Electro-optical devices with engineered electrodes

Abstract

An optical device including a waveguide and an electrode is described. The waveguide includes at least one optical material having an electro-optical effect. The electrode includes a channel region and an extension protruding from the channel region. The extension is closer to the waveguide than the channel region.

Description

[0001] Cross-references to other applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 62 / 941,139, filed on November 27, 2019, entitled “THIN-FILM ELECTRO-OPTICMODULATORS,” which is incorporated herein for all purposes. This application claims priority to U.S. Provisional Patent Application No. 63 / 033,666, filed on June 2, 2020, entitled “HIGH PERFORAMNCE OPTICAL MODULATORS,” which is incorporated herein for all purposes. This application claims priority to U.S. Provisional Patent Application No. 63 / 112,867, filed on November 12, 2020, entitled “BREAKING VOLTAGE-BANDWIDTH LIMIT IN INTEGRATED LITHIUMNIOBATE MODULATORS USING MICRO-STRUCTUREDELECTRODES,” which is incorporated herein for all purposes. Background Art

[0003] Optical modulators and other electro-optical devices are generally expected to meet certain performance benchmarks. For example, an optical modulator is expected to provide sufficient optical modulation at relatively low electrode drive voltages. Large optical modulation can correspond to a waveguide having a large length in the direction of transmission of the optical signal. However, it is also expected that the optical modulator consumes a small total area. It is also expected that the optical modulator has low electrode (e.g., microwave) signal loss for the electrical signal passing through the electrodes and low optical loss for the optical signal traversing the waveguide. Furthermore, it is expected that the optical modulator can provide low-loss transmission and large modulation at low voltages over a wide frequency bandwidth. Therefore, electro-optical devices are desired that can have low electrode loss, low optical loss, consume a controllable amount of area, and / or provide the desired optical modulation at low voltages. BRIEF DESCRIPTION OF THE DRAWINGS

[0004] Various embodiments of the invention are disclosed in the following detailed description and accompanying drawings.

[0005] Figures 1A-1E An embodiment of an optical device with engineered electrodes is shown.

[0006] Figure 2 Shown is a cross section of a portion of an embodiment of an optical device capable of improved performance.

[0007] Figure 3 Shown is a cross section of a portion of an embodiment of an optical device capable of improved performance.

[0008] Figure 4 Shown is a cross section of a portion of an embodiment of an optical device capable of improved performance.

[0009] Figure 5 Shown is a cross section of a portion of an embodiment of an optical device capable of improved performance.

[0010] Figure 6 Portions of an embodiment of an optical device indicating electrode configurations capable of improved performance are shown.

[0011] Figure 7 Portions of an embodiment of an optical device indicating electrode configurations capable of improved performance are shown.

[0012] Figure 8 Portions of an embodiment of an optical device indicating electrode configurations capable of improved performance are shown.

[0013] Figure 9 Portions of an embodiment of an optical device indicating electrode configurations capable of improved performance are shown.

[0014] Figure 10 Portions of an embodiment of an optical device indicating electrode configurations capable of improved performance are shown.

[0015] Figure 11 Portions of an embodiment of an optical device indicating electrode configurations capable of improved performance are shown.

[0016] Figures 12A-12D Portions of an embodiment of an optical device indicating various electrode configurations capable of improved performance are shown.

[0017] Figures 13A-13J Portions of an embodiment of an optical device indicating various electrode configurations capable of improved performance are shown.

[0018] Figures 14A-14K Portions of an embodiment of an optical device indicating various electrode configurations capable of improved performance are shown.

[0019] Figures 15A-15B Portions of an embodiment of an optical device capable of improved performance are shown.

[0020] Figure 16 Portions of an embodiment of an optical device capable of improved performance are shown.

[0021] Figure 17 Portions of an embodiment of an optical device capable of improved performance are shown.

[0022] Figure 18 Portions of an embodiment of an optical device capable of improved performance are shown.

[0023] Figure 19 Portions of an embodiment of an optical device capable of improved performance are shown.

[0024] Figure 20 Portions of an embodiment of an optical device capable of improved performance are shown.

[0025] Figure 21 Portions of an embodiment of an optical device capable of improved performance are shown.

[0026] Figure 22 Portions of an embodiment of an optical device capable of improved performance are shown.

[0027] Figure 23 Portions of an embodiment of an optical device capable of improved performance are shown.

[0028] Figure 24 Portions of an embodiment of an optical device capable of improved performance are shown.

[0029] Figure 25 Portions of an embodiment of an optical device capable of improved performance are shown.

[0030] Figure 26 Portions of an embodiment utilizing a subassembly of an optical modulator capable of improved performance are shown.

[0031] Figure 27 is a flow chart illustrating an embodiment of a method for providing an optical modulator capable of improved performance. DETAILED DESCRIPTION

[0032] The present invention may be implemented in a variety of ways, 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, such as a processor configured to execute instructions stored on and / or provided by a memory coupled to the processor. In this specification, these implementations, or any other form that the invention may take, may be referred to as techniques. In general, the order of the steps of the disclosed processes may be varied within the scope of the invention. Unless otherwise stated, a component such as a processor or memory described as being configured to perform a task may be implemented as a general-purpose component that is temporarily configured to perform a task at a given time, or as a specific component manufactured to perform a task. As used herein, the term 'processor' refers to one or more devices, circuits, and / or processing cores that are configured to process data, such as computer program instructions.

[0033] A detailed description of one or more embodiments of the present invention is provided below together with the accompanying drawings that illustrate the principles of the invention. The present invention is described in conjunction with these embodiments, but the present invention is not limited to any embodiment. The scope of the present invention is limited only by the claims, and the present invention encompasses many alternatives, modifications, and equivalents. In the following description, many specific details are set forth in order to provide a thorough understanding of the present invention. These details are provided for illustrative purposes, and the present invention can be implemented according to the claims without some or all of these specific details. For the sake of clarity, technical materials known in the technical field related to the present invention are not described in detail so as not to unnecessarily obscure the present invention.

[0034] The basic elements of an electro-optical device (also known as an optical device), such as an electro-optical modulator, include a waveguide and electrodes surrounding the waveguide. The waveguide carries the 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 waveguide's refractive index, which modulates the optical signal. For example, an electrode signal (such as a microwave signal) can be applied to the electrodes. Thus, the electrodes act as transmission lines. The electrode signal travels in the same direction as the optical signal propagating through the waveguide. The electrode signal generates a corresponding electric field in the waveguide, modulating the waveguide's refractive index. As a result, as the optical signal travels through the waveguide, it is modulated. Therefore, by driving the appropriate electrode signal through the electrodes, the desired modulation of the optical signal can be achieved.

[0035] While electro-optical devices function, their performance can be limited by many factors. For example, electrodes are desirable close to waveguides to increase the electric field strength at the waveguide. A higher electric field enhances the change in the waveguide's refractive index and increases the modulation of the optical signal. However, when microwave signals pass through the electrodes, the electrodes may suffer from electrode (e.g., microwave) signal losses. This loss may be increased by proximity to the waveguide. These losses can adversely affect the electrodes' ability to provide the desired electric field at the waveguide. These losses are exacerbated by absorption of the microwave signal by surrounding structures and resistive losses in the electrodes. Furthermore, the driving voltage required for the electrodes increases with increasing modulation frequency. For example, using an electrode voltage of less than two volts, optical signals at a frequency of 1 GHz can be easily modulated. However, for higher frequencies, such as in the 100 GHz range or higher, the required electrode voltage may be significantly higher (e.g., five volts or more). To achieve the desired change in refractive index, a higher voltage is applied to the electrodes. Consequently, the optical modulator may require a higher input voltage to the electrodes and consume more power than desired. Therefore, electro-optical devices with improved performance remain desirable.

[0036] Many techniques have been proposed to improve optical modulators. These include utilizing semiconductors (e.g., silicon and / or indium phosphide), bulk lithium niobate (LN), barium titanate (BTO), and / or waveguides using plasmonics. However, these and other techniques suffer from significant drawbacks in one or more of the aforementioned characteristics. For example, some modulators may not provide the desired modulation within a given area, may be so large as to provide only a weak electric field (and therefore a small electro-optical response), and / or suffer from unacceptable electrode or optical signal losses. A single limiting factor in the performance of an optical modulator may prevent it from functioning as desired. For example, even if the electrodes can be driven at low voltages, unacceptable electrode (microwave) losses may render the modulator unusable for a particular application. Therefore, mechanisms for providing optical modulators that exhibit low optical signal loss, low electrode signal loss, consume a manageable amount of area, and / or provide the desired optical modulation at relatively low voltages remain desirable.

[0037] An optical device that may have improved performance is described. The optical device includes a waveguide and an electrode. The waveguide includes at least one optical material having an electro-optic effect. In some embodiments, the waveguide includes a ridge portion and a thin film portion. The electrode includes a channel region and an extension protruding from the channel region. The extension is located closer to the waveguide than the channel region. In some embodiments, the extension has a spacing that is less than the microwave wavelength in the electrode divided by π. In some embodiments, the extension has a length that is less than the microwave wavelength in the electrode divided by π. The waveguide is configured to carry an optical signal, and the electrode is configured to carry an electrode signal. In some such embodiments, the optical material(s) have a microwave dielectric constant that is at least 1.5 times the optical dielectric constant of the optical signal and the electrode signal. As used herein, "dielectric constant" corresponds to relative permittivity, which is equal to the permittivity of a material divided by the permittivity of a vacuum. The microwave dielectric constant refers to the dielectric constant at the microwave frequency of interest. The optical dielectric constant refers to the dielectric constant at the optical frequency of interest that is equal to or approximately equal to the square of the refractive index. In some embodiments, each extension includes a connecting portion coupled to the channel region and a retrograde portion. The connecting portion is located between the retrograde portion and the channel region. In some embodiments, the optical device includes an additional electrode having an additional channel region and an additional plurality of extensions. The additional extensions are closer to a portion of the waveguide than the additional channel region. In some embodiments, the waveguide has a total optical loss of no more than 10 dB along the portion of the waveguide.

[0038] Thus, an optical device includes one or more electrodes fabricated with microstructures (i.e., extensions). The channel region(s) of the electrode(s) are configured to carry the majority of the current, while little to no current can be driven through the extensions. Consequently, losses caused by the proximity of the electrodes to the waveguide can be mitigated. However, because the extensions are closer to the waveguide, the amplitude of the electric field at the waveguide can be maintained or enhanced. Consequently, the electrodes can provide sufficient modulation of the optical signal at a lower electrode voltage.

[0039] In some embodiments, the optical performance may also be improved. The waveguide may have low optical loss, for example, an optical loss of no more than 1 dB / cm. In some such embodiments, in some cases, the waveguide has an optical loss of no more than 0.5 dB / cm (e.g., on average). In some embodiments, the waveguide has a total on-chip optical loss of no more than 4 dB. In some embodiments, the portion of the waveguide close to the electrode(s) has a total optical loss of no more than 3 dB. The optical efficiency of the device may be improved. Thus, the optical modulator may be made longer (e.g., longer than 2 cm and in some embodiments 3 cm or longer) and the modulation of the input optical signal enhanced. The waveguide may also be relatively small, for example, using thin film technology. In some embodiments, the waveguide has a wavelength less than the square of the wavelength of the optical signal in the nonlinear optical material(s) (e.g., λ 2 ) of the light mode cross-sectional area. In some embodiments, the light mode cross-sectional area is less than 3 times λ 2, where λ is the wavelength of the optical signal in the waveguide. Because the waveguide is small, the electrodes can be placed closer to the waveguide. This can increase the electric field at the waveguide and enhance the electro-optical effect. In some embodiments, the waveguide curved section(s) can have a curvature radius of no more than 500 μm. In some embodiments, the waveguide curved sections have a curved section optical loss of no more than 0.5 dB. Waveguide and electrode curved sections, if present, can be used to provide a longer region, where the electrodes are close to the waveguide, while controlling the length and / or area consumed by the device. In other words, the use of curved sections allows for a reduction in the maximum size of the optical modulator. The maximum size of an optical modulator is limited by the size of the package in which the optical modulator can be provided. Electrode and waveguide curved sections allow for a long optical path and a long region, where the electrodes are close to the waveguide, while reducing the maximum size of the optical modulator. For example, a straight optical modulator that is 4 cm long and 0.2 mm wide has the same length of optical path as an optical modulator with three curved sections (and four straight sections) occupying an area of ​​approximately 1 cm long and 0.8 mm wide. This second optical modulator has a smaller aspect ratio, is more compact, and can be mounted in a much smaller package, which is desirable. In some embodiments, the waveguide and electrodes can occupy an area of ​​no more than 50 square millimeters. In some embodiments, the waveguide and electrodes occupy an area of ​​no more than 20 square millimeters. In some embodiments, the waveguide and electrodes are located on an integrated circuit with a length of no more than 32 millimeters. Therefore, greater optical signal modulation can be achieved within a smaller footprint. In some embodiments, the electrode bend section(s) and the waveguide bend section(s) are configured to provide a path difference between the optical signal for the waveguide and the electrode signal for the electrode. The waveguide and electrode bend sections can be used to account for velocity mismatches between the electrode (microwave) signal and the optical signal. Therefore, device efficiency can be improved. The use of electrode(s) comprising a channel region and an extension allows the electrode to provide a high electric field at the waveguide. The extension also separates the edge of the channel region from the waveguide. As a result, current can be better confined to the channel region, thereby reducing electrode losses in the electrode and allowing for lower electrode drive voltages. The combination of reduced optical and electrode (e.g., microwave) losses, improved velocity matching between the electrodes and the optical signal, and the longer path over which the optical signal can be modulated allows for a reduced voltage amplitude input to the electrode(s). For example, in some embodiments, a microwave signal with an amplitude of 0.5-1.5 V can be input to the electrode(s) and provide the desired modulation of the refractive index for signals in the 50-100 GHz range. Consequently, device performance can be improved.

[0040] The waveguide carries the optical signal, while the electrode carries the electrode signal. In some embodiments, the extension is configured to reduce the velocity mismatch between the optical signal and the electrode signal. In some embodiments, the extension has at least one distance from the waveguide such that the total optical loss is less than 8 dB. For a frequency window in the frequency range from DC to no more than 500 GHz, the electrode may have a frequency-dependent electrode loss. In some embodiments, this frequency-dependent electrode loss is less than 0.8 dB per centimeter per square root of the electrode signal frequency. The electrode signal frequency is measured in GHz, and the frequency window may be at least 10 GHz. In other embodiments, the frequency-dependent electrode loss is less than 0.5 dB per centimeter per square root of the electrode signal frequency. The electrode signal frequency is measured in GHz, and the frequency window may be at least 10 GHz. In other embodiments, the frequency-dependent electrode loss is less than 0.3 dB per centimeter per square root of the electrode signal frequency. The electrode signal frequency is measured in GHz, and the frequency window may be at least 10 GHz. In some embodiments, for a frequency window in the frequency range from DC to no more than 500 GHz, the electrode has an absorptive electrode loss. In some embodiments, the absorbing electrode has a loss of less than 0.005 dB per centimeter per GHz and a frequency window of at least 10 GHz.

