Electro-optical device having an improved electrode

Abstract

An optical device is disclosed that includes a waveguide and an electrode. The waveguide includes at least one optical material having an electro-optic effect. The electrode includes a channel region and an extension that protrudes from the channel region. The extension is closer to a portion of the waveguide than the channel region.

Description

BACKGROUND ART

[0001] Cross-reference to other applications This application claims priority based on U.S. Provisional Patent Application No. 62 / 941,139, filed on November 7, 2019, entitled "THIN-FILM ELECTRO-OPTIC MODULATORS", which is incorporated herein by reference for all purposes. This application claims priority based on U.S. Provisional Patent Application No. 63 / 033,666, filed on June 2, 2020, entitled "HIGH PERFORAMNCE OPTICAL MODULATORS", which is incorporated herein by reference for all purposes. This application claims priority based on U.S. Provisional Patent Application No. 63 / 112,867, filed on November 12, 2020, entitled "BREAKING VOLTAGE-BANDWIDTH LIMIT IN INTEGRATED LITHIUM NIOBATE MODULATORS USING MICRO-STRUCTURED ELECTRODES", which is incorporated herein by reference for all purposes.

[0002] Optical modulators and other electro-optic devices generally desirably meet certain performance benchmarks. For example, it is desirable for an optical modulator to provide sufficient optical modulation at a lower electrode drive voltage. A large optical modulation may correspond to the waveguide having a large length in the optical signal transmission direction. However, it is also desirable for the optical modulator to consume a small total area. It is also desirable for the optical modulator to have low electrode (e.g., microwave) signal loss for an electrical signal passing through the electrode and low optical loss for an optical signal passing through the waveguide. Further, it is desirable for the optical modulator to provide low-loss transmission and large modulation at a low voltage over a wide frequency band. Accordingly, there is a desire for an electro-optic device that has low electrode loss, low optical loss, consumes a controlled amount of area, and / or provides a desired optical modulation at a low voltage.

BRIEF DESCRIPTION OF THE DRAWINGS

[0003] In the following detailed description and the accompanying drawings, various embodiments of the present invention are disclosed.

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Embodiments for Carrying Out the Invention

[0031] The present invention can be implemented in various forms, including a process, an apparatus, a system, a composition of matter, a computer program product embodied on a computer-readable storage medium, and / or a processor (a processor configured to execute instructions stored in and / or provided by a memory connected to the processor). In this specification, these embodiments or any other form that the present invention can take may be referred to as techniques. Generally, the order of the disclosed process steps may be changed within the scope of the present invention. Unless otherwise specified, components such as processors or memories described as being configured to perform tasks may be implemented as general components temporarily configured to perform the tasks at a certain time or as specific components manufactured to perform the tasks. In this specification, the term "processor" shall refer to one or more devices, circuits, and / or processing cores configured to process data such as computer program instructions.

[0032] Hereinafter, with reference to the drawings showing the principles of the present invention, a detailed description of one or more embodiments of the present invention will be given. The present invention is described in relation to such embodiments, but is not limited to any embodiment. The scope of the present invention is limited only by the claims, and the present invention includes many alternatives, modifications, and equivalents. In the following description, many specific details are set forth in order to provide a thorough understanding of the present invention. These details are for illustrative purposes only, and the present invention can be practiced according to the claims without some or all of these specific details. For the sake of simplicity, well-known technical matters in the technical field related to the present invention are not described in detail so as not to make the present invention unnecessarily difficult to understand.

[0033] The basic elements of an electro-optic device (also called an optical device) such as an electro-optic modulator include a waveguide and an electrode around the waveguide. The waveguide transmits an optical signal. The electrode is used to generate an electric field or a voltage difference in or near the waveguide. This electric field causes a change in the refractive index of the waveguide, and as a result, the optical signal is modulated. For example, an electrode signal (e.g., a microwave signal) may be applied to the electrode. The electrode functions as a transmission line. The electrode signal propagates in the same direction as the optical signal propagating through the waveguide. The electrode signal generates a corresponding electric field in the waveguide and modulates the refractive index of the waveguide. Thus, the optical signal is modulated when the optical signal passes through the waveguide. Therefore, the desired modulation of the optical signal can be achieved by driving an appropriate electrode signal through the electrode.

[0034] Electro-optic devices function, but their performance can be limited by a number of factors. For example, it is desirable for the electrode to be close to the waveguide in order to increase the strength of the electric field in the waveguide. A higher electric field increases the change in the refractive index of the waveguide and increases the modulation of the optical signal. However, the electrode can suffer electrode (e.g., microwave) signal loss when a microwave signal passes through the electrode. Such losses can be increased by proximity to the waveguide. These losses can adversely affect the ability of the electrode to provide the desired electric field in the waveguide. Absorption of the microwave signal by the surrounding structure and resistive losses in the electrode exacerbate these losses. Furthermore, the drive voltage required for the electrode increases as the modulation frequency increases. For example, an optical signal can be easily modulated at a frequency of 1 GHz using an electrode voltage of less than 2 volts. However, at higher frequencies (e.g., in the band above 100 GHz), the required electrode voltage can become quite high (e.g., 5 volts or more). A higher voltage is applied to the electrode to obtain the desired change in the refractive index. Thus, the optical modulator requires a larger input voltage to the electrode and can consume more power than desired. Therefore, there is still a need for an electro-optic device with improved performance.

[0035] Numerous techniques have been proposed to improve optical modulators. These techniques include waveguides using semiconductors (e.g., silicon and / or indium phosphide), bulk lithium niobate (LN), barium titanate (BTO), and / or plasmonics. However, these techniques and other techniques have significant drawbacks in one or more of the above-described features. For example, some modulators may not be able to provide the desired modulation in a given area, may be so large that only a weak electric field (and thus a smaller electro-optic response) is provided, and / or may suffer unacceptable electrode or optical signal losses. Signal limiting factors in the performance of an optical modulator can prevent the optical modulator from functioning as desired. For example, unacceptable electrode (microwave) losses can render the modulator unusable for a particular application even if the electrode can be driven at a low voltage. Therefore, a mechanism for providing an optical modulator having low optical signal loss, low electrode signal loss, consuming a controlled amount of area, and / or providing the desired optical modulation at a low voltage is still desired.

[0036] An optical device capable of improving performance is described. The optical device includes a waveguide and electrodes. The waveguide includes at least one optical material having an electro-optic effect. In some embodiments, the waveguide includes a ridge portion and a thin film portion. The electrodes include a channel region and an extension protruding from the channel region. The extension is closer to a part of the waveguide than the channel region. In some embodiments, the extension has a pitch, and the pitch may be shorter than the wavelength of the microwave in the electrode divided by π. In some embodiments, the extension has a length shorter than the wavelength of the microwave in the electrode divided by π. The waveguide is configured to transmit an optical signal, while the electrodes are configured to transmit an electrode signal. In some such embodiments, one or more optical materials have a microwave dielectric constant that is at least 1.5 times the optical dielectric constant for the optical signal and the electrode signal. As used herein, "dielectric constant" corresponds to relative dielectric constant, which is equal to the dielectric constant of the material divided by the vacuum dielectric constant. The microwave dielectric constant is the dielectric constant at the target microwave frequency. The optical dielectric constant is the dielectric constant at the target optical frequency and is equal to or approximately equal to the square of the refractive index. In some embodiments, each of the extensions includes a connection portion connected to the channel region and a reverse portion. The connection portion is between the reverse portion and the channel region. In some embodiments, the optical device includes additional electrodes having an additional channel region and a plurality of additional extensions. The additional extensions are closer to a part of the waveguide than the additional channel region. In some embodiments, the waveguide has a total optical loss of 10 dB or less along a part of the waveguide.

[0037] Accordingly, the optical device comprises one or more electrodes fabricated to have a micro-structure (i.e., an extension). One or more channel regions of the one or more electrodes are configured to conduct the bulk of the current, but the current can hardly or not at all be driven through the extension. Accordingly, losses due to the electrodes being in proximity to the waveguide can be mitigated. However, since the extension is close to the waveguide, the magnitude of the electric field in the waveguide can be maintained or increased. Accordingly, the electrodes can provide sufficient modulation of the optical signal at a lower electrode voltage.

[0038] In some embodiments, the optical performance can also be improved. The waveguide can have low optical loss (e.g., an optical loss of 1 dB / cm or less). In some such embodiments, the waveguide has an optical loss of 0.5 dB / cm or less in some cases (e.g., on average). In some embodiments, the waveguide has an on-chip total optical loss of 4 dB or less. In some embodiments, the portion of the waveguide proximate to the one or more electrodes has a total optical loss of 3 dB or less. The optical efficiency of the device can be improved. Accordingly, the optical modulator can be made longer (e.g., longer than 2 cm and, in some embodiments, 3 cm or more), and the modulation of the input optical signal is enhanced. Also, the waveguide can be made relatively small, e.g., using thin film technology. In some embodiments, the waveguide has an optical mode cross-sectional area smaller than the square of the wavelength of the optical signal in one or more non-linear optical materials (e.g., λ 2 )). In some embodiments, the optical mode cross-sectional area is λ 2Less than three times that, where λ is the wavelength of the optical signal in the waveguide. Since the waveguide is small, the electrodes may be placed closer to the waveguide. This may enable an increase in the electric field in the waveguide and an enhancement of the electro-optic effect. In some embodiments, one or more waveguide bending portions may have a bending radius of 500 μm or less. In some embodiments, the waveguide bending portion has a bending portion optical loss of 0.5 dB or less. When present, the bending portions of the waveguide and the electrodes may be used to increase the region where the electrodes are close to the waveguide while controlling the length and / or area consumed by the device. That is, the use of the bending portion enables reduction of the maximum dimension of the optical modulator. The maximum dimension of the optical modulator limits the reduction of the size of the package in which the optical modulator can be provided. The bending portions of the electrodes and the waveguide enable increasing the optical path and the region where the electrodes are close to the waveguide while reducing the maximum dimension of the optical modulator. For example, a linear optical modulator having a length of 4 centimeters and a width of 0.2 millimeters has the same optical path length as an optical modulator having three bending portions (and four straight portions) occupying an area of approximately 1 centimeter in length and 0.8 mm in width. This second optical modulator has a smaller aspect ratio, is more compact, and can fit into a much smaller package, which is desirable. In some embodiments, the waveguide and the electrodes may occupy an area of 50 square millimeters or less. The waveguide and the electrodes occupy an area of 20 square millimeters or less in some embodiments. In some embodiments, the waveguide and the electrodes are present on an integrated circuit having a length of 32 millimeters or less. Thus, a larger optical signal modulation can be achieved with a smaller footprint. In some embodiments, one or more electrode bending portions and one or more waveguide bending portions are configured to provide a path difference between the optical signal for the waveguide and the electrode signal for the electrodes. The bending portions of the waveguide and the electrodes may be used to account for the velocity mismatch between the electrode (microwave) signal and the optical signal. In this way, the efficiency of the device can be improved. The use of one or more electrodes with a channel region and an extension enables a high electric field to be provided by the electrodes in the waveguide.Also, the extension separates the edge of the channel region from the waveguide. Thus, the current can be better confined by the channel region, reducing the electrode loss at the electrode and making it possible to lower the drive voltage for the electrode. By combining the reduction of optical loss and electrode (e.g., microwave) loss, the improvement of the velocity matching between the electrode signal and the optical signal, and the extension of the path along which the optical signal can be modulated, it becomes possible to reduce the voltage amplitude input to one or more electrodes. For example, in some embodiments, a microwave signal with an amplitude of 0.5 to 1.5 V is input to one or more electrodes, and can provide a desired modulation of the refractive index for signals in the range of 50 to 100 GHz. Thus, the performance of the device can be improved.

[0039] The waveguide transmits the optical signal, while the electrode transmits the electrode signal. In some embodiments, the extension is configured to reduce the velocity mismatch between the optical signal and the electrode signal. In some embodiments, the extension has at least one distance from the waveguide such that the total optical loss is less than 8 dB. The electrode may have a frequency-dependent electrode loss for a frequency window in the frequency range from DC to 500 GHz or less. This frequency-dependent electrode loss is less than 0.8 dB per square root of the electrode signal frequency per centimeter in some embodiments. The electrode signal frequency is measured in GHz, and the frequency window may be at least 10 GHz. The frequency-dependent electrode loss is less than 0.5 dB per square root of the electrode signal frequency per centimeter in other embodiments. The electrode signal frequency is measured in GHz, and the frequency window may be at least 10 GHz. The frequency-dependent electrode loss is less than 0.3 dB per square root of the electrode signal frequency per centimeter in other embodiments. The electrode signal frequency is measured in GHz, and the frequency window may be at least 10 GHz. In some embodiments, the electrode has an absorption electrode loss for a frequency window of the electrode signal frequency from DC to 500 GHz or less. In some embodiments, the absorption electrode loss is less than 0.005 dB per GHz per centimeter, and the frequency window is at least 10 GHz.

[0040] The waveguide and the electrodes may be on a substrate. In some embodiments, the extension is between the substrate and the channel region. In some embodiments, the channel region is between the substrate and the plurality of extensions. In some embodiments, the substrate has a space therein. The space is aligned with a part of the waveguide and the plurality of extensions. In some embodiments, the waveguide and the electrodes are on a substrate structure. The substrate structure is selected from a first substrate having a low substrate microwave dielectric constant (e.g., less than 11), the first substrate combined with a lower layer between the substrate and the waveguide, and a second substrate having a high microwave dielectric constant greater than 11 combined with the lower layer. In such embodiments, the lower layer has a low lower layer microwave dielectric constant (e.g., less than 11).

[0041] The electrode may comprise an electrode bending portion. The waveguide may comprise a waveguide bending portion. The electrode bending portion and the waveguide bending portion are configured to provide a path difference between the optical signal for the waveguide and the electrode signal for the electrode.

[0042] In some embodiments, a sub-assembly such as an optical transmission sub-assembly (TOSA) is described. Such a sub-assembly comprises an optical modulator and a driver connected to the optical modulator. The optical modulator comprises a waveguide and electrodes. The waveguide comprises at least one optical material having an electro-optic effect. The electrode comprises a channel region and a plurality of extensions. The extensions are between the channel region and the waveguide. The driver is configured to electrically drive the electrode.

[0043] In some embodiments, a method of providing an optical device is described. The method comprises providing a waveguide and providing an electrode. The waveguide includes one or more optical materials having an electro-optic effect. The step of providing the electrode includes providing a channel region and providing an extension protruding from the channel region. The extension is closer to a part of the waveguide than the channel region. In some embodiments, the step of providing the extension includes processing an extension having a pitch shorter than the wavelength of the microwave in the electrode divided by π. The waveguide transmits an optical signal, while the electrode transmits an electrode signal. In some embodiments, the step of providing the extension includes configuring the extension to reduce a velocity mismatch between the optical signal and the electrode signal. In some embodiments, the electrode has a frequency-dependent electrode loss for a frequency window in a frequency range from DC to 500 GHz or less. The frequency-dependent electrode loss may be less than 0.8 dB per square root of the electrode signal frequency per centimeter, where the electrode signal frequency is measured in GHz and the frequency window is at least 10 GHz. In other embodiments, the frequency-dependent electrode loss is less than 0.5 dB per square root of the electrode signal frequency per centimeter. The electrode signal frequency is measured in GHz and the frequency window may be at least 10 GHz. In other embodiments, the frequency-dependent electrode loss is less than 0.3 dB per square root of the electrode signal frequency per centimeter. The electrode signal frequency is measured in GHz and the frequency window may be at least 10 GHz. In some embodiments, the electrode has an absorption electrode loss for a frequency window of the electrode signal frequency from DC to 500 GHz or less. In some embodiments, the absorption electrode loss is less than 0.005 dB per GHz per centimeter and the frequency window is at least 10 GHz.

[0044] Figures 1A - 1E illustrate embodiments of optical devices 100, 100', 100'', 100''', and 100'''' having improved electrodes. Figure 1A is a plan view showing an optical device (i.e., an electro - optical device) comprising a waveguide 110 and electrodes 120 and 130. Figures 1B, 1C, 1D, and 1E are perspective views showing optical devices 100', 100'', 100''', and 100'''' similar to optical device 100.

