Electrooptic device with improved electrode

Abstract

SOLUTION: To provide an optical device with a waveguide and an electrode, the waveguide including at least one optical material with an electrooptic effect and the electrode having a channel region and an extension part protruding from the channel region, the extension part being closer to a part of the waveguide than the channel region.SELECTED DRAWING: Figure 1B

Description

[Background technology]

[0001] CROSS-REFERENCE TO OTHER APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 62 / 941,139, entitled "THIN-FILM ELECTRO-OPTIC MODULATORS," filed November 7, 2019, which is incorporated by reference herein for all purposes. This application claims priority to U.S. Provisional Patent Application No. 63 / 033,666, entitled "HIGH PERFORAMNCE OPTICAL MODULATORS," filed June 2, 2020, which is incorporated by reference herein for all purposes. This application claims priority to U.S. Provisional Patent Application No. 63 / 112,867, filed 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-optical devices are generally desired to meet certain performance benchmarks. For example, it is desirable for the optical modulator to be able to provide sufficient optical modulation at lower electrode drive voltages. Large optical modulation may correspond to the waveguide having a large length in the direction of optical signal transmission. 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 the electrical signal through the electrodes and low optical loss for the optical signal through the waveguide. Furthermore, it is desirable for the optical modulator to be able to provide low-loss transmission and large modulation at low voltages over a wide frequency band. Thus, electro-optical devices that have low electrode loss, low optical loss, consume a controlled amount of area, and / or can provide the desired optical modulation at low voltages are desirable. [Brief description of the drawings]

[0003] Various embodiments of the invention are disclosed in the following detailed description and the accompanying drawings.

[0004] [Figure 1A] 1 illustrates an embodiment of an optical device having improved electrodes. [Figure 1B] 1 illustrates an embodiment of an optical device having improved electrodes. [Figure 1C] 1 illustrates an embodiment of an optical device having improved electrodes. [Figure 1D] 1 illustrates an embodiment of an optical device having improved electrodes. [Figure 1E] 1 illustrates an embodiment of an optical device having improved electrodes.

[0005] [Diagram 2] 1 is a cross-sectional view illustrating a portion of an embodiment of an optical device that may have improved performance.

[0006] [Diagram 3] 1 is a cross-sectional view illustrating a portion of an embodiment of an optical device that may have improved performance.

[0007] [Figure 4] 1 is a cross-sectional view illustrating a portion of an embodiment of an optical device that may have improved performance.

[0008] [Diagram 5] 1 is a cross-sectional view illustrating a portion of an embodiment of an optical device that may have improved performance.

[0009] [Figure 6] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance.

[0010] [Figure 7] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance.

[0011] [Figure 8]FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance.

[0012] [Figure 9] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance.

[0013] [Figure 10] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance.

[0014] [Figure 11] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance.

[0015] [Figure 12A] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 12B] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 12C] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 12D] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance.

[0016] [Figure 13A] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 13B] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 13C] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 13D] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 13E]FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 13F] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 13G] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 13H] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 13I] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 13J] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance.

[0017] [Figure 14A] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14B] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14C] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14D] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14E] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14F] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14G] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14H] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14I]FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14J] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance. [Figure 14K] FIG. 1 illustrates an electrode configuration in a portion of an embodiment of an optical device that may have improved performance.

[0018] [Figure 15A] 1A-1D illustrate portions of embodiments of optical devices that may have improved performance. [Figure 15B] 1A-1D illustrate portions of embodiments of optical devices that may have improved performance.

[0019] [Figure 16] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0020] [Figure 17] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0021] [Figure 18] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0022] [Figure 19] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0023] [Figure 20] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0024] [Figure 21] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0025] [Figure 22] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0026] [Diagram 23] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0027] [Figure 24] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0028] [Diagram 25] FIG. 1 illustrates a portion of an embodiment of an optical device that may have improved performance.

[0029] [Figure 26] FIG. 1 illustrates a portion of one embodiment of a subassembly utilizing an optical modulator that may have improved performance.

[0030] [Figure 27] 1 is a flow chart illustrating one embodiment of a method for providing an optical modulator that may have improved performance. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0031] The present invention may be embodied in various forms, including as 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 configured to execute instructions stored in and / or provided by a memory coupled to the processor. These embodiments or any other form the present invention may take may be referred to herein as techniques. In general, the order of steps of a disclosed process may be altered within the scope of the present invention. Unless otherwise noted, components such as a processor or memory described as configured to perform a task may be implemented as general components temporarily configured to perform the task at a given time, or as specific components manufactured to perform the task. As used herein, the term "processor" refers to one or more devices, circuits, and / or processing cores configured to process data, such as computer program instructions.

[0032] A detailed description of one or more embodiments of the present invention will now be given with reference to the drawings illustrating the principles of the present invention. The present invention will be described in connection with such embodiments, but is not limited to any of them. 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, numerous specific details are set forth in order to provide a thorough understanding of the present invention. These details are for the purpose of example, and the present invention may be practiced according to the claims without some or all of these specific details. For simplicity, technical matters well known in the art related to the present invention have not been described in detail so as not to unnecessarily obscure the present invention.

[0033] The basic elements of an electro-optical device (also called an optical device), such as an electro-optical modulator, include a waveguide and electrodes around the waveguide. The waveguide carries an optical signal. The electrodes are used to generate an electric field or voltage difference at or near the waveguide. This electric field causes a change in the refractive index of the waveguide, which results in the optical signal being modulated. For example, an electrode signal (e.g., a microwave signal) may be applied to the electrodes. The electrodes act as a transmission line. The electrode signal travels in the same direction as the optical signal propagating through the waveguide. The electrode signal creates a corresponding electric field in the waveguide, modulating the refractive index of the waveguide. Thus, the optical signal is modulated as it passes through the waveguide. Thus, a desired modulation of the optical signal may be achieved by driving the appropriate electrode signal through the electrodes.

[0034] Although electro-optical devices function, their performance may be limited by a number of factors. For example, it is desirable for the electrodes to be in close proximity to the waveguide to increase the strength of the electric field at the waveguide. A higher electric field enhances the change in the refractive index of the waveguide, increasing the modulation of the optical signal. However, the electrodes may experience electrode (e.g., microwave) signal losses as the microwave signal passes through the electrodes. Such losses may be increased by the proximity to the waveguide. These losses may adversely affect the ability of the electrodes to provide the desired electric field at the waveguide. Absorption of the microwave signal by surrounding structures and resistive losses at the electrodes exacerbate these losses. Furthermore, the drive voltage required for the electrodes increases as the frequency of the modulation increases. For example, optical signals can be easily modulated at frequencies of 1 GHz using electrode voltages of less than 2 volts. However, at higher frequencies (e.g., bands of 100 GHz and above), the required electrode voltages may be significantly higher (e.g., 5 volts or more). Higher voltages are applied to the electrodes to obtain the desired change in refractive index. Thus, the optical modulator may require a larger input voltage to the electrodes and consume more power than is desirable.Thus, electro-optical devices with improved performance remain desirable.

[0035] Many 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 and other techniques have significant shortcomings in one or more of the above-mentioned characteristics. 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 suffer from unacceptable electrode or optical signal loss. Signal-limiting factors in the performance of an optical modulator may prevent the optical modulator from functioning as desired. For example, unacceptable electrode (microwave) loss may render the modulator unusable for a particular application, even if the electrodes are capable of being driven at low voltages. Thus, a mechanism for providing an optical modulator that has low optical signal loss, low electrode signal loss, consumes a controlled amount of area, and / or provides the desired optical modulation at low voltages is still desired.

[0036] Optical devices are described that may have improved performance. The optical device comprises a waveguide and an electrode. The waveguide comprises at least one optical material having an electro-optic effect. In some embodiments, the waveguide comprises a ridge portion and a thin film portion. The electrode comprises a channel region and an extension portion protruding from the channel region. The extension portion is closer to a portion of the waveguide than the channel region. In some embodiments, the extension portion has a pitch, and the pitch may be less than a microwave wavelength at the electrode divided by pi. In some embodiments, the extension portion has a length less than a microwave wavelength at the electrode divided by pi. The waveguide is configured to transmit an optical signal, while the electrode is configured to transmit an electrode signal. In some such embodiments, the one or more optical materials have a microwave permittivity at least 1.5 times the optical permittivity for the optical signal and the electrode signal. As used herein, "dielectric constant" corresponds to the relative permittivity, which is equal to the dielectric constant of the material divided by the vacuum permittivity. The microwave permittivity refers to the permittivity at microwave frequencies of interest. The optical permittivity refers to the permittivity at optical frequencies of interest, which is equal to or approximately equal to the square of the refractive index. In some embodiments, each of the extensions comprises a connection portion connected to the channel region and a retrograde portion. The connection portion is between the retrograde portion and the channel region. In some embodiments, the optical device comprises a further electrode having a further channel region and a further plurality of extensions. The further extensions are closer to the portion of the waveguide than the further channel region. In some embodiments, the waveguide has a total optical loss of 10 dB or less along the portion of the waveguide.

[0037] Thus, the optical device comprises one or more electrodes fabricated with a microstructure (i.e., extensions). One or more channel regions of the one or more electrodes are configured to conduct the bulk of the current, but little or no current may be driven through the extensions. Thus, losses due to the proximity of the electrodes to the waveguide may be mitigated. However, because the extensions are closer to the waveguide, the magnitude of the electric field at the waveguide may be maintained or increased. Thus, the electrodes may be able to provide sufficient modulation of the optical signal at lower electrode voltages.

[0038] In some embodiments, optical performance may also be improved. The waveguide may have low optical loss (e.g., optical loss of 1 dB / cm or less). In some such embodiments, the waveguide may have an optical loss of 0.5 dB / cm or less (e.g., on average) in some cases. In some embodiments, the waveguide has a total optical loss on-chip of 4 dB or less. In some embodiments, the portion of the waveguide proximate to one or more electrodes has a total optical loss of 3 dB or less. The optical efficiency of the device may be improved. Thus, the optical modulator may be made longer (e.g., greater than 2 cm, and in some embodiments 3 cm or more), enhancing modulation of the input optical signal. Also, the waveguide may be made relatively small, for example, using thin film technology. In some embodiments, the waveguide may have a linearity of 100 nm to 100 nm, which is approximately equal to 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 area is smaller than λ 2, where λ is the wavelength of the optical signal in the waveguide. Because the waveguide is small, the electrodes may be placed closer to the waveguide. This may allow for an increase in the electric field in the waveguide and an enhancement of the electro-optic effect. In some embodiments, the one or more waveguide bends may have a bend radius of 500 μm or less. In some embodiments, the waveguide bends have a bend optical loss of 0.5 dB or less. When present, the bends in the waveguide and electrodes may be used to lengthen the area where the electrodes are in close proximity to the waveguide while controlling the length and / or area consumed by the device. That is, the use of bends allows for a reduction in the maximum dimensions of the optical modulator. The maximum dimensions of the optical modulator limit the reduction in the size of the package in which the optical modulator can be provided. The bends in the electrodes and waveguide allow for a lengthening of the optical path and the area where the electrodes are in close proximity to the waveguide while reducing the maximum dimensions of the optical modulator. For example, a linear optical modulator with a length of 4 centimeters and a width of 0.2 millimeters has the same length of optical path as an optical modulator with three bends (and four straight sections) occupying an area of ​​approximately 1 centimeter long and 0.8 mm wide. 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 electrodes can occupy an area of ​​50 square millimeters or less. In some embodiments, the waveguide and electrodes occupy an area of ​​20 square millimeters or less. In some embodiments, the waveguide and electrodes are present on an integrated circuit with a length of 32 millimeters or less. Thus, greater optical signal modulation can be achieved with a smaller footprint. In some embodiments, one or more electrode bends and one or more waveguide bends are configured to provide a path difference between the optical signal for the waveguide and the electrode signal for the electrode. The bends of the waveguide and electrode can be used to account for the mismatch in speed of 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 allows a high electric field to be provided in the waveguide by the electrodes.The extension also separates the edges of the channel region from the waveguide. Thus, the current may be better confined to the channel region, reducing electrode losses in the electrodes and allowing lower drive voltages for the electrodes. The combination of reduced optical and electrode (e.g., microwave) losses, improved velocity matching between electrode and optical signals, and an extension of the path along which the optical signal may be modulated allows for a reduction in the voltage amplitude input to one or more electrodes. For example, in some embodiments, a microwave signal of amplitude 0.5-1.5 V may be input to one or more electrodes to provide the desired modulation of the refractive index for signals in the 50-100 GHz range. Thus, device performance may 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 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. The frequency dependent electrode loss is in some embodiments 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 may be at least 10 GHz. The frequency dependent electrode loss is in other embodiments 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. The frequency dependent electrode loss is in other embodiments 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 electrodes have an absorptive electrode loss over a frequency window of the electrode signal frequency from DC to up to 500 GHz, hi some embodiments, the absorptive 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. The extension, in some embodiments, 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 portion 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 in combination with an underlayer between the substrate and the waveguide, and a second substrate in combination with the underlayer having a high microwave dielectric constant greater than 11. In such embodiments, the underlayer has a low underlayer microwave dielectric constant (e.g., less than 11).