[0041] The waveguide and electrodes may be on a substrate. In some embodiments, the extension is between the substrate and the channel region. In some embodiments, the channel region is between the substrate and the plurality of extensions. In some embodiments, the substrate has a void therein. The void is aligned with a portion of the waveguide and the plurality of extensions. In some embodiments, the waveguide and 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 being bonded to an underlying layer between the substrate and the waveguide; and a second substrate having a high microwave dielectric constant greater than 11 being bonded to the underlying layer. In such embodiments, the underlying layer has a low underlying microwave dielectric constant (e.g., less than 11).

[0042] The electrode may include an electrode bend section. The waveguide may include a waveguide bend section. The electrode bend section and the waveguide bend section are configured to provide a path difference between an optical signal for the waveguide and an electrode signal for the electrode.

[0043] In some embodiments, a subassembly, such as a transmission optical subassembly (TOSA), is described. The subassembly includes an optical modulator and a driver coupled to the optical modulator. The optical modulator includes a waveguide and an electrode. The waveguide includes at least one optical material exhibiting an electro-optical 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 electrode.

[0044] In some embodiments, a method for 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. Providing the electrode includes providing a channel region and providing an extension protruding from the channel region. The extension is located closer to the waveguide than the channel region. In some embodiments, providing the extension includes fabricating the extension with a spacing less than the wavelength of microwaves in the electrode divided by π. The waveguide carries an optical signal, while the electrode carries 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 within a range from DC to no more than 500 GHz. The frequency-dependent electrode loss can be less than 0.8 dB per centimeter per square root of the electrode signal frequency, where the electrode signal frequency is measured in GHz and the frequency window is at least 10 GHz. In other embodiments, the frequency-dependent electrode loss is less than 0.5 dB per centimeter per square root of the electrode signal frequency. The electrode signal frequency is measured in GHz, and the frequency window is at least 10 GHz. In other embodiments, the frequency-dependent electrode loss is less than 0.3 dB per centimeter per square root of the electrode signal frequency. The electrode signal frequency is measured in GHz, and the frequency window can be at least 10 GHz. In some embodiments, the electrode has an absorptive electrode loss for a frequency window of electrode signal frequencies from DC to no more than 500 GHz. In some embodiments, the absorptive electrode loss is less than 0.005 dB per centimeter per GHz, and the frequency window is at least 10 GHz.

[0045] Figures 1A-1E Embodiments of optical devices 100 , 100 ′, 100 ″, 100 ′″, and 100 ′″′ having engineered electrodes are shown. Figure 1A A plan view of an optical device (ie, electro-optical device) 100 including a waveguide 110 and electrodes 120 and 130 is depicted. Figure 1B 、 1C , 1D, and 1E show perspective views of optical devices 100 ′, 100 ″, 100 ′″, and 100 ′″″ that are similar to optical device 100 .

[0046] The optical devices 100, 100', 100''', and 100'''' can be part of an optical modulator having an electro-optic response (e.g., in picometers / volt) in the plane of the film (e.g., x-cut or y-cut lithium niobate) or perpendicular to the plane of the film. The optical device 100'' can be part of an optical modulator having an electro-optic response (e.g., in picometers / 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 that has an electro-optic effect in the plane of the film (e.g., even without using a material such as lithium niobate). Similarly, as used herein, a z-cut optical modulator has an electro-optic effect out of the plane of the film (e.g., perpendicular to the plane of the film) (e.g., even without using a material such as lithium niobate). Figures 1A-1E Not to scale. Other configurations are possible. For example, optical devices with 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. References Figure 1A An optical signal is input to the optical device 100. For example, the optical signal can 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. Therefore, 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.

[0047] refer to Figure 1A Optical device 100 includes a waveguide 110 and electrodes 120 and 130. Waveguide 110 is used to transmit an optical signal. More specifically, waveguide 110 receives an input optical signal and outputs a modulated optical signal. Electrode(s) 120 and / or 130 carry an electrode signal that applies a time-varying electric field to waveguide 110. This electric field modifies the refractive index of waveguide 110. In some embodiments, electrode 120 carries an electrode signal, such as a microwave signal, while electrode 130 is a ground. In some embodiments, electrode 130 carries an electrode (e.g., microwave) signal while electrode 120 is a ground. In some embodiments, both electrodes 120 and 130 carry electrode signals. Other configurations are possible. Thus, electrodes 120 and 130 are combined with waveguide 110 to provide a modulated optical signal. Electrodes 120 and 130 are depicted as surrounding waveguide 110 to indicate that waveguide 110 experiences an electric field applied between electrodes 120 and 130, but the physical locations of electrodes 120 and 130 are not indicated. For example, one could have electrode 120 directly on top of the waveguide or underneath the waveguide, with 130 to one side.

[0048] Waveguide 110 is shown as having a rectangular footprint and 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 beneath electrode(s) 120 and / or 130, and a ridge 112 between electrodes 120 and 130. Waveguide 110 includes at least one optical material exhibiting an electro-optic effect. In some embodiments, the optical material(s) are nonlinear. As used herein, a nonlinear optical material exhibits an electro-optic effect and has an effect of at least (e.g., greater than or equal to) 5 picometers / volt. 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 ferroelectric. In some embodiments, the electro-optic material effect includes a change in refractive index in response to an applied electric field due to the Pockels effect. Thus, in some embodiments, an optical material having an electro-optic effect within 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. A nonlinear optical material can be a non-centrosymmetric material. Thus, a nonlinear optical material can be piezoelectric.

[0049] In some embodiments, waveguide 110 is a low optical loss waveguide. For example, waveguide 110 can have a total optical loss of no more than 10 dB through a portion of waveguide 110 proximate electrodes 120 and 130 (e.g., when biased at maximum transmission and as a function of maximum loss). The total optical loss is the optical loss in the waveguide through a single continuous electrode region (e.g., as opposed to multiple devices cascaded together), such as Figure 1AAs shown in . In some embodiments, waveguide 110 has a total optical loss of no more than 8 dB. In some embodiments, the total optical loss does not exceed 4 dB. In some embodiments, the total optical loss is less than 3 dB. In some embodiments, the total optical loss is less than 2 dB. In some embodiments, waveguide 110 has an optical loss of no more than 3 dB / cm (e.g., average). In some embodiments, the nonlinear material in waveguide 110 has an optical loss of no more than 2.0 dB / cm. In some such embodiments, waveguide 110 has an optical loss of no more than 1.0 dB / cm. In some embodiments, waveguide 110 has an optical loss of no more than 0.5 dB / cm. In some embodiments, the nonlinear optical material in waveguide 110 comprises lithium niobate (LN) and / or lithium tantalate (LT). In some embodiments, the nonlinear optical material used in waveguide 110 consists of LN. In some embodiments, the nonlinear optical material used in waveguide 110 consists of LT. Such nonlinear optical materials may have an inert chemical etching reaction and can be conventionally etched using chemicals such as fluorine, chlorine, or bromine compounds. In some embodiments, the nonlinear optical material(s) include 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 with similar optical properties may be used.

[0050] Various other optical components may be incorporated into the waveguide 110 to provide desired phase modulation, polarization modulation, intensity modulation, IQ modulation, other modulation, and / or other functionality. For example, the waveguide 110 may have a wider portion(s) ( Figure 1A In some embodiments ( Figure 1A In the embodiment shown in FIG, the waveguide 110 may include a splitter to split the optical signal into multiple branches for modulation and recombining the modulated optical signals for output. Thus, the waveguide 110 and the electrodes 120 and 130 may be configured to provide desired functions.

[0051] A portion of waveguide 110 is located proximate electrodes 120 and 130 along the direction of optical signal transmission (e.g., from optical signal input through waveguide 110 to modulated optical signal output). This portion of the waveguide can have various lengths. In some embodiments, the length of the portion of waveguide 110 proximate electrodes 120 and 130 is at least 2 millimeters. In some embodiments, this portion of waveguide 110 is at least 5 millimeters long and no longer than 10 millimeters. Other embodiments may make this portion of waveguide 110 longer. The portion of waveguide 110 proximate electrodes 120 and 130 can have a length greater than 2 centimeters. In some embodiments, the length of the portion of waveguide 110 proximate electrodes 120 and 130 is at least 2.5 centimeters. In some embodiments, the length of this portion of waveguide 110 is at least 3 centimeters. These lengths are possible, at least in part, due to the low optical loss per unit length of waveguide 110 described above. Because waveguide 110 can be made longer, the total optical modulation provided by the electric field generated by electrodes 120 and 130 can be greater. Furthermore, due to low optical and microwave losses (described below), desired optical modulation (e.g., a change in refractive index) can be achieved using signals input to the electrode(s) 120 and / or 130 with relatively low voltages. For example, Vπ is the half-wave voltage, or the amplitude of the input electrode signal required to shift the phase of the optical signal by π. In some embodiments, Vπ does not exceed 6 volts for signals in the 50-100 GHz range. In some embodiments, Vπ does not exceed 3 volts for signals in the 50-100 GHz range. In some embodiments, Vπ is approximately the voltage provided by the CMOS circuitry, for example, in the range of 0.5 volts to 1.5 volts for signals in the 50-100 GHz range. For example, Vπ may not exceed 1.5 volts at 10 GHz. Thus, in some embodiments, Vπ does not exceed 1.5 volts. In some such embodiments, Vπ does not exceed 1 volt for signals in the 50-100 GHz range. Other voltages for other frequency ranges are possible. Thus, the performance of the optical modulator 110 can be improved.

[0052] In addition, the portion of waveguide 110 near electrodes 120 and 130 can have a small optical mode cross-sectional area. In some embodiments, the optical mode cross-sectional area is less than 3 times the square of the wavelength of the optical signal in the nonlinear optical material(s) (e.g., λ 2 In some embodiments, the optical mode cross-sectional area is less than 2 times the square of the wavelength of the optical signal in the nonlinear optical material(s). In some embodiments, the optical mode cross-sectional area is less than 1.5 times the square of the wavelength of the optical signal in the nonlinear optical material(s). In some embodiments, the optical mode cross-sectional area is less than 4 μm 2 In some such embodiments, the light mode cross-sectional area does not exceed 3 μm2 In some embodiments, thin films and fabrication techniques described herein can be used to provide such small light mode cross-sectional areas. The light mode cross-sectional areas can also allow for the low light losses described herein.

[0053] Electrodes 120 and 130 apply an electric field to the waveguide 110. Electrode 120 includes a channel region 122 and an extension 124 (at Figure 1A Only one of the extensions 124 is marked in FIG. 1 ). The electrode 130 includes a channel region 132 and an extension 134 (in FIG. Figure 1A Only one of the extensions 134 is labeled in FIG. 1 . In some embodiments, extension 124 or 134 may be omitted from electrode 120 or electrode 130, respectively. Extensions 124 and 134 protrude from channel regions 122 and 132, respectively. Thus, extensions 124 and 134 are closer to waveguide 110 than channel regions 122 and 132, respectively. Figure 1A Extensions 124 and 134 are shown as simple rectangular protrusions. In some embodiments, extensions 124 and 134 may have different shapes. For example, extension(s) 124 and / or 134 may have an L-shaped footprint, a T-shaped footprint, or 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. The distribution (e.g., spacing) and width of extensions 124 and 134 may also be irregular. In some embodiments, the distribution and / or width of extensions 124 and / or 134 may be regular. The distance between waveguide 110 and extensions 124 and 134 is shown as constant. In some embodiments, this distance may vary. Similarly, the distance between waveguide 110 and channels 122 and 132 is shown as constant. In some embodiments, this distance may vary. Electrodes 120 and 130 are shown as symmetrical. In some embodiments, electrodes 120 and 130 are asymmetrical. For example, extension 134 may be omitted while extension 124 is present.

[0054] Extensions 124 and 134 protrude from channel regions 122 and 132, respectively, and are located between channel regions 122 and 132 and waveguide 110. As a result, extensions 124 and 134 are sufficiently close to waveguide 110 to provide an enhanced electric field at waveguide 110, thereby increasing the change in refractive index caused by the electric field. In contrast, channel regions 122 and 132 are further away from waveguide 110 than extensions 124 and 134. Therefore, channel region 122 is less affected by the electric field generated by electrode 130 and extension 134. Charge tends to accumulate less at the edge of channel region 122, closest to electrode 130. Consequently, current is more easily driven through the center of channel region 122, and electrode losses in channel region 122 (and electrode 120) can be reduced. Similarly, channel region 132 is further away from electrode 120. The channel region 132 is less affected by the electric field generated by the electrode 120 / extension 124. Charge has a reduced tendency to accumulate at the edge of the channel region 132 closest to the electrode 120. Therefore, current is more easily driven through the channel region 132, and electrode losses in the channel region 132 (and the electrode 130) can be reduced. Since microwave signal losses through the electrodes 120 and 130 can be reduced, a smaller drive voltage can be used for the electrode(s) 120 and / or 130 and the optical device 100 can consume less power. In addition, the impedance of the electrode 120 can be improved to match the input voltage of the device ( Figure 1A This impedance matching can further reduce electrode signal loss in optical device 100. Furthermore, extensions 124 and 134 can influence the speed at which electrode signals pass through electrodes 120 and 130. Thus, extensions 124 and 134 can be configured to adjust the speed of the electrode signals to match the speed of the optical signal in waveguide 110. Consequently, the performance of optical device 100 can be improved.

[0055] Electrode(s) 120 and / or 130 can be fabricated using deposition techniques (such as evaporation and / or electroplating, as well as photolithography) to shape the extensions 124 and / or 134 of electrodes 120 and / or 130. The resulting electrodes 120 and / or 130 can have low frequency-dependent electrode losses. In some embodiments, the frequency-dependent electrode power loss can be as low as 0.8 dB per centimeter per square root of the electrode signal frequency within a specific frequency window (e.g., at least 10 GHz) within the frequency range between DC and 500 GHz, where the electrode signal frequency is measured in GHz. In other embodiments, the frequency-dependent electrode loss is less than 0.5 dB per centimeter per square root of the electrode signal frequency. The electrode signal frequency is measured in GHz, and the frequency window can be at least 10 GHz. In other embodiments, the frequency-dependent electrode loss is less than 0.3 dB per centimeter per square root of the electrode signal frequency. The electrode signal frequency is measured in GHz, and the frequency window can be at least 10 GHz. In some embodiments, the electrodes have absorptive electrode losses for a frequency window from DC to an electrode signal frequency not exceeding 500 GHz. In some embodiments, the absorption electrode loss is less than 0.005 dB per centimeter per GHz, and the frequency window is at least 10 GHz. In some embodiments, the frequency dependent electrode power loss for the same frequency window and frequency range can be as low as 0.75 dB per centimeter per electrode square root of the signal frequency for a particular frequency window (e.g., 10 GHz or more). In some embodiments, the electrode has an absorption electrode loss. In some embodiments, the absorption 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 centimeter per GHz. In some embodiments, the absorption electrode loss for the same frequency window and frequency range is less than 0.005 dB per centimeter per GHz for the frequency window in the frequency range between DC and 500 GHz. In some embodiments, the optical device 100 may include additional electrodes, such as DC electrodes ( Figure 1A (not shown in FIG. 1 ). Such additional electrodes may be used to optimize the optical device 100 for low frequency response. The electrodes may include one or more of electro-optical, thermal phase shifters, and / or MEMS phase shifters.