[0045] Optical devices 100, 100', 100'', 100''', and 100'''' may be part of a modulator having an electro - optical response (e.g., picometers per volt) in or perpendicular to a thin - film plane (e.g., x - cut or y - cut lithium niobate). Optical device 100'' may be part of a modulator having an electro - optical response (e.g., picometers per volt) out of the plane of the thin - film plane (e.g., z - cut lithium niobate). As used herein, an x - cut or y - cut modulator is a modulator having an electro - optical effect in the thin - film plane (even if no material such as lithium niobate is used). Similarly, as used herein, a z - cut optical modulator has an electro - optical effect out of (e.g., perpendicular to) the thin - film plane (even if no material such as lithium niobate is used). Figures 1A - 1E are not to exact scale. Other configurations are possible. For example, optical devices having different numbers of waveguides, other and / or additional waveguide components (such as splitters and branches), and / or different numbers of electrodes are possible. Referring to Figure 1A, an optical signal is input into optical device 100. For example, the optical signal may be provided by one or more lasers. An electrode signal having a voltage is also input into optical device 100. In some embodiments, the frequency of the electrode signal is in the microwave region. Therefore, the terms microwave signal and electrode signal are used synonymously herein. Optical device 100 utilizes the electrode signal to modulate the optical signal and outputs the modulated optical signal.

[0046] Referring to FIG. 1A, the optical device 100 includes a waveguide 110, and electrodes 120 and 130. The waveguide 110 is used to transmit an optical signal. More specifically, the waveguide 110 receives an input optical signal and outputs a modulated optical signal. The electrodes 120 and / or 130 transmit an electrode signal that applies a time-varying electric field to the waveguide 110. This electric field changes the refractive index of the waveguide 110. In some embodiments, the electrode 120 transmits an electrode signal (such as a microwave signal), while the electrode 130 is grounded. In some embodiments, the electrode 130 transmits an electrode (e.g., microwave) signal, while the electrode 120 is grounded. In some embodiments, both the electrodes 120 and 130 transmit an electrode signal. Other configurations are possible. Thus, the electrodes 120 and 130, together with the waveguide 110, provide a modulated optical signal. The electrodes 120 and 130 are depicted around the waveguide 110 to show that the waveguide 110 is subject to the electric field applied between 120 and 130, but this does not indicate the physical positions of the electrodes 120 and 130. For example, it is possible to place the electrode 120 immediately above or below the waveguide and place 130 on one side thereof.

[0047] The waveguide 110 is shown as having a rectangular footprint and extending only between the electrodes 120 and 130. The waveguide 110 may have other configurations. For example, the waveguide 110 may include a thin film portion that may extend under the electrodes 120 and / or 130, and a ridge 112 between the electrodes 120 and 130. The waveguide 110 includes at least one optical material having an electro - optic effect. In some embodiments, the optical material is a nonlinear material. As used herein, a nonlinear optical material exhibits an electro - optic effect and has an effect of at least 5 picometers / volt (e.g., 5 picometers / volt or more). In some embodiments, the nonlinear optical material has an effect of at least 10 picometers / volt. In some such embodiments, the nonlinear optical material has an effect of at least 20 picometers / volt. The nonlinear optical material undergoes a change in refractive index in response to an applied electric field. In some embodiments, the nonlinear optical material is a ferroelectric. In some embodiments, the effect of the electro - optic material includes a change in refractive index within an applied electric field due to the Pockels effect. Thus, in some embodiments, an optical material having an electro - optic effect in one or more of the ranges described herein is considered a nonlinear optical material, regardless of whether the effect depends linearly or non - linearly on the applied electric field. The nonlinear optical material may be a non - centrosymmetric material. Thus, the nonlinear optical material may be a piezoelectric material.

[0048] In some embodiments, waveguide 110 is a low optical loss waveguide. For example, waveguide 110 may have a total optical loss of 10 dB or less through a portion of waveguide 110 proximate to electrodes 120 and 130 (e.g., when biased at maximum transmission with maximum loss). The total optical loss is the optical loss in the waveguide through a single continuous electrode region (such as the region shown in FIG. 1A), as opposed to, e.g., a plurality of devices connected in cascade together. In some embodiments, waveguide 110 has a total optical loss of 8 dB or less. In some embodiments, the total optical loss is 4 dB or less. In some embodiments, the total optical loss is less than 3 dB. In some embodiments, the total optical loss is less than 2 dB. In some embodiments, waveguide 110 has an optical loss of 3 dB / cm or less (e.g., on average). In some embodiments, the non-linear material in waveguide 110 has an optical loss of 2.0 dB or less. In some such embodiments, waveguide 110 has an optical loss of 1.0 dB / cm or less. In some embodiments, waveguide 110 has an optical loss of 0.5 dB / cm or less. In some embodiments, the non-linear optical material in waveguide 110 includes lithium niobate (LN) and / or lithium tantalate (LT). In some embodiments, the non-linear optical material of waveguide 110 consists of LN. In some embodiments, the non-linear optical material of waveguide 110 consists of LT. Such non-linear optical materials may have an inert chemical etching reaction for conventional etching using a chemical such as a compound of fluorine, chlorine, or bromine. In some embodiments, the non-linear optical material includes one or more of LN, LT, potassium niobate, gallium arsenide, potassium titanyl phosphate, lead zirconate titanate, and barium titanate. In other embodiments, other non-linear optical materials having similar optical properties may be used.

[0049] Various other optical components may be incorporated into waveguide 110 to provide desired phase modulation, polarization modulation, intensity modulation, IQ modulation, other modulations, and / or other functions. For example, waveguide 110 may have one or more wider portions (not shown in FIG. 1A) to accommodate multiple modes. In some embodiments (not shown in FIG. 1A), waveguide 110 may include a splitter for splitting an optical signal into multiple branches for modulation and may recombine the modulated optical signals toward the output. Thus, waveguide 110 as well as electrodes 120 and 130 may be configured to provide the desired functions.

[0050] A portion of the waveguide 110 is close to the electrodes 120 and 130 along the optical signal transmission direction (e.g., from the input of the optical signal through the waveguide 110 to the output of the modulated optical signal). This portion of the waveguide may have various lengths. In some embodiments, the portion of the waveguide 110 close to the electrodes 120 and 130 is at least 2 millimeters in length. In some embodiments, this portion of the waveguide 110 is 5 millimeters or more and 10 millimeters or less in length. Other embodiments may have a longer portion of the waveguide 110. The portion of the waveguide 110 close to the electrodes 120 and 130 may have a length longer than 2 centimeters. In some embodiments, the length of the portion of the waveguide 110 close to the electrodes 120 and 130 is at least 2.5 cm. In some embodiments, the length of this portion of the waveguide 110 is at least 3 centimeters. Such a length is possible, at least in part, because the optical loss per unit length for the waveguide 110 described above is low. Since the waveguide 110 can be made longer, the total optical modulation that can be provided through the electric field generated by the electrodes 120 and 130 can be greater. Further, since the optical loss is low and the microwave loss is low (described later), the desired optical modulation (e.g., a change in refractive index) can be achieved with a signal input to the electrodes 120 and / or 130 having a lower voltage. For example, Vπ is the half-wave voltage, i.e., the amplitude of the input electrode signal required to shift the phase of the optical signal by π. In some embodiments, Vπ is 6 volts or less for signals in the range of 50 - 100 GHz. In some embodiments, Vπ is 3 volts or less for signals in the range of 50 - 100 GHz. In some embodiments, Vπ is on the order of the voltage provided through a CMOS circuit, e.g., in the range of 0.5 volts to 1.5 volts for signals in the range of 50 - 100 GHz. For example, Vπ may be 1.5 volts or less at 10 GHz. Thus, Vπ is 1.5 volts or less in some embodiments. In some such embodiments, Vπ is 1 volt or less for signals in the range of 50 - 100 GHz. Other voltages for other frequency ranges are also possible. Thus, the performance of the optical modulator 110 can be improved.

[0051] Furthermore, the portion of waveguide 110 proximate to electrodes 120 and 130 may have a small optical mode cross-sectional area. In some embodiments, the optical mode cross-sectional area is less than three times the square of the wavelength of the optical signal in one or more nonlinear optical materials (e.g., λ 2 ). In some embodiments, the optical mode cross-sectional area is less than two times the square of the wavelength of the optical signal in one or more nonlinear optical materials. In some embodiments, the optical mode cross-sectional area is less than 1.5 times the square of the wavelength of the optical signal in one or more nonlinear optical materials. In some embodiments, the optical mode cross-sectional area is less than 4 μm 2 . In some such embodiments, the optical mode cross-sectional area is 3 μm 2 or less. In some embodiments, such a small optical mode cross-sectional area can be provided using the thin films and manufacturing techniques described herein. Also, the optical mode cross-sectional area can enable the low optical losses described herein.

[0052] Electrodes 120 and 130 apply an electric field to waveguide 110. Electrode 120 includes a channel region 122 and an extension 124 (only one of which is labeled in FIG. 1A). Electrode 130 includes a channel region 132 and an extension 134 (only one of which is labeled in FIG. 1A). In some embodiments, extensions 124 or 134 may be omitted from electrodes 120 or 130, respectively. Extensions 124 and 134 protrude from channel regions 122 and 132, respectively. Thus, extensions 124 and 134 are each closer to waveguide 110 than channel regions 122 and 132. Extensions 124 and 134 shown in FIG. 1A are simple rectangular protrusions. In some embodiments, extensions 124 and 134 may have other shapes. For example, extensions 124 and / or 134 may have an L-shaped footprint, a T-shaped footprint, and / or another shaped footprint. Regardless of the shape, at least a portion of each of extensions 124 and 134 is closer to waveguide 110 than channel regions 122 and 132, respectively. Also, the distribution (e.g., pitch) and width of extensions 124 and 134 are irregular. In some embodiments, the distribution and / or width of extensions 124 and / or 134 may be regular. The distance between waveguide 110 and extensions 124 and 134 is shown as constant. In some embodiments, this distance may vary. Similarly, the distance between waveguide 110 and channels 122 and 132 is shown as constant. In some embodiments, this distance may vary. Electrodes 120 and 130 are shown as symmetric. In some embodiments, electrodes 120 and 130 are asymmetric. For example, extension 134 may be omitted while extension 124 is present.

[0053] The extensions 124 and 134 each protrude from the channel regions 122 and 132 and are located between the channel regions 122 and 132 and the waveguide 110, respectively. As a result, the extensions 124 and 134 are close enough to the waveguide 110 to provide an enhanced electric field to the waveguide 110. Thus, the change in refractive index caused by the electric field is increased. In contrast, the channel regions 122 and 132 are further away from the waveguide 110 than the extensions 124 and 134. Thus, the channel region 122 is not significantly affected by the electric field generated by the electrode 130 / extension 134. The tendency for charges to accumulate at the edge of the channel region 122 closest to the electrode 130 is reduced. Thus, current can be more easily driven through the central portion of the channel region 122, and electrode losses in the channel region 122 (and electrode 120) can be reduced. Similarly, the channel region 132 is away from the electrode 120. The channel region 132 is not significantly affected by the electric field generated by the electrode 120 / extension 124. The tendency for charges to accumulate at the edge of the channel region 132 closest to the electrode 120 is reduced. Thus, current can be more easily driven through the channel region 132, and electrode losses in the channel region 132 (and electrode 130) can be reduced. Since microwave signal losses through the electrodes 120 and 130 can be reduced, a smaller drive voltage may be used for the electrodes 120 and / or 130, and the power consumed by the optical device 100 can be reduced. Further, the ability to match the impedance of the electrode 120 to an input voltage device (not shown in FIG. 1A) can be improved. Such impedance matching can further reduce the electrode signal losses of the optical device 100. Further, the extensions 124 and 134 can affect the speed of the electrode signals passing through the electrodes 120 and 130. Thus, the extensions 124 and 134 may be configured to adjust the speed of the electrode signals to match the speed of the optical signal in the waveguide 110. Thus, the performance of the optical device 100 can be improved.

[0054] The electrodes 120 and / or 130 may be manufactured using deposition techniques (such as evaporation and / or electroplating) and photolithography to form the extensions 124 and / or 134 of the electrodes 120 and / or 130. The resulting electrodes 120 and / or 130 may have lower frequency-dependent electrode losses. In some embodiments, the frequency-dependent electrode power loss for a specific frequency window (e.g., at least 10 GHz) in the frequency range between DC and 500 GHz can be reduced to up to 0.8 dB per square root of the electrode signal frequency per centimeter. Here, the electrode signal frequency is measured in GHz. The frequency-dependent electrode loss is less than 0.5 dB per square root of the electrode signal frequency per centimeter in other embodiments. The electrode signal frequency is measured in GHz, and the frequency window may be at least 10 GHz. The frequency-dependent electrode loss is less than 0.3 dB per square root of the electrode signal frequency per centimeter in other embodiments. The electrode signal frequency is measured in GHz, and the frequency window may be at least 10 GHz. In some embodiments, the electrodes have absorption electrode losses for a frequency window of the electrode signal frequency from DC to up to 500 GHz. In some embodiments, the absorption electrode loss is less than 0.005 dB per GHz per centimeter, and the frequency window is at least 10 GHz. In some embodiments, the frequency-dependent electrode power loss for the same frequency window and frequency range can be reduced to up to 0.75 dB per square root of the electrode signal frequency per centimeter for a specific frequency window (e.g., 10 GHz or more). In some embodiments, the electrodes have absorption electrode losses. In some embodiments, the absorption electrode loss for a specific frequency window (e.g., 10 GHz or more) in the frequency range between DC and 500 GHz is less than 0.02 dB per GHz per centimeter. In some embodiments, the absorption electrode loss for the same frequency window and frequency range is less than 0.005 dB per GHz per centimeter for the frequency window in the frequency range between DC and 500 GHz. In some embodiments, the optical device 100 may include additional electrodes, such as a DC electrode (not shown in FIG. 1A).Such additional electrodes may be used to optimize the optical device 100 for low-frequency response. This electrode may comprise one or more of an electro-optic, a thermo-phase shifter, and / or a MEMS shifter.

[0055] During operation, a modulated optical signal is input into the waveguide 110. Also, an electrode signal (e.g., a microwave signal) is applied to the electrodes 120 and / or 130. For the purpose of explanation, it is assumed that the microwave signal is applied to the electrode 120 while the electrode 130 is grounded. Due to the time-varying microwave signal passing through the electrode 120, charges of a specific sign rapidly accumulate in the extension 124, decrease to zero at the extension 124, and charges of the opposite sign rapidly accumulate in the extension 124. The absence of negative charges in a specific extension 124 is regarded as the same as the accumulation of positive charges in the extension 124, and vice versa. This cycle is repeated at or near the frequency of the microwave signal. As a result of the charge accumulation in the extension 124, opposite charges accumulate in the nearby corresponding extension 134. A relatively large time-varying electric field is generated between the extensions 124 and 134. Since the electro-optic material of the waveguide 110 is exposed to a larger time-varying electric field, the refractive index of the waveguide 110 undergoes a larger change near the extensions 124 and 134. The optical signal is exposed to larger refractive index variations when passing through the extensions 124 and 134 through the waveguide 110. Therefore, for a given voltage amplitude microwave signal applied to the electrode 120, a larger modulation of the optical signal can be achieved. For example, the optical device 100 can provide sufficient optical modulation at a voltage amplitude of 1 volt or less provided to the electrode 120 at frequencies up to 100 - 300 GHz or more. Further, as described above, the presence of the extension 124 reduces the tendency for current to gather near the edge of the channel region 122 close to the waveguide 110, alleviating the loss at the electrode 120. Since the current can be more easily driven through the channel region 122 at a lower voltage, the microwave loss can be reduced. Therefore, the performance of the optical device 100 can be improved.

[0056] Furthermore, as described above, the optical device 100 can not only reduce the optical loss through the waveguide 110, but also increase the modulation of the optical signal by using a longer waveguide 110. The use of the electrodes 120 and 130 each having the extensions 124 and 134 reduces the microwave loss, enables a large electric field in the waveguide 110 / ridge 112, and can improve the propagation of the microwave signals through the electrodes 120 and 130, respectively. Also, the electrodes 120 and 130 can improve the performance by velocity and phase matching. Therefore, the performance of the optical device 100 can be significantly improved.

[0057] FIG. 1B is a perspective view of the optical device 100'. The optical device 100' is similar to the optical device 100. Therefore, similar parts of the optical device 100' are denoted by the same reference numerals. The optical device 100' includes a waveguide 110', an electrode 120', and an electrode 130' that are respectively similar to the waveguide 110, the electrode 120, and the electrode 130. The substrate / lower layer 101 is also shown. In some embodiments, the substrate 101 includes a silicon substrate and a silicon dioxide layer between the silicon substrate and the waveguide 110. Other substrates may be used in other embodiments. In some embodiments, the substrate 101 is a dielectric having a low microwave dielectric constant (e.g., a microwave dielectric constant of less than 11). In some embodiments, the substrate has a microwave dielectric constant of less than 8. In some such embodiments, the substrate has a microwave dielectric constant of less than 5. For example, the substrate 101 may include sapphire, quartz, and / or fused quartz. In some embodiments, one or more lower layers (such as silicon dioxide) having a low microwave dielectric constant are LowIt may be used on the microwave dielectric substrate 101. Other and / or additional lower layers may be used in other embodiments. Further, one or more low microwave dielectric lower layers may be used in combination with other substrates having a larger microwave dielectric constant. For example, a low microwave dielectric lower layer of silicon dioxide may be provided on a substrate 101 (such as silicon or LN) having a microwave dielectric constant greater than 11. In some embodiments, it is desirable that the provided lower layer be thick. For example, the lower layer may have a thickness of 3 micrometers or more and 100 micrometers or less. Further, other geometric configurations of the substrate and / or the lower layer may be used in some embodiments.