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

[0042] In some embodiments, a subassembly, such as a transmit optical subassembly (TOSA), is described. The subassembly includes an optical modulator and a driver connected to the optical modulator. The optical modulator 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 a plurality of extensions. The extensions are between the channel region and the waveguide. The driver is configured to electrically drive the electrodes.

[0043] In some embodiments, a method of providing an optical device is described. The method includes providing a waveguide and providing an electrode. The waveguide includes one or more optical materials having an electro-optic effect. The electrode includes providing a channel region and providing an extension protruding from the channel region. The extension is closer to a portion of the waveguide than the channel region. In some embodiments, providing the extension includes fabricating the extension with a pitch that is shorter than a wavelength of microwaves at the electrode divided by pi. The waveguide transmits an optical signal, while the electrode transmits an electrode signal. In some embodiments, 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. The frequency dependent electrode loss, in other embodiments, is less than 0.5 dB per square root of the electrode signal frequency per centimeter. The electrode signal frequency may be measured in GHz and the frequency window may be at least 10 GHz. The frequency dependent electrode loss, in other embodiments, is less than 0.3 dB per square root of the electrode signal frequency per centimeter. The electrode signal frequency may be measured in GHz and the frequency window may be at least 10 GHz. In some embodiments, the electrode has an absorptive electrode loss for a frequency window of the electrode signal frequency from DC to 500 GHz or less. In some embodiments, the absorptive electrode loss is less than 0.005 dB per GHz per centimeter and the frequency window is at least 10 GHz.

[0044] 1A-1E show embodiments of optical devices 100, 100', 100'', 100''', and 100'''' having improved electrodes. FIG. 1A shows a plan view of an optical device (i.e., an electro-optical device) with a waveguide 110 and electrodes 120 and 130. FIGS. 1B, 1C, 1D, and 1E show perspective views of optical devices 100', 100'', 100''', and 100'''', which are similar to optical device 100.

[0045] Optical devices 100, 100', 100'', 100''', and 100'''' may be part of an optical modulator having an electro-optic response (e.g., picometers per volt) in or perpendicular to the film plane (e.g., x-cut or y-cut lithium niobate). Optical device 100'' may be part of an optical modulator having an electro-optic response (e.g., picometers per volt) out of the plane of the film (e.g., z-cut lithium niobate). As used herein, an x-cut or y-cut modulator is a modulator having an electro-optic effect in the film plane (e.g., even if materials such as lithium niobate are not used). Similarly, as used herein, a z-cut optical modulator has an electro-optic effect out of the film plane (e.g., perpendicular to the film plane) (e.g., even if materials such as lithium niobate are not used). FIGS. 1A-1E are not to scale. Other configurations are possible. For example, optical devices having a different number of waveguides, other and / or additional waveguide components (such as splitters and branches), and / or a different number of electrodes are possible. Referring to FIG. 1A, an optical signal is input to the 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 to the optical device 100. In some embodiments, the frequency of the electrode signal is in the microwave range. Thus, the terms microwave signal and electrode signal are used synonymously herein. The optical device 100 modulates the optical signal using the electrode signal and outputs the modulated optical signal.

[0046] Referring to FIG. 1A, the optical device 100 comprises 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 electrode signals. Other configurations are possible. Thus, the electrodes 120 and 130, together with the waveguide 110, provide a modulated optical signal. Electrodes 120 and 130 are drawn around waveguide 110 to indicate that waveguide 110 experiences an electric field applied between 120 and 130, but this does not indicate the physical location of electrodes 120 and 130. For example, electrode 120 could be located just above or below the waveguide with 130 located to one side of it.

[0047] Waveguide 110 has a rectangular footprint and is shown extending only between electrodes 120 and 130. Waveguide 110 may have other configurations. For example, waveguide 110 may include a thin film portion that may extend under electrodes 120 and / or 130 and a ridge 112 between electrodes 120 and 130. 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 material. In some embodiments, the effect of the electro-optic material includes a change in the refractive index in 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 nonlinearly 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, the waveguide 110 is a low optical loss waveguide. For example, the waveguide 110 may have a total optical loss of 10 dB or less through the portion of the waveguide 110 proximate the electrodes 120 and 130 (e.g., when biased at maximum transmission and maximum loss). The total optical loss is the optical loss in the waveguide through a single continuous electrode area (as shown in FIG. 1A ) (as opposed to multiple devices cascaded together, for example). In some embodiments, the 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, the waveguide 110 has an optical loss of 3 dB / cm or less (e.g., on average). In some embodiments, the nonlinear material in the waveguide 110 has an optical loss of 2.0 dB or less. In some such embodiments, the waveguide 110 has an optical loss of 1.0 dB / cm or less. In some embodiments, the waveguide 110 has an optical loss of 0.5 dB / cm or less. In some embodiments, the nonlinear optical material in the waveguide 110 includes lithium niobate (LN) and / or lithium tantalate (LT). In some embodiments, the nonlinear optical material of the waveguide 110 is comprised of LN. In some embodiments, the nonlinear optical material of the waveguide 110 is comprised of LT. Such nonlinear optical materials may have an inert chemical etching reaction for conventional etching with chemicals such as compounds of fluorine, chlorine, or bromine. In some embodiments, the nonlinear 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 nonlinear optical materials having similar optical properties may be used.

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

[0050] A portion of the waveguide 110 is proximate to the electrodes 120 and 130 along the optical signal transmission direction (e.g., from the optical signal input through the waveguide 110 to the modulated optical signal output). This portion of the waveguide may have a variety of lengths. In some embodiments, the portion of the waveguide 110 proximate to the electrodes 120 and 130 is at least 2 millimeters long. In some embodiments, this portion of the waveguide 110 is at least 5 millimeters long and at most 10 millimeters long. Other embodiments may have this portion of the waveguide 110 longer. The portion of the waveguide 110 proximate to the electrodes 120 and 130 may have a length greater than 2 centimeters. In some embodiments, the length of the portion of the waveguide 110 proximate 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 lengths are possible, at least in part, due to the low optical loss per unit length for the waveguide 110 discussed above. Because the waveguide 110 can be longer, the total optical modulation that can be provided through the electric field generated by the electrodes 120 and 130 can be greater. Furthermore, because the optical losses are lower and the microwave losses are lower (discussed below), the desired optical modulation (e.g., 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 amplitude of the input electrode signal required to shift the phase of the optical signal by a half-wave voltage, i.e., 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 the CMOS circuitry, 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 less than or equal to 1 volt for signals in the range of 50-100 GHz. Other voltages for other frequency ranges are possible. In this manner, the performance of the optical modulator 110 may be improved.

[0051] Additionally, the portions of waveguide 110 proximate electrodes 120 and 130 may have a small optical mode cross-sectional area. In some embodiments, the optical mode cross-sectional area is a function of 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 area is less than 3 times the square of the wavelength of the optical signal in the one or more nonlinear optical materials. In some embodiments, the optical mode area is less than 1.5 times the square of the wavelength of the optical signal in the one or more nonlinear optical materials. In some embodiments, the optical mode area is less than 4 μm 2 In some such embodiments, the optical mode area is less than 3 μm 2 In some embodiments, such small optical mode areas can be provided using the thin films and fabrication techniques described herein, and the optical mode areas can enable low optical losses as described herein.

[0052] The electrodes 120 and 130 apply an electric field to the waveguide 110. The electrode 120 comprises a channel region 122 and extensions 124 (only one of which is labeled in FIG. 1A). The electrode 130 comprises a channel region 132 and extensions 134 (only one of which is labeled in FIG. 1A). In some embodiments, the extensions 124 or 134 may be omitted from the electrode 120 or electrode 130, respectively. The extensions 124 and 134 protrude from the channel regions 122 and 132, respectively. Thus, the extensions 124 and 134 are closer to the waveguide 110 than the channel regions 122 and 132, respectively. The extensions 124 and 134 shown in FIG. 1A are simple rectangular protrusions. In some embodiments, the extensions 124 and 134 may have another shape. For example, extensions 124 and / or 134 may have an L-shaped footprint, a T-shaped footprint, and / or a footprint of another shape. 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 is 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 illustrated as constant. In some embodiments, this distance may vary. Similarly, the distance between waveguide 110 and channels 122 and 132 is illustrated as constant. In some embodiments, this distance may vary. Electrodes 120 and 130 are illustrated as symmetric. In some embodiments, electrodes 120 and 130 are asymmetric. For example, decompressor 134 may be omitted while decompressor 124 is present.

[0053] The extensions 124 and 134 protrude from the channel regions 122 and 132, respectively, and are between the channel regions 122 and 132, respectively, and the waveguide 110. 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 greater. 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 less affected by the electric field generated by the electrode 130 / extensions 134. The tendency for charge to collect at the edge of the channel region 122 closest to the electrode 130 is reduced. Thus, current may be more easily driven through the central portion of the channel region 122, and electrode losses in the channel region 122 (and electrode 120) may be reduced. Similarly, the channel region 132 is further away from the electrode 120. The channel region 132 is less affected by the electric field generated by the electrode 120 / extension 124. The tendency for charge to collect at the edge of the channel region 132 closest to the electrode 120 is reduced. Thus, current may be more easily driven through the channel region 132, and electrode losses in the channel region 132 (and electrode 130) may be reduced. Because microwave signal losses through the electrodes 120 and 130 may be reduced, a smaller drive voltage may be used for the electrodes 120 and / or 130, and less power may be consumed by the optical device 100. Furthermore, the ability to match the impedance of the electrode 120 with an input voltage device (not shown in FIG. 1A) may be improved. Such impedance matching may further reduce electrode signal losses in the optical device 100. Furthermore, the extensions 124 and 134 may affect the speed of the electrode signal through the electrodes 120 and 130. Thus, extensions 124 and 134 may be configured to adjust the speed of the electrode signal to match the speed of the optical signal in waveguide 110. Thus, the performance of optical device 100 may be improved.

[0054] The electrodes 120 and / or 130 may be fabricated using deposition techniques (such as evaporation and / or electroplating) and photolithography to shape 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 particular frequency window (e.g., at least 10 GHz) in the frequency range between DC and 500 GHz may be down to 0.8 dB per square root of the electrode signal frequency per centimeter, where 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 may be measured in GHz and the frequency window may be at least 10 GHz. In some embodiments, the electrode has an absorbent electrode loss for a frequency window of the electrode signal frequency from DC to 500 GHz or less. In some embodiments, the absorbent 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 may be down to 0.75 dB per square root of the electrode signal frequency per centimeter for a particular frequency window (e.g., 10 GHz or more). In some embodiments, the electrode has an absorbent electrode loss. In some embodiments, the absorbent electrode loss for a particular 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 absorbent electrode loss for the same frequency window and frequency range is less than 0.005 dB per GHz per centimeter for a frequency window in the frequency range between DC and 500 GHz. In some embodiments, the optical device 100 may include additional electrodes, such as DC electrodes (not shown in FIG. 1A).Such additional electrodes may be used to optimize the optical device 100 for low frequency response. The electrodes may comprise one or more of electro-optical, thermal phase shifters, and / or MEMS shifters.

[0055] In operation, an optical signal to be modulated is input to the waveguide 110. Also, an electrode signal (e.g., a microwave signal) is applied to the electrodes 120 and / or 130. For purposes of illustration, the microwave signal is applied to the electrode 120, while the electrode 130 is grounded. A time-varying microwave signal passing through the electrode 120 causes a charge of a particular sign to rapidly accumulate in the extension 124, which then decays to zero at the extension 124, and a charge of the opposite sign rapidly accumulates at the extension 124. The absence of a negative charge at a particular extension 124 is considered the same as a positive charge accumulating at the extension 124, and vice versa. This cycle is repeated at or near the frequency of the microwave signal. As a result of the accumulation of charge at the extension 124, an opposite charge accumulates at the nearby corresponding extension 134. A relatively large time-varying electric field is generated between the extensions 124 and 134. Because 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 a larger variation in the refractive index as it passes through the waveguide 110 and through the extensions 124 and 134. Thus, for a microwave signal of a given voltage amplitude applied to the electrode 120, a larger modulation of the optical signal may be achieved. For example, the optical device 100 may provide sufficient optical modulation at frequencies from 100 to 300 GHz or higher with a voltage amplitude of 1 volt or less provided to the electrode 120. Furthermore, as discussed above, the presence of the extensions 124 reduces the tendency for current to collect near the edges of the channel region 122 close to the waveguide 110, mitigating losses in the electrode 120. Because current is more easily driven through the channel region 122 with a lower voltage, microwave losses may be reduced. Thus, the performance of the optical device 100 may be improved.