[0056] In operation, an optical signal desired to be modulated is input to waveguide 110. An electrode signal (e.g., a microwave signal) is also applied to electrode(s) 120 and / or 130. For purposes of explanation, it is assumed that the microwave signal is applied to electrode 120, while electrode 130 is ground. The time-varying microwave signal passing through electrode 120 causes a charge of a particular sign to rapidly accumulate in extension 124, then to fall back to zero in extension 124, and a charge of the opposite sign to rapidly accumulate in extension 124. The absence of negative charge in a particular extension 124 is considered equivalent to the accumulation of positive charge in that extension 124, and vice versa. This cycle repeats at or near the frequency of the microwave signal. As a result of the charge accumulation in extension 124, an opposite charge accumulates in a nearby corresponding extension 134. This generates a relatively large, time-varying electric field between extensions 124 and 134. Because the electro-optic material in waveguide 110 is exposed to a large, time-varying electric field, the refractive index of waveguide 110 undergoes a large change near extensions 124 and 134. As an optical signal traverses waveguide 110 and passes through extensions 124 and 134, it is exposed to a large change in refractive index. Consequently, for a microwave signal of a given voltage amplitude applied to electrode 120, a large modulation in the optical signal can be achieved. For example, optical device 100 can provide sufficient optical modulation at frequencies up to 100-300 GHz or higher, with a voltage amplitude of no more than one volt applied to electrode 120. Furthermore, as described above, the presence of extension 124 reduces the tendency of current to accumulate near the edge of channel region 122, closer to waveguide 110, and mitigates losses in electrode 120. Current can be driven more easily through channel region 122 at a lower voltage, reducing microwave losses. Consequently, the performance of optical device 100 can be improved.

[0057] Furthermore, as described above, optical device 100 can not only reduce light loss through waveguide 110, but also increase modulation of optical signals by using a longer waveguide 110. The use of electrodes 120 and 130 having extensions 124 and 134, respectively, can reduce microwave loss, allow for a large electric field at waveguide 110 / ridge 112, and improve the propagation of microwave signals through electrodes 120 and 130, respectively. Electrodes 120 and 130 can also improve performance through velocity and phase matching. Thus, the performance of optical device 100 can be significantly enhanced.

[0058] Figure 1Bis a perspective view of optical device 100'. Optical device 100' is similar to optical device 100. Therefore, similar portions of optical device 100' are labeled similarly. Optical device 100' includes waveguide 110', electrode 120', and electrode 130', which are similar to waveguide 110, electrode 120, and electrode 130, respectively. Also shown is substrate / underlying layer 101. In some embodiments, substrate 101 includes a silicon substrate and a silicon dioxide layer between the silicon substrate and waveguide 110. In other embodiments, other substrates may be used. In some embodiments, substrate 101 is a dielectric having a low microwave dielectric constant, for example, 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, underlying layer(s) having a low microwave dielectric constant, such as silicon dioxide, may be used on top of low microwave dielectric constant substrate 101. In other embodiments, other and / or additional underlayer(s) may be used. Furthermore, the low microwave dielectric constant underlayer(s) 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 provided underlayer to be thick. For example, the underlayer may be at least 3 microns thick and no more than 100 microns thick. Furthermore, in some embodiments, substrates and / or underlayers having other geometric configurations may be used.

[0059] The waveguide 110' is used to transmit optical signals. The waveguide 110' includes a ridge 112 and a thin film portion 114. Figure 1B In the embodiment shown in , the membrane portion 114 and the ridge portion are formed of the same material (eg, from the same membrane). The waveguide 110 ′ may be formed of similar materials as the waveguide 110 and may have similar properties.

[0060] In some embodiments, the waveguide 110' can have a different configuration. For example, the waveguide 110' can omit the thin film portion 114 or reduce the size of the thin film portion 114. The ridge 112 can have another configuration. For example, the ridge 112 can be trapezoidal, semi-circular, stacked rectangles and / or have another geometric shape that guides optical signals in a manner similar to that described herein. Other and / or additional materials can 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 can be formed from different materials. The thin film 114 can include a nonlinear optical material such as LN and / or LT, while the ridge 112 can be formed from a passive material such as silicon and / or silicon nitride. In some embodiments, the ridge 112 can be located below the thin film portion 114 (for example, the ridge 112 can be between the thin film portion 114 and the underlying substrate 101). Similarly, various other optical components can be introduced into the waveguide 110' to provide desired phase modulation, polarization modulation, intensity modulation, IQ modulation, other modulation and / or other functions. In some embodiments ( Figures 1B-1C In the embodiment shown in FIG, the waveguide 110 may include a splitter to split the optical signal into multiple branches for modulation and recombining the modulated optical signals for output. Thus, the waveguide 110 and the electrodes 120 and 130 may be configured to provide desired functions.

[0061] In some embodiments, the nonlinear optical material used in waveguide 110' is formed as a thin film. For example, the thin film can have a thickness no greater than 3 times the wavelength of the optical signal carried in waveguide 110' before processing (e.g., the thickness of thin film portion 114 and ridge portion 112). In some embodiments, the thin film has a thickness no greater than 2 times the wavelength of the optical signal (e.g., the thickness of thin film portion 114 and ridge portion 112). In some embodiments, the nonlinear optical material has a thickness no greater than 1 times the wavelength of the optical signal. In some embodiments, the nonlinear optical material has a thickness no greater than 0.5 times the wavelength of the optical signal. For example, the thin film can have a total thickness of no greater than three micrometers after deposition. In some embodiments, the thin film has a total thickness no greater than 2 micrometers. The thin film nonlinear optical material can be fabricated into waveguide 110' using photolithography. For example, ultraviolet (UV) and / or deep ultraviolet (DUV) photolithography can be used to pattern a mask for the nonlinear optical material. For DUV photolithography, the wavelength of light used is typically less than 250 nanometers. To fabricate the waveguide, the thin film nonlinear optical material can be physically etched, for example, using dry etching, reactive ion etching (RIE), or inductively coupled plasma (RIE). In some embodiments, chemical etching and / or electron beam etching can be used. Waveguide 110' can thus have an improved surface roughness. For example, the sidewall(s) of ridge 112 can have a reduced surface roughness. For example, the short-range root mean square surface roughness of the sidewalls of ridge 112 can be less than 10 nanometers. In some embodiments, the root mean square surface roughness does not exceed 5 nanometers. In some cases, the short-range root mean square surface roughness does not exceed 2 nanometers. Thus, waveguide 110' can have optical losses within the above-mentioned ranges. In some embodiments, the height of ridge 112 is selected to provide confinement of the optical mode such that at ten microns from the center of ridge 112, there is a 10 dB reduction in intensity from the intensity at the center of ridge 112. For example, in some cases, the height of ridge 112 is on the order of several hundred nanometers. However, in other embodiments, other heights are possible.

[0062] The portion of waveguide 110' proximate electrodes 120' and 130' along the direction of optical signal transmission (e.g., from the input of the optical signal through waveguide 110' to the modulated optical signal output). The portion of waveguide 110' proximate electrodes 120' and 130' can be of the aforementioned length, for example, a length greater than 2 millimeters in some embodiments, and greater than 2 centimeters or more in some such embodiments. Such a length is possible, at least in part, due to the low optical loss per unit length of waveguide 110 described above. Furthermore, the portion of waveguide 110' proximate electrodes 120' and 130' has a small optical mode cross-sectional area, as described above with respect to waveguide 110.

[0063] Electrodes 120' and 130' apply an electric field to waveguide 110. Electrode(s) 120' and / or 130' can be fabricated using deposition techniques such as electroplating and photolithography to shape electrodes 120 and / or 130. Within the scope of the above description of electrodes 120 and 130, the resulting electrodes 120' and / or 130' can have lower frequency-dependent electrode losses. Electrode 120' includes a channel region 122' and an extension 124' (at Figure 1B Only one of the extensions 124' is marked in FIG. 1 ). The electrode 130' includes a channel region 132' and an extension 134' (at Figure 1B Only one of the extensions 134' is labeled in FIG. 1 ). 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, the distance s from extensions 124' and 134' to waveguide ridge 112 is less than the distance w from channels 122' and 132' to waveguide ridge 112. Figure 1B In the embodiment shown in FIG, extensions 124' and 134' are at substantially the same level as channel regions 122' and 132', respectively. In some embodiments, in addition to or instead of being at the same level, the extensions may protrude above and / or below the channel regions.

[0064] Extensions 124' and 134' are close to waveguide 110'. For example, extensions 124' and 134' are a vertical distance d from waveguide 110'. The vertical distance to waveguide 110' may depend on the cladding used ( Figure 1B114). In some cases, distance d is highly customizable. For example, d can range from zero (or less if electrodes 120' and 130' contact or are embedded in membrane portion 114) to a height greater than ridge 112. However, it is still generally desirable that d be small enough so that electrodes 120' and 130' can apply a desired electric field to waveguide 110'. Extensions 124' and 134' are also spaced a distance s from ridge portion 112. It is desirable that extensions 124' and 134' be sufficiently close to waveguide 110' (e.g., close to ridge 112) so that the desired electric field and refractive index change can be achieved. However, it is desirable that extensions 124' and 134' be sufficiently far from waveguide 110' (e.g., from ridge 112) so that their presence does not result in excessive optical loss. While distance s is generally agnostic to the specific geometry or thickness of waveguide 110', it can be selected to allow for differently confined transverse electrical and transverse optical modes in waveguide 110'. However, it is desirable to reduce the optical field intensity at extensions 124' and 134' (and more particularly at sections 124B and 134B) to limit optical losses due to absorption of the optical field by the conductors in extensions 124' and 134'. Thus, s is sufficiently large that the total optical loss of waveguide 110' (including losses due to absorption at extensions 124' and 134') does not exceed the aforementioned range (e.g., 10 dB or less in some embodiments, 8 dB or less in some embodiments, and 4 dB or less in some embodiments). In some embodiments, s is selected such that the optical field intensity at extensions 124' and 134' is less than -10 dB of the maximum optical field intensity in waveguide 110'. In some embodiments, s is selected so that the optical field intensity at extensions 124' and 134' is less than its maximum value in the waveguide by -40 dB. For example, in some embodiments, extensions 124' and / or 134' may be at least 2 microns and no more than 2.5 microns from ridge 112.

[0065] exist Figure 1B In the embodiment shown in , the extension 124 has a connecting portion 124A and a retrograde portion 124B. The retrograde portion 124B is so named because portions of the retrograde portion may be antiparallel to the direction of signal transmission through the electrode 120. Similarly, the extension 134 has a connecting portion 1234A and a retrograde portion 134B. Thus, the extensions 124 and 134 have a "T" shape. In some embodiments, other shapes are possible. For example, the extensions 124 and / or 134 may have an "L" shape, may omit the retrograde portion, may be rectangular, trapezoidal, parallelogram-shaped, may partially or completely wrap around a portion of the waveguide 110, and / or have another shape. Similarly, the channel regions 122' and / or 132' shown as having a rectangular cross-section may have another shape. In addition, as Figure 1AAs shown, extensions 124' and / or 134' can be of different sizes. Although all extensions 124' and 134' are shown as being the same distance from ridge 112, some extensions 124' and / or some extensions 134' can be at different distances from ridge 112. Channel regions 122' and / or 132' can also have varying sizes. In some embodiments, it is desirable for extensions 124' and 134' to have a length l (e.g., l=ws) that corresponds to a frequency less than the Bragg frequency of the signal of electrodes 120' and 130', respectively. Therefore, it can be desirable that the length of extensions 124' and 134' does not exceed the microwave wavelength of the electrode signal divided by π at the highest operating frequency of electrodes 120' and 130'. In some embodiments, it is desirable that the length of extensions 124' and 134' is 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 microns in the substrate, it is desirable that extensions 124' and 134' be less than about 37 microns. Individual extensions 124' and / or 134' may be irregularly spaced or may be periodic. Periodic extensions have a constant spacing. In some embodiments, the desired spacing p is a distance corresponding to a frequency less than the Bragg frequency, as discussed above with respect to the lengths of extensions 124' and 134'. Thus, it may be desirable that the spacing of extensions 124' and 134' does not exceed the microwave wavelength of the electrode signal divided by π at the highest operating frequency of electrodes 120' and 130'. In some embodiments, the desired spacing is less than the microwave wavelength divided by 12. In some embodiments, the desired spacing is less than the microwave wavelength divided by 72, thereby allowing for low ripple in the group velocity.

[0066] Extensions 124' and 134' are closer to ridge 112 than channels 122' and 132', respectively (eg, s < w). In some embodiments, the dielectric cap ( Figure 1B 10'). As described above, it is desirable that extensions 124' and 134' have a length (ws) corresponding to a frequency less than the Bragg frequency of the signal of electrodes 120' and 130', respectively. As described above, it is also desirable that extensions 124' and 134' be spaced apart from ridge 112 (e.g., so that absorption losses in waveguide 110' can be maintained at a desired level, such as 10 dB or less). The length of extensions 124' and 134' and the desired spacing from ridge 112 (e.g., s) are taken into account in determining w. Although in Figures 1A-1C Although described in the context of a horizontal distance between the electrode structure and the waveguide, the distance between the electrode structure and the waveguide also applies to vertical configurations. Other distances between the waveguide 110 / ridge 112 and the channel regions 122 and / or 132 are possible.

[0067] The geometry of electrodes 120' and 130' is similar to that described with respect to electrodes 120 and 130. The dimensions of specific portions of extensions 124' and 134' can vary. For example, the length d2 of connecting portions 124A and / or 134A can be selected so that the impedance of electrodes 120' and 130', respectively, matches the impedance of a driver (not shown) (e.g., 50Ω). In some embodiments, the gap between extensions 134' and 124' (wherein waveguide ridge 112 is located) can be configured to increase the electric field at waveguide ridge 112. In some embodiments, the gap between extensions 124' and 134' is at least 1 and no more than 10 times the wavelength of the optical signal carried by waveguide 110'. However, a gap that is too small can lead to current crowding and microwave losses in electrode(s) 120' and / or 130'. In some embodiments, the width of channel regions 122' and / or 132' is selected to reduce microwave losses while attempting to match the microwave (electrode signal) speed with the optical signal speed in waveguide 110. For example, the electrode channel regions 122' and / or 132' can have a width of at least 2 microns and no more than 500 microns. The width of the retrograde portion 124B and / or 134B segment can be finely tuned to allow low microwave loss while maintaining velocity matching and high frequency response range. For example, the retrograde portion 124B and / or 134B can have a width (l-d2) of at least 10 nanometers and no more than 10 microns. The length d3 of each retrograde portion 124B and / or 134B and the gap between adjacent retrograde portions 124B and / or 134 are selected to allow efficient modulation and low microwave loss. For example, in some embodiments, a duty cycle d3 / (d3+d4) of at least 0.5 and no more than 0.9999 can be selected. In some embodiments, other dimensions can be selected, including but not limited to those described herein.