[0058] The waveguide 110’ is used for transmitting an optical signal. The waveguide 110’ includes a ridge 112 and a thin film portion 114. In the embodiment shown in FIG. 1B, the thin film portion 114 and the ridge portion are formed from the same material (for example, the same thin film). The waveguide 110’ may be formed from a material similar to that of the waveguide 110 and may have similar performance.

[0059] The waveguide 110' may have different configurations in some embodiments. For example, the waveguide 110' may omit the thin film portion 114 or may reduce the size of the thin film portion 114. The ridge 112 may have a different configuration. For example, the ridge 112 may have a trapezoidal, semi-circular, laminated rectangular, and / or another geometric shape that guides optical signals in a manner similar to those described herein. Other and / or additional materials may be used. In some embodiments, different portions of the waveguide 110' are formed from different materials. For example, the thin film portion 114 and the ridge 112 may be formed of different materials. The thin film 114 may include a non-linear optical material (such as LN and / or LT), while the ridge 112 may be formed of a passive material (such as silicon and / or silicon nitride). In some embodiments, the ridge 112 may be disposed below the thin film portion 114 (for example, the ridge 112 may be between the thin film portion 114 and the underlying substrate 101). Similarly, various other optical components may be incorporated into the waveguide 110 to provide desired phase modulation, polarization modulation, intensity modulation, IQ modulation, other modulations, and / or other functions. In some embodiments (not shown in FIGS. 1B-1C), the waveguide 110 may include a splitter for splitting an optical signal into a plurality of branches for modulation and may recombine the modulated optical signals towards the output. Thus, the waveguide 110 as well as the electrodes 120 and 130 may be configured to provide the desired functions.

[0060] In some embodiments, the nonlinear optical material of waveguide 110’ is formed as a thin film. For example, the thin film may have a thickness (e.g., of the thin film portion 114 and the ridge portion 112) that is three times or less the optical wavelength of the optical signal transmitted in waveguide 110’ before processing. In some embodiments, the thin film has a thickness (e.g., of the thin film portion 114 and the ridge portion 112) that is two times or less the optical wavelength. In some embodiments, the nonlinear optical material has a thickness that is one time or less the optical wavelength. In some embodiments, the nonlinear optical material has a thickness that is 0.5 times or less the optical wavelength. For example, the thin film may have a total thickness of 3 micrometers or less immediately after film formation. In some embodiments, the thin film has a total thickness of 2 micrometers or less. The thin film nonlinear optical material may be processed onto waveguide 110’ using photolithography. For example, ultraviolet (UV) and / or deep ultraviolet (DUV) photolithography may be used to pattern a mask for the nonlinear optical material. For DUV photolithography, the wavelength of the light utilized is typically less than 250 nanometers. To fabricate the waveguide, the thin film nonlinear optical material may be physically etched using, for example, dry etching, reactive ion etching (RIE), inductively coupled plasma RIE. In some embodiments, chemical etching and / or electron beam etching may also be used. Accordingly, waveguide 110’ may have an improved surface roughness. For example, one or more sidewalls of ridge 112 may have a reduced surface roughness. For example, the short-term root mean square surface roughness of the sidewall of ridge 112 is less than 10 nanometers. In some embodiments, this root mean square surface roughness is 5 nanometers or less. In some cases, the short-term root mean square surface roughness is 2 nanometers or less. Accordingly, waveguide 110’ may have optical losses within the ranges described above. In some embodiments, the height of ridge 112 is selected to provide optical mode confinement such that there is a 10 dB reduction in intensity at the center of ridge 112 at a position 10 micrometers from the center of ridge 112. For example, the height of ridge 112 is on the order of hundreds of nanometers in some cases.However, other heights are possible in other embodiments.

[0061] A part of the waveguide 110' is close to the electrodes 120 and 130 along the optical signal transmission direction (e.g., from the input of the optical signal through the waveguide 110' to the output of the modulated optical signal). The electrode 120 ’ and 130 ’ The portion of the waveguide 110' close to the electrodes 120 and 130 may have the above-described length (e.g., a length longer than 2 millimeters in some embodiments, and a length longer than 2 centimeters or more in some such embodiments). Such a length is possible at least in part because the optical loss per unit length for the waveguide 110 described above is low. Further, as described above for the waveguide 110, the electrodes 120 ’ and 130 ’ The portion of the waveguide 110' close to the electrodes 120 and 130 has a small optical mode cross-sectional area.

[0062] The electrodes 120' and 130' are the waveguide 110 ’An electric field is applied thereto. Electrodes 120’ and / or 130’ may be manufactured using deposition techniques (such as electroplating) and photolithography in order to form electrodes 120 and / or 130. The resulting electrodes 120’ and / or 130’ may have lower frequency-dependent electrode losses within the ranges described above with respect to electrodes 120 and 130. Electrode 120’ includes a channel region 122’ and an extension 124’ (only one of which is labeled in FIG. 1B). Electrode 130’ includes a channel region 132’ and an extension 134’ (only one of which is labeled in FIG. 1B). In some embodiments, extensions 124’ or 134’ may be omitted from electrodes 120’ or electrode 130’, respectively. Extensions 124’ and 134’ are each closer to waveguide 110’ than channel regions 122’ and 132’. For example, the distance s from extensions 124’ and 134’ to waveguide ridge 112 is shorter than the distance w from channels 122’ and 132’ to waveguide ridge 112. In the embodiment shown in FIG. 1B, extensions 124’ and 134’ are each at substantially the same height as channel regions 122’ and 132’. In some embodiments, in addition to or instead of being at the same height, the extensions may protrude above and / or below the channel regions.

[0063] The extensions 124’ and 134’ are close to the waveguide 110’. For example, the extensions 124’ and 134’ are at a vertical distance d from the waveguide 110’. The vertical distance to the waveguide 110’ may depend on the cladding material (not shown in FIG. 1B) used. The distance d can be highly customizable in some cases. For example, d can range from zero (less than zero if the electrodes 120’ and 130’ are in contact with or embedded in the thin film portion 114) to a value exceeding the height of the ridge 112. However, it is generally desirable that d is small enough so that the electrodes 120’ and 130’ can apply a desired electric field to the waveguide 110’. Also, the extensions 124’ and 134’ are at a distance s from the ridge 112. It is desirable that the extensions 124’ and 134’ are close enough to the waveguide 110’ (e.g., close to the ridge 112) to achieve the desired electric field and refractive index change. However, it is desirable that the extensions 124’ and 134’ are far enough from the waveguide 110’ (e.g., from the ridge 112) so that their presence does not cause excessive optical loss. The distance s generally does not depend on the specific geometry or thickness of the waveguide 110’, but s may be selected to allow both transverse electric modes and transverse optical modes to be confined differently within the waveguide 110’. However, the optical field intensity in the extensions 124’ and 134’ (more specifically, in the portions 124B and 134B) is desirably reduced to limit the optical loss due to absorption of the optical field by the conductors in the extensions 124’ and 134’. Thus, s is large enough so that the total optical loss of the waveguide 110’, including the loss due to absorption in the extensions 124’ and 134’, does not exceed the above-mentioned range (e.g., 10 dB or less in some embodiments, 8 dB or less in some embodiments, 4 dB or less in some embodiments). In some embodiments, s is selected such that the optical field intensity in the extensions 124’ and 134’ is less than -10 dB of the maximum optical field intensity in the waveguide 110. In some embodiments, s is selected such that the optical field intensity in the extensions 124’ and 134’ is less than -40 dB of its maximum value in the waveguide.For example, in some embodiments, the extension portion 124’ and / or 134’ may be at least 2 micrometers and at most 2.5 micrometers from the ridge 112.

[0064] In the embodiment shown in FIG. 1B, the extension portion 124 has a connection portion 124A and a reverse portion 124B. The reverse portion 124B is so called because a part of the reverse portion may be antiparallel to the direction of signal transmission through the electrode 120. Similarly, the extension portion 134 has a connection portion 134It has an extension part 124A and a reverse part 134B. Therefore, the extension parts 124 and 134 have a "T" shape. In some embodiments, other shapes are also possible. For example, the extension part 124 and / or 134 may have an "L" shape, the reverse part may be omitted, it may be rectangular, trapezoidal, parallelogram, may partially or completely wrap around a part of the waveguide 110, and / or may have another shape. Similarly, although the channel regions 122' and / or 132' are shown as having a rectangular cross-section, they may have another shape. Further, the extension parts 124' and / or 134' may have various sizes as shown by FIG. 1A. Although all the extension parts 124' and 134' are shown as being at the same distance from the ridge 122, a part of the extension part 124' and / or a part of the extension part 134' may be at different distances from the ridge 112. Also, the channel regions 122' and / or 132' may have various sizes. In some embodiments, it is desirable that the extension parts 124' and 134' each have a length l (for example, l = w - s) corresponding to a frequency lower than the Bragg frequency of the signal for the electrodes 120' and 130'. Therefore, it may be desirable that the lengths of the extension parts 124' and 134' are less than or equal to the value obtained by dividing the wavelength of the microwave of the electrode signal by π at the maximum operating frequency of the electrodes 120' and 130'. In some embodiments, it is desirable that the lengths of the extension parts 124' and 134' are less than the value obtained by dividing the wavelength of the microwave by 12. For example, when the maximum operating frequency is 300 GHz (which corresponds to a microwave wavelength of 440 micrometers on the substrate), it is desirable that the extension parts 124' and 134' are less than about 37 micrometers. The individual extension parts 124' and / or 134' may be irregularly spaced or may be periodic. The periodic extension parts have a certain pitch. In some embodiments, the pitch p is desirably a distance corresponding to a frequency lower than the Bragg frequency, as described above with respect to the lengths of the extension parts 124' and 134'.Therefore, it may be desirable for the pitch of the extensions 124' and 134' to be less than or equal to the value obtained by dividing the wavelength of the microwave of the electrode signal by π at the maximum operating frequency of the electrodes 120' and 130'. In some embodiments, it is desirable for the pitch to be less than the value obtained by dividing the wavelength of the microwave by 12. In some embodiments, it is desirable for the pitch to be less than the value obtained by dividing the wavelength of the microwave by 72, which enables low ripple in the group velocity.

[0065] The extensions 124' and 134' are each closer to the ridge 112 than the channels 122' and 132" (e.g., s < w). In some embodiments, a dielectric cladding material (not explicitly shown in FIG. 1B) is present between the electrodes 120' and 130' and the waveguide 110'. As described above, it is desirable for the extensions 124' and 134' to have lengths l(w - s) corresponding to frequencies less than the Bragg frequency of the signals for the electrodes 120' and 130', respectively. Also, it is desirable for the extensions 124' and 134' to be spaced apart from the ridge 112 as described above (e.g., so that the absorption loss in the waveguide 110' can be maintained at a desired level (such as 10 dB or less)). The lengths of the extensions 124' and 134', as well as the desired separation from the ridge 112 (e.g., s), are considered when determining w. Although FIGS. 1A - 1C are described in the context of horizontal distances, the distances between the electrode structure and the waveguide also apply to the vertical configuration. Other distances between the waveguide 110 / ridge 112 and the channel regions 122 and / or 132 are also possible.

[0066] The geometries of electrodes 120’ and 130’ are similar to the shapes described for electrodes 120 and 130. The sizes of specific portions of extensions 124’ and 134’ may vary. For example, the lengths d2 of connection portions 124A and / or 134A may be selected such that the impedances of electrodes 120’ and 130’ respectively match the impedance of a driver (not shown) (e.g., 50 Ω). In some embodiments, the gap between extensions 134’ and 124’ (where waveguide ridge 112 is present) may be configured to increase the electric field in waveguide ridge 112. In some embodiments, the gap between extensions 124’ and 134’ is between 1 times and 10 times the optical wavelength of the optical signal transmitted by waveguide 110’. However, a gap that is too small may cause current concentration and microwave loss in electrodes 120’ and / or 130’. In some embodiments, the widths of channel regions 122’ and / or 132’ are selected to reduce microwave loss while attempting to match the microwave (electrode signal) speed to the optical signal speed in waveguide 110. For example, electrode channel regions 122’ and / or 132’ may have widths between 2 micrometers and 500 micrometers. The widths of return portions 124B and / or 134B may be finely tuned to allow for low microwave loss while maintaining speed matching and a high-frequency response range. For example, return portions 124B and / or 134B may have widths (l - d2) between 10 nanometers and 10 micrometers. The length d3 of each return portion 124B and / or 134B, as well as the gap between adjacent return portions 124B and / or 134, are selected to allow for efficient modulation and low microwave loss. For example, a duty cycle d3 / (d3 + d4) between 0.5 and 0.9999 may be selected in some embodiments. Other dimensions (including but not limited to the dimensions described herein) may be selected in some embodiments.

[0067] The optical device 100’ operates in the same manner as the optical device 100. Thus, the optical device 100’ can share the advantages of the optical device 100. The use of the nonlinear optical material in the waveguide 110’ and the configuration of the waveguide 110’ (e.g., the smoother sidewalls of the ridge 112) can not only enhance the electro-optic effect (e.g., provide a greater modulation of the refractive index), but also reduce the optical loss. Thus, a longer waveguide 110, a greater total change in the refractive index, and hence an enhanced modulation of the optical signal can be achieved. The use of the electrodes 120’ and 130’ each having the extensions 124’ and 134’ can reduce the microwave loss, enable a large electric field in the waveguide 110’ / ridge 112’, and improve the propagation of the microwave signals through the electrodes 120’ and 130’ respectively. Thus, the performance of the optical device 100’ can be significantly improved.

[0068] This improvement in performance can be achieved for optical devices (e.g., 100 and / or 100') where the waveguide 110 and / or 110' includes or consists of an electro-optic material having a microwave dielectric constant that significantly exceeds the optical dielectric constant when utilized at the designed microwave frequency and optical frequency. Here, for a non-magnetic material, the optical index is equal to or approximately equal to the square root of the optical dielectric constant. For electro-optic materials (e.g., LN and LT) where the microwave dielectric constant significantly exceeds the optical dielectric constant, the microwave dielectric constant is 1.5 or more times the optical dielectric constant. In some cases, the microwave dielectric constant is 2 or more times the optical dielectric constant. In some examples, the microwave dielectric constant is 5 or more times the optical dielectric constant. In some such materials, the microwave dielectric constant is 10 or more times the optical dielectric constant. Thus, in some embodiments, the waveguide 110' that includes (or consists of) such a material has a microwave dielectric constant that exceeds the optical dielectric constant (e.g., at least 1.5 times, 2 times, 5 times, 10 times, or greater). The optical dielectric constant and the microwave dielectric constant respectively affect the transmission speeds of the optical signal and the microwave signal. The higher the optical dielectric constant, the lower the transmission speed of the optical signal. Similarly, the higher the microwave dielectric constant, the lower the transmission speed of the microwave signal.

[0069] Optical modes are generally well-confined by a waveguide, while microwave modes can spread out significantly outside the electrodes. For example, microwave modes can extend into the waveguide. For bulk optical devices and other optical devices comprising waveguides formed of materials having a microwave dielectric constant greater than the optical dielectric constant (e.g., LN and / or LT), the transmission speed of microwave signals in the waveguide material is significantly reduced compared to the speed of optical signals. Features (such as extensions) in the electrodes can also slow down the transmission of electrode signals in the electrodes. Thus, the velocity mismatch between the optical signal and the electrode signal is expected to be exacerbated by electrodes having features such as extensions. Generally, the use of features such as extensions is not preferred in situations where the waveguide material has a microwave dielectric constant significantly greater than the optical dielectric constant (e.g., in bulk LN and / or LT waveguides). That is, the use of features on the electrodes is generally limited to cases where the microwave dielectric constant of the waveguide material is not significantly greater (e.g., less than 1.5 times), approximately the same as, or smaller than the optical dielectric constant of the waveguide material (such as III-V compound materials like indium phosphide and gallium arsenide).