[0056] Additionally, as discussed above, the optical device 100 may not only reduce optical loss through the waveguide 110, but may also increase modulation of the optical signal through the use of a longer waveguide 110. The use of electrodes 120 and 130 with extensions 124 and 134, respectively, may reduce microwave loss and allow for a larger electric field in the waveguide 110 / ridge 112, improving the propagation of the microwave signal through electrodes 120 and 130, respectively. Additionally, the electrodes 120 and 130 may improve performance through velocity and phase matching. Thus, the performance of the optical device 100 may be significantly improved.

[0057] FIG. 1B is a perspective view of optical device 100'. Optical device 100' is similar to optical device 100. Thus, similar parts of optical device 100' are similarly labeled. Optical device 100' includes waveguide 110', electrode 120', and electrode 130', which are similar to waveguide 110, electrode 120, and electrode 130, respectively. Substrate / underlayer 101 is also shown. In some embodiments, substrate 101 includes a silicon substrate and a silicon dioxide layer between the silicon substrate and waveguide 110. Other substrates may be used in other embodiments. In some embodiments, substrate 101 is a dielectric material having a low microwave dielectric constant (e.g., a microwave dielectric constant less than 11). In some embodiments, the substrate has a microwave dielectric constant less than 8. In some such embodiments, the substrate has a microwave dielectric constant less than 5. For example, substrate 101 may include sapphire, quartz, and / or fused silica. In some embodiments, one or more underlayers having a low microwave dielectric constant (such as silicon dioxide) may be used on top of the microwave dielectric constant substrate 101. Other and / or additional underlayers may be used in other embodiments. Furthermore, one or more low microwave dielectric constant underlayers may be used in conjunction with other substrates having a larger microwave dielectric constant. For example, a low microwave dielectric constant underlayer of silicon dioxide may be provided on a substrate 101 having a microwave dielectric constant greater than 11 (such as silicon or LN). In some embodiments, it is desirable for the underlayer provided to be thick. For example, the underlayer may be greater than or equal to 3 micrometers and less than or equal to 100 micrometers thick. Furthermore, other geometries of substrates and / or underlayers may be used in some embodiments.

[0058] Waveguide 110' is used to transmit optical signals. Waveguide 110' comprises ridge 112 and thin film portion 114. In the embodiment shown in FIG. 1B, thin film portion 114 and ridge portion are formed from the same material (e.g., from the same thin film). Waveguide 110' may be formed from similar materials as waveguide 110 and may have similar performance.

[0059] The waveguide 110' may have a different configuration 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 another configuration. For example, the ridge 112 may have a trapezoidal shape, a semicircular shape, a stacked rectangular shape, and / or another geometric shape that guides the optical signal in a manner similar to that 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 from different materials. The thin film 114 may include a nonlinear optical material (such as LN and / or LT), while the ridge 112 may be formed from 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 (e.g., 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 waveguide 110 to provide desired phase, polarization, intensity, IQ, other modulation, and / or other functions. In some embodiments (not shown in FIGS. 1B-1C), waveguide 110 may include a splitter to split the optical signal into multiple branches for modulation and recombine the modulated optical signal for output. In this manner, waveguide 110 and electrodes 120 and 130 may be configured to provide a desired function.

[0060] In some embodiments, the nonlinear optical material of the 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) of less than or equal to three times the optical wavelength of the optical signal transmitted in the waveguide 110' prior to processing. In some embodiments, the thin film has a thickness (e.g., of the thin film portion 114 and the ridge portion 112) of less than or equal to two times the optical wavelength. In some embodiments, the nonlinear optical material has a thickness of less than or equal to one time the optical wavelength. In some embodiments, the nonlinear optical material has a thickness of less than or equal to 0.5 times the optical wavelength. For example, the thin film may have a total thickness of less than or equal to 3 micrometers immediately after deposition. In some embodiments, the thin film has a total thickness of less than or equal to 2 micrometers. The thin film nonlinear optical material may be fabricated into the 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 light utilized is typically less than 250 nanometers. To fabricate the waveguide, the thin-film nonlinear optical material may undergo physical etching, for example, using dry etching, reactive ion etching (RIE), inductively coupled plasma RIE. In some embodiments, chemical etching and / or electron beam etching may be used. Thus, the waveguide 110' may have improved surface roughness. For example, one or more sidewalls of the ridge 112 may have reduced surface roughness. For example, the short-term root-mean-square surface roughness of the sidewalls of the ridge 112 is less than 10 nanometers. In some embodiments, the 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. Thus, the waveguide 110' may have optical losses in the ranges described above. In some embodiments, the height of the ridge 112 is selected to provide confinement of the optical mode such that at a location 10 micrometers from the center of the ridge 112, there is a 10 dB reduction in intensity from the intensity at the center of the ridge 112. For example, the height of the ridge 112 is, in some cases, on the order of a few hundred nanometers.However, other heights are possible in other embodiments.

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

[0062] Electrodes 120' and 130' apply an electric field to waveguide 110. Electrodes 120' and / or 130' may be fabricated using deposition techniques (such as electroplating) and photolithography to shape electrodes 120 and / or 130. The resulting electrodes 120' and / or 130' may have lower frequency-dependent electrode losses in the ranges described above for electrodes 120 and 130. Electrode 120' comprises a channel region 122' and extensions 124' (only one of which is labeled in FIG. 1B). Electrode 130' comprises a channel region 132' and extensions 134' (only one of which is labeled in FIG. 1B). In some embodiments, extensions 124' or 134' may be omitted from electrode 120' or electrode 130', respectively. Extensions 124' and 134' are closer to waveguide 110' than channel regions 122' and 132', respectively. For example, a distance s from extensions 124' and 134' to waveguide ridge 112 is less than a distance w from channels 122' and 132' to waveguide ridge 112. In the embodiment shown in FIG. 1B, extensions 124' and 134' are substantially flush with channel regions 122' and 132', respectively. In some embodiments, the extensions may protrude above and / or below the channel regions in addition to or instead of being flush.

[0063] The extensions 124' and 134' are proximate 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 may be highly customizable in some cases. For example, d may range from zero (or less than zero if the electrodes 120' and 130' are in contact with or embedded in the membrane portion 114) to a value that exceeds the height of the ridge 112. However, it is generally desirable for d to be small enough to enable the electrodes 120' and 130' to apply a desired electric field to the waveguide 110'. Additionally, the extensions 124' and 134' are at a distance s from the ridge 112. The extensions 124' and 134' are desirably close enough to the waveguide 110' (e.g., close to the ridge 112) to achieve the desired electric field and refractive index change. However, the extensions 124' and 134' are desirably far enough away from the waveguide 110' (e.g., from the ridge 112) that their presence does not result in excessive optical loss. The distance s is generally independent of the particular geometry or thickness of the waveguide 110', but s may be selected to allow both transverse electric and transverse optical modes to be confined differently within the waveguide 110'. However, the optical field strength in the extensions 124' and 134' (and more specifically in the portions 124B and 134B) is desirably reduced to limit optical loss due to absorption of the optical field by the conductors in the extensions 124' and 134'. Thus, s is sufficiently large such that the total optical loss of waveguide 110', including losses due to absorption in extensions 124' and 134', is not greater than the ranges mentioned above (e.g., in some embodiments 10 dB or less, in some embodiments 8 dB or less, in some embodiments 4 dB or less). In some embodiments, s is selected such that the optical field strength in extensions 124' and 134' is less than -10 dB of the maximum optical field strength in waveguide 110. In some embodiments, s is selected such that the optical field strength in extensions 124' and 134' is less than -40 dB of its maximum in the waveguide.For example, extensions 124' and / or 134' may be between 2 micrometers and 2.5 micrometers from ridge 112 in some embodiments.

[0064] In the embodiment shown in FIG. 1B, extension 124 has a connecting portion 124A and a countercurrent portion 124B. Countercurrent portion 124B is so named because a portion of the countercurrent portion may be anti-parallel to the direction of signal transmission through electrode 120. Similarly, extension 134 has a connecting portion 1234A and a countercurrent portion 134B. Thus, extensions 124 and 134 have a "T" shape. In some embodiments, other shapes are possible. For example, extensions 124 and / or 134 may have an "L" shape, may omit the countercurrent portion, may be rectangular, trapezoidal, parallelogrammatic, may wrap partially or completely around a portion of waveguide 110, and / or may have another shape. Similarly, channel regions 122' and / or 132' are shown as having a rectangular cross-section, but may have another shape. Additionally, the extensions 124' and / or 134' may be of various sizes, as illustrated by FIG. 1A. Although all of the extensions 124' and 134' are shown as being the same distance from the ridge 122, some of the extensions 124' and / or some of the extensions 134' may be at different distances from the ridge 112. The channel regions 122' and / or 132' may also have various sizes. In some embodiments, it is desirable for the extensions 124' and 134' to have a length l (e.g., l=ws) that corresponds to a frequency that is less than the Bragg frequency of the signal for the electrodes 120' and 130', respectively. Thus, it may be desirable for the length of the extensions 124' and 134' to be less than or equal to the microwave wavelength of the electrode signal divided by π at the maximum operating frequency of the electrodes 120' and 130'. In some embodiments, it is desirable for the length of the extensions 124' and 134' to be less than the microwave wavelength divided by 12. For example, if the maximum operating frequency is 300 GHz (which corresponds to a microwave wavelength of 440 micrometers at the substrate), then extensions 124' and 134' should desirably be less than about 37 micrometers. Individual extensions 124' and / or 134' may be irregularly spaced or may be periodic. Periodic extensions have a constant pitch.In some embodiments, the pitch p is desirably a distance corresponding to a frequency below the Bragg frequency, as described above with respect to the lengths of the extensions 124' and 134'. Thus, the pitch of the extensions 124' and 134' may desirably 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, the pitch is desirably less than the value obtained by dividing the wavelength of the microwave by 12. In some embodiments, the pitch is desirably less than the value obtained by dividing the wavelength of the microwave by 72, enabling 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, the extensions 124' and 134' desirably each have a length l (w - s) corresponding to a frequency less than the Bragg frequency of the signal for the electrodes 120' and 130'. Also, the extensions 124' and 134' are desirably 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 distance between the electrode structure and the waveguide also applies to a vertical configuration. Other distances between the waveguide 110 / ridge 112 and the channel regions 122 and / or 132 are also possible.

[0066] The geometry of electrodes 120' and 130' is similar to that described for electrodes 120 and 130. The size of the particular portions of extensions 124' and 134' may vary. For example, the length d2 of connections 124A and / or 134A may be selected such that the impedance of electrodes 120' and 130', respectively, is matched to the impedance (e.g., 50 Ω) of a driver (not shown). In some embodiments, the gap between extensions 134' and 124' (where waveguide ridge 112 resides) may be configured to increase the electric field at waveguide ridge 112. In some embodiments, the gap between extensions 124' and 134' is between 1 and 10 times the optical wavelength of the optical signal transmitted by waveguide 110'. However, a gap that is too small may cause current crowding and microwave losses in electrodes 120' and / or 130'. In some embodiments, the width of the channel regions 122' and / or 132' is selected to reduce microwave losses while attempting to match the microwave (electrode signal) velocity with the optical signal velocity in the waveguide 110. For example, the electrode channel regions 122' and / or 132' may have a width of 2 micrometers or more and 500 micrometers or less. The width of the retrograde sections 124B and / or 134B may be fine-tuned to allow low microwave losses while maintaining velocity matching and a high frequency response range. For example, the retrograde sections 124B and / or 134B may have a width (l-d2) of 10 nanometers or more and 10 micrometers or less. The length d3 of each retrograde section 124B and / or 134B, as well as the gap between adjacent retrograde sections 124B and / or 134, are selected to allow efficient modulation and low microwave losses. For example, a duty cycle d3 / (d3+d4) of 0.5 or more and 0.9999 or less may be selected in some embodiments. Other dimensions, including but not limited to those described herein, may be selected in some embodiments.

[0067] The optical device 100' operates similarly to the optical device 100. Thus, the optical device 100' may share the advantages of the optical device 100. The use of nonlinear optical materials in the waveguide 110' and the configuration of the waveguide 110' (e.g., smoother sidewalls of the ridges 112) may not only enhance the electro-optic effect (e.g., provide a larger modulation of the refractive index) but also reduce optical losses. Thus, a longer waveguide 110, a larger total change in the refractive index, and thus an enhanced modulation of the optical signal may be achieved. The use of electrodes 120' and 130' with extensions 124' and 134', respectively, may reduce microwave losses and allow for a larger electric field in the waveguide 110' / ridges 112', improving the propagation of microwave signals through the electrodes 120' and 130', respectively. Thus, the performance of the optical device 100' may be significantly improved.

