High-gain differential electro-optic modulator

Abstract

To provide a differential electro-optic modulator that achieves very high modulation bandwidth and / or efficiency.SOLUTION: An optical modulator 100 includes a Mach-Zehnder interferometer including (i) a first optical waveguide including a first semiconductor junction diode, and (ii) a second optical waveguide including a second semiconductor junction diode. A semiconductor region connects the first and second semiconductor junction diodes such that a distance between the first and second optical waveguides is less than 2.0 μm for at least a portion of a longitudinal direction of the optical modulator. In another aspect, a method of modulating an optical signal includes splitting input light into first and second optical transmission paths; modulating a phase difference between light 102 in the first optical transmission path and light 104 in the second optical transmission path without applying a bias voltage through an impedance less than 100 Ω between the first and second optical transmission paths; and combining light that is output from the first and second optical transmission paths.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] (Technical field) FIELD OF THE DISCLOSURE The present disclosure relates generally to electro-optic differential modulators. [Background technology]

[0002] (background) In optical communication systems, electro-optic modulators provide the fundamental mechanism for modulating optical waveforms to transmit information. Generally, electro-optic modulators function by modulating one or more characteristics of an optical waveform in accordance with information, such as digital data, provided by an electrical signal. Summary of the Invention [Means for solving the problem]

[0003] (overview) FIELD OF THE DISCLOSURE Implementations of the present disclosure generally relate to electro-optic actuation modulators.

[0004] One general aspect includes an optical modulator comprising a Mach-Zehnder interferometer having (i) a first optical waveguide having a first semiconductor junction diode, and (ii) a second optical waveguide having a second semiconductor junction diode, the optical modulator also comprising a semiconductor region connecting the first semiconductor junction diode to the second semiconductor junction diode such that the distance between the first optical waveguide and the second optical waveguide is less than 2.0 μm along at least a portion of the length of the optical modulator.

[0005] Implementations may include one or more of the following features. In the optical modulator, the first semiconductor junction diode comprises a first anode and a first cathode, and the second semiconductor junction diode comprises a second anode and a second cathode. In the optical modulator, the first anode is connected to the second anode through a semiconductor region spanning the distance between the first optical waveguide and the second optical waveguide. In the optical modulator, the semiconductor region between the first anode and the second anode is configured without any external voltage connection with an impedance of less than 100 Ω. The optical modulator may further comprise: a first electrode connected to the first cathode and configured to apply a first electric field to the first optical waveguide; or a second electrode connected to the second cathode and configured to apply a second electric field to the second optical waveguide. The optical modulator further comprises a radio frequency (RF) transmission line configured to: (i) apply a first voltage to the first cathode via the first electrode, and (ii) apply a second voltage to the second cathode via the second electrode. In the optical modulator, the first optical waveguide comprises a plurality of first semiconductor junction diodes, and the second optical waveguide comprises a plurality of second semiconductor junction diodes. In the optical modulator, the RF transmission line is configured to (i) apply a first voltage to the plurality of first semiconductor junction diodes via the plurality of first electrodes, and (ii) apply a second voltage to the plurality of second semiconductor junction diodes via the second plurality of electrodes. In the optical modulator, in a first portion of the optical modulator, the first optical waveguide is at least 0.04 μm wider than the second optical waveguide, and in a second portion of the optical modulator, the second optical waveguide is at least 0.04 μm wider than the first optical waveguide. In an optical modulator, in at least a portion of the optical modulator: a first optical waveguide increases in width along a longitudinal direction of the optical modulator, and a second optical waveguide decreases in width along a longitudinal direction of the optical modulator. In the optical modulator, a first semiconductor junction diode comprises a first p-doped region and a first n-doped region, and a second semiconductor junction diode comprises a second p-doped region and a second n-doped region.In the optical modulator, the first p-doped region is connected to the second p-doped region through a third p-doped region of the semiconductor region connecting the first semiconductor junction diode to the second semiconductor junction diode. In the optical modulator, the third p-doped region is configured without any external voltage connection with an impedance of less than 100 Ω. In the optical modulator, the first semiconductor junction diode further comprises a first oxide layer between the first p-doped region and the first n-doped region, and the second semiconductor junction diode further comprises a second oxide layer between the second p-doped region and the second n-doped region. In the optical modulator, the Mach-Zehnder interferometer further comprises an optical splitter configured to receive input light and split the input light into the first optical waveguide and the second optical waveguide. The optical modulator may further include an optical combiner configured to receive the first output light from the first optical waveguide and the second output light from the second optical waveguide and combine the first output light into the second output light, wherein the distance between the first optical waveguide and the second optical waveguide is the distance between the inner wall of the first optical waveguide and the inner wall of the second optical waveguide.

[0006] Another general aspect includes an optical modulator comprising an optical splitter configured to split input light into a first optical transmission path and a second optical transmission path. The optical modulator also comprises means for modulating a phase difference between light in the first optical transmission path and light in the second optical transmission path without applying a bias voltage across an impedance of less than 100 ohms between the first optical transmission path and the second optical transmission path. The optical modulator also comprises an optical combiner configured to combine light output from the first optical transmission path and light output from the second optical transmission path.

[0007] Implementations may have one or more of the following features. The optical modulator further comprises a radio frequency (RF) transmission line configured to: (i) apply a first voltage to the first optical transmission line via a first electrode, and (ii) apply a second voltage to the second optical transmission line via a second electrode. In the optical modulator, the first optical transmission line comprises a first semiconductor junction diode and the second optical transmission line comprises a second semiconductor junction diode, and during modulation, the first semiconductor junction diode is at a voltage slightly below turn-on while the second semiconductor junction diode is at a maximum reverse voltage. In the optical modulator, the phase difference between light in the first optical transmission line and light in the second optical transmission line is modulated in a push-pull mode by applying a first electric field to the first optical transmission line and a second electric field to the second optical transmission line. In the optical modulator, the phase difference between the light in the first optical transmission line and the light in the second optical transmission line is modulated while maintaining the finite depletion regions of the semiconductor junction diodes in the first optical transmission line and the second optical transmission line.