[0070] In contrast, for the optical devices 100’ (and 100), a thin-film waveguide 110’ is used. Generally, the optical mode is well confined to the waveguide 110’ (e.g., to the ridge portion 112). This can be understood from the size of the optical mode shown in FIG. 2. Thus, returning to FIG. 1B, the optical permittivity of the waveguide 110’ determines the speed of the optical signal in the waveguide 110’. However, the microwave mode for the microwave signal in the electrodes 120’ and / or 130’ can spread over many structures. This can be understood from the size and position of the microwave mode shown in FIG. 2. Thus, returning to FIG. 1B, the speed of the microwave signal passing through the electrodes 120’ and 130’ can be understood using the microwave permittivities of a plurality of structures (the electrodes 120’ and 130’, the waveguide 110’, the cladding material (not shown in FIG. 1B) between the substrate / lower layer 101 and the electrodes 120’ and 130’, the substrate / lower layer 101, and the air or any structure (not shown) above the electrodes 120’ and 130’, etc.). Thus, the contribution of the (high) microwave permittivity of the material of the waveguide 110’ (e.g., LT and LN) can be mitigated by the (lower) microwave permittivity of the surrounding structures. In this way, even achieving other advantages of the extensions 124’ and / or 134’, the speed mismatch between the optical signal in the waveguide 110’ and the electrode signal for the electrodes 120’ and / or 130’ can be mitigated.

[0071] Figure 1C shows another embodiment 100'' of the optical device. The optical device 100'' is similar to the optical devices 100 and / or 100'. Therefore, similar structures have similar reference numerals. Thus, the optical device 100'' includes a waveguide 110 and waveguides 110' that are respectively similar to the electrodes 120 and 130, and electrodes 120' and 130'. Similarly, the electrodes 120' and 130' each include channel regions 122' and 132' that are respectively similar to the channel regions 122 and 132 of the electrodes 120 and 130. The electrodes 120' and 130' each include extensions 124' and 134' that are respectively similar to the extensions 124 and 134 of the electrodes 120 and 130. The extensions 124' and 134' include connections 124A' and 134A' and reversals 124B' and 134B' that are similar to the connections 124A and 134A and the reversals 124B and 134B, respectively.

[0072] In some embodiments, the optical devices 100 and 100' have an electro-optic effect in the plane of the thin film region 114 (e.g., an x-cut or y-cut modulator). The optical device 100'' has an electro-optic effect out of the plane of the thin film region 114'' (e.g., a z-cut optical modulator). Therefore, it is desirable to apply a vertical electric field to the waveguide 110''. Thus, the optical device 100'' includes an electrode 140' having an extension 144' with connections 144A' and reversals 144B'. The extension 144' is similar to the extensions 124, 134, 124', and 134'. Therefore, the discussions herein regarding the extensions 124 and 134 also apply to the extension 144'. For example, the distances s' and w' respectively correspond to the distances s and w. Thus, an optical device having an out-of-plane electro-optic effect and improved performance can also be provided.

[0073] Figure 1D shows an embodiment 100''' of an optical device. The optical device 100''' is similar to the optical devices 100, 100', and / or 100''. Therefore, similar structures have the same reference numerals. Thus, the optical device 100''' includes a waveguide 110 / 110' and electrodes 120 / 120' and 130 / 130, and a waveguide 110' and electrodes 120' and 130' that are respectively similar thereto. Similarly, the electrodes 120' and 130' each include channel regions 122' and 132' that are respectively similar to the channel regions 122 / 122' and 132 / 132' of the electrodes 120 / 120' and 130 / 130 of the optical devices 100 / 100'. The electrodes 120' and 130' each include extensions 124' and 134' that are respectively similar to the extensions 124 / 124' and 134 / 134' of the electrodes 120 / 120' and 130 / 130 of the optical devices 100 / 100'. The extensions 124' and 134' each include connection portions 124A' and 134A' and reverse portions 124B' and 134B' that are respectively similar to the connection portions 124A / 124A' and 134A / 134A' and the reverse portions 124B / 124 B ' and 134B / 134B' of the optical devices 100 / 100'.

[0074] In addition, the optical device 100''' includes a further waveguide 150 and a further electrode 140 having a channel region 142 and an extension 144. The electrode 150 and the extension 154 are respectively similar to the electrodes 120, 120', 13 0、 and, 130', and, the extensions 124, 124', 134, and, 134'. Similarly, the waveguide 150 is similar to the waveguides 110 and 110'. In some embodiments, the optical device 100''' may be part of an optical device such as a modulator or an interferometer. For example, the waveguides 110' and 150 may branch from a single waveguide upstream of the portion of the optical device 100''' shown in the figure and may merge downstream of the portion of the optical device 100''' shown in the figure.

[0075] The optical device 100''' operates in the same manner as the optical devices 100, 100', and / or 100''. Thus, the optical device 100''' may share the advantages of the optical devices 100, 100', and / or 100''. The use of the nonlinear optical material in the waveguides 110' and / or 150 and the configuration of the waveguides 110' and / or 150 (e.g., the smoother sidewalls of the ridge 112) can not only enhance the electro-optic effect but also reduce the optical loss. Thus, longer waveguides 110' and 150, a greater total change in the refractive index, and thus, an enhanced modulation of the optical signal can be achieved. The use of the electrodes 120', 130', and 140 each having the extensions 124', 134', and 144 can reduce the microwave loss and enable a large electric field in the waveguides 110' and 140. This can improve the propagation of the microwave signal through the electrodes 120', 130', and 140. Thus, the performance of the optical device 100''' can be significantly improved.

[0076] FIG. 1E shows an embodiment 100'''' of an optical device. The optical device 100'''' is similar to the optical devices 100, 100', 100'', and / or 100'''. Accordingly, similar structures have similar reference numerals. Thus, the optical device 100'''' includes a waveguide 110 / 110' and electrodes 120 / 120' and 130 / 130', and a waveguide 110' and electrodes 120'' and 130'' that are respectively similar thereto. Similarly, the electrodes 120'' and 130'' each include channel regions 122'' and 132'' that are respectively similar to the channel regions 122 / 122' and 132 / 132' of the electrodes 120 / 120' and 130 / 130' of the optical devices 100 / 100'. The electrodes 120'' and 130'' each include extensions 124'' and 134'' that are respectively similar to the extensions 124 / 124' and 134 / 134' of the electrodes 120 / 120' and 130 / 130' of the optical devices 100 / 100'. The extensions 124'' and 134'' each include connection portions 124A'' and 134A'' and reverse portions 124B'' and 134B'' that are respectively similar to the connection portions 124A / 124A' and 134A / 134A' and the reverse portions 124B / 124 B ' and 134B / 134B' of the optical devices 100 / 100'.

[0077] The electrodes 120'' and 130'' each further include additional conductive layers 126 and 136. Accordingly, the electrodes 120'' and 130'' may be capable of transmitting additional current in the conductive layers 126 and 136.

[0078] The optical device 100'''' operates in the same manner as the optical devices 100, 100', 100'', and / or 100'''. Thus, the optical device 100'''' can share the advantages of the optical devices 100, 100', 100'', and / or 100'''. The use of the nonlinear optical material in the waveguide 110' and the configuration of the waveguide 110' (e.g., the smoother sidewalls of the ridge 112) can not only enhance the electro-optic effect but also reduce the optical loss. Thus, a longer waveguide 110', a greater total change in the refractive index, and thus, an enhanced modulation of the optical signal can be achieved. The use of the electrodes 120'' and 130'' each having the extensions 124'' and 134'' can reduce the microwave loss and enable a large electric field in the waveguide 110'. This can improve the propagation of the microwave signal through the electrodes 120'' and 130''. Thus, the performance of the optical device 100'''' can be significantly improved.

[0079] FIG. 2 is a cross-sectional view showing a part of an embodiment 200 of an optical device whose performance can be improved. The optical device 200 includes a waveguide 210 on a substrate 201, as well as electrodes 220 and 230. An intermediate layer 202 and a cladding material 204 are also shown. In the illustrated embodiment, the substrate 201 is silicon, the intermediate layer 202 is silicon dioxide, and the cladding material 204 is silicon dioxide. In some embodiments, other and / or additional materials may be used for the substrate 201 and / or the intermediate layer 202. The portion of the waveguide 210 in the figure includes LN. However, other and / or additional electro-optic materials (such as LT) may be used. The waveguide 210 includes a ridge 212 and a thin film portion 214. The channel regions and extensions of the electrodes 220 and 230 are not shown. The optical device 200 is similar to the optical devices 100, 100', 100'', 100''', and / or 100'''. Thus, the waveguide 210 and the electrodes 220 and 230 are respectively similar to the waveguide 110 and / or 110' and the electrodes 120, 120', and / or 120'', and 130, 130', and / or 130''.

[0080] FIG. 2 shows the relative sizes of the optical mode for an optical signal and the high-frequency (RF) mode (or microwave mode) for a microwave. FIG. 2 is not to scale and only shows a part of the optical device 200. As shown in FIG. 2, the optical mode can be mainly confined in the waveguide 210, the intermediate layer 202, and the cladding material 204. In contrast, the microwave mode spreads through the plurality of stacks 201, 202, 210, 220, 230, and 204. Therefore, the microwave mode suffers absorption losses from the plurality of stacks 201, 202, 204, 210, 220, and 230. The absorption from the silicon substrate 201 can be particularly high. Also, the use of the silicon substrate 201 can affect the speed of the microwave signal through the electrodes 220 and 230. Since the size of the thin-film waveguide 210 is small, it is possible to design other parts of the optical device 200 to reduce the microwave absorption loss. For example, a part of the silicon substrate 201 may be removed or replaced, the electrodes 220 and / or 230 may be moved, the size of the waveguide 210 may be reduced, one or more other substrates may be used, and / or other changes are possible. For example, the intermediate layer 202 may be thick, such as having a thickness of 3 micrometers or more in some embodiments.

[0081] For example, FIGS. 3-5 show embodiments 300, 400, and 500 of an optical device capable of further reducing microwave absorption loss. FIG. 3 is a cross-sectional view showing a part of an embodiment 300 of an optical device whose performance can be improved. FIG. 3 is not to scale, and only a part of the optical device 300 is shown. The optical device 300 includes a waveguide 310, and electrodes 320 and 330 on a substrate 301. An intermediate layer 302 and a cladding material 304 are also shown. In the illustrated embodiment, the substrate 301 is silicon, the intermediate layer 302 is silicon dioxide, and the cladding material 304 is silicon dioxide. In some embodiments, other and / or additional materials may be used. The portion of the waveguide 310 in the figure contains LN. However, other and / or additional materials (such as LT) may be used. The waveguide 310 includes a ridge 312 and a thin film portion 314. The channel regions and extensions of the electrodes 320 and 330 are not shown. The optical device 300 is similar to the optical device 200. Thus, the waveguide 310 and the electrodes 320 and 330 are similar to the waveguide 210 and the electrodes 220 and 230, respectively. Also, the substrate 301, the intermediate layer 302, and the cladding material 304 are similar to the substrate 201, the intermediate layer 202, and the cladding material 204, respectively. However, in the optical device 300, the electrodes 320 and 330 are moved further away from the underlying silicon substrate 301. In some embodiments, the electrodes 320 and 330 may be moved further away from the silicon substrate 301 by increasing the thickness of the intermediate layer 302. For example, the intermediate layer 302 may be, in some embodiments, a thickness of 3 micrometers or more. This may be done in addition to or instead of moving the electrodes further away from the thin film portion 314. Further, the size of the thin film portion 314 of the waveguide 310 is reduced. Thus, absorption by the silicon substrate 301 and the waveguide 310 can be reduced. Further, the change in the speed of the microwave signal can also be reduced.

[0082] FIG. 4 is a cross-sectional view showing a part of an embodiment 400 of an optical device whose performance can be improved. FIG. 4 is not to scale and only a part of the optical device 400 is shown. The optical device 400 includes a waveguide 410 on a substrate 401, as well as electrodes 420 and 430. An intermediate layer 402 and a cladding material 404 are also shown. In the illustrated embodiment, the substrate 401 is silicon, the intermediate layer 402 is silicon dioxide, and the cladding material 404 is silicon dioxide. In some embodiments, other and / or additional materials may be used. The portion of the waveguide 410 in the figure includes LN. However, other and / or additional materials (such as LT) may be used. The waveguide 410 includes a ridge 412 and a thin film portion 414. The channel regions and extensions of the electrodes 420 and 430 are not shown. The optical device 400 is similar to the optical device 200. Accordingly, the waveguide 410 and the electrodes 420 and 430 are similar to the waveguide 210 and the electrodes 220 and 230, respectively. Also, the substrate 401, the intermediate layer 402, and the cladding material 404 are similar to the substrate 201, the intermediate layer 202, and the cladding material 204, respectively. However, in the optical device 400, the electrodes 420 and 430 are moved further away from the underlying silicon substrate 401. In some embodiments, the electrodes 420 and 430 may be moved further away from the silicon substrate 401 by increasing the thickness of the intermediate layer 402. This may be done in addition to or instead of moving the electrodes further away from the thin film portion 414. Accordingly, absorption by the silicon substrate 401 can be reduced. Further, a change in the speed of the microwave signal can also be reduced.

[0083] FIG. 5 is a cross-sectional view showing a part of an embodiment 500 of an optical device whose performance can be improved. FIG. 5 is not to scale and only a part of the optical device 500 is shown. The optical device 500 includes a waveguide 510 on a substrate 501, as well as electrodes 520 and 530. An intermediate layer 502 and a cladding material 504 are also shown. In the illustrated embodiment, the substrate 501 is silicon, the intermediate layer 502 is silicon dioxide, and the cladding material 504 is silicon dioxide. In some embodiments, other and / or additional materials may be used. The portion of the waveguide 510 in the figure includes LN. However, other and / or additional materials (such as LT) may be used. The waveguide 510 includes a ridge 512 and a thin film portion 514. The channel regions and extensions of the electrodes 520 and 530 are not shown. The optical device 500 is similar to the optical device 200. Therefore, the waveguide 510 and the electrodes 520 and 530 are similar to the waveguide 210 and the electrodes 220 and 230, respectively. The substrate 501, the intermediate layer 502, and the cladding material 504 are similar to the substrate 201, the intermediate layer 202, and the cladding material 204, respectively. However, in the optical device 500, the electrodes 520 and 530 are moved further away from the underlying silicon substrate 501 and are located further away. Further, a portion of the silicon substrate 501 below the ridge 512 is removed. Therefore, absorption by the silicon substrate 501 can be reduced. Further, the change in the speed of the microwave signal can also be reduced. In some embodiments, in addition to or instead of removing a portion of the substrate, another substrate may be selected.

[0084] In this way, the microwave loss can be further alleviated. Therefore, in addition to the advantages of the optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’’, the optical devices 300, 400, and 500 can further reduce the microwave absorption loss. As a result, the performance of the optical devices 300, 400, and 500 can be improved.

[0085] Figures 6, 7, 8, 9, 10, and 11 each show optical devices 600, 700, 800, 900, 1000, and 1100 whose performance can be improved. Figures 6 - 11 illustrate various electrode configurations. Figures 6 - 11 are not to scale and only show a portion of optical devices 600, 700, 800, 900, 1000, and 1100. Optical devices 600, 700, 800, 900, 1000, and 1100 are similar to optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’ and are similar. Similar components have similar reference numerals.

[0086] Referring to FIG. 6, waveguide 610 having electrodes 620 and 630 and ridge 612 is shown. FIG. 6 also shows extensions 624 and 634 (only one of each is labeled). As described above, extensions 624 and 634 of electrodes 620 and 630 can improve performance. In the embodiment shown in FIG. 6, extensions 624 and 634 are regularly spaced. Thus, extensions 624 and 634 are periodic and have a certain pitch. Also, extensions 624 and 634 are all the same size. However, other configurations are possible. For example, extensions 624 and 634 may have different sizes and different pitches. Thus, optical device 600 can share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’ and can share the advantages.

[0087] FIG. 7 shows an optical device 700. For clarity, only electrodes 720, 730, and 740 are shown. Generally, a waveguide / ridge is between electrode 720 and electrode 730. Another waveguide / ridge (or waveguide / ridge branch) is between electrode 720 and electrode 740. In some embodiments, electrode 720 transmits a microwave signal while electrodes 730 and 740 are grounded. However, other configurations are possible. In the illustrated embodiment, only electrode 720 has a channel region 722 and an extension 724. The extension 724 is rectangular. However, electrodes 730 and 740 do not have extensions. Because of the presence of the extension 724, current can be more easily driven through the channel region 722. Thus, the optical device 700 may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’.