[0068] This performance improvement can be achieved for optical devices (e.g., 100 and / or 100') in which the waveguides 110 and / or 110' include or consist of electro-optic materials that have microwave dielectric constants that significantly exceed the optical dielectric constant when utilized at the design microwave and optical frequencies, where for non-magnetic materials 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) whose microwave dielectric constants significantly exceed 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 times or more the optical dielectric constant. In some examples, the microwave dielectric constant is 5 times or more the optical dielectric constant. In some such materials, the microwave dielectric constant is 10 times or more the optical dielectric constant. Thus, in some embodiments, a waveguide 110' that includes (or consists of) such materials 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 more). The optical and microwave dielectric constants affect the transmission speeds of optical and microwave signals, respectively. The higher the optical dielectric constant, the slower the transmission speed of optical signals. Similarly, the higher the microwave dielectric constant, the slower the transmission speed of microwave signals.

[0069] While optical modes are generally well confined to the waveguide, microwave modes can extend significantly outside the electrode. For example, microwave modes can extend into the waveguide. For bulk optical devices and other optical devices with waveguides formed of materials (e.g., LN and / or LT) that have a microwave permittivity that is large compared to the optical permittivity, the transmission speed of microwave signals in the waveguide material is reduced more than the speed of optical signals. Features in the electrode (such as extensions) can also slow down the transmission of electrode signals in the electrode. Thus, the speed mismatch between optical and electrode signals is expected to be exacerbated by electrodes with features such as extensions. In general, the use of features such as extensions is not preferred in situations where the waveguide material has a microwave permittivity that is significantly larger than the optical permittivity (e.g., in bulk LN and / or LT waveguides). That is, the use of features on 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) than, approximately the same as, or less than the optical dielectric constant of the waveguide material (e.g., III-V compound materials such as indium phosphide and gallium arsenide).

[0070] In contrast, for optical device 100' (and 100), a thin film waveguide 110' is used. In general, optical modes are well confined to the waveguide 110' (e.g., in the ridge 112). This can be seen by the size of the optical modes 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, microwave modes for microwave signals in electrodes 120' and / or 130' can spread over many structures. This can be seen by the size and location of the microwave modes shown in FIG. 2. Thus, returning to FIG. 1B , the velocity of the microwave signal through electrodes 120′ and 130′ may be known using the microwave dielectric constants of multiple structures (electrodes 120′ and 130′, waveguide 110′, cladding material (not shown in FIG. 1B ) between substrate / underlayer 101 and electrodes 120′ and 130′, substrate / underlayer 101, and air or any structures (not shown) above electrodes 120′ and 130′, etc.). Thus, the contribution of the (high) microwave dielectric constant of the materials of waveguide 110′ (e.g., LT and LN) may be mitigated by the (lower) microwave dielectric constant of the surrounding structures. In this way, the velocity mismatch between the optical signal in waveguide 110′ and the electrode signal for electrodes 120′ and / or 130′ may be mitigated while still achieving other benefits of extensions 124′ and / or 134′.

[0071] FIG. 1C illustrates another embodiment of an optical device 100″. Optical device 100″ is similar to optical devices 100 and / or 100′. As such, like structures have like reference numerals. Thus, optical device 100″ includes waveguide 110′ and electrodes 120′ and 130′ that are similar to waveguide 110 and electrodes 120 and 130, respectively. Similarly, electrodes 120′ and 130′ include channel regions 122′ and 132′ that are similar to channel regions 122 and 132 of electrodes 120 and 130, respectively. Electrodes 120′ and 130′ include extensions 124′ and 134′ that are similar to extensions 124 and 134 of electrodes 120 and 130, respectively. Extensions 124' and 134' include connecting portions 124A' and 134A' and reverse portions 124B' and 134B' that are similar to connecting portions 124A and 134A and reverse portions 124B and 134B.

[0072] In some embodiments, optical devices 100 and 100' have an electro-optic effect in the plane of thin film region 114 (e.g., x-cut or y-cut modulators). Optical device 100'' has an electro-optic effect out of the plane of thin film region 114'' (e.g., z-cut optical modulators). Therefore, it is desirable to apply a perpendicular electric field to waveguide 110''. Thus, optical device 100'' comprises electrode 140' with extension 144' having connecting portion 144A' and retrograde portion 144B'. Extension 144' is similar to extensions 124, 134, 124', and 134'. Thus, the discussion herein regarding extensions 124 and 134 also applies to extension 144'. For example, distances s' and w' correspond to distances s and w, respectively. Thus, optical devices having out-of-plane electro-optic effects and improved performance may also be provided.

[0073] FIG. 1D illustrates one embodiment of an optical device 100'''. Optical device 100''' is similar to optical devices 100, 100', and / or 100'', such that similar structures have similar reference numbers. Thus, optical device 100''' includes waveguide 110' and electrodes 120' and 130' that are similar to waveguide 110 / 110' and electrodes 120 / 120' and 130 / 130', respectively. Similarly, electrodes 120' and 130' include channel regions 122' and 132', respectively, that are similar to channel regions 122 / 122' and 132 / 132', respectively, of electrodes 120 / 120' and 130 / 130', respectively, of optical device 100 / 100'. Electrodes 120' and 130' each include an extension 124' and 134', respectively, similar to extensions 124 / 124' and 134 / 134', respectively, of electrodes 120 / 120' and 130 / 130', respectively, of optical device 100 / 100'. Extensions 124' and 134' each include connecting portions 124A' and 134A' and counter portions 124B' and 134B', respectively, similar to connecting portions 124A / 124A' and 134A / 134A' and counter portions 124B / 124' and 134B / 134B', respectively, of optical device 100 / 100'.

[0074] The optical device 100'' also includes a further waveguide 150 and a further electrode 140 having a channel region 142 and an extension 144. The electrode 150 and extension 154 are similar to the electrodes 120, 120', 130', and 130' and extensions 124, 124', 134, and 134', respectively. 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 off 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] Optical device 100''' operates similarly to optical devices 100, 100', and / or 100''. Thus, optical device 100''' may share the advantages of optical devices 100, 100', and / or 100''. The use of nonlinear optical materials in waveguides 110' and / or 150 and the configuration of waveguides 110' and / or 150 (e.g., smoother sidewalls of ridges 112) may not only enhance the electro-optic effect but also reduce optical losses. Thus, longer waveguides 110' and 150, larger total changes in refractive index and thus enhanced modulation of optical signals may be achieved. The use of electrodes 120', 130', and 140 having extensions 124', 134', and 144, respectively, may reduce microwave losses and enable larger electric fields in waveguides 110' and 140. This may improve the propagation of microwave signals through the electrodes 120', 130', and 140. Thus, the performance of the optical device 100''' may be significantly improved.

[0076] FIG. 1E illustrates one embodiment of an optical device 100''''. Optical device 100'''' is similar to optical devices 100, 100', 100'', and / or 100'''. Accordingly, similar structures have similar reference numbers. Thus, optical device 100'''' includes waveguide 110' and electrodes 120'' and 130'', which are similar to waveguide 110 / 110' and electrodes 120 / 120' and 130 / 130', respectively. Similarly, electrodes 120'' and 130'' include channel regions 122'' and 132'', respectively, which are similar to channel regions 122 / 122' and 132 / 132', respectively, of electrodes 120 / 120' and 130 / 130', respectively, of optical device 100 / 100'. Electrodes 120'' and 130'' each include an extension 124'' and 134'', respectively, similar to extensions 124 / 124' and 134 / 134', respectively, of electrodes 120 / 120' and 130 / 130', respectively, of optical device 100 / 100'. Extensions 124'' and 134'' each include connecting portions 124A'' and 134A'' and retrograde portions 124B'' and 134B'', respectively, similar to connecting portions 124A / 124A' and 134A / 134A' and retrograde portions 124B / 124' and 134B / 134B', respectively, of optical device 100 / 100'.

[0077] Electrodes 120'' and 130'' each include an additional conductive layer 126 and 136, respectively. Thus, electrodes 120'' and 130'' may be capable of carrying additional current in conductive layers 126 and 136.

[0078] Optical device 100'''' operates similarly to optical devices 100, 100', 100'', and / or 100'''. Thus, optical device 100'''' may share the advantages of optical devices 100, 100', 100'', and / or 100'''. The use of nonlinear optical materials in waveguide 110' and the configuration of waveguide 110' (e.g., smoother sidewalls of ridge 112) may not only enhance the electro-optic effect but also reduce optical losses. Thus, a longer waveguide 110', a larger total change in refractive index, and thus enhanced modulation of the optical signal, may be achieved. The use of electrodes 120'' and 130'' having extensions 124'' and 134'', respectively, may reduce microwave losses and allow for a larger electric field in waveguide 110'. This may improve the propagation of microwave signals through electrodes 120'' and 130''. Therefore, the performance of the optical device 100'''' may be significantly improved.

[0079] FIG. 2 is a cross-sectional view of a portion of one embodiment 200 of an optical device that may have improved performance. The optical device 200 includes a waveguide 210 and electrodes 220 and 230 on a substrate 201. 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 illustrated waveguide 210 includes LN; however, other and / or additional electro-optical 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. Optical device 200 is similar to optical devices 100, 100', 100'', 100''', and / or 100''''. Thus, waveguide 210 and electrodes 220 and 230 are similar to waveguides 110 and / or 110', and electrodes 120, 120', and / or 120'', and 130, 130', and / or 130'', respectively.

[0080] FIG. 2 illustrates the relative sizes of optical modes for optical signals and radio frequency (RF) modes (or microwave modes) for microwaves. FIG. 2 is not to scale and only a portion of the optical device 200 is illustrated. As shown in FIG. 2, the optical modes may be primarily confined to the waveguide 210, the intermediate layer 202, and the cladding material 204. In contrast, the microwave modes propagate through the multiple stacks 201, 202, 210, 220, 230, and 204. Thus, the microwave modes experience absorption losses from the multiple stacks 201, 202, 204, 210, 220, and 230. Absorption from the silicon substrate 201 may be particularly high. The use of the silicon substrate 201 may also affect the speed of the microwave signal through the electrodes 220 and 230. Due to the small size of the thin film waveguide 210, it is possible to design other parts of the optical device 200 to reduce microwave absorption losses. For example, portions of silicon substrate 201 may be removed or replaced, electrodes 220 and / or 230 may be moved, waveguide 210 may be reduced in size, one or more other substrates may be used, and / or other modifications are possible. For example, intermediate layer 202 may be thick, such as 3 micrometers or greater in thickness, in some embodiments.

[0081] For example, Figures 3-5 show optical device embodiments 300, 400, and 500 that may further reduce microwave absorption losses. Figure 3 is a cross-sectional view of a portion of an optical device embodiment 300 that may improve performance. Figure 3 is not to scale, and only a portion of optical device 300 is shown. Optical device 300 includes a waveguide 310 and electrodes 320 and 330 on a substrate 301. Intermediate layer 302 and cladding material 304 are also shown. In the illustrated embodiment, substrate 301 is silicon, intermediate layer 302 is silicon dioxide, and cladding material 304 is silicon dioxide. In some embodiments, other and / or additional materials may be used. The portion of waveguide 310 shown includes LN. However, other and / or additional materials (such as LT) may be used. Waveguide 310 includes ridge 312 and thin film portion 314. Channel regions and extensions of electrodes 320 and 330 are not shown. Optical device 300 is similar to optical device 200. Thus, waveguide 310 and electrodes 320 and 330 are similar to waveguide 210 and electrodes 220 and 230, respectively. Also, substrate 301, intermediate layer 302, and cladding material 304 are similar to substrate 201, intermediate layer 202, and cladding material 204, respectively. However, in optical device 300, electrodes 320 and 330 have been moved farther from the underlying silicon substrate 301. In some embodiments, electrodes 320 and 330 may be moved farther from silicon substrate 301 by increasing the thickness of intermediate layer 302. For example, intermediate layer 302 may be 3 micrometers or thicker in some embodiments. This may be done in addition to or instead of moving the electrodes farther from thin film portion 314. Additionally, thin film portion 314 of waveguide 310 has been reduced in size. Therefore, absorption may be reduced by the silicon substrate 301 and the waveguide 310. Additionally, changes in the velocity of the microwave signal may also be reduced.

[0082] FIG. 4 is a cross-sectional view of a portion of an embodiment 400 of an optical device that may have improved performance. FIG. 4 is not to scale, and only a portion of the optical device 400 is shown. The optical device 400 includes a waveguide 410 and electrodes 420 and 430 on a substrate 401. 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 illustrated waveguide 410 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. Thus, 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 have been 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 membrane portion 414. Thus, absorption by the silicon substrate 401 may be reduced. Additionally, changes in the velocity of the microwave signal may also be reduced.