[0008] Another general aspect includes a method of modulating an optical signal, the method including: splitting input light into a first optical transmission line and a second optical transmission line. The method also includes modulating a phase difference between light in the first optical transmission line and light in the second optical transmission line without applying a bias voltage across an impedance of less than 100 ohms between the first optical transmission line and the second optical transmission line. The method also includes combining light output from the first optical transmission line and light output from the second optical transmission line.

[0009] Implementations may include one or more of the following features: In a method, a phase difference between light in a first optical transmission line and light in a second optical transmission line is modulated while maintaining finite depletion regions of semiconductor junction diodes in each of the first optical transmission line and the second optical transmission line.

[0010] Another general aspect includes an optical modulator comprising a Mach-Zehnder interferometer having (i) a first optical waveguide having a first semiconductor junction diode, and (ii) a second optical waveguide having a second semiconductor junction diode. The optical modulator also comprises a semiconductor region connecting a terminal of the first semiconductor junction diode to a terminal of the second semiconductor junction diode. The terminal of the first semiconductor junction diode and the terminal of the second semiconductor junction diode are either both p-doped anodes or both n-doped cathodes. The semiconductor region is not connected to other circuit elements through an impedance of less than 100 Ω.

[0011] The details of one or more implementations of the subject matter of this disclosure are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the following description, drawings, and claims. [Brief explanation of the drawings]

[0012] BRIEF DESCRIPTION OF THE DRAWINGS [Figure 1] FIG. 1 shows an example of a top view of a differential modulator implementing a bias voltage connection between waveguides.

[0013] [Figure 2] FIG. 2 shows an example cross section of a modulator implementing a bias voltage connection between the waveguides.

[0014] [Figure 3] FIG. 3 shows an example of an equivalent circuit along a cross section of a modulator implementing bias voltage connections between the waveguides.

[0015] [Figure 4] FIG. 4 shows another example of a cross section of a modulator implementing a bias voltage connection between the waveguides.

[0016] [Figure 5] FIG. 5 illustrates an example of a top view of a modulator according to an implementation of the present disclosure.

[0017] [Figure 6] FIG. 6 illustrates another example of a top view of a modulator according to an implementation of the present disclosure.

[0018] [Figure 7] FIG. 7 illustrates an example of a top view of a modulator showing variations in the width of an optical waveguide, according to an implementation of the present disclosure.

[0019] [Figure 8] FIG. 8 illustrates an example cross section of a modulator according to an implementation of the present disclosure.

[0020] [Figure 9] FIG. 9 shows an example of an equivalent circuit along a cross section of a modulator according to an implementation of the present disclosure.

[0021] [Figure 10] FIG. 10 illustrates another example cross section of a modulator according to an implementation of the present disclosure.

[0022] [Figure 11] FIG. 11 shows an example of the performance of different modulators in terms of conductance per unit length between the V+ and V− terminals as a function of the distance between the waveguides.

[0023] [Figure 12] FIG. 12 shows an example of the performance of different modulators in terms of the voltage across each semiconductor junction diode as a function of an applied differential voltage ΔV across the two terminals of the modulator.

[0024] [Figure 13] FIG. 13 shows an example of the performance of a modulator according to an implementation of the present disclosure in terms of the normalized differential refractive index change between the two waveguides of the modulator as a function of the distance between the waveguides for various waveguide widths.

[0025] [Figure 14] FIG. 14 is a flowchart illustrating an example of modulating an optical signal according to an implementation of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0026] (Detailed explanation) Disclosed herein are systems and techniques that provide novel differential electro-optic modulators capable of achieving very high modulation bandwidths and / or efficiencies. This is achieved through novel implementations that allow for a significant reduction in the physical distance between the modulator's waveguides. In some implementations, the reduction in the physical distance between the waveguides is achieved by eliminating bias voltage connections between the semiconductor junction diodes of the modulator's waveguides while maintaining a finite depletion region in the semiconductor junction diodes. In turn, the reduction in the physical distance between the diodes allows for a significant reduction in the electrical resistance between the diodes, thereby increasing the modulator's modulation bandwidth and / or efficiency. In some implementations, to mitigate potentially detrimental optical coupling between closely spaced waveguides, the waveguides have alternating widths along the length of the modulator.

[0027] 1 shows an example top view of a differential modulator 100 implementing a bias voltage connection between waveguides. This example provides a comparison with modulators according to implementations of the present disclosure, which are further described below with reference to FIGS. 5-14.

[0028] The modulator 100 is based on a Mach-Zehnder interferometer (MZI) implementation in which an optical signal propagates along the length of the modulator 100 (e.g., from left to right in FIG. 1 ) along two optical transmission lines 102 and 104. At the input of the modulator 100, an optical splitter 106 splits the input light into the two optical transmission lines 102 and 104. At the output of the modulator 100, an optical combiner 108 combines the output light from the two optical transmission lines 102 and 104. The optical splitter 106 and the optical combiner 108 can be implemented in various ways, for example, using symmetric, asymmetric, or tunable optical intensity couplers. The optical transmission lines 102 and 104 can be implemented by waveguides formed in a semiconductor structure 116, as described in further detail below with reference to FIG. 2 . In some implementations, the optical core of the waveguide, and / or the optical splitter 106, and / or the optical combiner 108 may include silicon ribs.

[0029] The modulator 100 uses a traveling-wave configuration in which a voltage applied to terminals 110 and 112 generates an electrical signal that propagates along a radio frequency (RF) transmission line 114, which is terminated in an RF termination resistor. The electrical signal in the RF transmission line 114 travels at the same speed as the light propagating along the two optical transmission lines 102 and 104, inducing electro-optic modulation in the light. Specifically, the RF transmission line 114 is connected to a semiconductor structure 116 via electrodes (described in more detail below with reference to FIG. 2 ), which apply respective voltages, and the resulting electric field spans one or both of the optical transmission lines 102 and 104. The applied voltage(s) induce a phase shift in the light propagating along one or both of the optical transmission lines 102 and 104. In some implementations, the phase shift is differential, in that the magnitude of the phase shift is equal and the sign of the phase shift is opposite between the optical transmission lines 102 and 104.