[0088] FIG. 8 shows an optical device 800. For clarity, only electrodes 820, 830, and 840 are shown. Generally, a waveguide / ridge is between electrode 820 and electrode 830. Another waveguide / ridge (or waveguide / ridge branch) is between electrode 820 and electrode 840. In some embodiments, electrode 820 transmits a microwave signal while electrodes 830 and 840 are grounded. However, other configurations are possible. In the illustrated embodiment, only electrode 820 has a channel region 822 and an extension 824. The extension 824 is in a “T” shape. Thus, the extension 824 has a connection portion 824A and a retrograde portion 824B. Electrodes 830 and 840 do not have extensions. Because of the presence of the extension 824, current can be more easily driven through the channel region 822. Thus, the optical device 800 may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’ and may share the advantages of.

[0089] FIG. 9 shows an optical device 900. Electrodes 920, 930, and 940 are shown. A waveguide / ridge 910 is between electrode 920 and electrode 930. Another waveguide / ridge (or waveguide / ridge branch) 950 is between electrode 920 and electrode 940. In some embodiments, electrode 920 transmits a microwave signal, while electrodes 930 and 940 are grounded. However, other configurations are possible. In the illustrated embodiment, electrode 920 has a channel region 922 and an extension 924. Similarly, electrode 930 has a channel region 932 and an extension 934. Electrode 940 has a channel region 942 and an extension 944. Extensions 924, 934, and 944 are generally in a "T" shape, but have different lengths and are not periodic (e.g., irregularly spaced and having various pitches). Due to the presence of extensions 924, 934, and 944, current can be more easily driven through channel regions 922, 932, and 942. Thus, optical device 900 may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’ and may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’

[0090] FIG. 10 shows an optical device 1000. Electrodes 1020, 1030, and 1040 are shown. A waveguide / ridge 1010 is between electrode 1020 and electrode 1030. Another waveguide / ridge (or waveguide / ridge branch) 1050 is between electrode 1020 and electrode 1040. In some embodiments, electrode 1020 transmits a microwave signal while electrodes 1030 and 1040 are grounded. However, other configurations are possible. In the illustrated embodiment, electrode 1020 has a channel region 1022 and an extension 1024. Electrode 1030 has a channel region 1032 and an extension 1034. Electrode 1040 has a channel region 1042 and an extension 1044. Extensions 1024, 1034, and 1044 have various shapes and are irregularly spaced. Further, channel 1022 has a notch. However, even so, channel 1022 has a straight central region capable of conducting current. Due to the presence of extensions 1024, 1034, and 1044, current can be more easily driven through channel regions 1022, 1032, and 1042, respectively. Thus, optical device 1000 may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’ and may share the advantages of

[0091] FIG. 11 shows an optical device 1100. Electrodes 1120, 1130, and 1140 are shown. A waveguide / ridge 1110 is between electrode 1120 and electrode 1130. Another waveguide / ridge (or waveguide / ridge branch) 1150 is between electrode 1120 and electrode 1140. In some embodiments, electrode 1120 transmits a microwave signal while electrodes 1130 and 1140 are grounded. However, other configurations are possible. In the illustrated embodiment, electrode 1120 has a channel region 1122 and an extension 1124. Electrode 1130 has a channel region 1132 and an extension 1134. Electrode 1140 has a channel region 1142 and an extension 1144. Extensions 1124, 1134, and 1144 have various shapes and are irregularly spaced. Due to the presence of extensions 1124, 1134, and 1144, current can be more easily driven through channel regions 1122, 1132, and 1142, respectively. Thus, optical device 1100 can share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’. ’ Thus, as shown by optical devices 600, 700, 800, 900, 1000, and 1100, extensions of various configurations may be used for the electrodes.

[0092] FIGS. 12A - 12D show various electrode configurations in diagrams showing a part of embodiments 1200A, 1200B, 1200C, and 1200D of an optical device whose performance can be improved. FIGS. 12A - 12D are not to scale and only show a part of optical devices 1200A, 1200B, 1200C, and 1200D. Optical devices 1200A, 1200B, 1200C, and 1200D are optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’. ’is similar to. Therefore, similar components have the same labels (e.g., waveguide 1210 is similar to waveguide 110’). FIG. 12A is a plan view of optical device 1200A. FIGS. 12B - 12D are cross-sectional views showing parts of optical devices 1200B, 1200C, and 1200D. FIGS. 12A - 12D show that even though the cross-sectional views of several optical devices are different, those devices can share the same plan view. Conversely, even if the cross-sectional views can be similar, several optical devices can have different plan views.

[0093] Referring to FIG. 12A, electrodes 1220A, 1230A, and 1240A, and waveguides 1210A and 1250A are shown. A part of waveguides 1210A and 1250A shown in FIG. 12A corresponds to a ridge in some embodiments. Electrodes 1220A, 1230A, and 1240A each have channel regions 1222A, 1232A, and 1242A. Also, electrodes 1220A, 1230A, and 1240A include extensions 1224A, 1234A, and 1244A. As described above, the extensions 1224A, 1234A, and 1244A of electrodes 1220A, 1230A, and 1240A can improve performance. In some embodiments, channels 1222A, 1232A, and 1242A are each at the same height as extensions 1224A, 1234A, and 1244A.

[0094] FIG. 12B shows optical device 1200B that shares the plan view of optical device 1200A. Therefore, optical device 1200B includes electrodes 1220B, 1230B, and 1240B and waveguides 1210B and 1250B. Waveguides 1210B and 1250B each include ridges 12 1 2B and 1252B. Waveguides 1210B and 1250B have a common thin film portion 1214 BThey are shared. Electrodes 1220B, 1230B, and 1240B each have channel regions 1222B, 1232B, and 1242B, respectively. Also, electrodes 1220B, 1230B, and 1240B include extension portions 1224B, 1234B, and 1244B. As described above, the extension portions 1224B, 1234B, and 1244B of electrodes 1220B, 1230B, and 1240B can improve performance. Although it shares the same plan view as optical device 1200A, the channel regions 1222B, 1232B, and 1242B are raised to a height higher than that of the extension portions 1224B, 1234B, and 1244B (farther from the substrate). Optical device 1200B functions in the same manner as optical device 1200A and thus can share the advantages of optical device 100.

[0095] FIG. 12C shows an optical device 1200C having a cross-sectional view very similar to that of optical device 1200B. Optical device 1200C includes electrodes 1220C, 1230C, and 1240C, and waveguides 1210C and 1250C. Waveguides 1210C and 1250C each include ridges 12 1 2C and 1252C. Waveguides 1210 C and 1250 C share a common thin film portion 1214C. Electrodes 1220C, 1230C, and 1240C each have channel regions 1222C, 1232C, and 1242C, respectively. Also, electrodes 1220C, 1230C, and 1240C include extension portions 1224C, 1234C, and 1244C. As described above, the extension portions 1224C, 1234C, and 1244C of electrodes 1220C, 1230C, and 1240C can improve performance. Although it shares a similar cross-sectional view, optical device 1200C has a different plan view from optical devices 1200A and 1200B. As can be seen from the dotted line in FIG. 12C, the outer edges of the extension portions 1224C, 1234C, and 1244C are respectively the channel regions 1222C, 1232C, and 1 2It is aligned with the outer edge of 42C. Therefore, electrodes 1220C, 1230C, and 1240C appear rectangular when viewed from above. That is, the extension portions 1224C, 1234C, and 1244C are not visible in the plan view. However, even so, the extension portions 1224C, 1234C, and 1244C are closer to the waveguide 1210C / ridge 1212C and the waveguide 1250C / ridge 1252C than the corresponding channel regions 1222C, 1232C, and 1242C. The optical device 1200C functions in the same manner as the optical devices 1200A and 1200B. Therefore, despite having different plan views, the optical device 1200C may share the advantages of the optical devices 100, 1200A, and / or 1200B.

[0096] FIG. 12D shows an optical device 1200D that shares the plan view of the optical device 1200A. Therefore, the optical device 1200D includes electrodes 1220D, 1230D, and 1240B, and waveguides 1210D and 1250D. The waveguides 1210D and 1250D each include ridges 12 1 2D and 1252D. The waveguides 1210D and 1250D each include thin film portions 1214D and 1254D, respectively. The electrodes 1220D, 1230D, and 1240D each have channel regions 1222D, 1232D, and 1242D. Also, the electrodes 1220D, 1230D, and 1240D each include extension portions 1224D, 1234D, and 1244D. As described above, the extension portions 1224D, 1234D, and 1244D of the electrodes 1220D, 1230D, and 1240D can improve performance. Although sharing the same plan view as the optical device 1200A, the thin film portions 1214D and 1254D of the waveguides 1210D and 1250D are each reduced in size. The optical device 1200D functions in the same manner as the optical devices 1200A, 1200B, and 1200C. Therefore, the optical device 1200D may share the advantages of the optical devices 100, 1200A, 1200B, and / or 1200C.

[0097] Figures 13A through 13J show various electrode configurations in diagrams depicting portions of embodiments of optical devices 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 1300I, and 1300J that can have improved performance. Figures 13A through 13J are not to scale and show only portions of optical devices 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 1300I, and 1300J. Figures 13A through 13J show various configurations of electrodes that can be used in x-cut or y-cut waveguide structures. Optical devices 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 1300I, and 1300J are similar to optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’. ’ Accordingly, similar components have similar labels (e.g., waveguide ridge 1312A is similar to waveguide ridge 112). For clarity, electrodes are generally illustrated as rectangles in Figures 13A through 13I. However, such electrodes may include the channel regions, extensions, and / or other features described herein. Thus, the electrodes shown in Figures 13A through 13I primarily show the positions of the electrodes.

[0098] Figure 13A shows optical device 1300A having a waveguide with ridge 1312A and thin film portion 1314A, and electrodes 1320A and 1330A. Substrate 1301A and intermediate layer 1302A are also shown. It is desirable for the extensions of the electrodes to be close to the corresponding waveguides. In some embodiments, it is desirable for a portion of the extension of the electrode to be between the upper end of the waveguide ridge and the upper end of the thin film portion. Accordingly, electrodes 1320A and 1330A share a contact surface with thin film portion 1314A of the waveguide. More specifically, electrodes 1320A and 1330A contact the upper surface of thin film portion 1314A.

[0099] FIG. 13B shows an optical device 1300B including a waveguide having a ridge 1312B and a thin film portion 1314B, and electrodes 1320B and 1330B. A substrate 1301B and an intermediate layer 1302B are also shown. The extension of the electrode is desirably close to the corresponding waveguide. Electrodes 1320B and 1330B extend from above the upper end of the waveguide ridge 1312B through the thin film portion 1314B of the waveguide into the intermediate layer 1302B.

[0100] FIG. 13C shows an optical device 1300C including a waveguide having a ridge 1312C and a thin film portion 1314C, and electrodes 1320C and 1330C. A substrate 1301C and an intermediate layer 1302C are also shown. The extension of the electrode is desirably close to the corresponding waveguide. Electrodes 1320C and 1330C extend from above the upper end of the waveguide ridge 1312C through the thin film portion 1314C of the waveguide into the substrate 1301C.

[0101] FIG. 13D shows an optical device 1300D including a waveguide having a ridge 1312D and a thin film portion 1314D, and electrodes 1320D and 1330D. A substrate 1301D and an intermediate layer 1302D are also shown. The extension of the electrode is desirably close to the corresponding waveguide. Electrode extensions 1320D and 1330D extend from between the upper end of the waveguide ridge 1312D and the upper end of the waveguide thin film portion 1314D through the thin film portion 1314D into the substrate 1301D.

[0102] FIG. 13E shows an optical device 1300E including a waveguide having a ridge 1312E and a thin film portion 1314E, and electrodes 1320E and 1330E. A substrate 1301E and an intermediate layer 1302E are also shown. The extension of the electrode is desirably close to the corresponding waveguide. Electrodes 1320E and 1330E extend from above the upper end of the waveguide ridge 1312E to between the upper end of the waveguide ridge 1312E and the upper end of the waveguide thin film portion 1314E.

[0103] Figure 13F shows an optical device 1300F including a waveguide having a structure 1312F and a thin film portion 1314F, and electrodes 1320F and 1330F. A substrate 1301F and an intermediate layer 1302F are also shown. The extensions of the electrodes desirably are close to the corresponding waveguides. Electrodes 1320F and 1330F extend from above the upper end of the structure 1312F to between the upper end of the waveguide structure 1312F and the upper end of the waveguide thin film portion 1314F. Further, the structure 1312F corresponds to a waveguide ridge. However, in the illustrated embodiment, the structure 1312 may be another component (such as a heater).

[0104] Figure 13G shows an optical device 1300G including a waveguide having a ridge 1312G and a thin film portion 1314G, and electrodes 1320G and 1330G. A substrate 1301G and an intermediate layer 1302G are also shown. The extensions of the electrodes desirably are close to the corresponding waveguides. Electrodes 1320G and 1330G extend from above the thin film portion 1314G into the waveguide thin film portion 1314G. Further, the waveguide ridge 1312G is below the waveguide thin film portion 1314G.

[0105] Figure 13H shows an optical device 1300H including a waveguide having a structure 1312H and a thin film portion 1314H, and electrodes 1320H and 1330H. A substrate 1301H and an intermediate layer 1302H are also shown. The extensions of the electrodes desirably are close to the corresponding waveguides. Electrodes 1320H and 1330H extend from above the upper end of the thin film portion 1314H into the waveguide thin film portion 1314H. The structure 1312H may be a heater or a similar component corresponding to a waveguide ridge. Further, the structure 1312H is below the waveguide thin film portion 1314H.

[0106] FIG. 13I shows an optical device 1300I comprising a waveguide having a structure 1312I and a thin film portion 1314I, and electrodes 1320I and 1330I. A substrate 1301I and an intermediate layer 1302I are also shown. The extensions of the electrodes are desirably close to the corresponding waveguides. Electrodes 1320I and 1330I extend from below the lower end of the structure 1312I to the bottom surface of the waveguide thin film portion 1314I. The structure 1312i may be a heater or a similar component corresponding to the waveguide ridge and is below the waveguide thin film portion 1314I.

[0107] FIG. 13J shows an optical device 1300J comprising a waveguide having a ridge 1312J and a thin film portion 1314J, and electrodes 1320J and 133 0J and. A substrate 1301I and an intermediate layer 1302I are also shown. Electrode 1320J comprises a channel region 1322J and an extension 1324J. Electrode 1330J comprises a channel region 1332J and an extension 1334J. As seen in the optical device 1330J, the channel regions 1322J and / or 1332J need not have a rectangular cross-section.

[0108] Thus, regardless of the various electrode and waveguide configurations, the optical devices 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 1300I, and 1300J are similar to the optical device 100. Accordingly, the optical devices 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 1300I, and 1300J may share the advantages of the optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’ and.

[0109] Figures 14A - 14K show various electrode configurations in diagrams depicting portions of embodiments 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400I, 1400J, and 1400K of an optical device whose performance can be improved. Figures 14A - 14K are not to scale and show only portions of optical devices 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400I, 1400J, and 1400K. Optical devices 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400I, 1400J, and 1400K are similar to optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’ and are similar. Accordingly, similar components have similar labels (e.g., waveguide ridge 1412A is similar to waveguide ridge 112). Although present, the channel regions and extensions are not shown separately in Figures 14A - 14D. Figures 14A - 14K show various configurations of electrodes that can be used in waveguide structures (e.g., z - cut waveguides) where the electro - optic effect occurs outside the thin - film plane. For clarity, the electrodes are generally shown as rectangles in Figures 14A - 14D. However, such electrodes may comprise the channel regions, extensions, and / or other features described herein. Accordingly, the electrodes shown in Figures 14A - 14D mainly indicate the positions of the electrodes. The extensions and other features of some embodiments are shown more clearly in Figures 14E - 14K.

[0110] Figure 14A shows an optical device 1400A comprising a waveguide having a ridge 1412A and a thin - film portion 1414A, and electrodes 1420A and 1430A. Substrate 1401A and intermediate layer 1402A are also shown. The electrodes are desirably close to the corresponding waveguide and provide a vertical field in the region of ridge 1412A. Accordingly, electrode 1420A is above ridge 1412A, while electrode 1430A is a film below ridge 1412A and extends horizontally.

[0111] FIG. 14A shows an optical device 1400A including a waveguide having ridges 1412A and a thin film portion 1414A, and electrodes 1420A and 1430A. Substrate 1401A and intermediate layer 1402A are also shown. The electrodes are desirably close to the corresponding waveguide and provide a vertical field in the region of ridge 1412A. Thus, electrode 1420A is above ridge 1412A, while electrode 1430A is a film below ridge 1412A and extends horizontally.