[0083] FIG. 5 is a cross-sectional view of a portion of an embodiment 500 of an optical device that may have improved performance. FIG. 5 is not to scale, and only a portion of the optical device 500 is shown. The optical device 500 includes a waveguide 510 and electrodes 520 and 530 on a substrate 501. 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 illustrated waveguide 510 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. Thus, 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 have been moved farther away from the underlying silicon substrate 301. Furthermore, the portion of the silicon substrate 501 below the ridge 512 has been removed. Thus, the absorption by the silicon substrate 501 may be reduced. Furthermore, the change in the velocity of the microwave signal may also be reduced. In some embodiments, in addition to or instead of removing a portion of the substrate, a different substrate may be selected.

[0084] In this manner, microwave losses may be further mitigated. Thus, in addition to the advantages of optical devices 100, 100', 100'', 100''', and / or 100'''', optical devices 300, 400, and 500 may further reduce microwave absorption losses. As a result, the performance of optical devices 300, 400, and 500 may be improved.

[0085] 6, 7, 8, 9, 10, and 11 show optical devices 600, 700, 800, 900, 1000, and 1100, respectively, that may have improved performance. FIGS. 6-11 illustrate various electrode configurations. FIGS. 6-11 are not to scale and only portions of optical devices 600, 700, 800, 900, 1000, and 1100 are shown. Optical devices 600, 700, 800, 900, 1000, and 1100 are similar to optical devices 100, 100', 100'', 100''', and / or 100'''. Similar components have similar reference numbers.

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

[0087] FIG. 7 illustrates optical device 700. For clarity, only electrodes 720, 730, and 740 are shown. Typically, a waveguide / ridge is between electrodes 720 and 730. Another waveguide / ridge (or waveguide / ridge branch) is between electrodes 720 and 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. Extension 724 is rectangular. However, electrodes 730 and 740 do not have an extension. Due to the presence of extension 724, current may be more easily driven through channel region 722. Thus, 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. Typically, a waveguide / ridge is between electrodes 820 and 830. Another waveguide / ridge (or waveguide / ridge branch) is between electrodes 820 and 840. In some embodiments, electrode 820 carries 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. Extension 824 is "T" shaped. Thus, extension 824 has a connection portion 824A and a return portion 824B. Electrodes 830 and 840 are devoid of extensions. Due to the presence of extension 824, current may be more easily driven through channel region 822. Thus, optical device 800 may share the advantages of optical devices 100, 100', 100'', 100'''', and / or 100''''.

[0089] FIG. 9 shows an optical device 900. Electrodes 920, 930, and 940 are shown. A waveguide / ridge 910 is between electrodes 920 and 930. Another waveguide / ridge (or waveguide / ridge branch) 950 is between electrodes 920 and 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 "T" shaped, but have different lengths and are not periodic (e.g., irregularly spaced and with a varying pitch). Due to the presence of extensions 924, 934, and 944, current may 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'''.

[0090] FIG. 10 shows an optical device 1000. Electrodes 1020, 1030, and 1040 are shown. A waveguide / ridge 1010 is between electrodes 1020 and 1030. Another waveguide / ridge (or waveguide / ridge branch) 1050 is between electrodes 1020 and 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. The extensions 1024, 1034, and 1044 have various shapes and are irregularly spaced apart. Additionally, channel 1022 has a notch. However, channel 1022 still has a straight central region that can transmit current. Due to the presence of extensions 1024, 1034, and 1044, current may 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'''.

[0091] FIG. 11 shows an optical device 1100. Electrodes 1120, 1130, and 1140 are shown. A waveguide / ridge 1110 is between electrodes 1120 and 1130. Another waveguide / ridge (or waveguide / ridge branch) 1150 is between electrodes 1120 and 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. The extensions 1124, 1134, and 1144 have various shapes and are irregularly spaced apart. Due to the presence of extensions 1124, 1134, and 1144, current may be more easily driven through channel regions 1122, 1132, and 1142, respectively. Thus, optical device 1100 may share the advantages of optical devices 100, 100', 100'', 100'''', and / or 100'''. Thus, various configurations of extensions may be used for the electrodes, as illustrated by optical devices 600, 700, 800, 900, 1000, and 1100.

[0092] 12A-12D show various electrode configurations in a diagram illustrating portions of optical device embodiments 1200A, 1200B, 1200C, and 1200D that may have improved performance. FIGS. 12A-12D are not to scale, and only portions of optical devices 1200A, 1200B, 1200C, and 1200D are shown. Optical devices 1200A, 1200B, 1200C, and 1200D are similar to optical devices 100, 100', 100'', 100''', and / or 100''', and thus similar components have similar labels (e.g., waveguide 1210 is similar to waveguide 110'). FIG. 12A is a plan view of optical device 1200A. 12B-12D are cross-sectional views of portions of optical devices 1200B, 1200C, and 1200D. FIGURES 12A-12D illustrate that some optical devices may share the same plan view even though the cross-sections of the devices may differ. Conversely, some optical devices may have different plan views even though the cross-sections may be similar.

[0093] 12A, electrodes 1220A, 1230A, and 1240A and waveguides 1210A and 1250A are shown. Portions of waveguides 1210A and 1250A shown in FIG. 12A correspond to ridges in some embodiments. Electrodes 1220A, 1230A, and 1240A have channel regions 1222A, 1232A, and 1242A, respectively. Electrodes 1220A, 1230A, and 1240A also include extensions 1224A, 1234A, and 1244A. As discussed above, extensions 1224A, 1234A, and 1244A of electrodes 1220A, 1230A, and 1240A can improve performance. In some embodiments, channels 1222A, 1232A, and 1242A are at the same height as extensions 1224A, 1234A, and 1244A, respectively.

[0094] 12B shows optical device 1200B sharing a plan view of optical device 1200A. Thus, optical device 1200B includes electrodes 1220B, 1230B, and 1240B and waveguides 1210B and 1250B. Waveguides 1210B and 1250B include ridges 1222B and 1252B, respectively. Waveguides 1210B and 1250B share a common thin film portion 1214C. Electrodes 1220B, 1230B, and 1240B include channel regions 1222B, 1232B, and 1242B, respectively. Electrodes 1220B, 1230B, and 1240B also include extensions 1224B, 1234B, and 1244B. As mentioned above, the extensions 1224B, 1234B, and 1244B of electrodes 1220B, 1230B, and 1240B may improve performance. Although sharing the same plan view as optical device 1200A, channel regions 1222B, 1232B, and 1242B are elevated to a higher height (further away from the substrate) than extensions 1224B, 1234B, and 1244B. Optical device 1200B functions similarly to optical device 1200A and may therefore share the advantages of optical device 100.

[0095] 12C shows optical device 1200C having a cross-sectional view very similar to optical device 1200B. Optical device 1200C includes electrodes 1220C, 1230C, and 1240C and waveguides 1210C and 1250C. Waveguides 1210C and 1250C include ridges 1222C and 1252C, respectively. Waveguides 1210B and 1250B share a common thin film portion 1214C. Electrodes 1220C, 1230C, and 1240C include channel regions 1222C, 1232C, and 1242C, respectively. Electrodes 1220C, 1230C, and 1240C also include extensions 1224C, 1234C, and 1244C. As mentioned above, the extensions 1224C, 1234C, and 1244C of the electrodes 1220C, 1230C, and 1240C may improve performance. Although sharing a similar cross-sectional view, the optical device 1200C has a different plan view than the optical devices 1200A and 1200B. As can be seen by the dotted lines in FIG. 12C, the outer edges of the extensions 1224C, 1234C, and 1244C are aligned with the outer edges of the channel regions 1222C, 1232C, and 142C, respectively. Thus, the electrodes 1220C, 1230C, and 1240C appear rectangular when viewed from above. That is, the extensions 1224C, 1234C, and 1244C are not visible in the plan view. However, extensions 1224C, 1234C, and 1244C are still closer to waveguide 1210C / ridge 1212C and waveguide 1250C / ridge 1252C than corresponding channel regions 1222C, 1232C, and 1242C. Optical device 1200C functions similarly to optical devices 1200A and 1200B. Thus, despite having a different plan view, optical device 1200C may share the advantages of optical devices 100, 1200A, and / or 1200B.

[0096] 12D shows optical device 1200D, which shares a plan view with optical device 1200A. Thus, optical device 1200D includes electrodes 1220D, 1230D, and 1240B, and waveguides 1210D and 1250D. Waveguides 1210D and 1250D include ridges 1222D and 1252D, respectively. Waveguides 1210D and 1250D include thin-film portions 1214D and 1254D, respectively. Electrodes 1220D, 1230D, and 1240D have channel regions 1222D, 1232D, and 1242D, respectively. Electrodes 1220D, 1230D, and 1240D also include extensions 1224D, 1234D, and 1244D. As mentioned above, the extensions 1224D, 1234D, and 1244D of electrodes 1220D, 1230D, and 1240D may improve performance. While sharing the same plan view as optical device 1200A, the thin film portions 1214D and 1254D of waveguides 1210D and 1250D, respectively, are reduced in size. Optical device 1200D functions similarly to optical devices 1200A, 1200B, and 1200C. Thus, optical device 1200D may share the advantages of optical devices 100, 1200A, 1200B, and / or 1200C.

[0097] 13A-13J show various electrode configurations in diagrams illustrating portions of embodiments of optical devices 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 1300I, and 1300J that may have improved performance. Figures 13A-13J are not to scale and only portions of optical devices 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 1300I, and 1300J are shown. Figures 13A-13J show various configurations of electrodes that may be utilized with 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''', and thus similar components have similar labels (e.g., waveguide ridge 1312A is similar to waveguide ridge 112). For clarity, electrodes are generally illustrated as rectangular in FIGS. 13A-13I, although such electrodes may include channel regions, extensions, and / or other features as described herein. Thus, the electrodes illustrated in FIGS. 13A-13I are primarily intended to illustrate the location of the electrodes.

[0098] FIG. 13A shows an optical device 1300A with a waveguide having a ridge 1312A and a thin film portion 1314A, and electrodes 1320A and 1330A. Substrate 1301A and intermediate layer 1302A are also shown. The electrode extensions are preferably in close proximity to the corresponding waveguide. In some embodiments, a portion of the electrode extension is preferably between the top of the ridge and the top of the thin film portion of the waveguide. Thus, electrodes 1320A and 1330A share a contact surface with the thin film portion 1314A of the waveguide. More specifically, electrodes 1320A and 1330A contact the top surface of thin film portion 1314A.

[0099] 13B shows an optical device 1300B with a waveguide having a ridge 1312B and a thin film portion 1314B, and electrodes 1320B and 1330B. Substrate 1301B and intermediate layer 1302B are also shown. The electrode extensions are preferably adjacent to the corresponding waveguides. Electrodes 1320B and 1330B extend above the top of the waveguide ridge 1312B, through the thin film portion 1314B of the waveguide, and into the intermediate layer 1302B.

[0100] 13C shows an optical device 1300C with a waveguide having a ridge 1312C and a membrane 1314C, and electrodes 1320C and 1330C. Also shown is a substrate 1301C and an intermediate layer 1302C. The electrode extensions are preferably adjacent to the corresponding waveguides. The electrodes 1320C and 1330C extend above the top of the waveguide ridge 1312C, through the membrane 1314C of the waveguide, and into the substrate 1301C.

[0101] 13D shows an optical device 1300D with a waveguide having a ridge 1312D and a membrane portion 1314D, and electrodes 1320D and 1330D. Substrate 1301D and intermediate layer 1302D are also shown. Electrode extensions are preferably adjacent to the corresponding waveguide. Electrode extensions 1320D and 1330D extend between the top of waveguide ridge 1312D and the top of waveguide membrane portion 1314D, through membrane portion 1314D, and into substrate 1301D.

[0102] 13E shows an optical device 1300E with a waveguide having a ridge 1312E and a membrane portion 1314E, and electrodes 1320E and 1330E. Substrate 1301E and intermediate layer 1302E are also shown. The electrode extensions are preferably adjacent to the corresponding waveguide. Electrodes 1320E and 1330E extend from above the top of waveguide ridge 1312E to between the top of waveguide ridge 1312E and the top of waveguide membrane portion 1314E.

[0103] FIG. 13F shows an optical device 1300F with a waveguide having a structure 1312F and a membrane portion 1314F, and electrodes 1320F and 1330F. Substrate 1301F and intermediate layer 1302F are also shown. The electrode extensions are preferably close to the corresponding waveguide. Electrodes 1320F and 1330F extend from above the top of structure 1312F to between the top of the waveguide structure 1312F and the top of the waveguide membrane portion 1314F. Furthermore, structure 1312F corresponds to a waveguide ridge. However, in the illustrated embodiment, structure 1312 may be another component (such as a heater).