[0030] Electro-optic modulation is achieved by varying the voltage at one or both of terminals 110 and 112 to modulate the differential phase shift between the phase of the first optical transmission line 102 and the phase of the second optical transmission line 104. For example, when the terminal voltages are controlled so that the differential phase shift causes destructive interference at the optical combiner 108, this corresponds to an "off" or logic "0" state of the modulator 100. In contrast, when the terminal voltages are controlled so that the differential phase shift between the two optical transmission lines 102 and 104 causes constructive interference at the optical combiner 108, this corresponds to an "on" or logic "1" state of the modulator 100.

[0031] The differential phase shift between the two optical transmission lines 102 and 104 may also be affected by other factors. For example, the physical lengths of the optical transmission lines 102 and 104 may be the same to provide a unique differential phase shift of zero, or may be different to provide a unique differential phase shift that is not zero. Furthermore, in some implementations, direct current (DC) phase shifters 122 and 124 (e.g., thermo-optic phase shifters such as optical waveguide heaters) may be implemented near the ends of the optical transmission lines 102 and 104 to control the relative phase of the two optical signals before they are combined at the optical combiner 108.

[0032] In some implementations, phase modulation can be performed by a "push-pull" mechanism, in which the phase of light in both of the two optical transmission lines 102 and 104 is modulated to control the relative phase shift between the two optical transmission lines. In push-pull operation, the voltage V+ at terminal 110 increases and the voltage V− at terminal 112 decreases (or vice versa), resulting in a corresponding phase shift of the light in each of the optical transmission lines 102 and 104. Push-pull modulation can offer various advantages over non-push-pull modulation, such as reduced average energy consumption and reduced chirp in the modulated signal.

[0033] In some scenarios, a direct current (DC) bias connection 118 may be connected between the two optical transmission lines 102 and 104. The DC bias connection 118 is implemented such that the semiconductor junction diodes in each of the optical transmission lines 102 and 104 maintain a reverse bias even when the data signals applied to the terminals 110 and 112 vary between a logic 1 and a logic 0. Further details of the DC bias connection 118 and the semiconductor junction diodes are provided below with reference to FIG.

[0034] 2 shows an example cross-sectional view of a modulator 200 (e.g., modulator 100 of FIG. 1) that implements a bias voltage connection between waveguides. This example is provided for comparison with modulators according to implementations of the present disclosure, which are further described below with reference to FIGS. 5-14.

[0035] A cross-sectional view of modulator 200 shows details of the MZI structure. The MZI comprises a first optical waveguide 202 and a second optical waveguide 204. Optical waveguides 202 and 204 may be implemented, for example, as silicon ribbed waveguides on a slab. In some implementations, modulator 200 comprises a substrate 206 (e.g., a silicon substrate), an insulating structure 208 (e.g., a dielectric such as an oxide), and a semiconductor structure 210 (e.g., a silicon layer comprising optical waveguides 202 and 204).

[0036] Each of the optical waveguides 202 and 204 includes a semiconductor junction. The semiconductor junction diodes may be implemented, for example, by PIN (P-type / Intrinsic / N-type) junction diodes or P / N junction diodes. In the modulator 200, a P / N junction is embedded in each of the optical waveguides 202 and 204 to form a diode for each waveguide. These diodes are shown as a first semiconductor junction diode 212 and a second semiconductor junction diode 214.

[0037] The modulator 200 also includes electrodes 216 and 218 (e.g., metal electrodes) in physical contact with the silicon layer 210. In some implementations, the electrodes 216 and 218 are in physical contact with P-doped contact regions 220 and 222 of the silicon layer 210. The electrodes 216 and 218 may be formed, for example, by etching the insulating layer 208 to form metal (e.g., tungsten, copper, and / or aluminum) contacts.

[0038] Modulator 200 may also include metal layers 224 and 226 on electrodes 216 and 218. In some implementations, metal layers 224 and 226 may form segments of an RF transmission line (e.g., RF transmission line 114 of FIG. 1).

[0039] In some scenarios, a DC bias connection 228 is implemented between the two optical waveguides 202 and 204. The DC bias connection 228 ensures that the semiconductor junction diodes 212 and 214 maintain a reverse bias during modulation. For example, in a push-pull mode of modulation, a differential voltage (e.g., V+ and V−) is applied to the metal layers 224 and 226 (and thus to the electrodes 216 and 218). As the voltage (e.g., V+) at the first electrode 216 increases and the voltage (e.g., V−) at the second electrode 218 decreases, the width of the depletion region in the first optical waveguide 202 decreases while the width of the depletion region in the second optical waveguide 204 increases (and vice versa). As the depletion width changes, the effective refractive index experienced by light traveling along each of the optical waveguides 202 and 204 changes, resulting in a corresponding phase shift of the light. As a result, push-pull modulation can be achieved with the modulator 200.

[0040] In the example modulator 200, a DC bias connection 228 is formed at the cathodes 230 and 232 (N-doped regions) of the semiconductor junction diodes 212 and 214, while varying voltages V+ and V− are applied to the anodes 234 and 236 (P-doped regions) of the semiconductor junction diodes 212 and 214. The DC bias connection 228 ensures that the semiconductor junction diodes 212 and 214 maintain a reverse bias. For example, in the example modulator 200, if the bias voltage applied to the DC bias connection 228 is too low (or non-existent), a large number of carriers injected into the depletion region of the first semiconductor junction diode 212 may cause the first semiconductor junction diode 212 to operate (e.g., a forward bias of greater than 0.6 V for silicon), resulting in forward bias and slow operation. Implementing the DC bias connection 228 with a sufficiently large bias voltage ensures that the semiconductor junction diodes 212 and 214 maintain a reverse bias under modulation.

[0041] However, the structure of modulator 200 imposes various limitations on modulation performance. Specifically, the structure of modulator 200 imposes significant series electrical resistance in various regions of modulator 200.

[0042] Specifically, the presence of DC bias connection 228 increases the physical distance of semiconductor (e.g., silicon) region 238 between semiconductor junction diodes 212 and 214. This results in significant series electrical resistance in semiconductor region 238 connecting semiconductor junction diodes 212 and 214. Furthermore, typical techniques for reducing such series electrical resistance, such as increasing the silicon doping of the semiconductor structure, can have other adverse effects, such as increased optical absorption.