[0112] FIG. 14B shows an optical device 1400B including a waveguide having ridges 1412B and a thin film portion 1414B, and electrodes 1420B, 1430B, and 1440B. Substrate 1401B and intermediate layer 1402B are also shown. The electrodes are desirably close to the corresponding waveguide and provide a vertical field in the region of ridge 1412B. Thus, electrode 1420B is above ridge 1412B, while electrodes 1430B and 1440B are B on the side of ridge 1412 and extend below it. Electrodes 1430B and 1440B terminate near or within thin film portion 1414B. Thus, the electric field in the region of ridge 1412B is substantially vertical (z direction).

[0113] FIG. 14C shows an optical device 1400C including a waveguide having ridges 1412C and a thin film portion 1414C, and electrodes 1420C, 1430C, and 1440C. Substrate 1401C and intermediate layer 1402C are also shown. The electrodes are desirably close to the corresponding waveguide and provide a vertical field in the region of ridge 1412C. Thus, electrode 1420C is above ridge 1412C, while electrodes 1430C and 1440C are on the side of ridge 1412C and extend below it. Electrodes 1430C and 1440C extend through waveguide thin film portion 1414C. Thus, the electric field in the region of ridge 1412C is substantially vertical (z direction).

[0114] FIG. 14D shows an optical device 1400D comprising a waveguide having a structure 1412D and a thin film portion 1414D, and electrodes 1420D and 1430D. A substrate 1401D and an intermediate layer 1402D are also shown. The electrodes are desirably proximate to the corresponding waveguide and provide a vertical field in the region of the structure 1412D. Thus, electrode 1420D is above the structure 1412D, while electrode 1430D is a film below the structure 1412D and extends horizontally. The structure 1412D is below the waveguide thin film portion 1414D and may be a heater or a similar component.

[0115] FIG. 14E shows an optical device 1400E comprising a waveguide 1410E having a ridge 1412E and a thin film portion 1414E, and electrodes 1420E and 1430E. A substrate 1401E and an intermediate layer 1400E are also shown. The electrodes are desirably proximate to the corresponding waveguide and provide a vertical field in the region of the structure 1412E. Thus, electrode 1420E is above the structure 1412 E while electrodes 1430E and 1440E are on the sides of the structure 1412E. In the illustrated embodiment, electrodes 1430E and 1440E are ground electrodes, while electrode 1420E transmits a signal. The positions of the ground electrodes 1430E and 1440E are exemplary. Other grounding positions may be used as long as a vertical electric field is established within the waveguide 1412E. Also shown are the channel regions 1422E, 1432E, and 1442E, and the extensions 1424E, 1434E, and 1444E of electrodes 1420E, 1430E, and 1440E, respectively. The channel regions 1422E, 1432E, and 1442E, and the extensions 1424E, 1434E, and 1444E are similar to the channel regions and extensions described above. Thus, the optical device 1400E may share the advantages of the optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ that utilize extensions. ’ which utilize extensions.

[0116] FIG. 14F shows a differential optical device 1400F comprising a waveguide 1410F having ridges 1412F and a thin film portion 1414F, and electrodes 1420F and 1430F. A substrate 1401F and an intermediate layer 1400F are also shown. The electrodes are desirably proximate to the corresponding waveguides and provide a vertical field in the region of structure 1412F. Thus, electrode 1420F is above structure 1412F, while electrodes 1430F and 1440F are lateral to structure 1412F. Since optical device 1400F is a differential modulator, additional waveguides 1460F (e.g., additional ridges) and additional electrodes 1450F are present. In the illustrated embodiment, electrodes 1430F and 1440F are ground electrodes, while electrodes 1420F and 1450F carry signals. The positions of ground electrodes 1430F and 1440F are exemplary. Other ground positions may be used as long as a vertical electric field is established within waveguides 1412F and 1460F. Channel regions 1422F, 1432F, 1442F, and 1452F, and extensions 1424F, 1434F, 1444F, and 1454F of electrodes 1420F, 1430F, 1440F, and 1450F, respectively, are also shown. Channel regions 1422F, 1432F, 1442F, and 1452F, and extensions 1424F, 1434F, 1444F, and 1454F are similar to the channel regions and extensions described above. Thus, optical device 1400F may share the advantages of optical devices 100, 100', and / or 150 that utilize extensions.

[0117] FIG. 14G shows a differential optical device 1400G comprising a waveguide 1410G having ridges 1412G and a thin film portion 1414G, and electrodes 1420G and 1430G. A substrate 1401G and an intermediate layer 1400G are also shown. The electrodes are desirably proximate to the corresponding waveguides and provide a vertical field in the region of structure 1412G. Thus, electrode 1420G is above structure 1412G, while electrodes 1430G and 1440G are on the sides of structure 1412G. Since optical device 1400G is a differential modulator, there are additional waveguides 1460G (e.g., additional ridges) and additional electrodes 1450G. In the illustrated embodiment, electrodes 1430G and 1440G are ground electrodes, while electrodes 1420G and 1450G carry signals. The positions of ground electrodes 1430G and 1440G are exemplary. Other grounding positions may be used as long as a vertical electric field is established within waveguides 1412G and 1460G. Channel regions 1422G, 1432G, 1442G, and 1452G, and extensions 1424G, 1434G, 1444G, and 1454G of electrodes 1420G, 1430G, 1440G, and 1450G, respectively, are also shown. Channel regions 1422G, 1432G, 1442G, and 1452G, and extensions 1424G, 1434G, 1444G, and 1454G are similar to the channel regions and extensions described above. Optical device 1400G is similar to optical device 1400F. However, extensions 1424G and 1454G are offset from channel regions 1422G and 1452G, respectively. As a result, the interaction between channel regions 1422G and 1452G can be reduced. Thus, optical device 1400G can share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ that utilize extensions. ’ which can share the advantages.

[0118] FIG. 14H shows an optical device 1400H including a waveguide 1410H having a structure 1412H and a thin film portion 1414H, and electrodes 1420H and 1430H. A substrate 1401H and an intermediate layer 1400H are also shown. The electrodes are desirably close to the corresponding waveguides and provide a vertical field in the region of the structure 1412H. The structure 1412H may be a material other than a nonlinear optical material, such as a passive material or a heater described herein. An optional buffer layer may exist between the thin film region 1414H including the nonlinear optical material and the structure 1412H. In some embodiments, the structure 1412H may simply be an embedded ridge including a nonlinear optical material. The electrode 1420H is below the structure 1412H, while the electrodes 1430H and 1440H are on the sides of the structure 1412H. In the illustrated embodiment, the electrodes 1430H and 1440H are ground electrodes, while the electrode 1420H transmits a signal. The positions of the ground electrodes 1430H and 1440H are exemplary. Other grounding positions may be used as long as a vertical electric field is established within the waveguide 1412H. The channel regions 1422H, 1432H, and 1442H, and the extensions 1424H, 1434H, and 1444H of the electrodes 1420H, 1430H, and 1440H, respectively, are also shown. The channel regions 1422H, 1432H, and 1442H, and the extensions 1424H, 1434H, and 1444H are similar to the channel regions and extensions described above. Thus, the optical device 1400H may share the advantages of the optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ that utilize extensions. ’ may share.

[0119] FIG. 14I shows a differential optical device 1400I including a waveguide 1410I having a structure 1412I and a thin film portion 1414I, and electrodes 1420I and 1430I. A substrate 1401I and an intermediate layer 1400I are also shown. The electrodes are desirably close to the corresponding waveguides and provide a vertical field in the region of the structure 1412I. Thus, the electrode 1420I is in the structure 1412Below I, while electrodes 1430I and 1440I are on the sides of structure 1412I. Structure 1412I may be a material other than a nonlinear optical material, such as a passive material or a heater described herein. In some embodiments, structure 1412I may simply be an embedded ridge containing a nonlinear optical material. Since optical device 1400I is a differential modulator, there are additional waveguides / structures 1460I (e.g., additional ridges, passive materials, or heaters) and additional electrodes 1450I. In the illustrated embodiment, electrodes 1430I and 1440I are ground electrodes, while electrodes 1420I and 1450I transmit signals. The positions of ground electrodes 1430I and 1440I are exemplary. Other grounding positions may be used as long as a vertical electric field is established within waveguides 1412I and 1460I. An optional buffer layer may be present between the thin film region 1414I containing the nonlinear optical material and structures 1412I and 1460I. Also shown are the channel regions 1422I, 1432I, 1442F, and 1452I, and the extensions 1424I, 1434I, 1444I, and 1454I of electrodes 1420I, 1430I, 1440I, and 1450I, respectively. Channel regions 1422I, 1432I, 1442I, and 1452I, and extensions 1424I, 1434I, 1444I, and 1454I are similar to the channel regions and extensions described above. Thus, optical device 1400I may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ that utilize extensions. ’ may share.

[0120] FIG. 14J shows an optical device 1400J comprising a waveguide 1410J having a ridge 1412J and a thin film portion 1414J, and electrodes 1420J and 1430J. Substrate 1401J and intermediate layer 140 2J) is also shown. The electrodes are desirably close to the corresponding waveguides and provide a vertical field in the region of structure 1412J. Thus, electrode 1420J is above structure 1412J, while electrodes 1430J and 1440J are on the sides of structure 1412J. In the illustrated embodiment, electrodes 1430J and 1440J are ground electrodes, while electrode 1420J transmits a signal. The positions of ground electrodes 1430J and 1440J are exemplary. Other grounding positions may be used as long as a vertical electric field is established within waveguide 1412J. Channel regions 1432J and 1442J of electrodes 1430J and 1440J, respectively, and extensions 1434J and 1444J are also shown. Thus, signal electrode 1420J does not have an extension in this embodiment. Channel regions 1432J and 1442J, and extensions 1434J and 1444J are similar to the channel regions and extensions described above. Thus, optical device 1400J may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ that utilize extensions. ’ Furthermore, not all electrodes necessarily need to have extensions to improve performance.

[0121] FIG. 14K shows a differential optical device 1400K comprising a waveguide 1410K having a ridge 1412K and a thin film portion 1414K, and electrodes 1420K and 1430K. Substrate 1401K and intermediate layer 140 2K is also shown. The electrodes are desirably close to the corresponding waveguides and provide a vertical field in the region of structure 1412K. Thus, electrode 1420K is above structure 1412K, while electrodes 1430K and 1440K are on the sides of structure 1412K. Since optical device 1400K is a differential modulator, there are additional waveguides 1460K (e.g., additional ridges) and additional electrodes 1450K. In the illustrated embodiment, electrodes 1430FK and 1440K are ground electrodes, while electrodes 1420K and 1450K transmit signals. The positions of ground electrodes 1430K and 1440K are exemplary. Other grounding positions may be used as long as a vertical electric field is established within waveguides 1412K and 1460K. Channel regions 1432K and 1442K of electrodes 1430K and 1440K, respectively, and extensions 1434K and 1444K are also shown. Channel regions 1432K and 1442K, and extensions 1434K and 1444K are similar to the channel regions and extensions described above. However, signal electrodes 1420K and 1450K do not have extensions. Optical device 1400K may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’. ’ can share. Further, not all electrodes necessarily need to have extensions to improve performance.

[0122] Thus, regardless of the configurations of the various electrodes and waveguides, optical devices 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400I, 1400J, and 1400K are similar to optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’. ’ Therefore, optical devices 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400I、 1400J, and 1400K can share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’. ’

[0123] Figures 15A and 15B respectively show a part of embodiments 1500A and 1500B of an optical device. Optical devices 1500A and 1500B are similar to optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’’. Figures 15A and 15B are not to scale and only show a part of optical devices 1500A and 1500B. Optical devices 1500A and 1500B are similar to optical devices 100, 100’, 100’’, and / or 100’’’’. Therefore, similar components have the same reference numerals. Optical device 1500A includes a waveguide 110 / 110’ having a ridge 112, and a waveguide 1510 having a ridge 1512, which is similar to electrodes 120, 120’, 120’’, 130, 130’, and 130’, and electrodes 1520 and 1530. Electrodes 1520 and 1530 respectively include channel regions 1522 and 1532, which are similar to channel regions 122, 122’, 122’’, and 132, 132’, 132’’ of electrodes 120, 120’, 120’’, and 130, 130’, 130’’. Electrodes 1520 and 1530 respectively include extensions 1524 and 1534, which are similar to extensions 124, 124’, 124’’, and 134, 134’, 134’’ of electrodes 120, 120’, 120’’, and 130, 130’, 130’’. Extensions 1524 and 1534 include connection parts 1524A and 1534A, which are similar to connection parts 124A, 124A’, 124A’’, and 134A, 134A’, 134A’’, and reverse parts 1524B and 1534B, which are similar to reverse parts 124B, 124B’, 124B’’, and 134B, 134B’, 134B’’.

[0124] In addition, the waveguide 1510 includes a waveguide bent portion 1515. Although multiple waveguide bent portions are shown in FIG. 15A, only one waveguide bent portion 1515 is labeled. Each waveguide bent portion 1515 may have a bending radius of 1 mm or less. In some embodiments, each waveguide bent portion 1515 may also have a bending radius of 500 μm or less. In some embodiments, each waveguide bent portion 1515 has a bent portion optical loss of 0.5 dB or less. The bent portions of the waveguide (and electrodes) may be used to increase the region where the electrodes 1520 and 1530 are close to the waveguide 1510 while suppressing the size of the device incorporating the optical device 1500A. For example, the waveguide 1510 and the electrodes 1520 and 1530 may occupy an area of 50 square millimeters or less. In some embodiments, the waveguide 1510 and the electrodes 1520 and 1530 occupy an area of 20 square millimeters or less. In some embodiments, the waveguide 1510 and the electrodes 1520 and 1530 are present on an integrated circuit having a length of 32 millimeters or less. In some such embodiments, the waveguide 1510 and the electrodes 1520 and 1530 are present on an integrated circuit having a length of 22 millimeters or less. This holds even if the length of the waveguide 1510 is longer. Thus, a larger optical signal modulation can be achieved with a smaller overall device.

[0125] The electrode 1520 may include an electrode bent portion 1525 (only one of which is labeled in FIG. 15A). Similarly, the electrode 1530 may include an electrode bent portion 1535 (only one of which is labeled in FIG. 15A). Similar to the waveguide bent portion 1515 of the waveguide 1510, the electrode bent portions 1525 and 1535 enable longer electrodes 1520 and 1530, respectively, with a smaller footprint. Thus, the optical device 1500A can consume less space at a specific length in the package.

[0126] In some embodiments, the electrode bending portions 1525 and 1535 may be used to improve performance. More specifically, the electrode bending portions 1525 and 1535 and the waveguide bending portion 1515 can be configured to provide a path difference between the optical signal for the waveguide 1510 and the electrode signal for the electrodes 1520 and / or 1530. Such a path difference may be used to compensate for the difference in transmission speed between the microwave signal in the electrodes 1520 and / or 1530 and the transmission speed of the optical signal in the waveguide 1510. The speed of the optical signal passing through the waveguide 1510 is affected by the refractive index of the waveguide 1510. The speed of the microwave signal in the electrodes 1520 and / or 1530 is affected by the presence of the extensions 1524 and / or 1534. The extensions 1524 and / or 1534 tend to slow down the propagation of the microwave signal through the electrodes 1520 and / or 1530. Surrounding materials such as the substrate / lower layer (not shown in FIGS. 15A - 15B) can also affect the speed of the electrode signal. The materials used for the waveguide 1510 and the electrodes 1520 and / or 1530, the processing techniques used for the waveguide 1510 and the electrodes 1520 and / or 1530, the cladding material and the substrate / lower layer, and the configuration of the extensions 1524 and / or 1534 may be selected to reduce the difference in speed between the optical signal in the waveguide 1510 and the electrode signal in the electrodes 1520 and / or 1530.

[0127] Furthermore, it may be relatively far from the ridge 1512 (e.g., farther from the ridge 15 than the channels 1522 and / or 1532) 1Additional extensions may be added that are far enough from 2. Such extensions (not shown in FIGS. 15A-15B) may improve the velocity matching between the optical signal in waveguide 1510 and the electrode signals in electrodes 1520 and / or 1530. However, there may still be some mismatch between the optical signal velocity and the electrode signal velocity. Bending portions 1515, 1525, and 1535 can compensate for these mismatches. For example, in some embodiments, waveguide bend portion 1515 may be configured such that the optical signal travels a longer path in waveguide 1510 than the path through which the microwave signal travels in electrodes 1520 and / or 1530. This path difference can compensate for the optical signal traveling faster in waveguide 1510 than the microwave signal traveling in electrodes 1520 and / or 1530. In some embodiments, waveguide bend portion 1515 may be configured such that the optical signal travels a shorter path in waveguide 1510 than the path through which the microwave signal travels in electrodes 1520 and / or 1530. This path difference can compensate for the optical signal traveling slower in waveguide 1510 than the microwave signal traveling in electrodes 1520 and / or 1530. Such path differences may be used in addition to or instead of the serpentine path of the waveguide (described below). Thus, for a given velocity mismatch between the microwave (electrode) signal and the optical (waveguide) signal, the lengths of bending portions 1515, 1525, and 1535 can be calculated to mitigate the difference caused by the electrode signal and the optical signal traveling at different velocities in the straight portion. By configuring the straight portion and the bending portion, the velocity mismatch can be mitigated and the desired performance can be obtained. Thus, waveguide bend portion 1515 and electrode bend portions 1525 and 1535 can be utilized to account for the velocity mismatch between the electrode (microwave) signal and the optical signal. Accordingly, in addition to the advantages described herein with respect to optical devices such as optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’’, optical device 1500A can have improved performance because it has improved velocity matching.