[0104] FIG. 13G shows an optical device 1300G with a waveguide having a ridge 1312G and a membrane portion 1314G, and electrodes 1320G and 1330G. Substrate 1301G and intermediate layer 1302G are also shown. The electrode extensions are preferably adjacent to the corresponding waveguide. Electrodes 1320G and 1330G extend from above membrane portion 1314G into the waveguide membrane portion 1314G. Additionally, the waveguide ridge 1312G is below the waveguide membrane portion 1314G.

[0105] FIG. 13H shows an optical device 1300H with a waveguide having a structure 1312H and a membrane portion 1314H, and electrodes 1320H and 1330H. Substrate 1301H and intermediate layer 1302H are also shown. The electrode extensions are preferably close to the corresponding waveguide. Electrodes 1320H and 1330H extend from above the top end of membrane portion 1314H into the waveguide membrane portion 1314H. Structure 1312H may be a heater or similar component corresponding to a waveguide ridge. Additionally, structure 1312H is below the waveguide membrane portion 1314H.

[0106] FIG. 13I shows an optical device 1300I with a waveguide having a structure 1312I and a membrane portion 1314I, and electrodes 1320I and 1330I. Substrate 1301I and intermediate layer 1302I are also shown. The electrode extensions are preferably adjacent to the corresponding waveguide. Electrodes 1320I and 1330I extend from below the bottom end of structure 1312I to the bottom surface of the waveguide membrane portion 1314I. Structure 1312i may be a heater or similar component corresponding to a waveguide ridge and is below the waveguide membrane portion 1314I.

[0107] 13J shows an optical device 1300J comprising a waveguide having a ridge 1312J and a thin film portion 1314J, and electrodes 1320J and 1330IJ. Substrate 1301I and 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 optical device 1330J, channel regions 1322J and / or 1332J need not have a rectangular cross-section.

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

[0109] Figures 14A-14K show various electrode configurations in diagrams illustrating portions of optical device embodiments 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400I, 1400J, and 1400K that may provide improved performance. Figures 14A-14K are not to scale and only portions of optical devices 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400I, 1400J, and 1400K are shown. 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'''. Thus, similar components have similar labels (e.g., waveguide ridge 1412A is similar to waveguide ridge 112). Although present, channel regions and extensions are not separately illustrated in Figures 14A-14D. Figures 14A-14K show various configurations of electrodes that can be utilized for waveguide structures where the electro-optic effect occurs outside the plane of the thin film (e.g., z-cut waveguides). For clarity, the electrodes are generally illustrated as rectangular in Figures 14A-14D. However, such electrodes may include channel regions, extensions, and / or other features as described herein. Thus, the electrodes shown in Figures 14A-14D are primarily illustrative of the location of the electrodes. The extensions and other features of some embodiments are more clearly shown in Figures 14E-14K.

[0110] 14A shows an optical device 1400A with a waveguide having a ridge 1412A and a membrane portion 1414A, and electrodes 1420A and 1430A. Substrate 1401A and intermediate layer 1402A are also shown. The electrodes are preferably adjacent to the corresponding waveguide and provide a vertical field in the region of the ridge 1412A. Thus, electrode 1420A is above ridge 1412A, while electrode 1430A is a membrane below ridge 1412A and extends horizontally.

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

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

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

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

[0116] FIG. 14F shows a differential optical device 1400F with a waveguide 1410F having a ridge 1412F and a thin film portion 1414F, and electrodes 1420F and 1430F. Substrate 1401F and intermediate layer 1400F are also shown. The electrodes are preferably close to the corresponding waveguide and provide a vertical field in the region of structure 1412F. Thus, electrode 1420F is above structure 1412F, while electrodes 1430F and 1440F are to the sides of structure 1412F. Since optical device 1400F is a differential modulator, there is a further waveguide 1460F (e.g., a further ridge) and a further electrode 1450F. 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 locations may be used so long as a vertical electric field is established within the waveguides 1412F and 1460F. Also shown are channel regions 1422F, 1432F, 1442F, and 1452F and extensions 1424F, 1434F, 1444F, and 1454F of electrodes 1420F, 1430F, 1440F, and 1450F, respectively. 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 with a waveguide 1410G having a ridge 1412G and a thin film portion 1414G, and electrodes 1420G and 1430G. The substrate 1401G and intermediate layer 1400G are also shown. The electrodes are preferably close to the corresponding waveguides and provide a vertical field in the region of the structure 1412G. Thus, the electrodes 1420G are above the structure 1412G, while the electrodes 1430G and 1440G are to the sides of the structure 1412G. Since the optical device 1400G is a differential modulator, there is a further waveguide 1460G (e.g., a further ridge) and a further electrode 1450G. In the illustrated embodiment, the electrodes 1430G and 1440G are ground electrodes, while the electrodes 1420G and 1450G carry the signal. The positions of the ground electrodes 1430G and 1440G are exemplary. Other ground locations may be used as long as a vertical electric field is established within the waveguides 1412G and 1460G. Also shown are channel regions 1422G, 1432G, 1442G, and 1452G and extensions 1424G, 1434G, 1444G, and 1454G of electrodes 1420G, 1430G, 1440G, and 1450G, respectively. 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, interaction between channel regions 1422G and 1452G may be reduced. Thus, optical device 1400G may share the advantages of optical devices 100, 100', 100'', 100''', and / or 100''' that utilize extensions.

[0118] FIG. 14H shows an optical device 1400H with a waveguide 1410H having a structure 1412H and a thin film portion 1414H, and electrodes 1420H and 1430H. Substrate 1401H and intermediate layer 1400H are also shown. The electrodes are preferably adjacent to the corresponding waveguide and provide a vertical field in the region of structure 1412H. Structure 1412H may be a material other than a nonlinear optical material, such as a passive material or a heater as described herein. An optional buffer layer may be present between thin film region 1414H containing the nonlinear optical material and structure 1412H. In some embodiments, structure 1412H may simply be a buried ridge containing a nonlinear optical material. Electrode 1420H is below structure 1412H, while electrodes 1430H and 1440H are on the sides of structure 1412H. In the illustrated embodiment, electrodes 1430H and 1440H are ground electrodes, while electrode 1420H carries the signal. The locations of ground electrodes 1430H and 1440H are exemplary. Other locations of the grounds may be used as long as a vertical electric field is established within waveguide 1412H. Also shown are channel regions 1422H, 1432H, and 1442H and extensions 1424H, 1434H, and 1444H of electrodes 1420H, 1430H, and 1440H, respectively. Channel regions 1422H, 1432H, and 1442H and extensions 1424H, 1434H, and 1444H are similar to the channel regions and extensions described above. Thus, optical device 1400H may share the advantages of optical devices 100, 100', 100'', 100''', and / or 100''' that utilize extensions.

[0119] FIG. 14I shows a differential optical device 1400I with 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 preferably close to the corresponding waveguides and provide a vertical field in the region of the structure 1412I. Thus, the electrode 1420I is below the structure I, while the electrodes 1430I and 1440I are on the sides of the structure 1412I. The structure 1412I may be a material other than a nonlinear optical material, such as a passive material or a heater as described herein. In some embodiments, the structure 1412I may simply be a buried ridge that includes a nonlinear optical material. Because the 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 carry signals. The locations of ground electrodes 1430I and 1440I are exemplary. Other locations of the grounds may be used as long as a vertical electric field is established within the waveguides 1412I and 1460I. An optional buffer layer may be present between the thin film region 1414I containing the nonlinear optical material and the structures 1412I and 1460I. Also shown are channel regions 1422I, 1432I, 1442F, and 1452I, and 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''', which utilize extensions.

[0120] FIG. 14J shows an optical device 1400J with a waveguide 1410J having a ridge 1412J and a thin film portion 1414J, and electrodes 1420J and 1430J. Substrate 1401J and intermediate layer 1400J are also shown. The electrodes are preferably adjacent to the corresponding waveguide 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 carries the signal. The locations of ground electrodes 1430J and 1440J are exemplary. Other locations of the grounds may be used, so long as a vertical electric field is established within waveguide 1412J. Also shown are channel regions 1432J and 1442J and extensions 1434J and 1444J of electrodes 1430J and 1440J, respectively. Thus, signal electrode 1420J does not include extensions 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 need to include extensions to improve performance.

[0121] FIG. 14K shows a differential optical device 1400K with a waveguide 1410K having a ridge 1412K and a thin film portion 1414K, and electrodes 1420K and 1430K. Substrate 1401K and intermediate layer 1400K are also shown. The electrodes are preferably 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 to the sides of structure 1412K. Since optical device 1400K is a differential modulator, there is a further waveguide 1460K (e.g., a further ridge) and a further electrode 1450K. In the illustrated embodiment, electrodes 1430FK and 1440K are ground electrodes, while electrodes 1420K and 1450K carry signals. The locations of ground electrodes 1430K and 1440K are exemplary. Other locations of grounds may be used so long as a vertical electric field is established within waveguides 1412K and 1460K. Also shown are channel regions 1432K and 1442K and extensions 1434K and 1444K of electrodes 1430K and 1440K, respectively. 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 include extensions. Optical device 1400K may share the advantages of optical devices 100, 100', 100'', 100''', and / or 100''', which utilize extensions. Furthermore, not all electrodes need to include extensions to improve performance.

[0122] In this manner, despite the various electrode and waveguide configurations, 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'''. Thus, optical devices 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400J, and 1400K may share the advantages of optical devices 100, 100', 100'', 100'''', and / or 100'''.

[0123] 15A and 15B show portions of optical device embodiments 1500A and 1500B, respectively. Optical devices 1500A and 1500B are similar to optical devices 100, 100', 100'', 100''', and / or 100''''. FIGS. 15A and 15B are not to scale and only portions of optical devices 1500A and 1500B are shown. Optical devices 1500A and 1500B are similar to optical devices 100, 100', 100'', and / or 100'''', respectively. As such, similar components have similar reference numbers. Optical device 1500A includes waveguide 1510 with ridge 1512 similar to waveguide 110 / 110' with ridge 112 and electrodes 120, 120', 120'', 130, 130', and 130', and electrodes 1520 and 1530. Electrodes 1520 and 1530 include channel regions 1522 and 1532 similar to channel regions 122, 122', 122'', and 132, 132', 132'', respectively, of electrodes 120, 120', and 120'', and 130, 130', and 130'', respectively. Electrodes 1520 and 1530 include extensions 1524 and 1534, respectively, that are similar to extensions 124, 124', 124'', and 134, 134', 134'', of electrodes 120, 120', 120'', and 130, 130', 130'', respectively. Extensions 1524 and 1534 include connecting portions 1524A and 1534A, and retrograde portions 1524B and 1534B, that are similar to connecting portions 124A, 124A', 124A'', and 134A, 134A', 134A'', and retrograde portions 124B, 124B', 124B'', and 134B, 134B', 134B'', respectively.

[0124] The waveguide 1510 also includes a waveguide bend 1515. Although multiple waveguide bends are shown in FIG. 15A, only one waveguide bend 1515 is labeled. Each waveguide bend 1515 may have a bend radius of 1 mm or less. In some embodiments, each waveguide bend 1515 has a bend radius of 500 μm or less. In some embodiments, each waveguide bend 1515 has a bend optical loss of 0.5 dB or less. The bends in the waveguide (and electrodes) may be used to lengthen the area in which the electrodes 1520 and 1530 are adjacent to the waveguide 1510 while limiting the size of a 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. The waveguide 1510 and electrodes 1520 and 1530, in some embodiments, occupy an area of ​​20 square millimeters or less. In some embodiments, the waveguide 1510 and electrodes 1520 and 1530 reside on an integrated circuit having a length of 32 millimeters or less. In some such embodiments, the waveguide 1510 and electrodes 1520 and 1530 reside on an integrated circuit having a length of 22 millimeters or less. This is true even if the length of the waveguide 1510 is longer. Thus, greater optical signal modulation can be achieved with a smaller overall device.

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

[0126] In some embodiments, the electrode bends 1525 and 1535 may be used to improve performance. More specifically, the electrode bends 1525 and 1535 and the waveguide bends 1515 may 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 at the electrodes 1520 and / or 1530 and the transmission speed of the optical signal at the waveguide 1510. The speed of the optical signal through the waveguide 1510 is affected by the refractive index of the waveguide 1510. The speed of the microwave signal at 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 / underlayer (not shown in FIGS. 15A-15B) may also affect the velocity of the electrode signal. The materials used for the waveguide 1510 and electrodes 1520 and / or 1530, the processing techniques used for the waveguide 1510 and electrodes 1520 and / or 1530, the cladding material and substrate / underlayer, and the configuration of the extensions 1524 and / or 1534 may be selected to reduce the difference in velocity between the optical signal in the waveguide 1510 and the electrode signal in the electrodes 1520 and / or 1530.