[0043] Furthermore, semiconductor regions 240 and 242 (which connect semiconductor junction diodes 212 and 214, respectively, to their respective electrodes 216 and 218) are P-doped semiconductor materials, which have a higher resistivity (for the same optical absorption) than N-doped semiconductor materials, resulting in a significant series electrical resistance in semiconductor regions 240 and 242 between electrodes 216 and 218 and semiconductor junction diodes 212 and 214.

[0044] As a result, the total series electrical resistance between electrodes 216 and 218 can significantly attenuate the voltage along modulator 200 due to charging and discharging of the diode capacitance. Furthermore, this attenuation typically increases as the modulation frequency increases. The resulting RF losses along modulator 200 can adversely affect the bandwidth of modulator 200.

[0045] 3 shows an example of an equivalent circuit 300 along a cross section of a modulator (e.g., a cross section of modulator 200 of FIG. 2) implementing a bias voltage connection between waveguides. This example is shown for comparison with modulators according to implementations of the present disclosure, which are further described below with reference to FIGS. 5-14.

[0046] 3, the series electrical resistance 340 between the first electrode 316 and the first semiconductor junction diode 312 (e.g., corresponding to semiconductor region 240 in FIG. 2) is 7.2 mΩ·m. The series electrical resistance 342 between the second electrode 318 and the second semiconductor junction diode 314 (e.g., corresponding to semiconductor region 242 in FIG. 2) is 7.2 mΩ·m. The series electrical resistance 338 between the semiconductor junction diodes 312 and 314 (e.g., corresponding to semiconductor region 238 in FIG. 2) is 7.4 mΩ·m (the series resistance between each of the semiconductor junction diodes 312 and 314 and the DC bias voltage connection 328 is 3.7 mΩ·m).

[0047] 4 illustrates another example cross section of a modulator 400 (e.g., another example cross section of modulator 100 of FIG. 1) implementing a bias voltage connection between waveguides. This example is provided for comparison with modulators according to implementations of the present disclosure, as further described below with reference to FIGS. 5-14.

[0048] The structure of modulator 400 is referred to as a silicon-insulator-silicon capacitor (SISCAP) modulator structure. Compared to modulator 200 of FIG. 2, modulator 400 implements thin oxide layers 444 and 446 on semiconductor junction diodes 412 and 414 of optical waveguides 402 and 404. Furthermore, in modulator 400, DC bias connection 428 applies a bias voltage to anodes 434 and 436 (P-doped regions) of semiconductor junction diodes 412 and 414, while electrodes 416 and 418 apply a varying voltage to cathodes 430 and 432 (N-doped regions) of semiconductor junction diodes 412 and 414. DC bias connection 428 ensures that semiconductor junction diodes 412 and 414 are maintained in reverse bias.

[0049] Figures 5-14 relate to modulators according to implementations of the present disclosure. In contrast to the modulators of Figures 1-4, the modulators of Figures 5-14 do not require any bias voltage connections between the waveguides, resulting in significantly lower series resistance between the electrodes and therefore wider modulation bandwidth. Furthermore, in Figures 5-14, the modulators implement a waveguide structure with varying width to mitigate detrimental optical coupling between closely spaced waveguides.

[0050] FIG. 5 illustrates an example of a top view of a modulator 500 according to an implementation of the present disclosure.

[0051] Modulator 500 is based on an MZI implementation comprising two optical transmission lines 502 and 504, an optical splitter 506, and an optical combiner 508. Modulator 500 further comprises terminals, such as terminal 510 and terminal 512, through which a voltage can be applied. The voltage travels along RF transmission line 514, which is connected to semiconductor structure 516 via respective voltage-applying electrodes, and the resulting electric field spans one or both of optical transmission lines 502 and 504.

[0052] In contrast to the modulator 100 of FIG. 1 , the modulator 500 does not implement any DC bias connection between the two optical transmission lines 502 and 504. This allows the two optical transmission lines 502 and 504 to be closer together, thus reducing the series electrical resistance between them. For example, in some implementations, the distance between the waveguides of the two optical transmission lines 502 and 504 is less than 0.5 μm along at least a portion of the length of the optical transmission lines 502 and 504. In some implementations, the distance between the waveguides is less than 2.0 μm along at least a portion of the length of the optical transmission lines 502 and 504. In some implementations, the distance between the waveguides is in the range of 0.1 μm to 2.0 μm along at least a portion of the length of the optical transmission lines 502 and 504. In some implementations, the distance between the waveguides is defined as the distance between the inner walls of two waveguides at a given point along the length of the modulator 500 (eg, point 505 in FIG. 5).

[0053] However, because the two optical transmission lines 502 and 504 are closer together, there is a risk of greater detrimental optical coupling between the light in optical transmission line 502 and the light in optical transmission line 504. To mitigate such optical coupling, in some implementations, the waveguide of one of the optical transmission lines (502 or 504) is designed to have a wider width than the other optical transmission line at the same distance along the length of the modulator 500. This helps ensure that the light traveling through the waveguides of optical transmission lines 502 and 504 is not phase-matched, thus reducing optical coupling between the two waveguides. An alternative way to understand the importance of using different waveguide widths is to look at the two eigenmodes of the coupled waveguides of optical transmission lines 502 and 504. If the waveguides have equal widths, the lowest eigenmode is an even eigenmode, and the next lowest eigenmode is an odd eigenmode. In such a scenario, differential modulation cannot occur. However, if one waveguide is significantly wider than the other, the lowest eigenmode will be composed of light primarily in the wider waveguide, and the next lowest eigenmode will be primarily in the narrower waveguide. This allows differential modulation to occur despite the close spacing of the waveguides. For example, in some implementations, one waveguide in optical transmission lines 702 or 704 is at least 0.04 μm wider than the waveguide in the other optical transmission line. In some implementations, the difference in waveguide width is in the range of 0.04 μm to 0.4 μm.

[0054] Furthermore, in such implementations, the width variations of the two waveguides can be swapped along the modulator 500, usefully ensuring that the overall length of the wider portion of each waveguide is equal and that the overall length of the narrower portion of each waveguide is equal. In the example of FIG. 5, from left to right, the waveguide of the first optical transmission line 502 is wider than the waveguide of the second optical transmission line 504 but later becomes narrower than the waveguide of the second optical transmission line 504 (alternatively, the first optical transmission line 502 may start narrow and later become wider). While the example of FIG. 5 shows one width swap in the middle of the modulator 500, some implementations may include additional width swaps. Further details of the waveguide width variations are described below with reference to FIG. 7.