[0128] Optical device 1500B is similar to optical device 1500A. Therefore, similar structures have the same reference numerals. Accordingly, optical device 1500B includes a waveguide 1510 having a ridge 1512, as well as a waveguide 1510' having a ridge 1512' and electrodes 1520' and 1530' that are similar to electrodes 1520 and 1530. Electrodes 1520' and 1530' each include extensions 1524' and 1534' that are similar to extensions 1524 ’ and 1534 ’ Extensions 1524 ’ and 1534 ’ include connection portions 1524A ’ and 1534A ’ and reverse portions 1524B

[0129] and 1534B. The bent portions 115', 125', and 135' of waveguide 110' and electrodes 120' and 130' are each similar to bent portions 115, 125, and 135. In some embodiments, the bent portions may be omitted so that waveguide 1510' and electrodes 1520' and 1530' are straight. , light Optical device 1500B has an electro-optic effect out-of-plane of the thin film region (e.g., is a z-cut optical device). Therefore, it is desirable to apply a vertical electric field to waveguide 1510'. Accordingly, electrode 1540 is also shown. Although not shown, electrode 1540 may have extensions. Electrode bent portions 1525', 1535', and 1545, and waveguide bent portions 1515' and 1545 are also shown. Accordingly, in addition to the advantages described herein with respect to optical devices such as optical devices 100, 100', 100'', 100''', 100'''', and / or 1500A

[0130] FIG. 16 shows a part of an optical device 1600 including a waveguide 1610 and electrodes 1620 and 1630. Electrodes 1620 and 1630 each include an extension 1624 and 1634, respectively. Only one extension 1624 and one extension 1634 are labeled. The channel regions of electrodes 1620 and 1630 are not labeled. The waveguide 1610 includes a bent portion 1615, and only one of them is labeled. Similarly, electrodes 1620 and 1630 include bent portions 1625 and 1635, and only one bent portion per electrode is labeled therein. The bent portions 1615, 1625, and 1635 make it possible to reduce the area occupied by the long waveguide 1610 and the long electrodes 1620 and 1630. Further, as will be described later, the bent portions 1615, 1625, and 1635 may be used to mitigate velocity and thus phase mismatches between the microwave signals transmitted by electrodes 1620 and / or 1630 and the optical signals transmitted by the waveguide 1610. The positions of 1624 and 1634 shown in the figure may not correspond to physical positions. For example, in a z-cut modulator device, 1624 or 1634 may be disposed above the waveguide 1610, and additional electrodes may be introduced to provide the required electric field profile.

[0131] FIG. 17 shows a part of an optical device 1700 including a waveguide 1710 and electrodes 1720 and 1730. The optical device 1700 is the optical device 100, 100’, 100’’, 100’’’, and / or 100’’’ ’is similar. Therefore, similar structures have similar reference numerals. Accordingly, the optical device 1700 includes a waveguide 1710 having ridges 1712 and a thin film portion 1714, which are similar to the waveguide 110' having ridges 112 and a thin film portion 114, and electrodes 1720 and 1730. The electrodes 1720 and 1730 each include extensions 1724 and 1734 that are similar to the extensions 124, 124', 124'', and 134, 134', 134''. The extensions 1724 and 1734 may be etched partially in, completely in, or through the thin film portion 1714 of the waveguide 1712. The optical device 1700 may share the advantages of the optical devices 100, 100', 100'', and 100''' ’ and may share the advantages of the optical devices 100, 100', 100'', 100''', and / or 100''''

[0132] FIG. 18 shows a portion of an optical device 1800 including a waveguide 1810 and electrodes 1820 and 1830. The optical device 1800 may share the advantages of the optical devices 100, 100', 100'', 100''', and / or 100'''' ’is similar. Therefore, similar structures have similar reference numerals. Accordingly, optical device 1800 includes waveguide 110’ having ridge 112 and thin film portion 114, and waveguide 1810 having ridge 1812 and thin film portion 1814, which are respectively similar to electrode 120 and electrode 130, and electrodes 1820 and 1830. Electrodes 1820 and 1830 respectively include extension portions 1824 and 1834 that are similar to extension portions 124, 124’, 124’’, and 134, 134’, 134’’. Substrate 1801 is similar to substrate 101. Space 1802 within substrate 1801 and additional layer 1803 are also shown. Space 1801 is at least partially filled with layer 1803. Layer 1803 may be a dielectric in some embodiments. In some embodiments, layer 1803 may be a metal layer or other layer. Layer 1803 may be used to design the mechanical integrity or microwave characteristics of optical device 1800. In some embodiments, substrate 1802 may be completely removed. In such embodiments, layer 1803, if present, may extend across optical device 1800. In some embodiments, space 1802 may have a different shape (e.g., semi-cylindrical, etc.), multiple spaces 1802 may be formed, and / or layer 1803 may be omitted. Further, space 1802 need not extend across the full height of the substrate. In some embodiments, space 1802 is formed from the front side of substrate 1801, for example, by etching substrate 1801 from the same side as waveguide 1810. Also, space 1802 may extend across multiple waveguides and / or electrodes in some embodiments. Optical device 1800 may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’ and may share the advantages of.

[0133] FIG. 19 shows a portion of optical device 1900 including waveguide 1910 and electrodes 1920 and 1930. Optical device 1900 may share the advantages of optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’It is similar. Therefore, similar structures have similar reference numerals. Thus, the optical device 1900 includes a waveguide 110' having a ridge 112 and a thin film portion 114, a waveguide 1910 having a ridge 1912 and a thin film portion 1914 that are respectively similar to the electrodes 120 and 130, and electrodes 1920 and 1930. The electrodes 1920 and 1930 respectively include extension portions 1924 and 1934 that are similar to the extension portions 124, 124', 124'', and 134, 134', 134''. The substrate 1901 is similar to the substrate 101. Also shown are a space 1902 in the substrate 1901 and a further layer 1903 that are similar to the space 1802 and the further layer 1803 in the substrate 1801. Further, a second layer 1904 is provided, which may be a metal support layer or other layer. The layers 1903 and 1904 may be used to design the mechanical integrity or microwave characteristics of the optical device 1900. The optical device 1900 may share the advantages of the optical devices 100, 100', 100'', and 100'''.

[0134] FIG. 20 shows a part of an optical device 2000 including a waveguide 2010 and electrodes 2020 and 2030. The optical device 2000 is the optical device 100, 100', 100'', 100''', and / or 100''' ’is similar. Therefore, similar structures have the same reference numerals. Accordingly, optical device 2000 includes waveguide 110’ having ridge 112 and thin film portion 114, waveguide 2010 having ridge 2012 and thin film portion 2014 which are respectively similar to electrode 120 and electrode 130, and electrodes 2020 and 2030. Electrodes 2020 and 2030 each include extension portions 2024 and 2034 which are similar to extension portions 124, 124’, 124’’, and 134, 134’, 134’’. Substrate 2005 may be similar to substrate 101 and / or may be an underlying layer such as silicon dioxide. The optical device is moved onto another substrate 2006 for large-scale processing on another material platform such as Si. In this case, the original optical device is turned over and attached onto the second substrate 206. Further, the second substrate 2006 may undergo further processing. For example, a space similar to space 1802 may be formed and may be completely or partially refilled. Further, the underlying layer / substrate 2005 may be removed in some embodiments. Optical device 2000 may share the advantages of optical devices 100, 100’, 100’’, and 100’’’.

[0135] FIG. 21 is a rear view showing a part of an optical device 2100 including waveguide 2110 and electrodes (not shown). Optical device 2100 is similar to optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’ ’ is similar. Therefore, similar structures have the same reference numerals. Accordingly, optical device 2100 includes waveguide 110’ having ridge 112 and thin film portion 114, waveguide 2110 having ridge 2112 and a thin film portion (not shown) which are respectively similar to electrode 120 and electrode 130, and electrodes (not shown). Substrate 2 1 01 is similar to substrate 101. Also, the space 2 within substrate 2 1 01 102 is shown. Also, structural feature portions 2160, 2162, and 2164 are shown. As shown in FIG. 21, such structural feature portions may extend completely or partially across the space 2002, may be parallel to some or all of other structural feature portions, may be arranged in a pattern, and / or may form a right angle or another angle with the optical signal transmission direction. For example, the structural feature portions 2160, 2162, and 2164 may extend across the space 2002 by 10% or more and 90% or less. In some such embodiments, the structural feature portions 2160, 2162, and 2164 may extend across the space 2002 by 30% or more and 80% or less. The support structures 2160, 2162, and 2164 may be formed by partially removing the substrate 2101 when forming the space 2102. Thus, the structural feature portions 2160, 2162, and / or 2164 may remain after the formation of the space 210 2 . In some embodiments, the structural feature portions 2160, 2162, and 2164 may be formed of other materials. The optical device 2100 may share the advantages of the optical devices 100, 100', 100'', and 100'''.

[0136] FIG. 22 is a plan view showing a part of the optical device 2200. The optical device 2100 is similar to the optical devices 100, 100', 100'', 100''', and / or 100''' ’ . Therefore, similar structures have similar reference numerals. The optical device 2200 includes waveguide tubes 110' and 150, and electrodes 120, 130, and electrode 1 4It includes waveguide 2210 and 2250 which are similar to 0 respectively, and electrodes 2220, 2230, and 2240. Electrodes 2220, 2230, and 2240 each include channel portions 2222, 2232, and 2242 which are similar to channel portions 122, 132, and 142 respectively, and extension portions 2224, 2234, and 2244 which are similar to extension portions 224, 234, and 244 respectively. Also, splitter 2216 and combiner 2218 are shown. Therefore, optical device 2200 can be considered to be configured as an interferometer. Thus, the optical devices described in this specification can be incorporated into various devices. Such devices (such as optical device 2200) can share the advantages of optical devices 100, 100’, 100’’, and 100’’’.

[0137] FIG. 23 is a plan view showing a part of optical device 2300. Optical device 2300 is similar to optical devices 100, 100’, 100’’, 100’’’, and / or 100’’’. ’ Therefore, similar structures have similar reference numerals. Optical device 2300 includes waveguide 2310 and 2350 which are similar to waveguide 110’ and 150 respectively (for example, the arms of the waveguide), and electrodes 2320 and 2330. Electrodes 2320 and 2330 each include channel portions 2322 and 2332 which are similar to channel portions 122, 132, and 142 respectively, and extension portions 2324 and 2334 which are similar to extension portions 224, 234, and 244 respectively. As seen in FIG. 23, extension portions 2334 and 2324 include metal bridges that extend beyond the upper portions of waveguide 2310 and 2350 in order to arrange extension portions 2324 and 2334 so that the fields on waveguide 2310 and 2350 are more symmetric. Optical device 2300 can share the advantages of optical devices 100, 100’, 100’’, and 100’’’.

[0138] FIG. 24 is a plan view showing a part of the optical device 2400. The optical device 2400 is similar to the optical devices 100, 100', 100'', 100''', and / or 100'''. Therefore, similar structures have similar reference numerals. The optical device 2400 includes waveguides 2410 and 2450, which are respectively similar to the waveguides 110' and 150, and electrodes 2420 and 2430, which are respectively similar to the electrodes 120 and 130. The electrodes 2420 and 2430 each include channel portions 2422 and 2432, and extension portions 2424 and 2434, which are respectively similar to the channel portions 122 and 132, and the extension portions 224 and 234. As seen in FIG. 24, the extension portions 2434 and 2424 include a metal bridge extending over the upper portions of the waveguides 2410 and 2450 and further reverse features in order to arrange and configure the extension portions 2424 and 2434 so that the fields on the waveguides 2410 and 2450 are more symmetric. ’ Specifically, in order to induce opposite shifts in the waveguides 2410 and 2450, the extension portions 2424 and 2434 are connected with opposite polarities by a first positive metal bridge extending over the upper portions of the waveguides 2450 and 2410, respectively. The metal bridge connects the reverse portions of the extension portions 2424 and 2434 to the channel regions 2422 and 2432, respectively, while causing minimal optical loss in the waveguides 2410 and 2450. Further, a second set of reverse features for the extension portions 2424 and 2434 are provided on the opposite sides sandwiching the waveguides 2410 and 2450 so that the geometry of the optical device 2400 is symmetric. The optical device 2400 has a smaller modulator chirp (the difference in modulation intensity in the two waveguides 2410 and 2450) than the optical device 2300, at the cost of increased design complexity and possibly a narrower microwave bandwidth. The optical device 2400 may share the advantages of the optical devices 100, 100', 100'', and 100'''. 4

[0139]

[0140] ​​FIG. 25 is a plan view showing a part of the optical device 2500. The optical device 2500 is similar to the optical devices 100, 100', 100'', 100''', and / or 100''''. ’ Therefore, similar structures have similar reference numerals. The optical device 2500 includes waveguide 2510 and 2550, and electrodes 2520, 2530, and 2540, which are similar to the waveguide 110' and 150, and the electrodes 120, 130, and 140, respectively. 540 The electrodes 2520, 2530, and 2540 include channel portions 2522, 2532, and 2542, and extension portions 2524, 2534, and 2544, which are similar to the channel portions 122, 132, and 142, and the extension portions 224, 234, and 244, respectively. Further, the electrodes 2520, 2530, and 2540 are divided into three segments along the waveguides 2510 and 2550. Also, the divided electrodes 2520, 2530, and 2540 may be used in a distributed driver scheme where each electrode pair (2520 and 2530, or 2530 and 2540) includes a plurality of electrode sections. Each set of segments is driven by separate driver amplifiers 2570, 2572, and 2574 connected between a common source and the signal electrode 2530. Physical or electronic electrical delays 2580, 2582, and 2584, any of 110a - 110c, may be introduced between each separate driver 2570, 2572, and 2574 to mitigate the velocity mismatch between the optical signals in the waveguides 2510 and 2550 and the electrode signals in the electrodes 2520, 2530, and 2540. The optical device 2500 may share the advantages of the optical devices 100, 100', 100'', and 100'''.

[0141] Thus, various combinations of feature portions for an optical device have been described in the context of FIGS. 1A to 25. These feature portions may be combined in many ways. Accordingly, a low-loss waveguide including a thin-film nonlinear optical material processed as described herein, an electrode having an extension portion and a channel region, velocity matching between a microwave signal and an optical signal, low microwave loss characteristics, a low-voltage electrode signal, low optical loss, a waveguide bending portion and an electrode bending portion enabling a longer waveguide occupying a smaller area, and / or other features described herein may be combined in ways not explicitly shown. As a result, high-performance optical devices such as optical modulators can be provided.

[0142] For example, FIG. 26 is a block diagram showing an exemplary embodiment of a device 2600 formed using an optical modulator 2610. In some embodiments, the device 2600 is an optical transmission subassembly (TOSA). The TOSA 2600 includes an optical modulator 2610 and an optional driver 2620. Also shown is an optical signal source 2602 (such as one or more lasers). The optical modulator 2610 is similar to one or more of the optical devices shown in FIGS. 1A to 25. Accordingly, an optical modulator 2610 having one or more of a low-loss waveguide including a thin-film nonlinear optical material processed as described herein, an electrode having an extension portion and a channel region, velocity matching between a microwave signal and an optical signal, low microwave loss characteristics, a low-voltage electrode signal, low optical loss, a waveguide bending portion and an electrode bending portion enabling a longer waveguide occupying a smaller area, and / or other features described herein may be combined in ways not explicitly shown. As a result, a high-performance optical modulator 2610 can be utilized in the device 2600.

[0143] Also shown is an optional driver 2620 used to drive the electrodes of the optical modulator 2610. Thus, driver 2620 may be a high-frequency driver. Since the electrodes for the optical modulator 2610 may be driven using a lower voltage, driver 2620 may be omitted. Thus, in some embodiments, the optical modulator 2610 may be driven by an input data signal for the TOSA 2600. In other embodiments, driver 2620 may be utilized. However, a lower voltage may be used. Similarly, since the optical modulator 2610 utilizes a low-loss waveguide, the input optical signal (e.g., a signal from one or more lasers) may have lower power. Thus, a device with improved performance can be provided using an optical modulator as described herein.