[0127] Additionally, further extensions may be added that may be relatively far from the ridge 1512 (e.g., farther from the ridge 1512 than the channels 1522 and / or 1532). Such extensions (not shown in FIGS. 15A-15B) may improve the velocity matching between the optical signal in the waveguide 1510 and the electrode signal in the electrodes 1520 and / or 1530. However, there may still be some mismatch between the optical signal velocity and the electrode signal velocity. The bends 1515, 1525, and 1535 may compensate for these mismatches. For example, in some embodiments, the waveguide bends 1515 may be configured such that the optical signal travels a longer path in the waveguide 1510 than the microwave signal travels in the electrodes 1520 and / or 1530. This path difference may ensure that the optical signal travels faster in the waveguide 1510 than the microwave signal travels in the electrodes 1520 and / or 1530. In some embodiments, the waveguide bends 1515 may be configured to cause the optical signal to travel a shorter path in the waveguide 1510 than the path the microwave signal travels in the electrodes 1520 and / or 1530. This path difference may compensate for the optical signal traveling slower in the waveguide 1510 than the microwave signal travels in the 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) and optical (waveguide) signals, the lengths of the bends 1515, 1525, and 1535 can be calculated to mitigate the difference caused by the electrode and optical signals traveling at different speeds in the straight sections. By configuring the straight and bend sections, the velocity mismatch can be mitigated to obtain the desired performance. In this manner, waveguide bends 1515 and electrode bends 1525 and 1535 may be utilized to account for mismatch in the velocities of the electrode (microwave) and optical signals. Thus, in addition to the advantages described herein for optical devices such as optical devices 100, 100', 100'', 100''', and / or 100'''', optical device 1500A may have improved performance because it has improved velocity matching.

[0128] Optical device 1500B is similar to optical device 1500A. As such, similar structures have similar reference numbers. Thus, optical device 1500B includes a waveguide 1510 with ridge 1512 and a waveguide 1510' with ridge 1512', which are similar to electrodes 1520 and 1530, and electrodes 1520' and 1530'. Electrodes 1520' and 1530' include extensions 1524' and 1534', which are similar to extensions 1524 and 1534, respectively. Extensions 1524 and 1534 include connecting portions 1524A and 1534A and counter portions 1524B and 1534B, which are similar to connecting portions 1524A and 1534A and counter portions 1524B and 1534B. Bent portions 115', 125', and 135' of waveguide 110' and electrodes 120' and 130' are similar to bent portions 115, 125, and 135, respectively. In some embodiments, the bent portions may be omitted such that waveguide 1510' and electrodes 1520' and 1530' are straight.

[0129] Optical device 1500B has an electro-optic effect out of the plane of the thin film region (e.g., it is a z-cut optical device). Therefore, it is desirable to apply a perpendicular electric field to the waveguide 1510'. Thus, electrode 1540 is also shown. Although not shown, electrode 1540 may have an extension. Electrode bends 1525', 1535', and 1545 and waveguide bends 1515' and 1545 are also shown. Thus, in addition to the advantages described herein for optical devices such as optical devices 100, 100', 100'', 100''', 100'''', and / or 1500A, optical device 1500B may have improved performance due to improved velocity matching.

[0130] FIG. 16 shows a portion of an optical device 1600 with a waveguide 1610 and electrodes 1620 and 1630. The electrodes 1620 and 1630 have extensions 1624 and 1634, respectively. Only one extension 1624 and one extension 1634 are labeled. The channel regions of the electrodes 1620 and 1630 are not labeled. The waveguide 1610 has bent portions 1615, only one of which is labeled. Similarly, the electrodes 1620 and 1630 have bent portions 1625 and 1635, only one of which is labeled per electrode. The bent portions 1615, 1625, and 1635 allow the area occupied by the long waveguide 1610 and the long electrodes 1620 and 1630 to be small. Additionally, as will be explained later, bends 1615, 1625, and 1635 may be used to mitigate velocity mismatch and therefore phase mismatch between the microwave signal carried by electrodes 1620 and / or 1630 and the optical signal carried by waveguide 1610. The locations of 1624 and 1634 shown in the figure may not correspond to physical locations. For example, in a z-cut modulator device, 1624 or 1634 may be located at the top of waveguide 1610 and additional electrodes may be introduced to provide the required electric field profile.

[0131] FIG. 17 shows a portion of an optical device 1700 including a waveguide 1710 and electrodes 1720 and 1730. The optical device 1700 is similar to optical devices 100, 100', 100'', 100''', and / or 100'''. As such, similar structures have similar reference numbers. Thus, the optical device 1700 includes a waveguide 110' having a ridge 112 and a thin film portion 114, and a waveguide 1710 having a ridge 1712 and a thin film portion 1714, which are similar to electrodes 120 and 130, respectively, and electrodes 1720 and 1730. The electrodes 1720 and 1730 include extensions 1724 and 1734, respectively, which are similar to extensions 124, 124', 124'', and 134, 134', 134'', respectively. The extensions 1724 and 1734 may be etched on, partially in, completely in, or through the thin film portion 1714 of the waveguide 1712. The optical device 1700 may share the advantages of optical devices 100, 100', 100'', and 100'''.

[0132] FIG. 18 shows a portion of an optical device 1800 comprising a waveguide 1810 and electrodes 1820 and 1830. The optical device 1800 is similar to optical devices 100, 100', 100'', 100''', and / or 100'''. As such, similar structures have similar reference numbers. Thus, the optical device 1800 comprises a waveguide 110' having a ridge 112 and a thin film portion 114, and a waveguide 1810 having a ridge 1812 and a thin film portion 1814, which are similar to electrodes 120 and 130, respectively, and electrodes 1820 and 1830. The electrodes 1820 and 1830 comprise extensions 1824 and 1834, respectively, which are similar to extensions 124, 124', 124'', and 134, 134', 134'', respectively. The substrate 1801 is similar to the substrate 101. A space 1802 within the substrate 1801 and an additional layer 1803 are also shown. The space 1801 is at least partially filled with the layer 1803. The layer 1803 may be a dielectric in some embodiments. In some embodiments, the layer 1803 may be a metal layer or other layer. The layer 1803 may be used to design the mechanical integrity or microwave properties of the optical device 1800. In some embodiments, the substrate 1802 may be completely removed. In such embodiments, the layer 1803, if present, may extend across the optical device 1800. In some embodiments, the space 1802 may have a different shape (e.g., semi-cylindrical, etc.), multiple spaces 1802 may be formed, and / or the layer 1803 may be omitted. Furthermore, the space 1802 may not extend across the entire height of the substrate. In some embodiments, the space 1802 is formed from the front side of the substrate 1801, for example, by etching the substrate 1801 from the same side as the waveguide 1810. Also, the space 1802 may extend across multiple waveguides and / or electrodes in some embodiments. The optical device 1800 may share the advantages of the optical devices 100, 100', 100'', and 100'''.

[0133] FIG. 19 shows a portion of an optical device 1900 including a waveguide 1910 and electrodes 1920 and 1930. The optical device 1900 is similar to optical devices 100, 100', 100'', 100''', and / or 100'''. As such, similar structures have similar reference numbers. Thus, the optical device 1900 includes a waveguide 1910 including a ridge 112 and a thin film portion 114, and electrodes 1920 and 1930 including electrodes 1920 and 1930. The electrodes 1920 and 1930 include extensions 1924 and 1934, respectively, similar to extensions 124, 124', 124'', and 134, 134', 134'', respectively. Substrate 1901 is similar to substrate 101. Also shown is space 1902 in substrate 1901 and further layer 1903, which are similar to space 1802 and further layer 1803 in substrate 1801. Also provided is a second layer 1904, which may be a metal support layer or other layer. Layers 1903 and 1904 may be used to design the mechanical integrity or microwave properties of optical device 1900. Optical device 1900 may share the advantages of optical devices 100, 100', 100'', and 100'''.

[0134] FIG. 20 shows a portion of an optical device 2000 comprising a waveguide 2010 and electrodes 2020 and 2030. The optical device 2000 is similar to optical devices 100, 100', 100'', 100''', and / or 100''', such that similar structures have similar reference numbers. Thus, the optical device 2000 comprises a waveguide 2010 having a ridge 112 and a thin film portion 2014, which are similar to electrodes 120 and 130, respectively, as well as electrodes 2020 and 2030. The electrodes 2020 and 2030 comprise extensions 2024 and 2034, respectively, which are similar to extensions 124, 124', 124'', and 134, 134', 134'', respectively. Substrate 2005 may be similar to substrate 101 and / or may be an underlayer such as silicon dioxide. The optical device is transferred onto another substrate 2006 for larger scale processing on another material platform such as Si. In this case, the original optical device is flipped over and mounted onto the second substrate 206. Furthermore, the second substrate 2006 may undergo further processing. For example, spaces similar to space 1802 may be formed and fully or partially refilled. Furthermore, the underlayer / 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 back view of a portion of an optical device 2100 with a waveguide 2110 and an electrode (not shown). The optical device 2100 is similar to the optical devices 100, 100', 100'', 100''', and / or 100'''. As such, similar structures have similar reference numbers. Thus, the optical device 2100 includes a waveguide 2110 with a ridge 2112 and a thin film portion (not shown) that are similar to the waveguide 110' with the ridge 112 and the thin film portion 114, and the electrodes 120 and 130, respectively, and an electrode (not shown). The substrate 2001 is similar to the substrate 101. Also shown is the space 2002 within the substrate 2001. Also shown are structural features 2160, 2162, and 2164. As shown in FIG. 21, such structural features may extend completely or partially across the space 2002, may be parallel to some or all of the other structural features, may be arranged in a pattern, and / or may be perpendicular or at another angle to the direction of transmission of the optical signal. For example, the structural features 2160, 2162, and 2164 may extend across the space 2002 by 10% to 90%. In some such embodiments, the structural features 2160, 2162, and 2164 may extend across the space 2002 by 30% to 80%. The support structures 2160, 2162, and 2164 may be formed by partially removing the substrate 2101 when forming the space 2102. Thus, the structural features 2160, 2162, and / or 2164 may remain after the formation of the space 2106. In some embodiments, structural features 2160, 2162, and 2164 may be formed of other materials. Optical device 2100 may share the advantages of optical devices 100, 100', 100'', and 100'''.

[0136] 22 is a plan view of a portion of an optical device 2200. Optical device 2100 is similar to optical devices 100, 100', 100'', 100''', and / or 100''', such that similar structures have similar reference numbers. Optical device 2200 includes waveguides 2210 and 2250 similar to waveguides 110' and 150 and electrodes 120, 130, and 150, respectively, and electrodes 2220, 2230, and 2240. Electrodes 2220, 2230, and 2240 include channel portions 2222, 2232, and 2242 and extensions 2224, 2234, and 2244 similar to channels 122, 132, and 142 and extensions 224, 234, and 244, respectively. Also shown is a splitter 2216 and a combiner 2218. Thus, optical device 2200 may be considered to be configured as an interferometer. As such, the optical devices described herein may be incorporated into a variety of devices. Such devices (such as optical device 2200) may share the advantages of optical devices 100, 100', 100'', and 100'''.

[0137] 23 is a plan view of a portion of optical device 2300. Optical device 2300 is similar to optical devices 100, 100', 100'', 100''', and / or 100''', such that similar structures have similar numbers. Optical device 2300 includes waveguides 2310 and 2350 (e.g., arms of the waveguides) and electrodes 2320 and 2330 that are similar to waveguides 110' and 150 and electrodes 120 and 130, respectively. Electrodes 2320 and 2330 include channel portions 2322 and 2332 and extensions 2324 and 2334 that are similar to channel portions 122, 132, and 142 and extensions 224, 234, and 244, respectively. 23, extensions 2334 and 2324 include metal bridges that extend beyond the tops of waveguides 2310 and 2350 to position extensions 2324 and 2334 so that the fields on waveguides 2310 and 2350 are more symmetrical. Optical device 2300 may share the advantages of optical devices 100, 100', 100'', and 100'''.

[0138] 24 is a plan view of a portion of optical device 2400. Optical device 2400 is similar to optical devices 100, 100', 100'', 100''', and / or 100''', such that similar structures have similar numbers. Optical device 2400 includes waveguides 2410 and 2450 similar to waveguides 110' and 150 and electrodes 120 and 130, respectively, and electrodes 2420 and 2430. Electrodes 2420 and 2430 include channel portions 2422 and 2432 and extensions 2424 and 2434 similar to channel portions 122 and 132 and extensions 224 and 234, respectively. As can be seen in FIG. 24, the extensions 2434 and 2424 include metal bridges that extend beyond the tops of the waveguides 2410 and 2450, as well as further retrograde features, to position and configure the extensions 2424 and 2434 so that the fields on the waveguides 2410 and 2450 are more symmetrical.