[0055] Although the depiction of Figure 5 above shows an example of a modulator 500 in which the waveguide widths of the two optical transmission lines 502 and 504 are different, in other implementations the waveguides may have a constant width along the length of the modulator 500.

[0056] Furthermore, while the depiction of FIG. 5 shows an example of modulator 500 without a physical DC bias connection, in some implementations, a DC bias connection can be implemented between the two optical transmission lines 502 and 504, but via a high impedance. For example, in some implementations, the high impedance is achieved with an impedance greater than 1 kΩ. As another example, in some implementations, the high impedance is achieved with an impedance greater than 100 Ω. In such a scenario of a DC bias connection via a high impedance, a current will be generated due to the voltage difference between (i) the external voltage and (ii) the voltage that would be generated between the optical transmission lines 502 and 504 if no external voltage was applied. This generated current will be less than the sum of the diode leakage current and all photo-generated currents in the diodes, and therefore the circuit will operate primarily as if there were no applied external DC bias voltage (e.g., similar to a true floating voltage). Therefore, it should be understood that implementations of the present disclosure, such as those shown in FIGS. 5-10, in which no physical DC bias connection is present, can also be implemented with a DC bias connection, but via a high impedance.

[0057] Modulator 500 implements an example of a continuous traveling wave structure in which RF transmission line 514 is continuously connected to semiconductor structure 516. Alternatively, a segmented traveling wave structure can be implemented as described below with reference to FIG.

[0058] 6 illustrates another example of a top view of a modulator 600 according to an implementation of the present disclosure. Modulator 600 is an example of an implementation of a segmented traveling wave structure.

[0059] The modulator 600 is also based on an MZI implementation, which includes two optical transmission lines 602 and 604, an optical splitter 606, and an optical combiner 608. The modulator 600 further includes terminals, such as terminal 610 and terminal 612, through which a voltage can be applied. The voltage travels along an RF transmission line 614, which is connected to a semiconductor structure 616 via respective voltage-applying electrodes, and the resulting electric field spans one or both of the optical transmission lines 602 and 604. The modulator 600 also does not implement any DC bias connection between the two optical transmission lines 602 and 604, which would shorten the distance between them. For example, in some implementations, the distance between the waveguides of the two optical transmission lines 602 and 604 is less than 0.5 μm along at least a portion of the length of the optical transmission lines 602 and 604. In some implementations, the distance between the waveguides is less than 2.0 μm along at least a portion of the length of the optical transmission lines 602 and 604. In some implementations, the distance between the waveguides is in the range of 0.1 μm to 2.0 μm along at least a portion of the length of the optical transmission lines 602 and 604. In some implementations, the distance between the waveguides is defined as the distance between the inner walls of two waveguides at a given point along the length of the modulator 600 (e.g., point 605 in FIG. 6).

[0060] The differences between the modulator 500 of FIG. 5 and the modulator 600 of FIG. 6 arise from the configuration of the semiconductor structures (516, 616) and the manner in which the RF transmission lines (514, 614) are connected to the semiconductor structures (516, 616). The modulator 500 of FIG. 5 implements a continuous traveling wave structure, in which the RF transmission line 514 is continuously and directly connected to the semiconductor structure 516. In contrast, the modulator 600 of FIG. 6 implements a segmented traveling wave structure, in which the RF transmission line 614 is intermittently connected to segments of the semiconductor structure 616, with no semiconductor structure present in the intermittent regions 620 along the optical transmission paths 602 and 604. This structure of the modulator 600, sometimes referred to as a capacitively loaded traveling wave structure, has the advantage of providing additional degrees of freedom in the implementation of the RF transmission line 614, e.g., the average capacitance per unit length of the RF transmission line 614. Lumped-element modulators can also benefit from the techniques disclosed herein.

[0061] Furthermore, in modulator 600, the waveguides of optical transmission lines 602 and 604 have different widths in different portions of modulator 600, similar to the waveguide structure of modulator 500 of Figure 5. Further details of the variations in waveguide width are provided below with reference to Figure 7.

[0062] 7 shows an example of a top view of a width swap region of a modulator 700 illustrating the variation in width of an optical waveguide according to an implementation of the present disclosure (e.g., modulator 500 of FIG. 5 or modulator 600 of FIG. 6). In some implementations, the width swap region is implemented between semiconductor regions 616 of FIG. 6.

[0063] The modulator 700 comprises two optical transmission lines 702 and 704, which may be implemented by silicon ribbed waveguides. Furthermore, as discussed above with reference to Figures 5 and 6, the modulator 700 does not implement any DC bias connections, thus allowing the two optical transmission lines 702 and 704 to be closer together, thereby reducing the series electrical resistance between them.

[0064] To reduce detrimental optical coupling between the closer waveguides of optical transmission lines 702 and 704, one of optical transmission lines 702 or 704 has a wider waveguide than the waveguide of the other optical transmission line. This is useful to ensure that optical coupling between the two waveguides is reduced because the light traveling in the waveguides of optical transmission lines 702 and 704 is not phase-matched. For example, in some implementations, the waveguide of one of optical transmission lines 702 or 704 is at least 0.04 μm wider than the waveguide of the other optical transmission line.

[0065] Additionally, the variations in the widths of the two waveguides can be interchanged along the modulator 700. For example, in FIG. 7, in portion 722 of modulator 500, the waveguide of second optical transmission line 704 is wider than the waveguide of first optical transmission line 702. Then, in portion 724 of modulator 700, the waveguide of first optical transmission line 702 is wider than the waveguide of second optical transmission line 704. In some implementations, the difference in the widths of the waveguides is at least 0.04 μm. In some implementations, the difference in the widths of the waveguides is in the range of 0.04 μm to 0.4 μm.

[0066] 7 shows one width interchange section in the middle of the modulator 700, in some implementations additional width interchange sections can be provided, for example, if the distance between the width interchange sections is significantly longer than the beat length between the two eigenmodes of the two waveguides, which is typically 10 μm. This is useful to ensure reduced optical coupling between the two waveguides. In some implementations, an odd number of interchange sections is preferred, as it is useful to ensure that the start and end transitions cancel each other out.