[0068] Optical device 100' operates in a similar manner to optical device 100. Therefore, optical device 100' can share the benefits of optical device 100. The use of nonlinear optical materials in waveguide 110' and the configuration of waveguide 110' (e.g., smoother sidewalls of ridge 112) can not only increase the electro-optic effect (e.g., providing greater modulation of the refractive index) but also reduce optical losses. Consequently, longer waveguides 110, greater total refractive index changes, and thus enhanced optical signal modulation can be achieved. The use of electrodes 120' and 130' having extensions 124' and 134', respectively, can reduce microwave losses, allow for large electric fields at waveguide 110' / ridge 112, and improve the propagation of microwave signals through electrodes 120' and 130', respectively. Consequently, the performance of optical device 100' can be significantly enhanced.

[0069] This improvement in performance can be achieved for optical devices (e.g., 100 and / or 100') where waveguides 110 and / or 110' include or consist of an electro-optic material having a microwave dielectric constant that significantly exceeds the optical dielectric constant when used at the design microwave and optical frequencies. Here, for non-magnetic materials, the optical index is equal to or approximately the square root of the optical dielectric constant. For electro-optic materials where the microwave dielectric constant significantly exceeds the optical dielectric constant (e.g., LN and LT), the microwave dielectric constant is at least 1.5 times the optical dielectric constant. In some cases, the microwave dielectric constant is at least 2 times the optical dielectric constant. In some cases, the microwave dielectric constant is at least 5 times the optical dielectric constant. In some such materials, the microwave dielectric constant is at least 10 times the optical dielectric constant. Therefore, in some embodiments, the waveguide 110' comprising (or composed of) such a material has a microwave dielectric constant that exceeds the optical dielectric constant (e.g., by a factor of at least 1.5, 2, 5, 10, or more). The optical dielectric constant and the microwave dielectric constant affect the transmission speeds of optical and microwave signals, respectively. The higher the optical dielectric constant, the lower the transmission speed of optical signals. Similarly, the higher the microwave dielectric constant, the lower the transmission speed of microwave signals.

[0070] While optical modes are generally well confined to waveguides, microwave modes can extend significantly beyond the electrodes. For example, microwave modes can extend into the waveguide. For bulk and other optical devices that include waveguides formed from materials with microwave permittivity that is large compared to the optical permittivity (e.g., LN and / or LT), the propagation speed of microwave signals in the waveguide material is reduced to a greater extent than the speed of optical signals. Features in the electrodes, such as extensions, can also slow the propagation of electrode signals in the electrodes. Therefore, the velocity mismatch between optical and electrode signals can be expected to be exacerbated by electrodes with features such as extensions. Generally, the use of features such as extensions is disadvantageous in cases where the waveguide material has a microwave permittivity that is significantly larger than the optical permittivity (e.g., in the case of bulk LN and / or LT waveguides). In other words, the use of features on electrodes is generally limited to cases where the microwave permittivity of the waveguide material(s) is not significantly greater (e.g., less than 1.5 times) and is approximately equal to or less than the optical permittivity of the waveguide material(s) (e.g., III-V compound materials such as indium phosphide and gallium arsenide).

[0071] In contrast, for optical device 100' (and 100), a thin film waveguide 110' is used. Typically, the light mode is well confined to the waveguide 110' (eg, to the ridge portion 112). This can be due to Figure 2 The dimensions of the light patterns are shown in Figure 2. Return to Reference Figure 1B, the optical dielectric constant of the waveguide 110' thus determines the speed of the optical signal in the waveguide 110'. However, the microwave mode of the microwave signal in the electrodes 120' and / or 130' may extend over many structures. This can be determined by Figure 2 The size and position of the microwave patterns are shown in Figure 2. Return to Reference Figure 1B , the speed of the microwave signal passing through the electrodes 120' and 130' can therefore be found using the microwave dielectric constants of a plurality of structures such as the electrodes 120' and 130', the waveguide 110', the cladding ( Figure 1B ), substrate / underlying layer 101, and the air or any structure (not shown) above electrodes 120' and 130'. Thus, the contribution of the (large) microwave dielectric constant of the waveguide 110' material (e.g., LT and LN) can be mitigated by the (lower) microwave dielectric constant of the surrounding structure. In this way, the velocity mismatch between the optical signal in waveguide 110' and the electrode signal of electrode(s) 120' and / or 130' can still be mitigated, while achieving the other benefits of extensions 124' and / or 134'.

[0072] Figure 1C Another embodiment of an optical device 100' is shown. Optical device 100' is similar to optical device(s) 100 and / or 100'. Therefore, similar structures are labeled similarly. Thus, optical device 100' includes a 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', respectively, that are similar to channel regions 122 and 132 of electrodes 120 and 130, respectively. Electrodes 120' and 130' include extensions 124' and 134', respectively, 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 retrograde portions 124B′ and 134B′, which are similar to connecting portions 124A and 134A and retrograde portions 124B and 134B.

[0073] In some embodiments, optical devices 100 and 100' exhibit an electro-optic effect in the plane of thin film region 114 (e.g., an x-cut or y-cut modulator). Optical device 100' exhibits an electro-optic effect out of the plane of thin film region 114' (e.g., a z-cut optical modulator). Therefore, it is desirable to apply a perpendicular electric field to waveguide 110'. Therefore, optical device 100' includes electrode 140', which includes an extension 144' having a connecting portion 144A' and a retrograde portion 144B'. Extension 144' is similar to extensions 124, 134, 124', and 134'. Therefore, 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, an optical device exhibiting an out-of-plane electro-optic effect and improved performance can also be provided.

[0074] Figure 1D An embodiment of an optical device 100''' is shown. Optical device 100''' is similar to optical device(s) 100, 100', and / or 100'. Accordingly, similar structures have been labeled similarly. Thus, optical device 100''' includes a 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, for electrodes 120 / 120' and 130 / 130', respectively, of optical devices 100 / 100'. Electrodes 120' and 130' include extensions 124' and 134', respectively, which are similar to extensions 124 / 124' and 134 / 134', respectively, for electrodes 120 / 120' and 130 / 130', respectively, of optical devices 100 / 100'. Extensions 124' and 134' include connecting portions 124A' and 134A', respectively, and retrograde portions 124B' and 134B', respectively, which are similar to connecting portions 124A / 124A' and 134A / 134A' and retrograde portions 124B / 124' and 134B / 134B', respectively, of optical devices 100 / 100'.

[0075] Optical device 100''' also includes an additional waveguide 150 and an additional electrode 140 having a channel region 142 and an extension 144. Electrode 150 and extension 154 are similar to electrodes 120, 120', 130', and 130', and extensions 124, 124', 134, and 134', respectively. Similarly, waveguide 150 is similar to waveguides 110 and 110'. In some embodiments, optical device 100''' can be part of an optical device such as a modulator or an interferometer. For example, waveguides 110' and 150 can separate from a single waveguide upstream of the portion of optical device 100''' shown and can converge downstream of the portion of optical device 100''' shown.

[0076] Optical device 100''' operates in a similar manner to optical devices 100, 100', and / or 100''. Thus, optical device 100''' can share the benefits of optical device(s) 100, 100', and / or 100''. The use of nonlinear optical materials in waveguide(s) 110' and / or 150 and the configuration of waveguide(s) 110' and / or 150 (e.g., smoother sidewalls of ridge 112) can not only increase the electro-optic effect but also reduce optical losses. Consequently, longer waveguides 110' and 150, a greater total refractive index change, and thus enhanced optical signal modulation can be achieved. The use of electrodes 120', 130', and 140 having extensions 124', 134', and 144, respectively, can reduce microwave losses, allowing for a large electric field at waveguides 110' and 140. This can improve the propagation of microwave signals through electrodes 120', 130', and 140. Therefore, the performance of the optical device 100 ′″ can be significantly improved.

[0077] Figure 1EAn embodiment of an optical device 100''' is shown. Optical device 100'''' is similar to optical device(s) 100, 100', 100'', and / or 100''. Accordingly, similar structures have been labeled similarly. Accordingly, optical device 100''' includes a 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, for electrodes 120 / 120' and 130 / 130', respectively, of optical devices 100 / 100'. Electrodes 120" and 130" include extensions 124" and 134", respectively, which are similar to extensions 124 / 124' and 134 / 134', respectively, for electrodes 120 / 120' and 130 / 130', respectively, of optical devices 100 / 100'. Extensions 124" and 134" include connecting portions 124A" and 134A", respectively, and retrograde portions 124B" and 134B", respectively, which are similar to connecting portions 124A / 124A' and 134A / 134A' and retrograde portions 124B / 124' and 134B / 134B', respectively, of optical devices 100 / 100'.

[0078] Electrodes 120 ″ and 130 ″ each include an additional conductive layer 126 and 136 , respectively. Therefore, electrodes 120 ″ and 130 ″ may be able to carry additional current in conductive layers 126 and 136 .

[0079] Optical device 100''' operates in a similar manner to optical devices 100, 100', 100", and / or 100''. Thus, optical device 100'' can share the benefits of optical device(s) 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) can not only increase the electro-optic effect but also reduce optical losses. Consequently, a longer waveguide 110', a greater total refractive index change, and thus enhanced optical signal modulation can be achieved. The use of electrodes 120'' and 130'' having extensions 124'' and 134'', respectively, can reduce microwave losses, allowing for a large electric field at waveguide 110'. This can improve the propagation of microwave signals through electrodes 120'' and 130''. Consequently, the performance of optical device 100''' can be significantly improved.

[0080] Figure 2A cross-section of a portion of an embodiment of an optical device 200 capable of improved performance is shown. Optical device 200 includes a waveguide 210 and electrodes 220 and 230 located on a substrate 201. Also shown are an intermediate layer 202 and a cladding layer 204. In the illustrated embodiment, substrate 201 is silicon, intermediate layer 202 is silicon dioxide, and cladding layer 204 is silicon dioxide. In some embodiments, other and / or additional materials may be used for substrate 201 and / or intermediate layer 202. The portion of waveguide 210 shown includes LN. However, other and / or additional electro-optical materials, such as LT, may be used. Waveguide 210 includes a ridge 212 and a thin film portion 214. The channel region and extensions of electrodes 220 and 230 are not shown. Optical device 200 is similar to optical devices 100, 100', 100", 100''', and / or 100''''. Thus, the waveguide 210 and the electrodes 220 and 230 are similar to the waveguide 110 and / or 110 ′ and the electrodes 120 , 120 ′ and / or 120 ″ and 130 , 130 ′ and / or 130 ″, respectively.

[0081] Figure 2 Indicates the relative sizes of the optical mode of an optical signal and the radio frequency (RF) mode (or microwave mode) of microwaves. Figure 2 It is not to scale and only a portion of the optical device 200 is shown. Figure 2 As shown, the optical mode can be primarily confined to the waveguide 210, the intermediate layer 202, and the cladding layer 204. In contrast, the microwave mode extends through the multiple stacks 201, 202, 210, 220, 230, and 204. Therefore, the microwave mode experiences absorption losses from the multiple stacks 201, 202, 204, 210, 220, and 230. Absorption from the silicon substrate 201 can be particularly high. The use of the silicon substrate 201 can also affect the speed at which microwave signals pass through the electrodes 220 and 230. Due to the small size of the thin-film waveguide 210, other portions of the optical device 200 can be engineered to reduce microwave absorption losses. For example, portions of the silicon substrate 201 can be removed or replaced, electrodes 220 and / or 230 can be moved, the waveguide 210 can be reduced in size, other substrates (one or more) can be used, and / or other modifications are possible. For example, the intermediate layer 202 can be thick, such as at least 3 microns in some embodiments.

[0082] For example, Figure 3-5 Embodiments of optical devices 300 , 400 , and 500 are shown that may have further reduced microwave absorption losses. Figure 3 Shown is a cross-section of a portion of an embodiment of an optical device 300 capable of improved performance. Figure 3Not to scale, and only a portion of optical device 300 is shown. Optical device 300 includes a waveguide 310 and electrodes 320 and 330 located on substrate 301. Also shown are an intermediate layer 302 and a cladding layer 304. In the illustrated embodiment, substrate 301 is silicon, intermediate layer 302 is silicon dioxide, and cladding layer 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 a ridge 312 and a thin film portion 314. The channel region 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. Substrate 301, intermediate layer 302, and cladding layer 304 are also similar to substrate 201, intermediate layer 202, and cladding layer 204, respectively. However, for optical device 300, electrodes 320 and 330 have been moved further from the underlying silicon substrate 301. In some embodiments, electrodes 320 and 330 can be moved further from silicon substrate 301 by increasing the thickness of intermediate layer 302. For example, in some embodiments, intermediate layer 302 can be at least 3 microns thick. This can be achieved in addition to or in lieu of moving the electrodes further from thin film portion 314. Furthermore, thin film portion 314 of waveguide 310 has been reduced in size. Therefore, absorption due to silicon substrate 301 and waveguide 310 can be reduced. Furthermore, velocity variations of microwave signals can be reduced.

[0083] Figure 4 A cross-section of a portion of an embodiment of an optical device 400 having improved performance is shown. Figure 4Not to scale, and only a portion of optical device 400 is shown. Optical device 400 includes a waveguide 410 and electrodes 420 and 430 located on substrate 401. Also shown are an intermediate layer 402 and a cladding layer 404. In the illustrated embodiment, substrate 401 is silicon, intermediate layer 402 is silicon dioxide, and cladding layer 404 is silicon dioxide. In some embodiments, other and / or additional materials may be used. The portion of waveguide 410 shown includes LN. However, other and / or additional materials such as LT may be used. Waveguide 410 includes a ridge 412 and a thin film portion 414. The channel region and extensions of electrodes 420 and 430 are not shown. Optical device 400 is similar to optical device 200. Thus, waveguide 410 and electrodes 420 and 430 are similar to waveguide 210 and electrodes 220 and 230, respectively. Substrate 401, intermediate layer 402, and cladding layer 404 are also similar to substrate 201, intermediate layer 202, and cladding layer 204, respectively. However, for optical device 400, electrodes 420 and 430 have been moved further away from underlying silicon substrate 401. In some embodiments, electrodes 420 and 430 can be moved further away from silicon substrate 401 by increasing the thickness of intermediate layer 402. This can be achieved in addition to or in lieu of moving the electrodes further away from thin film portion 414. Thus, absorption due to silicon substrate 401 can be reduced. Furthermore, speed variations of microwave signals can also be reduced.