[0144] FIG. 27 is a flowchart showing one embodiment of a method 2700 for forming an optical modulator having improved performance. Method 2700 is described in the context of a process that may have sub-processes. Although described in a particular order, another order that is consistent with the description herein may be used.

[0145] An optical waveguide is provided in step 2702. In some embodiments, a thin film of a nonlinear optical material (such as LN and / or LT) is provided and patterned to form a low-loss waveguide. In some embodiments, ultraviolet (UV) and / or deep ultraviolet (DUV) photolithography may be used to pattern a mask for the nonlinear optical material. For example, a hard mask layer is provided on the nonlinear optical thin film. A UV or DUV mask layer is provided on the hard mask layer and patterned using UV or DUV photolithography. The hard mask is formed from the hard mask layer by transferring the pattern of the mask to the hard mask layer. For example, portions of the hard mask layer exposed by the openings of the mask may be selectively etched. The hard mask may have recesses or openings in the regions where the hard mask layer is etched. The pattern of the hard mask may be transferred to the nonlinear optical material thin film layer using, for example, physical etching. In some cases, the processing is performed in a stitch region of at least 10 millimeters by 10 millimeters. In some embodiments, the stitch region may be at least 15 millimeters by 15 millimeters. In some embodiments, each stitch region is at least 20 millimeters by 20 millimeters. In some embodiments, bent portions are also provided. Thus, a high electro-optic effect waveguide that may have bent portions may be provided.

[0146] Electrodes having a desired configuration are provided in step 2704. For example, the electrodes may be deposited or electroplated in step 2704. In some embodiments, step 2704 includes the step of providing one or more electrodes having a channel region and extensions. The extensions may be configured as described herein. In some embodiments, the one or more electrodes are further configured to have bent portions. Then, the manufacture of the optical modulator may be completed.

[0147] For example, the optical modulator 100' may be provided using the method 2700. The waveguide 110' may be processed in step 2702. A thin film of a nonlinear optical material is provided and etched to form the ridge 112. Further, the bent portions (such as the bent portion 1515) are also provided by etching in step 2 7 02. The electrodes 120 and 130 are formed in step 2704. Accordingly, the channel regions 122 and 132 and the extensions 124 and 134 are formed. The electrode bent portions (such as the portion 1525) are also processed in step 2704.

[0148] For example, using the method 2700, an electrode having an extension may be utilized, and an optical modulator similar to those of FIGS. 1A to 25 may be manufactured. An example of such a modulator is one processed with an etching depth of 300 nm in a 600 nm thick x-cut thin film LN on a quartz wafer. In some embodiments, the RF Vπ measured at 1 GHz is 2.3 V and 1.3 V for modulators having lengths of 10 millimeters and 20 millimeters using an electrode gap of 5 micrometers (for example, the distance between the extensions 124 and 134), resulting in RF voltage-length products (Vπ·L) of 2.3 and 2.6 V·cm, respectively. The attenuation of some embodiments of such modulators is measured to be greater than 25 dB, and the on-chip loss is estimated to be less than 1 dB. In some embodiments, an optical device provided using an electrode with an extension has an RF loss (microwave loss) of only 2 dB / cm at 50 GHz compared to 7 dB / cm for a normal electrode design (for example, without an extension) having the same thickness (for example, 800 nm) and material used (for example, Au) for the electrode. The resistive loss α0 at the electrode is ∝L -1 f -1 / 2 due to the skin effect of the metal, where L is the length of the electrode and f is the microwave frequency. A conventional electrode on the LN thin film has α 0,reg = 0.69 dBcm -1 GHz -1 / 2 whereas for the processed electrode with an extension, α 0,ext = 0.26 dBcm -1 GHz -1 / 2It is. In some embodiments, the ultra-low RF loss enabled a measured EO response with only 0.8 (1.7) dB of attenuation for a 10 mm (20 mm) modulator at 50 GHz compared to the reference Vπ at 1 GHz. In other words, the RF Vπ at 50 GHz is 2.5 V (1.6 V) for embodiments of a 10 mm (20 mm) optical modulator that utilize segmented electrodes. The electrical reflection from the electrodes is maintained below -15 dB for all frequencies. In some embodiments, by using a lower-index substrate (such as fused silica or air), further separation of the extension can be achieved while maintaining velocity matching with the optical signal.

[0149] Thus, using method 2700, an optical modulator is provided that has a low-loss, thin-film, nonlinear optical material waveguide including bends. Further, electrodes are also fabricated that include a channel region, an extension, and a bent portion. As a result, an optical modulator can be provided that has low optical signal loss, low electrode signal loss, consumes a controlled amount of area, and / or provides a desired optical modulation at a low voltage. Accordingly, the performance of the optical modulator can be improved.

[0150] The above embodiments have been described in some detail for ease of understanding, but the present invention is not limited to the details provided. There are many alternative ways to implement the present invention. The disclosed embodiments are illustrative and not intended to be limiting. [Application Example 1] An optical device comprising: a waveguide including at least one optical material having an electro-optic effect; and an electrode having a channel region and a plurality of extensions protruding from the channel region, wherein the plurality of extensions are closer to a part of the waveguide than the channel region. A waveguide including at least one optical material having an electro-optic effect; and an electrode having a channel region and a plurality of extensions protruding from the channel region, wherein the plurality of extensions are closer to a part of the waveguide than the channel region. [Application Example 2] The optical device according to Application Example 1, wherein the plurality of extensions have a pitch shorter than a value obtained by dividing the wavelength of microwaves in the electrode by π. [Application Example 3] The optical device according to Application Example 2, wherein the waveguide is configured to transmit an optical signal, the electrode is configured to transmit an electrical signal, and the at least one optical material has a microwave dielectric constant at least 1.5 times the optical dielectric constant with respect to the optical signal and the electrode signal. [Application Example 4] The optical device according to Application Example 1, wherein the waveguide transmits an optical signal, the electrode transmits an electrical signal, and the plurality of extensions are configured to reduce the velocity mismatch between the optical signal and the electrode signal. [Application Example 5] The optical device according to Application Example 1, wherein the plurality of extensions have at least one distance from the waveguide such that the total optical loss is less than 8 dB. ​ [Applicable Example 6] The optical device according to Applicable Example 1, wherein the waveguide and the electrode are present on a substrate, the plurality of extension portions have positions, and the positions are selected from a first position and a second position, the first position is between the substrate and the channel region, and the second position is a position where the channel region is present between the substrate and the plurality of electrodes. [Applicable Example 7] The optical device according to Applicable Example 1, wherein the waveguide and the electrode are present on a substrate structure, and the substrate structure is selected from a first substrate having a low substrate microwave dielectric constant lower than 11, the first substrate combined with a lower layer between the substrate and the waveguide, and a second substrate having a high microwave dielectric constant higher than 11 combined with the lower layer, and the lower layer has a reduced layer microwave dielectric constant less than 11. [Applicable Example 8] The optical device according to Applicable Example 1, wherein the waveguide and the electrode are present on a substrate having a space therein, and the space is aligned with the part of the waveguide and the plurality of extension portions. [Applicable Example 9] The optical device according to Applicable Example 1, wherein the plurality of extension portions have a length shorter than a value obtained by dividing the wavelength of microwaves in the electrode by π. [Applicable Example 10] The optical device according to Applicable Example 1, wherein the waveguide includes a ridge portion and a thin film portion. [Applicable Example 11] The optical device according to Applicable Example 1, wherein each of the plurality of extension portions includes a connection portion and a reverse portion coupled to the channel region, and the connection portion is between the reverse portion and the channel region. [Applicable Example 12] The optical device according to Applicable Example 1, wherein the electrode has a frequency-dependent electrode loss with respect to a frequency window in a frequency range from DC to 500 GHz or less, the frequency-dependent electrode loss is less than 0.8 dB per square root of the electrode signal frequency per centimeter, the electrode signal frequency is measured in GHz, and the frequency window is at least 10 GHz. [Applicable Example 13] An optical device according to Applicable Example 1, wherein the electrode has an absorption electrode loss with respect to a frequency window of an electrode signal frequency from DC to 500 GHz or less, the absorption electrode loss is less than 0.005 dB per centimeter per GHz, and the frequency window is at least 10 GHz. [Applicable Example 14] An optical device according to Applicable Example 1, wherein the electrode includes an electrode bent portion, the waveguide includes a waveguide bent portion, and the electrode bent portion and the waveguide bent portion are configured to provide a path difference between an optical signal for the waveguide and an electrode signal for the electrode. [Applicable Example 15] An optical device according to Applicable Example 1, further comprising a further electrode having a further channel region and a further plurality of extensions, wherein the further plurality of extensions are closer to the part of the waveguide than the further channel region. [Applicable Example 16] A subassembly, comprising an optical modulator, the optical modulator including a waveguide and an electrode, the waveguide including at least one optical material having an electro-optic effect, the electrode including a channel region and a plurality of extensions, the plurality of extensions existing between the channel region and the waveguide, the plurality of extensions being closer to a part of the waveguide than the channel region, a driver connected to the optical modulator and configured to electrically drive the electrode, and comprising a subassembly. [Applicable Example 17] A method, comprising providing a waveguide including at least one optical material having an electro-optic effect, providing an electrode, the providing of the electrode including providing a channel region, providing a plurality of extensions protruding from the channel region, wherein the plurality of extensions are closer to a part of the waveguide than the channel region. [Applicable Example 18] The method according to Applicable Example 17, wherein the providing of the plurality of extensions further includes fabricating the plurality of extensions at a pitch shorter than a value obtained by dividing the wavelength of microwaves in the electrode by π. [Applicable Example 19] The method according to Applicable Example 17, wherein the waveguide transmits an optical signal, the electrode transmits an electrode signal, and the providing of the plurality of extensions further includes configuring the plurality of extensions to reduce a velocity mismatch between the optical signal and the electrode signal. [Application Example 20] The method according to Application Example 17, wherein the electrode has a frequency-dependent electrode loss with respect to a frequency window in a frequency range from DC to 500 GHz or less, the frequency-dependent electrode loss is less than 0.8 dB per square root of the electrode signal frequency per centimeter, the electrode signal frequency is measured in GHz, and the frequency window is at least 10 GHz.

Claims

1. An optical device comprising: A waveguide including at least one optical material having an electro - optical effect and lithium, the waveguide transmitting an optical signal; An electrode having a channel region and a plurality of extensions protruding from the channel region, the plurality of extensions being closer to a part of the waveguide than the channel region, the electrode transmitting an electrode signal; The waveguide and the electrode are on a substrate structure having a substrate microwave dielectric constant of less than 11, the substrate structure including a substrate and a lower layer between the substrate and the waveguide, the substrate having a high microwave dielectric constant greater than 11, the lower layer having a reduced - layer microwave dielectric constant of less than 11 and a thickness of at least 3 microns, the lower layer including silicon dioxide; The electrode is an improved electrode configured such that a microwave mode of the electrode signal transmitted through the channel region reaches the at least one optical material and a part of the substrate structure, and a part of the substrate structure includes a part of the lower layer and a part of the substrate. An optical device.

2. The optical device according to claim 1, wherein the plurality of extensions have a pitch shorter than a value obtained by dividing the wavelength of microwaves in the electrode by π.

3. The optical device according to claim 2, wherein the waveguide is configured to transmit the optical signal, the electrode is configured to transmit the electrode signal, and the at least one optical material has a microwave dielectric constant at least 1.5 times the optical dielectric constant with respect to the optical signal and the electrode signal. An optical device.

4. The optical device according to claim 1, wherein the plurality of extensions are configured to reduce a velocity mismatch between the optical signal and the electrode signal.

5. The optical device according to claim 1, wherein the plurality of extensions have at least one distance from the waveguide such that the total optical loss is less than 8 dB.

6. The optical device according to claim 1, wherein the waveguide and the electrode are present on the substrate structure, the plurality of extensions have positions, and the positions are selected from a first position and a second position, the first position being between the substrate structure and the channel region, and the second position being a position such that the channel region is between the substrate structure and the plurality of electrodes. An optical device.

7. An optical device according to claim 1, wherein the substrate structure has a space therein, and the space is aligned with the part of the waveguide and the plurality of extensions.

8. An optical device according to claim 1, wherein the plurality of extensions have a length shorter than a value obtained by dividing the wavelength of the microwave in the electrode by π, and the length is at least one distance of the plurality of extensions from the channel region toward the waveguide.

9. An optical device according to claim 1, wherein the waveguide includes a ridge portion and a thin film portion.

10. An optical device according to claim 1, wherein each of the plurality of extensions includes a connection portion and a reverse portion coupled to the channel region, and the connection portion is between the reverse portion and the channel region.

11. An optical device according to claim 1, wherein the electrode has a frequency-dependent electrode loss with respect to a frequency window in a frequency range from DC to 500 GHz or less, the frequency-dependent electrode loss is less than 0.8 dB per square root of the electrode signal frequency per centimeter, the electrode signal frequency is measured in GHz, and the frequency window is at least 10 GHz.

12. An optical device according to claim 1, wherein the electrode has an absorption electrode loss with respect to a frequency window of the electrode signal frequency from DC to 500 GHz or less, the absorption electrode loss is less than 0.005 dB per GHz per centimeter, and the frequency window is at least 10 GHz.

13. An optical device according to claim 1, wherein the electrode includes an electrode bending portion, the waveguide includes a waveguide bending portion, and the electrode bending portion and the waveguide bending portion are configured to provide a path difference between an optical signal for the waveguide and an electrode signal for the electrode.

14. An optical device according to claim 1, further comprising a further electrode including a further channel region and a further plurality of extensions, wherein the further plurality of extensions are closer to the part of the waveguide than the further channel region.

15. A subassembly, An optical modulator, the optical modulator comprising a waveguide and an electrode, the waveguide including at least one optical material having an electro-optic effect and lithium, the waveguide transmitting an optical signal, the electrode comprising a channel region and a plurality of extensions, the plurality of extensions being present between the channel region and the waveguide, the plurality of extensions being closer to a part of the waveguide than the channel region, the electrode transmitting an electrode signal, the waveguide and the electrode being on a substrate structure having a substrate microwave dielectric constant of less than 11, the substrate structure including a substrate and a lower layer between the substrate and the waveguide, the substrate having a high microwave dielectric constant greater than 11 in combination with the lower layer, the lower layer having a reduced layer microwave dielectric constant of less than 11 and a thickness of at least 3 microns, the lower layer including silicon dioxide, the electrode being configured such that a microwave mode of the electrode signal transmitted through the channel region reaches the at least one optical material and a part of the substrate structure, a part of the substrate structure including a part of the lower layer and a part of the substrate, the at least one optical material including lithium, the plurality of extensions being configured to reduce a velocity mismatch between the optical signal and the electrode signal, A driver connected to the optical modulator and configured to electrically drive the electrode, A sub-assembly comprising.

16. A method comprising: Providing a waveguide including at least one optical material having an electro-optic effect and lithium, the waveguide transmitting an optical signal, Providing an electrode, wherein providing the electrode comprises: Providing a channel region, Providing a plurality of extensions protruding from the channel region, The plurality of extensions being closer to a part of the waveguide than the channel region, The electrode transmitting an electrode signal, the waveguide and the electrode being on a substrate structure having a substrate microwave dielectric constant of less than 11, the substrate structure including a substrate and a lower layer between the substrate and the waveguide, the substrate having a high microwave dielectric constant greater than 11 in combination with the lower layer, the lower layer having a reduced layer microwave dielectric constant of less than 11 and a thickness of at least 3 microns, the lower layer including silicon dioxide, The electrode is configured such that a microwave mode of the electrode signal transmitted through the channel region extends to the at least one optical material and to a part of the substrate structure, a part of the substrate structure including a part of the lower layer and a part of the substrate, and the plurality of extensions are configured to reduce a velocity mismatch between the optical signal and the electrode signal.

17. The method according to claim 16, wherein providing the plurality of extensions further comprises fabricating the plurality of extensions along the channel region at a pitch shorter than a value obtained by dividing the wavelength of the microwave in the electrode by π.

18. The method according to claim 16, wherein the waveguide transmits an optical signal, the electrode transmits an electrode signal, and providing the plurality of extensions further comprises configuring the plurality of extensions to reduce a velocity mismatch between the optical signal and the electrode signal.

19. The method according to claim 16, wherein the electrode has a frequency-dependent electrode loss with respect to a frequency window in a frequency range from DC to 500 GHz or less, the frequency-dependent electrode loss being less than 0.8 dB per square root of the electrode signal frequency per centimeter, the electrode signal frequency being measured in GHz, and the frequency window being at least 10 GHz.

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