[0067] A potential complication resulting from variations in the waveguide widths of optical transmission lines 702 and 704 is that wider waveguides have a higher effective refractive index than narrower waveguides. As a result, the phase of light within the waveguides affects the wider portions of the waveguides differently compared to the narrower portions of the waveguides. Thus, if the two optical transmission lines 702 and 704 have wider portions of different lengths (e.g., if the length of portion 722 is longer than the length of portion 724, or vice versa), this can result in different inherent phase shifts of the light within the two waveguides due to, for example, differences in wavelength or temperature, or the different speeds of light in the two waveguides.

[0068] To alleviate such complications, the widths of the two waveguides can be swapped to ensure that the overall length of the wider portion of each waveguide is equal, and that the overall length of the narrower portion of each waveguide is equal. This is useful for ensuring that the overall effective path length of optical transmission line 702 is the same as the overall effective path length of optical transmission line 704. As a result, this can be useful for ensuring a unique, non-zero differential phase shift between the light propagating along the two optical transmission lines 702 and 704.

[0069] In some implementations, the transition between the width swaps can be gradual. For example, from left to right in FIG. 7, the distance between the waveguides of the two optical transmission lines 702 and 704 gradually increases. This is useful to keep the light in the two optical transmission lines 702 and 704 largely uncoupled. This increased separation changes the width of each waveguide so that the wider waveguide becomes narrower and the narrower waveguide becomes wider. As the waveguide widths swap, the two waveguides gradually move closer to each other again.

[0070] In some implementations, the distance between the waveguides of the two optical transmission lines 702 and 704 is less than 0.5 μm along at least a portion of the length of the optical transmission lines 702 and 704. In some implementations, the distance between the waveguides is less than 2.0 μm along at least a portion of the length of the optical transmission lines 702 and 704. In some implementations, the distance between the waveguides is in the range of 0.1 μm to 2.0 μm along at least a portion of the length of the optical transmission lines 702 and 704. In some implementations, the distance between the waveguides is defined as the distance between the inner walls of the two waveguides at a given point along the length of the modulator 700 (e.g., point 705 in FIG. 7).

[0071] FIG. 8 illustrates an example cross-section of a modulator 800 (eg, a cross-section at point 505 of modulator 500 in FIG. 5 or a cross-section at point 605 of modulator 600 in FIG. 6) according to an implementation of the present disclosure.

[0072] A cross section of modulator 800 shows details of the MZI structure. The MZI comprises a first optical waveguide 802 and a second optical waveguide 804. The optical waveguides 802 and 804 may be implemented, for example, as silicon ribbed waveguides on a slab. In some implementations, modulator 800 comprises a substrate 806 (e.g., a silicon substrate), an insulating structure 808 (e.g., a dielectric such as an oxide), and a semiconductor structure 810 (e.g., a silicon layer comprising the optical waveguides 802 and 804).

[0073] In some implementations, one of the optical waveguides 802 and 804 is wider than the other optical waveguide, as discussed above with respect to Figures 5-7. For example, in Figure 8, the second optical waveguide 804 is at least 0.04 μm wider than the first optical waveguide 802. In some implementations, the difference in the widths of the waveguides is in the range of 0.04 μm to 0.4 μm.

[0074] Each of the optical transmission lines 802 and 804 comprises a semiconductor junction. The semiconductor junction diodes may be implemented, for example, by PIN (P-type / Intrinsic / N-type) junction diodes or P / N junction diodes. In the modulator 800, a P / N junction is embedded in each of the optical waveguides 802 and 804 to form a diode in each waveguide. These diodes are shown as a first semiconductor junction diode 812 and a second semiconductor junction diode 814.

[0075] Modulator 800 also includes electrodes 816 and 818 (e.g., metal electrodes) in physical contact with silicon layer 810. In some implementations, electrodes 816 and 818 are in physical contact with N-doped contact regions 820 and 822 of silicon layer 810. Electrodes 816 and 818 may be formed, for example, by etching insulating layer 808 and forming metal (e.g., tungsten, copper, and / or aluminum) contacts. Modulator 800 may also include metal layers 824 and 826 on electrodes 816 and 818. In some implementations, metal layers 824 and 826 may form segments of an RF transmission line (e.g., RF transmission line 114 of FIG. 1 ).

[0076] There are a number of differences between modulator 800 and modulator 200 of FIG. 2. Most notably, modulator 800 does not implement any DC bias voltage connection between semiconductor junction diodes 812 and 814 (compared to modulator 200, which implements DC bias connection 228). Instead, semiconductor junction diodes 812 and 814 are connected in series with opposite polarity (anodes 834 and 836 are connected together). This ensures that continuous current never flows through semiconductor junction diodes 812 and 814. This configuration allows the voltage across the two semiconductor junction diodes 812 and 814 to naturally self-regulate, ensuring that diodes 812 and 814 maintain a reverse bias despite variations in the modulation voltages (e.g., V+ and V−) that may be applied to electrodes 816 and 818. Implementing a floating voltage across semiconductor junction diodes 812 and 814 automatically biases the diodes 812 and 814 at the most efficient point of the modulator, at a voltage phase shift slightly below the value at which the diodes 812 and 814 turn on. In some implementations, this voltage phase shift is the "gain" of the modulator.

[0077] 2 is that the polarities of semiconductor junction diodes 812 and 814 are reversed compared to modulator 200. Specifically, semiconductor junction diodes 812 and 814 have respective (P-doped) anodes 834 and 836 near the center of modulator 800 and respective (N-doped) cathodes 830 and 832 near the edges of modulator 800. Thus, semiconductor region 838 between semiconductor junction diodes 812 and 814 is P-doped, while semiconductor regions 840 and 842 (connecting semiconductor junction diodes 812 and 814 to respective electrodes 816 and 818) are N-doped.