[0084] Figure 5 A cross-section of a portion of an embodiment of an optical device 500 having improved performance is shown. Figure 5Not to scale, and only a portion of optical device 500 is shown. Optical device 500 includes a waveguide 510 and electrodes 520 and 530 located on a substrate 501. Also shown are an intermediate layer 502 and a cladding layer 504. In the illustrated embodiment, substrate 501 is silicon, intermediate layer 502 is silicon dioxide, and cladding layer 504 is silicon dioxide. In some embodiments, other and / or additional materials may be used. The portion of waveguide 510 shown includes LN. However, other and / or additional materials such as LT may be used. Waveguide 510 includes a ridge 512 and a thin film portion 514. The channel region and extensions of electrodes 520 and 530 are not shown. Optical device 500 is similar to optical device 200. Thus, waveguide 510 and electrodes 520 and 530 are similar to waveguide 210 and electrodes 220 and 230, respectively. Substrate 501, intermediate layer 502, and cladding layer 504 are similar to substrate 201, intermediate layer 202, and cladding layer 204, respectively. However, for optical device 500, electrodes 520 and 530 have been moved further away from the underlying silicon substrate 301. In addition, the portion of silicon substrate 501 below ridge 512 has been removed. Therefore, absorption due to silicon substrate 501 can be reduced. In addition, the speed variation of the microwave signal can also be reduced. In some embodiments, another substrate can be selected in addition to or instead of removing the portion of the substrate.

[0085] Therefore, microwave loss can be further mitigated. Thus, in addition to the benefits of optical device(s) 100, 100', 100", 100''', and / or 100''', optical devices 300, 400, and 500 can have further reduced microwave absorption loss. Therefore, the performance of optical devices 300, 400, and 500 can be improved.

[0086] Figure 6 、 7 , 8, 9, 10 and 11 show optical devices 600, 700, 800, 900, 1000 and 1100, respectively, which can have improved performance. Figure 6-11 Various electrode structures are shown. Figure 6-11 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 device(s) 100, 100', 100", 100'", and / or 100'". Similar components have similar references.

[0087] refer to Figure 6 , showing electrodes 620 and 630 and waveguide 610 having ridge 612. Figure 6Extensions 624 and 634 are also indicated in FIG. (only one of each is labeled). As described above, the extensions 624 and 634 of electrodes 620 and 630 can improve performance. Figure 6 In the embodiment shown in FIG, extensions 624 and 634 are regularly spaced. Thus, extensions 624 and 634 are periodic and have a constant spacing. Extensions 624 and 634 are also all the same size. However, other configurations are possible. For example, extensions 624 and 634 can have different sizes and different spacings. Thus, optical device 600 can share the benefits of optical device(s) 100, 100', 100", 100'", and / or 100''.

[0088] Figure 7 Optical device 700 is shown. For clarity, only electrodes 720, 730, and 740 are shown. Typically, a waveguide / ridge is located between electrode 720 and electrode 730. Another waveguide / ridge (or waveguide / ridge branch) is located between electrode 720 and electrode 740. In some embodiments, electrode 720 carries the microwave signal, while electrodes 730 and 740 are grounds. 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 in shape. However, electrodes 730 and 740 do not have extensions. Due to the presence of extension 724, current can be more easily driven through channel region 722. Thus, optical device 700 can share the benefits of optical device(s) 100, 100', 100", 100'", and / or 100'''.

[0089] Figure 8 Optical device 800 is shown. For clarity, only electrodes 820, 830, and 840 are shown. Typically, a waveguide / ridge is located between electrode 820 and electrode 830. Another waveguide / ridge (or waveguide / ridge branch) is located between electrode 820 and electrode 840. In some embodiments, electrode 820 carries the microwave signal, while electrodes 830 and 840 are grounds. 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 includes a connecting portion 824A and a retrograde portion 824B. Electrodes 830 and 840 do not have extensions. Due to the presence of extension 824, current can be more easily driven through channel region 822. Thus, optical device 800 can share the benefits of optical device(s) 100, 100', 100", 100'", and / or 100'''.

[0090] Figure 9An optical device 900 is shown. Electrodes 920, 930, and 940 are shown. A waveguide / ridge 910 is located between electrode 920 and electrode 930. Another waveguide / ridge (or waveguide / ridge branch) 950 is located between electrode 920 and electrode 940. In some embodiments, electrode 920 carries the microwave signal, while electrodes 930 and 940 are grounds. 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 varying lengths and are not periodic (e.g., irregularly spaced and with varying spacing). The presence of extensions 924, 934, and 944 allows current to be driven more easily through channel regions 922, 932, and 942. Thus, the optical device 900 may share the benefits of the optical device(s) 100 , 100 ′, 100 ″, 100 '″, and / or 100 '''.

[0091] Figure 10 An optical device 1000 is shown. Electrodes 1020, 1030, and 1040 are shown. A waveguide / ridge 1010 is located between electrode 1020 and electrode 1030. Another waveguide / ridge (or waveguide / ridge branch) 1050 is located between electrode 1020 and electrode 1040. In some embodiments, electrode 1020 carries the microwave signal, while electrodes 1030 and 1040 are grounds. However, other configurations are possible. In the illustrated embodiment, electrode 1020 has a channel region 1022 and an extension 1024. Electrode 1030 has a channel region 1032 and an extension 1034. Electrode 1040 has a channel region 1042 and an extension 1044. Extensions 1024, 1034, and 1044 have various shapes and are irregularly spaced. Furthermore, channel 1022 has a notch. However, channel 1022 still has a straight center region that can carry current. Due to the presence of extensions 1024, 1034, and 1044, current can still be driven more easily through channel regions 1022, 1032, and 1042, respectively. Thus, optical device 1000 can share the benefits of optical device(s) 100, 100', 100", 100'", and / or 100'''.

[0092] Figure 11An optical device 1100 is shown. Electrodes 1120, 1130, and 1140 are shown. A waveguide / ridge 1110 is located between electrode 1120 and electrode 1130. Another waveguide / ridge (or waveguide / ridge branch) 1150 is located between electrode 1120 and electrode 1140. In some embodiments, electrode 1120 carries the microwave signal, while electrodes 1130 and 1140 are grounds. However, other configurations are possible. In the illustrated embodiment, electrode 1120 has a channel region 1122 and an extension 1124. Electrode 1130 has a channel region 1132 and an extension 1134. Electrode 1140 has a channel region 1142 and an extension 1144. Extensions 1124, 1134, and 1144 have various shapes and are irregularly spaced. Due to the presence of extensions 1124, 1134, and 1144, current can still be driven more easily through channel regions 1122, 1132, and 1142, respectively. Thus, optical device 1100 can share the benefits of optical device(s) 100, 100', 100", 100'", and / or 100'". Thus, as indicated by optical devices 600, 700, 800, 900, 1000, and 1100, various configurations of extensions can be used for electrodes.

[0093] Figures 12A-12D Portions of embodiments of optical devices 1200A, 1200B, 1200C, and 1200D are shown indicating various electrode configurations capable of improved performance. Figures 12A-12D 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 device(s) 100, 100', 100", 100'", and / or 100'". Accordingly, similar components have similar references (e.g., waveguide 1210 is similar to waveguide 110'). Figure 12A A plan view of optical device 1200A is shown. Figures 12B-12D Cross-sectional views of portions of optical devices 1200B, 1200C, and 1200D are shown. Figures 12A-12D It shows that some optical devices can share the same plan view even though their cross-sectional views are different. Conversely, some optical devices can have different plan views even though their cross-sectional views may be similar.

[0094] refer to Figure 12A , showing electrodes 1220A, 1230A, and 1240A and waveguides 1210A and 1250A. In some embodiments, Figure 12AThe portions of waveguides 1210A and 1250A shown correspond to ridges. 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 described 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 level as extensions 1224A, 1234A, and 1244A, respectively.

[0095] Figure 12B Optical device 1200B is shown, sharing the 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 described above, extensions 1224B, 1234B, and 1244B of electrodes 1220B, 1230B, and 1240B can improve performance. Although sharing the same plan view as optical device 1200A, channel regions 1222B, 1232B, and 1242B have been elevated to a higher level (further from the substrate) than extensions 1224B, 1234B, and 1244B. Optical device 1200B functions in a similar manner to optical device 1200A and thus shares the benefits of optical device 100.

[0096] Figure 12COptical device 1200C is shown, 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 described above, extensions 1224C, 1234C, and 1244C of electrodes 1220C, 1230C, and 1240C can improve performance. Despite sharing a similar cross-sectional view, optical device 1200C has a different plan view than optical devices 1200A and 1200B. Figure 12C As seen by the dashed lines in FIG, the outer edges of extensions 1224C, 1234C, and 1244C are aligned with the outer edges of channel regions 1222C, 1232C, and 142C, respectively. Therefore, electrodes 1220C, 1230C, and 1240C appear rectangular from above. In other words, extensions 1224C, 1234C, and 1244C would not be readily apparent from a plan view. However, extensions 1224C, 1234C, and 1244C are still closer to waveguide 1210C / ridge 1212C and waveguide 1250C / ridge 1252C than the corresponding channel regions 1222C, 1232C, and 1242C. Optical device 1200C functions in a manner similar to optical devices 1200A and 1200B. Thus, despite having a different plan view, optical device 1200C may share the benefits of optical devices 100, 1200A, and / or 1200B.

[0097] Figure 12DAn optical device 1200D is shown, sharing the same plan view as 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 each include a thin film portion 1214D and 1254D, respectively. Electrodes 1220D, 1230D, and 1240D include channel regions 1222D, 1232D, and 1242D, respectively. Electrodes 1220D, 1230D, and 1240D also include extensions 1224D, 1234D, and 1244D. As described above, the extensions 1224D, 1234D, and 1244D of the electrodes 1220D, 1230D, and 1240D can improve performance. While sharing the same planar layout as the optical device 1200A, the thin film portions 1214D and 1254D of the waveguides 1210D and 1250D, respectively, are reduced in size. The optical device 1200D functions in a similar manner to the optical devices 1200A, 1200B, and 1200C. Thus, the optical device 1200D can share the benefits of the optical devices 100, 1200A, 1200B, and / or 1200C.

[0098] Figures 13A-13J Portions of embodiments of optical devices 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 1300I, and 1300J are shown that can have improved performance and indicate various electrode configurations. Figures 13A-13J Not to scale, and only portions of optics 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 13001, and 1300J are shown. Figures 13A-13J Various configurations of electrodes that can be used for x-cut or y-cut waveguide structures are shown. Optical devices 1300A, 1300B, 1300C, 1300D, 1300E, 1300F, 1300G, 1300H, 1300I, and 1300J are similar to optical device(s) 100, 100', 100", 100'" and / or 100'"'. Therefore, similar components have similar references (e.g., waveguide ridge 1312A is similar to waveguide ridge 112). For clarity, Figures 13A-13I The middle electrode is generally shown as a rectangle. However, such an electrode may include a channel region, an extension, and / or other features described herein. Figures 13A-13I The electrodes shown in FIG. 1 primarily illustrate the positions of the electrodes.

[0099] Figure 13AAn optical device 1300A is shown including a waveguide having a ridge 1312A and a thin film portion 1314A, as well as electrodes 1320A and 1330A. Also shown are a substrate 1301A and an intermediate layer 1302A. It is desirable for the extended portions of the electrodes to be proximate to the corresponding waveguides. In some embodiments, it is desirable for portions of the extended portions of the electrodes to be between the top of the ridge and the top of the thin film portion of the waveguide. Thus, electrodes 1320A and 1330A share an interface with the thin film portion 1314A of the waveguide. More specifically, electrodes 1320A and 1330A contact the top surface of the thin film portion 1314A.

[0100] Figure 13B An optical device 1300B is shown that includes a waveguide having a ridge 1312B and a thin film portion 1314B, as well as electrodes 1320B and 1330B. Also shown are a substrate 1301B and an intermediate layer 1302B. It is desirable that the electrodes extend proximate to the corresponding waveguides. Electrodes 1320B and 1330B extend from above the top of the waveguide ridge 1312B, through the waveguide's thin film portion 1314B, and into the intermediate layer 1302B.

[0101] Figure 13C An optical device 1300C is shown that includes a waveguide having a ridge 1312C and a thin film portion 1314C, as well as electrodes 1320C and 1330C. Also shown are a substrate 1301C and an intermediate layer 1302C. It is desirable that the electrodes extend proximate to the corresponding waveguides. Electrodes 1320C and 1330C extend from over the top of the waveguide ridge 1312C, through the waveguide's thin film portion 1314C, and into the substrate 1301C.

[0102] Figure 13D An optical device 1300D is shown that includes a waveguide having a ridge 1312D and a thin film portion 1314D, as well as electrodes 1320D and 1330D. Also shown are a substrate 1301D and an intermediate layer 1302D. It is desirable for the electrode extensions to be proximate to the corresponding waveguides. Electrode extensions 1320D and 1330D extend from between the top of the waveguide ridge 1312D and the top of the waveguide thin film portion 1314D, through the thin film portion 1314D, and into the substrate 1301D.

[0103] Figure 13E An optical device 1300E is shown that includes a waveguide having a ridge 1312E and a thin film portion 1314E, as well as electrodes 1320E and 1330E. Also shown are a substrate 1301E and an intermediate layer 1302E. It is desirable that the electrodes extend proximate to the corresponding waveguides. Electrodes 1320E and 1330E extend from above the top of the waveguide ridge 1312E to between the top of the waveguide ridge 1312E and the top of the waveguide thin film portion 1314E.

[0104] Figure 13FAn optical device 1300F is shown that includes a waveguide having a structure 1312F and a thin film portion 1314F, as well as electrodes 1320F and 1330F. Also shown are a substrate 1301F and an intermediate layer 1302F. It is desirable that the extended portions of the electrodes be proximate to the corresponding waveguides. 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 thin film portion 1314F. Furthermore, structure 1312F corresponds to a waveguide ridge. However, in the illustrated embodiment, structure 1312F may be another component, such as a heater.

[0105] Figure 13G An optical device 1300G is shown that includes a waveguide having a ridge 1312G and a thin film portion 1314G, as well as electrodes 1320G and 1330G. Also shown are a substrate 1301G and an intermediate layer 1302G. It is desirable that the extended portions of the electrodes approach the corresponding waveguides. Electrodes 1320G and 1330G extend from above the thin film portion 1314G into the waveguide thin film portion 1314G. Furthermore, the waveguide ridge 1312G is below the waveguide thin film portion 1314G.

[0106] Figure 13H An optical device 1300H is shown that includes a waveguide having a structure 1312H and a thin film portion 1314H, as well as electrodes 1320H and 1330H. Also shown are a substrate 1301H and an intermediate layer 1302H. It is desirable that the extended portions of the electrodes approach the corresponding waveguides. Electrodes 1320H and 1330H extend from above the top of thin film portion 1314H into the waveguide thin film portion 1314H. Structure 1312H can be a heater or similar component corresponding to a waveguide ridge. Furthermore, structure 1312H is located below the waveguide thin film portion 1314H.

[0107] Figure 13I An optical device 1300I is shown that includes a waveguide having a structure 1312I and a thin film portion 1314I, as well as electrodes 1320I and 1330I. Also shown are a substrate 1301I and an intermediate layer 1302I. It is desirable that the electrodes extend proximate to the corresponding waveguides. Electrodes 1320I and 1330I extend from beneath the bottom of structure 1312I to the bottom surface of waveguide thin film portion 1314I. Structure 1312I can be a heater or similar component corresponding to a waveguide ridge and is located beneath waveguide thin film portion 1314I.