[0139] More specifically, to induce opposite shifts in the waveguides 2410 and 2450, the extensions 2424 and 2434 are connected in opposite polarity by a first positive metal bridge that extends over the tops of the waveguides 2450 and 2410, respectively. The metal bridge connects the retrograde portions of the extensions 2424 and 2434 with the channel regions 2422 and 2432, respectively, while causing minimal optical loss in the waveguides 2410 and 2450. Additionally, a second set of retrograde portions for the extensions 2424 and 2434 are provided on opposite sides of the waveguides 2410 and 2450 such that the geometry of the optical device 2400 is symmetrical. Optical device 2400 has a smaller modulator chirp (difference in modulation strength in the two waveguides 2410 and 2450) than optical device 2300, at the cost of increased design complexity and possibly narrower microwave bandwidth. Optical device 2400 may share the advantages of optical devices 100, 100', 100'', and 100'''.

[0140] 25 is a plan view of a portion of optical device 2500. Optical device 2500 is similar to optical devices 100, 100', 100'', 100''', and / or 100''', such that like structures have like reference numbers. Optical device 2500 includes waveguides 2510 and 2550, which are similar to waveguides 110' and 150, and electrodes 120, 130, and 140, respectively, and electrodes 2520, 2530, and 254. The electrodes 2520, 2530, and 2540 each include a channel portion 2522, 2532, and 2542, and an extension portion 2524, 2534, and 2544, respectively, similar to the channel portion 122, 132, and 142, and the extension portion 224, 234, and 244. Furthermore, the electrodes 2520, 2530, and 2540 are divided into three segments along the waveguides 2510 and 2550. The divided electrodes 2520, 2530, and 2540 may also be used in a distributed driver scheme, where each electrode pair (2520 and 2530 or 2530 and 2540) includes multiple electrode sections. Each set of segments is driven by a separate driver amplifier 2570, 2572, and 2574 connected between a common source and the signal electrode 2530. Electrical delays 2580, 2582, and 2584, either physical or electronic 110a-110c, may be introduced between each separate driver 2570, 2572, and 2574 to mitigate velocity mismatch between the optical signals in the waveguides 2510 and 2550 and the electrode signals in the electrodes 2520, 2530, and 2540. Optical device 2500 may share the advantages of optical devices 100, 100', 100'', and 100'''.

[0141] Thus, various combinations of features for optical devices have been described in the context of Figures 1A-25. These features may be combined in many ways. Thus, low loss waveguides including thin film nonlinear optical materials processed as described herein, electrodes with extensions and channel regions, velocity matching of microwave and optical signals, low microwave loss characteristics, low voltage electrode signals, low optical losses, waveguide bends and electrode bends allowing longer waveguides occupying less area, and / or other features described herein may be combined in ways not expressly shown. As a result, high performance optical devices such as optical modulators may be provided.

[0142] For example, FIG. 26 is a block diagram illustrating an example embodiment of a device 2600 formed with an optical modulator 2610. In some embodiments, the device 2600 is a Transmitter Optical 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 illustrated in FIGS. 1A-25. Thus, an optical modulator 2610 having one or more of low-loss waveguides including thin-film nonlinear optical materials processed as described herein, electrodes with extensions and channel regions, velocity matching of microwave and optical signals, low microwave loss characteristics, low voltage electrode signals, low optical losses, waveguide bends and electrode bends that allow longer waveguides occupying less area, and / or other features described herein may be combined in a manner not explicitly shown. As a result, a high performance optical modulator 2610 may 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, the driver 2620 may be a high frequency driver. Because the electrodes for the optical modulator 2610 may be driven using a lower voltage, the 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, the driver 2620 may be used, but a lower voltage may be used. Similarly, because the optical modulator 2610 utilizes a low loss waveguide, the input optical signal (e.g., a signal from one or more lasers) may have a lower power. Thus, using an optical modulator as described herein, a device with improved performance may be provided.

[0144] 27 is a flow chart illustrating one embodiment of a method 2700 for forming an optical modulator with improved performance. Method 2700 is described in the context of a process that may have sub-processes. Although described in a particular order, other orders may be used that are not consistent with the description herein.

[0145] An optical waveguide is provided in step 2702. In some embodiments, a thin film of 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. A hard mask is formed from the hard mask layer by transferring a pattern of the mask to the hard mask layer. For example, portions of the hard mask layer exposed by the openings in the mask may be selectively etched. The hard mask may have recesses or openings in the areas where the hard mask layer was 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 with a stitch area of ​​at least 10 millimeters by 10 millimeters. In some embodiments, the stitched regions may be at least 15 millimeters by 15 millimeters. In some embodiments, each stitched region is at least 20 millimeters by 20 millimeters. In some embodiments, bends are also provided. In this manner, a high electro-optic effect waveguide may be provided that may have bends.

[0146] An electrode having a desired configuration is provided at step 2704. For example, the electrode may be evaporated or electroplated at step 2704. In some embodiments, step 2704 includes providing one or more electrodes having a channel region and an extension. The extension may be configured as described herein. In some embodiments, the one or more electrodes are further configured to have a bent portion. Fabrication of the light modulator may then be completed.

[0147] For example, optical modulator 100' may be provided using method 2700. Waveguide 110' may be fabricated in step 2702. A thin film of nonlinear optical material is provided and etched to form ridge 112. Additionally, bent portions (such as bent portion 1515) are also provided by etching in step 2202. Electrodes 120 and 130 are formed in step 2704. Thus, channel regions 122 and 132 and extensions 124 and 134 are formed. Electrode bent portions (such as portion 1525) are also fabricated in step 2704.

[0148] For example, method 2700 may be used to fabricate optical modulators similar to those of FIGS. 1A-25 using electrodes with extensions. An example of such a modulator is fabricated in 600 nm thick x-cut thin film LN on a quartz wafer with an etch depth of 300 nm. In some embodiments, the RF Vπ measured at 1 GHz is 2.3 V and 1.3 V for 10 mm and 20 mm long modulators with a 5 micrometer electrode gap (e.g., distance between extensions 124 and 134), resulting in RF voltage-length products (Vπ·L) of 2.3 and 2.6 V·cm, respectively. Attenuation of some embodiments of such modulators is measured to be greater than 25 dB, and on-chip losses are estimated to be less than 1 dB. In some embodiments, an optical device provided with electrodes with extensions has RF losses (microwave losses) of only 2 dB / cm at 50 GHz, compared to 7 dB / cm for a conventional electrode design (e.g., without extensions) with the same thickness (e.g., 800 nm) and material used (e.g., Au) for the electrode. The resistive losses in the electrodes, α, are ∝L as a result of the skin effect of the metal. -1 f -1 / 2 where L is the length of the electrode and f is the microwave frequency. Conventional electrodes on LN thin films have a 0,reg =0.69dBcm -1 GHz -1 / 2 whereas, in the case of the machining electrode with an extension, α 0,ext =0.26dBcm -1 GHz -1 / 2In some embodiments, the ultra-low RF loss enabled a measured EO response of only 0.8 (1.7) dB attenuation for the 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 the 10 mm (20 mm) optical modulator embodiment utilizing split electrodes. Electrical reflection from the electrodes is maintained below -15 dB for all frequencies. In some embodiments, further isolation of the extensions can be achieved while maintaining velocity matching with the optical signal by utilizing a lower index substrate (such as fused silica or air).

[0149] Thus, using method 2700, an optical modulator having a low-loss, thin-film, nonlinear optical material waveguide that includes bends is provided. Additionally, electrodes with channel regions, extensions, and bends are also fabricated. As a result, an optical modulator may be provided that has low optical signal loss, low electrode signal loss, consumes a controlled amount of area, and / or provides the desired optical modulation at low voltages. Thus, the performance of the optical modulator may be improved.

[0150] Although the above embodiments have been described in some detail for ease of understanding, the invention is not limited to the details provided. There are many alternative ways of implementing the invention. The disclosed embodiments are illustrative and are not intended to be limiting.

Claims

1. An optical device, comprising: a waveguide that includes at least one optical material containing lithium and having an electro-optic effect, and that transmits an optical signal; and a plurality of electrodes including a first electrode and a second electrode, wherein the first electrode includes a first channel region and a plurality of first extensions protruding from the first channel region, the second electrode includes a second channel region and a plurality of second extensions protruding from the second channel region, and the plurality of first extensions are closer to the plurality of second extensions than the first channel region is; the waveguide has a waveguide loss of 1 dB / cm or less, the plurality of electrodes have 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. An optical device.

2. The optical device according to Claim 1, wherein the waveguide has a sidewall surface roughness of 10 nanometers or less. An optical device.

3. The optical device according to Claim 2, wherein the waveguide includes a ridge portion and a thin film portion, and the ridge portion has the sidewall surface roughness. An optical device.

4. The optical device according to Claim 2, wherein the total height of the waveguide is less than 1 micrometer. An optical device.

5. The optical device according to Claim 1, wherein the first 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 the optical signal for the waveguide and the electrode signal for the first electrode. An optical device.

6. The optical device according to Claim 5, wherein the waveguide bending portion has an optical loss of 0.5 dB or less. An optical device.

7. The optical device according to Claim 1, wherein the waveguide and the plurality of electrodes are present on a substrate structure including a substrate and an underlying layer on the substrate, and the underlying layer includes silicon dioxide. An optical device.

8. The optical device according to Claim 7, wherein The waveguide has a waveguide microwave permittivity, the substrate structure has a substrate microwave permittivity of less than 11, and the microwave mode for the electrode signal for the first electrode traverses a part of the substrate structure, an optical device.

9. The optical device according to claim 1, wherein the waveguide and the first electrode are present on a substrate structure, the substrate structure being a first substrate having a low microwave permittivity of less than 11, the first substrate being combined with a lower layer between the first substrate and the waveguide, and a first substrate selected from a second substrate having a high microwave permittivity greater than 11 combined with the lower layer, the lower layer having a low lower-layer microwave permittivity of less than 11, an optical device.

10. The optical device according to claim 1, further comprising cladding adjacent to at least a part of the waveguide and at least a part of the first electrode, the cladding having a cladding microwave permittivity, the waveguide having a waveguide microwave permittivity, the first electrode transmitting an electrode signal, the waveguide microwave permittivity being greater than the cladding microwave permittivity, the microwave mode for the electrode signal traversing a part of the cladding, and the cladding having a cladding microwave velocity in the cladding that is greater than or equal to the waveguide microwave velocity of the microwave mode for the waveguide, an optical device.

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

12. The optical device according to claim 1, wherein the first electrode has an absorption electrode loss for the frequency window, and the absorption electrode loss is less than 0.005 dB per GHz per centimeter, an optical device.

13. The optical device according to claim 1, wherein the waveguide includes a ridge portion and a thin film portion, an optical device.

14. The optical device according to claim 1, wherein each of the plurality of extensions includes a connection portion connected to the channel region and the retrograde portion, and the connection portion is between the retrograde portion and the channel region, an optical device.

15. A subassembly, An optical modulator including a waveguide and a plurality of electrodes, wherein the waveguide includes at least one optical material having an electro-optic effect and containing lithium, the waveguide transmits an optical signal, the plurality of electrodes includes a first electrode and a second electrode, the first electrode includes a first channel region and a plurality of first extensions protruding from the first channel region, the second electrode includes a second channel region and a plurality of second extensions protruding from the second channel region, and the plurality of first extensions are closer to the plurality of second extensions than the first channel region. A driver connected to the optical modulator and configured to electrically drive the plurality of electrodes. The waveguide has a waveguide loss of 1 dB / cm or less, the plurality of electrodes have 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, the subassembly. **Claim 16** A method comprising: Providing a waveguide including at least one optical material having an electro-optic effect and containing lithium. Providing a plurality of electrodes including a first electrode and a second electrode, and providing the plurality of electrodes further includes: Providing a first channel region for the first electrode and a plurality of first extensions protruding from the first channel region, and providing a second channel region for the second electrode and a plurality of second extensions protruding from the second channel region, wherein the plurality of first extensions are closer to the plurality of second extensions than the first channel region. The waveguide has a waveguide loss of 1 dB / cm or less, the plurality of electrodes have 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, the method. **Claim 17** The method according to claim 16, The waveguide and the plurality of electrodes are present on a substrate structure including a substrate and a lower layer on the substrate, the lower layer includes silicon dioxide, and the substrate structure has a substrate microwave dielectric constant of less than 11, method. **Claim 18**: The method according to claim 16, wherein the first 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 first electrode, method. **Claim 19**: The method according to claim 18, wherein the waveguide bent portion has an optical loss of 0.5 dB or less, method.

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