[0078] These aforementioned differences provide modulator 800 with numerous technical advantages over modulator 200 of FIG. 2. One advantage is that, because modulator 800 does not have a DC bias voltage connection, the two optical waveguides 802 and 804 can be implemented much closer to each other than modulator 200 of FIG. 2. This allows the size of semiconductor region 838 connecting semiconductor junction diodes 812 and 814 to be significantly reduced, thereby significantly reducing the series electrical resistance between the semiconductor junction diodes 812 and 814. For example, in some implementations, the distance between the two optical waveguides 802 and 804 (shown as 805 in FIG. 8) is less than 0.5 μm. In some implementations, the distance 805 between the two optical waveguides 802 and 804 is less than 2.0 μm. In some implementations, the distance 805 between the two optical waveguides 802 and 804 is in the range of 0.1 μm to 2.0 μm. In some implementations, the distance 805 between the waveguides can be defined as the distance between the inner walls of two waveguides at a given point along the length of the modulator 800 (e.g., measured at a cross-section of the modulator 800 shown in FIG. 8).

[0079] Another advantage is that P-doped silicon has a higher resistivity than N-doped silicon (for the same optical absorption), so a highly resistive P-doped material is used for the small semiconductor region 838 (between semiconductor junction diodes 812 and 814) and a less resistive N-doped material is used for the large semiconductor regions 840 and 842 (connecting semiconductor junction diodes 812 and 814 to electrodes 816 and 818). Alternatively, in some implementations, an N-doped material can be used for the small semiconductor region 838 and a P-doped material can be used for the large semiconductor regions 840 and 842.

[0080] As a result, the total series resistance between electrodes 816 and 818 is significantly reduced, and therefore the bandwidth and speed of modulation are significantly improved.

[0081] Although the absence of a DC bias voltage connection in modulator 800 negates a degree of freedom in the ability to adjust the degree of reverse bias of semiconductor junction diodes 812 and 814, in some scenarios the significant benefits, such as improved bandwidth and speed of modulation, provided by the configuration of modulator 800 outweigh such limitations.

[0082] FIG. 9 illustrates an example of an equivalent circuit 900 along a cross section of a modulator (eg, a cross section of modulator 800 of FIG. 8) according to an implementation of the present disclosure.

[0083] 9, the series electrical resistance 940 between the first electrode 916 and the first semiconductor junction diode 912 (e.g., corresponding to semiconductor region 840 in FIG. 8) is 3.7 mΩ·m. The series electrical resistance 942 between the second electrode 918 and the second semiconductor junction diode 914 (e.g., corresponding to semiconductor region 842 in FIG. 8) is 3.7 mΩ·m. The series electrical resistance 938 between the first semiconductor junction diodes 912 and 914 (e.g., corresponding to semiconductor region 838 in FIG. 8) is 4.6 mΩ·m (without any DC bias voltage connection between the diodes).

[0084] As can be seen in this example, the total series resistance between electrodes 916 and 918 is reduced by approximately a factor of two compared to equivalent circuit 300 of FIG. 3. This reduction in total series resistance can significantly improve the performance of the modulator. For example, modulation bandwidth is increased due to reduced RF losses along the modulator. Alternatively, modulation efficiency can be improved. For example, a thin slab can be used, which increases the total series resistance but also improves the confinement of light within optical waveguides 802 and 804, thus improving modulation efficiency. Alternatively, a thicker waveguide can be used, which increases the capacity but also improves the confinement of light.

[0085] FIG. 10 illustrates another example cross section of a modulator 1000 (eg, another example cross section of modulator 500 of FIG. 5 or modulator 600 of FIG. 6) according to an implementation of the present disclosure.

[0086] The structure of modulator 1000 is a silicon-insulator-silicon capacitor (SISCAP) modulator structure. Compared to modulator 800 of Figure 8, modulator 1000 implements thin oxide layers 1044 and 1046 on semiconductor junction diodes 1012 and 1014 of optical waveguides 1002 and 1004. Furthermore, similar to modulator 800 of Figure 8, the anodes 1034 and 1036 (P-doped regions) of semiconductor junction diodes 1012 and 1014 are connected to each other (without a DC bias connection between them), and electrodes 1016 and 1018 apply a varying voltage to the cathodes 1030 and 1032 (N-doped regions) of semiconductor junction diodes 1012 and 1014.

[0087] These features provide modulator 1000 with a number of technical advantages over modulator 200 of Figure 2. One advantage is that, because there is no DC bias voltage connection in modulator 1000, the two optical waveguides 1002 and 1004 can be implemented much closer to each other than in modulator 200 of Figure 2. This allows the size of semiconductor region 1038 connecting semiconductor junction diodes 1012 and 1014 to be significantly reduced, thereby significantly lowering the series electrical resistance between semiconductor junction diodes 1012 and 1014. Another advantage is that a highly resistive P-doped material is used for the small semiconductor region 1038 (between semiconductor junction diodes 1012 and 1014) and a less resistive N-doped material is used for the large semiconductor regions 1040 and 1042 (connecting semiconductor junction diodes 1012 and 1014 to electrodes 1016 and 1018). As a result, the total series resistance between the electrodes 1016 and 1018 is significantly reduced, and therefore the bandwidth and modulation speed are significantly improved. For example, in some implementations, the distance between the two optical waveguides 1002 and 1004 (shown as 1005 in FIG. 10 ) is less than 0.5 μm. In some implementations, the distance 1005 between the two optical waveguides 1002 and 1004 is less than 2.0 μm. In some implementations, the distance 1005 between the two optical waveguides 1002 and 1004 is in the range of 0.1 μm to 2.0 μm. In some implementations, the inter-waveguide distance 1005 can be defined as the distance between the inner walls of the two waveguides at a given point along the length of the modulator 1000 (e.g., as measured at a cross-section of the modulator 1000 shown in FIG. 10 ).

[0088] Additionally, in some implementations, one of the optical waveguides 1002 and 1004 is wider than the other optical waveguide, as discussed above with respect to Figures 5-8. For example, in Figure 10, the second optical waveguide 1004 is at least 0.04 μm wider than the first optical waveguide 1002. In some implementations, the difference in the widths of the waveguides is in the range of 0.04 μm to 0.4 μm.

[0089] Modulators according to implementations of the present disclosure can be used in many applications. For example, one application is a high-speed optical intensity modulator implementing an intensity-modulated direct-detection (IM-DD) scheme, such as non-return-to-zero (NRZ) or pulse amplitude modulation (PAM). Another application is using the modulator with a second modulator with a 90-degree relative phase shift as part of a larger interferometer to implement more complex modulation schemes for coherent detection, such as quadrature phase-shift keying (QPSK) modulation or quadrature amplitude modulation (QAM). For example, this can be achieved with an in-phase / quadrature (IQ) modulator structure including a nested modulator, where each of the two branches of a modulator (the outer modulator) implements another modulator (the inner modulator). In some implementations, a phase adjuster can be implemented to set the inner and outer modulators to a 180-degree and 90-degree phase difference, respectively. Each modulator in such a nested modulator structure can be implemented as described in this disclosure (e.g., as the modulators described with reference to Figures 5-10).