[0108] Figure 13JAn optical device 1300J is shown that includes a waveguide having a ridge 1312J and a thin film portion 1314J, as well as electrodes 1320J and 1330IJ. Also shown are a substrate 1301I and an intermediate layer 1302I. Electrode 1320J includes a channel region 1322J and an extension 1324J. Electrode 1330J includes a channel region 1332J and an extension 1334J. As can be seen in optical device 1330J, channel regions 1322J and / or 1332J need not have rectangular cross-sections.

[0109] Thus, despite the varying 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 benefits of optical device(s) 100, 100', 100", 100'", and / or 100''".

[0110] Figures 14A to 14K Portions of embodiments of optical devices 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400I, 1400J, and 1400K are shown that can have improved performance and indicate various electrode configurations. Figures 14A-14K 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 device(s) 100, 100', 100", 100'", and / or 100'". Accordingly, similar components have similar references (e.g., waveguide ridge 1412A is similar to waveguide ridge 112). Although present, the channel region and extensions are not shown. Figures 14A-14D are shown separately. Figures 14A-14K Various configurations of electrodes that can be used in waveguide structures where the electro-optic effect is out of the film plane (e.g., z-cut waveguides) are shown. Figures 14A-14D The middle electrode is generally shown as a rectangle. However, such an electrode may include a channel region, an extension, and / or other features described herein. Figures 14A-14D The electrodes shown in FIG. 1 primarily indicate the locations of the electrodes. The extensions and other features of some embodiments are shown in FIG. Figures 14E-14K More clearly shown in .

[0111] Figure 14A An optical device 1400A is shown that includes a waveguide having a ridge 1412A and a thin film portion 1414A, as well as electrodes 1420A and 1430A. Also shown are a substrate 1401A and an intermediate layer 1402A. It is desirable that the electrodes be close to the corresponding waveguides and provide a vertical field in the region of the ridge 1412A. Thus, electrode 1420A is above the ridge 1412A, while electrode 1430A is a thin film that extends horizontally below the ridge 1412A.

[0112] Figure 14A An optical device 1400A is shown that includes a waveguide having a ridge 1412A and a thin film portion 1414A, as well as electrodes 1420A and 1430A. Also shown are a substrate 1401A and an intermediate layer 1402A. It is desirable that the electrodes be close to the corresponding waveguides and provide a vertical field in the region of the ridge 1412A. Thus, electrode 1420A is above the ridge 1412A, while electrode 1430A is a thin film that extends horizontally below the ridge 1412A.

[0113] Figure 14B An optical device 1400B is shown, including a waveguide having a ridge 1412B and a thin film portion 1414B, as well as electrodes 1420B, 1430B, and 1440B. Also shown are a substrate 1401B and an intermediate layer 1402B. It is desirable that the electrodes be proximate to the corresponding waveguide and provide a perpendicular field in the region of ridge 1412B. Therefore, electrode 1420B is above ridge 1412B, while electrodes 1430B and 1440B extend to the sides of and below ridge 1412B. Electrodes 1430B and 1440B terminate near or within thin film portion 1414B. Consequently, the electric field in the region of ridge 1412B is substantially vertical (in the z-direction).

[0114] Figure 14C An optical device 1400C is shown that includes a waveguide having a ridge 1412C and a thin film portion 1414C, as well as electrodes 1420C, 1430C, and 1440C. Also shown are a substrate 1401C and an intermediate layer 1402C. It is desirable that the electrodes be proximate to the corresponding waveguide and provide a perpendicular field in the region of ridge 1412C. Therefore, electrode 1420C is above ridge 1412C, while electrodes 1430C and 1440C extend to the sides of and below ridge 1412C. Electrodes 1430C and 1440C extend through the waveguide thin film portion 1414C. Consequently, the electric field in the region of ridge 1412C is substantially vertical (in the z-direction).

[0115] Figure 14DAn optical device 1400D is shown that includes a waveguide having a structure 1412D and a thin film portion 1414D, as well as electrodes 1420D and 1430D. Also shown are a substrate 1401D and an intermediate layer 1402D. It is desirable that the electrodes be proximate to the corresponding waveguide and provide a vertical field in the region of the structure 1412D. Thus, electrode 1420D is above the structure 1412D, while electrode 1430D is a membrane extending horizontally below the structure 1412D. The structure 1412D is below the waveguide thin film portion 1414D and may be a heater or similar component.

[0116] Figure 14E An optical device 1400E is shown that includes a waveguide 1410E having a ridge 1412E and a thin film portion 1414E, as well as electrodes 1420E and 1430E. Also shown are a substrate 1401E and an intermediate layer 1400E. It is desirable that the electrodes be located proximate to the corresponding waveguides and provide a perpendicular field in the region of structure 1412E. Therefore, electrode 1420E is located above structure 1412E, while electrodes 1430E and 1440E are located to the sides of structure 1412E. In the illustrated embodiment, electrodes 1430E and 1440E are ground electrodes, while electrode 1420E carries a signal. The locations of ground electrodes 1430E and 1440E are exemplary. Other ground locations may be used as long as a perpendicular electric field is established in waveguide 1412E. Also shown are channel regions 1422E, 1432E, and 1442E, and extensions 1424E, 1434E, and 1444E, for 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 can share the benefits of optical devices 100, 100', 100", 100'", and / or 100''' utilizing extensions.

[0117] Figure 14FA differential optical device 1400F is shown, including a waveguide 1410F having a ridge 1412F and a thin film portion 1414F, and electrodes 1420F and 1430F. Also shown are a substrate 1401F and an intermediate layer 1400F. It is desirable that the electrodes be proximate to their respective waveguides and provide a perpendicular field in the region of structure 1412F. Therefore, electrode 1420F is above structure 1412F, while electrodes 1430F and 1440F are to the sides of structure 1412F. Because optical device 1400F is a differential modulator, additional waveguides 1460F (e.g., additional ridges) and additional electrodes 1450F are present. In the illustrated embodiment, electrodes 1430F and 1440F are ground electrodes, while electrodes 1420F and 1450F carry signals. The placement of ground electrodes 1430F and 1440F is exemplary. Other ground locations can be used as long as a perpendicular electric field is established in waveguides 1412F and 1460F. Also shown are channel regions 1422F, 1432F, 1442F, and 1452F, and extensions 1424F, 1434F, 1444F, and 1454F, for 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 can share the benefits of optical devices 100, 100', and / or 150 that utilize extensions.

[0118] Figure 14GA differential optical device 1400G is shown, including a waveguide 1410G having a ridge 1412G and a thin film portion 1414G, and electrodes 1420G and 1430G. Also shown are a substrate 1401G and an intermediate layer 1400G. It is desirable that the electrodes be proximate to their respective waveguides and provide a perpendicular field in the region of structure 1412G. Therefore, electrode 1420G is above structure 1412G, while electrodes 1430G and 1440G are to the sides of structure 1412G. Because optical device 1400G is a differential modulator, additional waveguides 1460G (e.g., additional ridges) and additional electrodes 1450G are present. In the illustrated embodiment, electrodes 1430G and 1440G are ground electrodes, while electrodes 1420G and 1450G carry signals. The placement of ground electrodes 1430G and 1440G is exemplary. Other ground positions can be used as long as a perpendicular electric field is established in waveguides 1412G and 1460G. Also shown are channel regions 1422G, 1432G, 1442G, and 1452G, and extensions 1424G, 1434G, 1444G, and 1454G, for electrodes 1420G, 1430G, 1440G, and 1450G, respectively. Channel regions 1422G, 1432G, 1442G, and 1452G, and extensions 1424G, 1434G, 1444G, and 1454G, are similar to those 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 can be reduced. Thus, the optical device 1400G may share the benefits of the optical devices 100 , 100 ′, 100 ″, 100 ′″, and / or 100 ′″′ that utilize extensions.

[0119] Figure 14HAn optical device 1400H is shown including a waveguide 1410H having a structure 1412H and a thin film portion 1414H, and electrodes 1420H and 1430H. Also shown are a substrate 1401H and an intermediate layer 1400H. It is desirable that the electrodes be proximate to the corresponding waveguides and provide a perpendicular field in the region of the structure 1412H. The structure 1412H may be a material other than a nonlinear optical material, such as a passive material or heater as described herein. An optional buffer layer may be between the thin film region 1414H comprising nonlinear optical material and the structure 1412H. In some embodiments, the structure 1412H may simply be an embedded ridge comprising nonlinear optical material. Electrode 1420H is below the structure 1412H, while electrodes 1430H and 1440H are to the sides of the structure 1412H. In the illustrated embodiment, electrodes 1430H and 1440H are ground electrodes, while electrode 1420H carries a signal. The locations of the ground electrodes 1430H and 1440H are exemplary. Other ground locations can be used as long as a perpendicular electric field is established in waveguide 1412H. Also shown are channel regions 1422H, 1432H, and 1442H, and extensions 1424H, 1434H, and 1444H for 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 can share the benefits of optical devices 100, 100', 100", 100'", and / or 100''' utilizing extensions.

[0120] Figure 14IA differential optical device 1400I is shown, including a waveguide 1410I having a structure 1412I and a thin film portion 1414I, and electrodes 1420I and 1430I. Also shown are a substrate 1401I and an intermediate layer 1400I. It is desirable that the electrodes be proximate to the corresponding waveguides and provide a perpendicular field in the region of the structure 1412I. Therefore, electrode 1420I is below the structure 1412I, while electrodes 1430I and 1440I flank the structure 1412I. The structure 1412I may be a material other than a nonlinear optical material, such as a passive material or heater as described herein. In some embodiments, the structure 1412I may simply be an embedded ridge comprising a nonlinear optical material. Because the optical device 1400I is a differential modulator, additional waveguides / structures 1460I (e.g., additional ridges, passive materials, or heaters) and additional electrodes 1450I are present. 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 ground locations may be used as long as a perpendicular electric field is established in waveguides 1412I and 1460I. An optional buffer layer may be provided between thin film region 1414I comprising nonlinear optical material and structures 1412I and 1460I. Channel regions 1422I, 1432I, 1442F, and 1452I, as well as extensions 1424I, 1434I, 1444I, and 1454I, are also shown for 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 can share the benefits of optical devices 100, 100', 100", 100'", and / or 100''' utilizing extensions.

[0121] Figure 14JAn optical device 1400J is shown including a waveguide 1410J having a ridge 1412J and a thin film portion 1414J, as well as electrodes 1420J and 1430J. Also shown are a substrate 1401J and an intermediate layer 1400J. It is desirable that the electrodes be located proximate to their respective waveguides and provide a perpendicular field in the region of structure 1412J. Therefore, electrode 1420J is located above structure 1412J, while electrodes 1430J and 1440J are located to the sides of structure 1412J. In the illustrated embodiment, electrodes 1430J and 1440J are ground electrodes, while electrode 1420J carries a signal. The locations of ground electrodes 1430J and 1440J are exemplary. Other ground locations may be used as long as a perpendicular electric field is established in waveguide 1412J. Also shown are channel regions 1432J and 1442J, as well as extensions 1434J and 1444J, for electrodes 1430J and 1440J, respectively. Thus, in this embodiment, signal electrode 1420J does not include an extension. Channel regions 1432J and 1442J, as well as extensions 1434J and 1444J, are similar to the channel regions and extensions described above. Thus, optical device 1400J can share the benefits of optical devices 100, 100', 100", 100'", and / or 100''" that utilize extensions. Furthermore, not all electrodes need to include extensions to provide improved performance.

[0122] Figure 14KA differential optical device 1400F is shown, including a waveguide 1410K having a ridge 1412K and a membrane portion 1414K, and electrodes 1420K and 1430K. Also shown are a substrate 1401K and an intermediate layer 1400K. It is desirable that the electrodes be proximate to their respective waveguides and provide a perpendicular field in the region of structure 1412K. Therefore, electrode 1420K is above structure 1412K, while electrodes 1430K and 1440K are to the sides of structure 1412K. Because optical device 1400K is a differential modulator, additional waveguides 1460K (e.g., additional ridges) and additional electrodes 1450K are present. 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 ground locations may be used as long as a perpendicular electric field is established in the waveguides 1412K and 1460K. Also shown are channel regions 1432K and 1442K and extensions 1434K and 1444K for electrodes 1430K and 1440K, respectively. The channel regions 1432K and 1442K and extensions 1434K and 1444K are similar to the channel regions and extensions described above. However, the signal electrodes 1420K and 1450K do not include extensions. The optical device 1400K can share the benefits of optical devices 100, 100', 100", 100'", and / or 100''" utilizing extensions. Furthermore, not all electrodes need include extensions in order to provide improved performance.

[0123] Thus, despite the varying electrode and waveguide configurations, the optical devices 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400I, 1400J, and 1400K are similar to the optical devices 100, 100', 100", 100'", and / or 100'". Thus, the optical devices 1400A, 1400B, 1400C, 1400D, 1400E, 1400F, 1400G, 1400H, 1400J, and 1400K may share the benefits of the optical device(s) 100, 100', 100", 100'", and / or 100'".

[0124] Figure 15A and 15B Portions of embodiments of optical devices 1500A and 1500B are shown, respectively. The optical devices 1500A and 1500B are similar to the optical device(s) 100, 100', 100", 100'", and / or 100'''. Figure 15A and 15BNot to scale, and only portions of optical devices 1500A and 1500B are shown. Optical devices 1500A and 1500B are similar to optical device(s) 100, 100', 100", and / or 100'". Accordingly, similar components have been labeled similarly. Optical device 1500A includes a waveguide 1510 having a ridge 1512 and electrodes 1520 and 1530, which are similar to waveguides 110 / 110' having a ridge 112 and electrodes 120, 120', 120", 130, 130', and 130". Electrodes 1520 and 1530 include channel regions 1522 and 1532, respectively, which are similar to channel regions 122, 122', 122" and 132, 132', 132" of electrodes 120, 120', 120" and 130, 130', 130", respectively. Electrodes 1520 and 1530 include extensions 1524 and 1534, respectively, which 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″.

[0125] Waveguide 1510 also includes a waveguide bend section 1515. Figure 15AMultiple waveguide bends are shown, but only one waveguide bend 1515 is labeled. Each waveguide bend 1515 can have a bend radius of no more than 1 mm. In some embodiments, each waveguide bend 1515 has a bend radius of no more than 500 μm. In some embodiments, each waveguide bend 1515 has a bend optical loss of no more than 0.5 dB. Waveguide (and electrode) bends can be used to provide a longer region in which electrodes 1520 and 1530 are close to waveguide 1510 while controlling the size of the device incorporated into optical device 1500A. For example, waveguide 1510 and electrodes 1520 and 1530 can occupy an area of ​​no more than 50 square millimeters. In some embodiments, waveguide 1510 and electrodes 1520 and 1530 occupy an area of ​​no more than 20 square millimeters. In some embodiments, waveguide 1510 and electrodes 1520 and 1530 are located on an integrated circuit having a length of no more than 32 millimeters. In some such embodiments, waveguide 1510 and electrodes 1520 and 1530 are located on an integrated circuit that is no longer than 22 mm. This is true despite the higher length of waveguide 1510. Thus, greater optical signal modulation can be achieved in a smaller overall device.

[0126] Electrode 1520 may include an electrode bend section 1525 (at Figure 15A Similarly, electrode 1530 includes an electrode bend 1535 (at Figure 15A (Only one of them is labeled in FIG. ). Similar to waveguide bend section 1515 of waveguide 1510, electrode bend sections 1525 and 1535 allow for longer lengths of electrodes 1520 and 1530, respectively, within a smaller footprint. Thus, optical device 1500A can consume less space, and in particular, less length, within a package.

[0127] In some embodiments, electrode bends 1525 and 1535 and waveguide bend 1515 can also be used to improve performance. More specifically, electrode bends 1525 and 1535 and waveguide bend 1515 can be configured to provide a path difference between the optical signal for waveguide 1510 and the electrode signal(s) for electrode(s) 1520 and / or 1530. This path difference can be used to compensate for the difference in transmission speed(s) between the microwave signal in electrode(s) 1520 and / or 1530 and the optical signal in waveguide 1510. The speed of the optical signal passing through waveguide 1510 is affected by the refractive index of waveguide 1510. The speed(s) of the microwave signal(s) in electrode(s) 1520 and / or 1530 is affected by the presence of extensions 1524 and / or 1534. Extensions 1524 and / or 1534 tend to slow the propagation of microwave signals through electrode(s) 1520 and / or 1530. Surrounding materials such as substrate / underlayer ( Figures 15A-15B The speed of the electrode signal may also be affected by the materials used for waveguide 1510 and electrodes 1520 and / or 1530, the manufacturing techniques used for waveguide 1510 and electrodes 1520 and / or 1530, the cladding and substrate / underlayer, and the configuration of extensions 1524 and / or 1534. The configuration of extensions 1524 and / or 1534 may be selected to reduce the speed difference between the optical signal in waveguide 1510 and the electrode signal in electrodes 1520 and / or 1530.

[0128] Furthermore, additional extensions may be added that may be relatively far from ridge 1512 (eg, further from ridge 152 than channels 1522 and / or 1532). Such extensions ( Figures 15A-15B(not shown) may improve the match between the speed of the optical signal in waveguide 1510 and the speed of the electrode signal in electrodes 1520 and / or 1530. However, some mismatch may still exist between the optical and electrode signal speeds. Curved sections 1515, 1525, and 1535 can compensate for this mismatch. For example, in some embodiments, waveguide curved section 1515 can be configured so that the path traversed by the optical signal in waveguide 1510 is longer than the path traversed by the microwave signal in electrode(s) 1520 and / or 1530. This path difference can compensate for the optical signal traveling faster in waveguide 1510 than the microwave signal traveling in electrode(s) 1520 and / or 1530. In some embodiments, waveguide curved section 1515 can be configured so that the path traversed by the optical signal in waveguide 1510 is shorter than the path traversed by the microwave signal in electrode(s) 1520 and / or 1530. This path difference can compensate for the optical signal traveling more slowly in waveguide 1510 than the microwave signal traveling in electrode(s) 1520 and / or 1530. Such a path difference can be used in addition to or in place of the waveguide's tortuous path (discussed below). Thus, for a given velocity mismatch between the microwave (electrode) and optical (waveguide) signals, the lengths of curved sections 1515, 1525, and 1535 can be calculated to mitigate the difference introduced by the electrode and optical signals traveling at different speeds in the straight sections. By configuring the straight and curved sections, the velocity mismatch can be mitigated and the desired performance achieved. Thus, the waveguide curved section 1515 and the electrode curved sections 1525 and 1535 can be used to account for the velocity mismatch between the electrode (microwave) and optical signals. Thus, in addition to the benefits described herein with respect to optical devices such as optical devices 100 , 100 ′, 100 ″, 100 '″, and / or 100 ''″, optical device 1500A may have improved velocity matching and, therefore, improved performance.

[0129] Optical device 1500B is similar to optical device 1500A. Thus, similar structures are labeled similarly. Thus, optical device 1500B includes a waveguide 1510′ having a ridge 1512′ and electrodes 1520′ and 1530′, which are similar to waveguide 1510 having a ridge 1512 and electrodes 1520 and 1530. Electrodes 1520′ and 1530′ include extensions 1524′ and 1534′, respectively, which are similar to extensions 1524 and 1534. Extensions 1524 and 1534 include connecting portions 1524A and 1534A and retrograde portions 1524B and 1534B, which are similar to connecting portions 1524A and 1534A and retrograde portions 1524B and 1534B. Curved portions 115', 125', and 135' of waveguide 110' and electrodes 120' and 130' are similar to curved portions 115, 125, and 135, respectively. In some embodiments, the curved portions may be omitted such that waveguide 1510' and electrodes 1520' and 1530' are straight.

[0130] Optical device 1500B has an electro-optic effect that occurs 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 waveguide 1510'. Therefore, electrode 1540 is also shown. Although not shown, electrode 1540 may have an extension. Also shown are electrode curved sections 1525', 1535', and 1545, as well as waveguide curved sections 1515' and 1545. Therefore, in addition to the benefits described herein with respect to optical devices (such as optical devices 100, 100', 100", 100'", 100''", and / or 1500A), optical device 1500B may have improved velocity matching and, therefore, improved performance.

[0131] Figure 16A portion of optical device 1600 is shown, including waveguide 1610 and electrodes 1620 and 1630. Electrodes 1620 and 1630 include extensions 1624 and 1634, respectively. Only one extension 1624 and one extension 1634 are labeled. The channel regions of electrodes 1620 and 1630 are not labeled. Waveguide 1610 includes curved segments 1615, only one of which is labeled. Similarly, electrodes 1620 and 1630 include curved segments 1625 and 1635, only one of which is labeled for each electrode. Curved segments 1615, 1625, and 1635 allow a long waveguide 1610 and long electrodes 1620 and 1630 to occupy a smaller area. Furthermore, as described below, curved sections 1615, 1625, and 1635 can be used to mitigate velocity mismatches, and therefore phase mismatches, between microwave signals carried by electrode(s) 1620 and / or 1630 and optical signals 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 on top of waveguide 1610, and additional electrodes may be introduced to provide the necessary electric field distribution.

[0132] Figure 17 A portion of an optical device 1700 is shown, including a waveguide 1710 and electrodes 1720 and 1730. Optical device 1700 is similar to optical device(s) 100, 100', 100", 100'", and / or 100'". Accordingly, similar structures have been labeled similarly. Thus, optical device 1700 includes a waveguide 1710 having a ridge 1712 and a thin film portion 1714, and electrodes 1720 and 1730, which are similar to waveguide 110' having a ridge 112 and a thin film portion 114, and electrodes 120 and 130, respectively. Electrodes 1720 and 1730 include extensions 1724 and 1734, respectively, which are similar to extensions 124, 124', 124", and 134, 134', 134". Extensions 1724 and 1734 may be etched onto, partially into, completely into, or through the membrane portion 1714 of the waveguide 1712. Optical device 1700 may share the benefits of optical device(s) 100, 100', 100", and 100'".

[0133] Figure 18A portion of an optical device 1800 is shown, including a waveguide 1810 and electrodes 1820 and 1830. Optical device 1800 is similar to optical device(s) 100, 100', 100", 100'", and / or 100''. Accordingly, similar structures are labeled similarly. Optical device 1800 thus includes a waveguide 1810 having a ridge 1812 and a thin film portion 1814, and electrodes 1820 and 1830, which are similar to waveguide 110' having a ridge 112 and a thin film portion 114, and electrodes 120 and 130, respectively. Electrodes 1820 and 1830 include extensions 1824 and 1834, respectively, that are similar to extensions 124, 124', 124", and 134, 134', 134". Substrate 1801 is similar to substrate 101. Also indicated is a void 1802 in substrate 1801 and an additional layer 1803. Void 1801 is at least partially filled with layer 1803. In some embodiments, layer 1803 may be a dielectric. In some embodiments, layer 1803 may be a metal or other layer. Layer 1803 may be used to engineer the mechanical integrity or microwave properties of optical device 1800. In some embodiments, substrate 1802 may be completely removed. In such embodiments, layer 1803 (if present) may extend across optical device 1800. In some embodiments, void 1802 may have different shapes, such as a semi-cylindrical shape, multiple voids 1802 may be formed, and / or layer 1803 may be omitted. Furthermore, void(s) 1802 may not extend the entire height of the substrate. In some embodiments, void(s) 1802 are formed from the front side of substrate 1801, for example, by etching substrate 1801 from the same side as waveguide 1810. In some embodiments, void(s) 1802 may also extend across multiple waveguides and / or electrodes. Optical device 1800 may share the benefits of optical device(s) 100 , 100 ′, 100 ″, and 100 '″.

[0134] Figure 19A portion of an optical device 1900 is shown, including a waveguide 1910 and electrodes 1920 and 1930. Optical device 1900 is similar to optical device(s) 100, 100', 100", 100'", and / or 100''. Accordingly, similar structures are labeled similarly. Optical device 1900 thus includes a waveguide 1910 having a ridge 1912 and a thin film portion 1914, and electrodes 1920 and 1930, which are similar to waveguide 110' having a ridge 112 and a thin film portion 114, and electrodes 120 and 130, respectively. Electrodes 1920 and 1930 include extensions 1924 and 1934, respectively, which are similar to extensions 124, 124', 124", and 134, 134', 134". Substrate 1901 is similar to substrate 101. Also indicated is a void 1902 in substrate 1901 and an additional layer 1903, which are similar to void 1802 and additional layer 1803 in substrate 1801. A second layer 1904 is also provided, which may be a metal support or other layer. Layers 1903 and 1904 may be used to engineer the mechanical integrity or microwave properties of optical device 1900. Optical device 1900 may share the benefits of optical device(s) 100, 100', 100", and 100'".

[0135] Figure 20 A portion of an optical device 2000 is shown, including a waveguide 2010 and electrodes 2020 and 2030. Optical device 2000 is similar to optical device(s) 100, 100', 100", 100'", and / or 100''. Accordingly, similar structures are labeled similarly. Thus, optical device 2000 includes a waveguide 2010 having a ridge 2012 and a thin film portion 2014, and electrodes 2020 and 2030, which are similar to waveguide 110' having a ridge 112 and a thin film portion 114, and electrodes 120 and 130, respectively. Electrodes 2020 and 2030 include extensions 2024 and 2034, respectively, which are similar to extensions 124, 124', 124", and 134, 134', 134". Substrate 2005 can be similar to substrate 101 and / or can be an underlying layer such as silicon dioxide. The optical device is transferred to a different substrate 2006 for large-scale processing on another material platform, such as Si. In this case, the original optical device is flipped and mounted on the second substrate 206. Furthermore, the second substrate 2006 may undergo additional processing. For example, voids similar to void 1802 may be formed and fully or partially refilled. Furthermore, in some embodiments, the underlying layer / substrate 2005 may be removed. Optical device 2000 may share the benefits of optical device(s) 100, 100', 100", and 100'".

[0136] Figure 21 A rear view of a portion of an optical device 2100 including a waveguide 2110 and electrodes (not shown) is shown. The optical device 2100 is similar to the optical device(s) 100, 100', 100", 100''' and / or 100''''. Accordingly, similar structures have similar references. The optical device 2100 thus includes a waveguide 2110 having a ridge 2112 and a thin film portion (not shown), and electrodes (not shown) that are similar to the waveguide 110' having a ridge 112 and a thin film portion 114, the electrode 120, and the electrode 130, respectively. The substrate 2001 is similar to the substrate 101. A void 2002 in the substrate 2001 is also indicated. Structural features 2160, 2162, and 2164 are also shown. As shown in FIG. Figure 21 As shown in , such structural features may extend completely or partially across void 2002, may be parallel to some or all of the other structural features, may be arranged in a pattern, and / or may be perpendicular to the direction of transmission of the optical signal or at another angle. For example, structural features 2160, 2162, and 2164 may extend across void 2002 by at least ten percent and no more than ninety percent. In some such embodiments, structural features 2160, 2162, and 2164 may extend across void 2002 by at least thirty percent and no more than eighty percent. Support structures 2160, 2162, and 2164 may be formed by partially removing substrate 2101 when forming void 2102. Thus, structural features 2160, 2162, and / or 2164 may remain after void 2106 is formed. In some embodiments, structural features 2160, 2162, and 2164 may be formed from other materials. Optical device 2100 may share the benefits of optical device(s) 100 , 100 ′, 100 ″, and 100 '″.

[0137] Figure 22A plan view of a portion of an optical device 2200 is shown. Optical device 2100 is similar to optical device(s) 100, 100', 100", 100'", and / or 100''. Accordingly, similar structures are labeled similarly. Optical device 2200 includes waveguides 2210 and 2250 and electrodes 2220, 2230, and 2240, which are similar to waveguides 110' and 150, and electrodes 120, 130, and 150, respectively. Electrodes 2220, 2230, and 2240 include channel portions 2222, 2232, and 2242, and extensions 2224, 2234, and 2244, respectively, which are similar to channel portions 122, 132, and 142, and extensions 224, 234, and 244. Also shown are a splitter 2216 and a combiner 2218. Thus, optical device 2200 can be considered to be configured as an interferometer. Thus, the optical devices described herein can be incorporated into various devices. Devices such as optical device 2200 can share the benefits of (one or more) optical devices 100, 100', 100", and 100'".

[0138] Figure 23 A plan view of a portion of an optical device 2300 is shown. The optical device 2300 is similar to the optical device(s) 100, 100', 100", 100''', and / or 100'''. Accordingly, similar structures have been labeled similarly. The optical device 2300 includes waveguides 2310 and 2350 (e.g., arms of the waveguides) and electrodes 2320 and 2330, which are similar to the waveguides 110' and 150 and electrodes 120 and 130, respectively. The electrodes 2320 and 2330 include channel portions 2322 and 2332, respectively, and extensions 2324 and 2334, which are similar to the channel portions 122, 132, and 142, and extensions 224, 234, and 244, respectively. Figure 23 As can be seen in FIG, extensions 2334 and 2324 include metal bridges that extend on top 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 can share the benefits of optical device(s) 100, 100', 100", and 100'".

[0139] Figure 24A plan view of a portion of an optical device 2400 is shown. Optical device 2400 is similar to optical device(s) 100, 100', 100", 100''', and / or 100'''. Accordingly, similar structures have been labeled similarly. Optical device 2400 includes waveguides 2410 and 2450 and electrodes 2420 and 2430, which are similar to waveguides 110' and 150 and electrodes 120 and 130, respectively. Electrodes 2420 and 2430 include channel portions 2422 and 2432, and extensions 2424 and 2434, respectively, which are similar to channel portions 122 and 132 and extensions 224 and 234. Figure 24 As can be seen in FIG, extensions 2434 and 2424 include metal bridges extending over the tops of waveguides 2410 and 2550 and additional retrograde features to position and configure extensions 2424 and 2434 so that the fields on waveguides 2410 and 2450 are more symmetric.

[0140] More specifically, to induce opposite motions in waveguides 2410 and 2450, extensions 2424 and 2434 are connected to opposite polarities via a first positive metal bridge extending atop waveguides 2450 and 2410, respectively. The metal bridges connect the retrograde portions of extensions 2424 and 2434 to channel regions 2422 and 2432, respectively, while inducing minimal optical loss in waveguides 2410 and 2450. Furthermore, providing a second set of retrograde portions of extensions 2424 and 2434 on opposite sides of waveguides 2410 and 2450 makes the geometry of optical device 2400 symmetrical. Optical device 2400 exhibits smaller modulator chirp (the difference in modulation intensity between the two waveguides 2410 and 2450) than optical device 2300, at the expense of increased design complexity and potentially reduced microwave bandwidth. Optical device 2400 may share the benefits of optical device(s) 100 , 100 ′, 100 ″, and 100 '″.

[0141] Figure 25A plan view of a portion of an optical device 2500 is shown. Optical device 2500 is similar to optical device(s) 100, 100', 100", 100'", and / or 100''. Accordingly, similar structures have been labeled similarly. Optical device 2500 includes waveguides 2510 and 2550 and electrodes 2520, 2530, and 2540, which are similar to waveguides 110' and 150, and electrodes 120, 130, and 140, respectively. Electrodes 2520, 2530, and 2540 include channel portions 2522, 2532, and 2542, and extensions 2524, 2534, and 2544, respectively, which are similar to channel portions 122, 132, and 142, and extensions 224, 234, and 244. Furthermore, the electrodes 2520, 2530, and 2540 are divided into three segments along the waveguides 2510 and 2550. The segmented electrodes 2520, 2530, and 2540 can also be used with a distributed driver scheme, where each electrode pair (2520 and 2530 or 2530 and 2540) includes multiple electrode segments. 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. Physical or electronic 110a-110c electrical delays 2580, 2582, and 2584 can be introduced between each individual driver 2570, 2572, and 2574 to mitigate velocity mismatches between the optical signal in the waveguides 2510 and 2550 and the electrode signals in the electrodes 2520, 2530, and 2540. Optical device 2500 may share the benefits of optical device(s) 100 , 100 ′, 100 ″, and 100 '″.

[0142] Therefore, already in Figure 1A-25 Various combinations of features of optical devices are described in the context of

[0014] These features can be combined in a variety of ways. Thus, low-loss waveguides comprising thin-film nonlinear optical materials fabricated as described herein, electrodes having extensions and channel regions, curved waveguide and electrode sections that allow for velocity matching between microwave and optical signals, low microwave loss characteristics, low voltage electrode signals, low optical loss, longer waveguides that occupy a smaller amount of area, and / or other features described herein can be combined in ways (one or more) not explicitly shown. Thus, high-performance optical devices, such as optical modulators, can be provided.

[0143] For example, Figure 26 26 is a block diagram illustrating an exemplary embodiment of a device 2600 formed using an optical modulator 2610. In some embodiments, the device 2600 is a transmissive 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 Figure 1A-25

[00105] Thus, optical modulator 2610 having one or more of the following can be combined in a manner not explicitly shown: a low-loss waveguide comprising thin-film nonlinear optical material fabricated as described herein, an electrode having an extension and a channel region, curved sections of waveguide and electrode that allow for velocity matching between microwave and optical signals, low microwave loss characteristics, a low voltage electrode signal, low optical loss, a longer waveguide that occupies a smaller amount of area, and / or other characteristics described herein. Thus, a high-performance optical modulator 2610 can be used in device 2600.

[0144] Also shown is an optional driver 2620 for driving the electrodes of optical modulator 2610. Driver 2620 can be a radio frequency driver. Because lower voltages can be used to drive the electrodes of optical modulator 2610, driver 2620 can be omitted. Therefore, in some embodiments, optical modulator 2610 can be driven by the input data signal from TOSA 2600. In other embodiments, driver 2620 can be utilized. However, lower voltages can be employed. Similarly, because optical modulator 2610 utilizes low-loss waveguides, input optical signals, such as from one or more lasers, can have lower power. Thus, using optical modulators such as those described herein can provide devices with improved performance.

[0145] Figure 27 2 is a flow chart illustrating an embodiment of a method 2700 for forming an optical modulator with improved performance. The method 2700 is described in the context of a process that may have sub-processes. Although described in a particular order, another order that is inconsistent with the description herein may be utilized.

[0146] At 2702, an optical waveguide is provided. 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, a mask for the nonlinear optical material can be patterned using ultraviolet (UV) and / or deep ultraviolet (DUV) lithography. 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 lithography. A hard mask is formed from the hard mask layer by transferring the mask pattern to the hard mask layer. For example, portions of the hard mask layer exposed by holes in the mask can be selectively etched. The hard mask can have recesses or holes in the areas where the hard mask layer is etched. The hard mask pattern can be transferred to the thin film layer of nonlinear optical material, for example using one or more physical etching processes. In some cases, fabrication is performed in a stitching area of ​​at least 10 mm by 10 mm. In some embodiments, the stitching area can be at least 15 mm by 15 mm. In some embodiments, each stitching area is at least 20 mm by 20 mm. In some embodiments, a curved section is also provided. Thus, a low-loss, high electro-optical effect waveguide can be provided that can have a curved section.

[0147] At 2704, electrodes having the desired configuration are provided. For example, the electrodes may be evaporated or electroplated at 2704. In some embodiments, 2704 includes providing an electrode(s) having a channel region and an extension. The extension may be configured as described herein. In some embodiments, the electrode(s) are further configured to have a curved section. Fabrication of the optical modulator may then be completed.

[0148] For example, method 2700 can be used to provide optical modulator 100'. Waveguide 110' can be fabricated at 2702. A thin film of nonlinear optical material is provided and etched to form ridge 112. Furthermore, curved segments, such as curved segment 1515, are also provided via etching at 2202. Electrodes 120 and 130 are formed at 2704. Thus, channel regions 122 and 132 and extensions 124 and 134 are formed. Electrode curved segments, such as segment 1525, are also fabricated at 2704.

[0149] For example, using method 2700, a device using an electrode having an extension and similar to Figures 1A to 25An example of such a modulator is fabricated on a 600 nm thick x-cut thin film LN on a quartz wafer with a 300 nm etch depth. In some embodiments, the RF Vπ measured at 1 GHz for 10 and 20 mm long modulators using a 5 micron electrode gap (e.g., the distance between extensions 124 and 134) is 2.3 V and 1.3 V, translating to RF voltage-length products (Vπ*L) of 2.3 and 2.6 V*cm, respectively. The extinction of some embodiments of such a modulator was measured to be greater than 25 dB, and on-chip losses were estimated to be less than 1 dB. In some embodiments, optical devices provided using electrodes including extensions have an RF loss (microwave loss) of only 2 dB / cm at 50 GHz, compared to 7 dB / cm for a conventional electrode design (e.g., without extensions) of the same electrode thickness (e.g., 800 nm) and material used (e.g., Au). As a result of the skin effect in the metal, the ohmic loss α0 in the electrode is ∞L -1 f -1 / 2 , where L is the length of the electrode and f is the microwave frequency. 0,ext =0.26dBcm -1 GHz -1 / 2 In contrast, conventional electrodes on thin film LN have α 0,reg =0.69dBcm -1 GHz -1 / 2 In some embodiments, the ultra-low RF loss enables an EO response of only 0.8 (1.7) dB attenuation measured for a 10 mm (20 mm) modulator at 50 GHz, compared to a reference Vπ at 1 GHz. In other words, the RF Vπ at 50 GHz is 2.5 V (1.6 V) for an embodiment of a 10 mm (20 mm) optical modulator utilizing segmented electrodes. The electrical reflection from the electrodes remains below -15 dB for all frequencies. In some embodiments, the use of a lower refractive index substrate such as fused silica or air allows for further separation of the extensions while maintaining velocity matching to the optical signal.

[0150] Thus, using method 2700, an optical modulator having a low-loss thin-film nonlinear optical material waveguide including a bend is provided. Furthermore, an electrode including a channel region, an extension, and a bend section is fabricated. Thus, an optical modulator can be provided that exhibits low optical signal loss, low electrode loss, consumes a controllable amount of area, and / or provides desired optical modulation at low voltages. Consequently, the performance of the optical modulator can be improved.

[0151] Although the foregoing embodiments have been described in some detail for purposes of clarity of understanding, the invention is not limited to the details provided. There are many alternative ways of implementing the invention. The disclosed embodiments are exemplary and not restrictive.

Claims

1. An optical device comprising: a waveguide comprising at least one optical material having an electro-optical effect, the at least one optical material comprising lithium, the waveguide comprising a ridge portion; as well as an electrode comprising a channel region and a plurality of extensions protruding from the channel region, the plurality of extensions being closer to the ridge portion of the waveguide than the channel region, the electrode being configured to carry an electrical signal having a microwave mode, the waveguide and the electrode being located on a substrate structure having a substrate microwave dielectric constant of less than 11 in a region intersecting the microwave mode, the substrate structure comprising a combination of a substrate having a high microwave dielectric constant greater than 11 and an underlying layer having a dielectric constant less than 11; wherein the electrode is configured such that a microwave mode of an electrical signal carried in the channel region intersects the at least one optical material comprising lithium and intersects a portion of the substrate structure comprising a first portion of the underlying layer and a second portion of the substrate, and Wherein, the plurality of extensions are spaced apart from the ridge portion.

2. The optical device according to claim 1, wherein The plurality of extensions have a pitch smaller than a wavelength of microwaves in the electrode divided by π, and the pitch is no greater than a length corresponding to a Bragg frequency of the electrode.

3. The optical device according to claim 2, wherein: The waveguide is configured to carry an optical signal, and wherein the at least one optical material has a microwave dielectric constant of at least 1.5 times the optical dielectric constant of the optical and electrical signals.

4. The optical device according to claim 1, wherein The waveguide carries an optical signal, and wherein the plurality of extensions are configured to reduce a path difference between the electrical signal and the optical signal due to a velocity mismatch between the optical signal and the electrical signal.

5. The optical device according to claim 1, wherein The plurality of extensions have at least one distance from the waveguide such that a total optical loss is less than 8 dB, the at least one distance corresponding to an optical intensity of an optical signal at the plurality of extensions being less than -10 dB of a maximum optical intensity in the waveguide. The optical device according to claim 1 , wherein: The plurality of extensions have positions selected from a first position between the substrate structure and the channel region and a second position such that the channel region is located between the substrate structure and the plurality of extensions.

7. The optical device according to claim 1, wherein The substrate structure has a void therein that is aligned with the ridge portion and the plurality of extensions of the waveguide.

8. The optical device according to claim 1, wherein The plurality of extensions have a length that is less than a wavelength of microwaves in the electrode divided by π.

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

10. The optical device according to claim 1, wherein Each of the plurality of extensions includes a retrograde portion and a connection portion coupled to the channel region, the connection portion being between the retrograde portion and the channel region.

11. The optical device according to claim 1, wherein The electrode has a frequency-dependent electrode loss of less than 0.8 dB per square root of the electrical signal frequency per centimeter for a frequency window within a frequency range from DC to no more than 500 GHz, the frequency window being at least 10 GHz.

12. The optical device according to claim 1, wherein The electrode has an absorptive electrode loss of less than 0.005 dB per centimeter per GHz for a frequency window in electrical signal frequencies from DC to no more than 500 GHz, the frequency window being at least 10 GHz.

13. The optical device according to claim 1, wherein The electrode comprises an electrode bend section, wherein the waveguide comprises a waveguide bend section, and wherein the electrode bend section and the waveguide bend section are configured to provide a path difference between an optical signal for the waveguide and an electrical signal for the electrode.

14. The optical device according to claim 1, further comprising: An additional electrode includes an additional channel region and an additional plurality of extensions, the additional plurality of extensions being located closer to the ridge portion of the waveguide than the additional channel region.

15. A subassembly comprising: An optical modulator, the optical modulator comprising a waveguide and an electrode, the waveguide comprising at least one optical material having an electro-optic effect, the at least one optical material comprising lithium, the waveguide comprising a ridge portion, the electrode comprising a channel region and a plurality of extensions, the plurality of extensions being located between the channel region and the waveguide, the plurality of extensions being closer to the ridge portion of the waveguide than to the channel region, the electrode being configured to carry an electrical signal having a microwave mode, the waveguide and the electrode being located on a substrate structure having a substrate microwave dielectric constant of less than 11 in a region intersecting the microwave mode, the substrate structure comprising a combination of a substrate having a high microwave dielectric constant greater than 11 and a lower layer having a dielectric constant less than 11; wherein the electrode is configured such that a microwave mode of an electrical signal carried in the channel region intersects the at least one optical material comprising lithium and intersects a portion of the substrate structure, the portion of the substrate structure comprising a first portion of the underlying layer and a second portion of the substrate; and a driver coupled to the optical modulator and configured to electrically drive the electrode, Wherein, the plurality of extensions are spaced apart from the ridge portion.

16. A method for providing an optical device, comprising: providing a waveguide comprising at least one optical material, the at least one optical material comprising lithium and having an electro-optic effect, providing the waveguide comprising providing a ridge portion of the waveguide; as well as Provide electrodes including: providing a channel region; and providing a plurality of extensions protruding from the channel region, the plurality of extensions being closer to the ridge portion of the waveguide than the channel region, the electrode being configured to carry an electrical signal having a microwave mode, the waveguide and the electrode being located on a substrate structure having a substrate microwave dielectric constant of less than 11 in a region intersecting the microwave mode, the substrate structure comprising a combination of a substrate having a high microwave dielectric constant greater than 11 and an underlying layer having a dielectric constant less than 11; wherein the electrode is configured such that a microwave mode of an electrical signal carried in the channel region intersects the at least one optical material comprising lithium and intersects a portion of the substrate structure comprising a first portion of the underlying layer and a second portion of the substrate, and Wherein, the plurality of extensions are spaced apart from the ridge portion.

17. The method according to claim 16, wherein Providing the plurality of extensions further comprises: The plurality of extensions are fabricated at a pitch less than a wavelength of microwaves in the electrode divided by π, the pitch being no greater than a length corresponding to a Bragg frequency of the electrode.

18. The method according to claim 16, wherein The waveguide carries an optical signal, the electrode carries an electrical signal, and wherein providing the plurality of extensions further comprises: The plurality of extensions are configured to reduce a path difference between the electrical signal and the optical signal due to a speed mismatch between the optical signal and the electrical signal.

19. The method according to claim 16, wherein The electrode has a frequency-dependent electrode loss of less than 0.8 dB per square root of the electrical signal frequency per centimeter for a frequency window within a frequency range from DC to no more than 500 GHz, the frequency window being at least 10 GHz.

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