[0090] FIG. 11 shows examples of modulators with different performance in terms of conductance per unit length between the V+ and V− terminals depending on the distance between the waveguides.

[0091] The plot shown in Figure 11 typically compares the performance of a modulator with a DC bias connection (e.g., modulator 100 of Figure 1) with the performance of a modulator implemented with a floating anode (e.g., the modulators of Figures 5-10) and a modulator implemented with a floating cathode, for various semiconductor doping levels. As shown in Figure 11, when the distance between the waveguides is 0.1 μm, the floating anode implementation doubles the conductance compared to the DC bias connection implementation. The floating cathode implementation also provides an improvement over the DC bias connection implementation, but the improvement is significantly smaller due to the predominance of P-doped regions in the modulator's semiconductor structure.

[0092] FIG. 12 shows an example of the performance of different modulators in terms of the voltage across each semiconductor junction diode as a function of an applied differential voltage ΔV (ΔV=V+−V−) across the two terminals of the modulator, which is the voltage across the two diodes in series of FIGS. 3 and 9.

[0093] The dotted curves represent the voltage across each of the two diodes in a modulator with a DC bias connection (e.g., modulator 100 of FIG. 1), and the solid curves represent the voltage across each of the two diodes in a modulator in which a floating anode is implemented (e.g., the modulators of FIGS. 5-10).

[0094] For the dotted curves (modulators with DC bias connections, e.g., modulator 100 of FIG. 1), the bias voltage is adjusted to keep the diode below the voltage at which it turns on. For these curves, the voltage across each diode is approximately a straight line with a slope equal in magnitude to about ½ (i.e., +½ and −½ for the two dotted curves).

[0095] In the solid curves (modulators implemented with floating anodes, e.g., those shown in Figures 5-10), when the applied differential voltage ΔV is equal to zero, the voltage across each diode is also zero, so the curves for the two diodes intersect at point (0, 0) on the graph. When the applied differential voltage ΔV is large, one diode is slightly lower than its on voltage, and the other diode has a large reverse voltage. This allows the modulator to automatically operate at the highest possible gain despite changes in the environment or manufacturing process. The solid curves for both diodes initially vary with a slope of magnitude 1 (i.e., +1 and -1 at the slopes of the two solid curves). The overall result is a nonlinear behavior of the voltage across each diode as a function of the applied differential voltage ΔV. Although the difference in voltage across the two diodes is strictly proportional to the applied differential voltage ΔV in both cases, the modulator's MZI configuration is no longer driven by equal but opposite voltages in each optical transmission line. This introduces a small nonlinear chirp into the resulting optical signal output from the optical combiner, which can affect transmission in the presence of chromatic dispersion, however this effect should be very small.

[0096] FIG. 13 shows an example of the performance of a modulator according to an implementation of the present disclosure (e.g., the modulator of FIGS. 5-10) in terms of the normalized differential refractive index change between the two waveguides of the modulator as a function of the distance between the waveguides for various waveguide widths.

[0097] In the example of Figure 13, the nominal waveguide width is 0.45 μm and the wavelength is 1.31 μm. The waveguide thickness is 0.22 μm and the slab thickness is 0.10 μm. The results in Figure 13 were generated by simulating a depletion region in the center of each waveguide, with the size of the depletion region being 0.2 μm wide and 0.22 μm high. The depletion region has a refractive index of 3×10 in one waveguide. -4 The refractive index of the other waveguide increases by 3 × 10 -4The refractive index of the two waveguide modes is calculated. When the sign of the refractive index change changes, the refractive index of the two waveguide modes is calculated again. The mode refractive indices for the two cases are subtracted and averaged for the two waveguides, and the result is normalized to the largest value to obtain the differential refractive index plot in Figure 13.

[0098] 14 is a flowchart illustrating an exemplary method 1400 for modulating an optical signal according to an implementation of the present disclosure. Method 1400 can be implemented using a modulator disclosed herein (e.g., a modulator described with reference to FIGS. 5-10).

[0099] The method 1400 includes splitting (1402) input light into a first optical transmission path and a second optical transmission path.

[0100] The method 1400 further includes modulating 1404 a phase difference between the light of the first optical transmission line and the light of the second optical transmission line without applying a bias voltage between the first optical transmission line and the second optical transmission line. In some implementations, the phase difference between the light of the first optical transmission line and the light of the second optical transmission line is modulated while maintaining the finite depletion region of the semiconductor junction diode in each of the first optical transmission line and the second optical transmission line. For example, this modulation can be performed using the floating anode structure of the modulator described above with reference to Figures 5-10.

[0101] The method 1400 further includes combining 1406 the light output from the first optical transmission path and the light output from the second optical transmission path.

[0102] While this disclosure includes details of numerous specific implementations, these should not be construed as limitations on the scope of all inventions or what may be claimed, but rather as descriptions of features that may be specific to particular implementations of a particular invention. Certain features described in this disclosure in the context of separate implementations may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented separately in multiple implementations or in any suitable subcombination. Furthermore, while features may be described above as functioning in a particular combination and even initially claimed as such, one or more features of a claimed combination may, in some cases, be excluded from the combination, and the claimed combination may be in terms of a subcombination or a variation of a subcombination.

[0103] Similarly, although acts are shown in a particular order in the figures, this should not be construed as requiring that such acts be performed in the particular order or sequence shown to achieve desired results, nor should it be construed as requiring that all illustrated acts be performed.

Claims

1. An optical modulator comprising: (i) a first optical waveguide having a first semiconductor junction diode, and (ii) a Mach-Zehnder interferometer comprising a second optical waveguide having a second semiconductor junction diode; and A semiconductor region connecting the first semiconductor junction diode to the second semiconductor junction diode such that a distance between the first optical waveguide and the second optical waveguide is less than 2.0 μm in at least a part of a longitudinal direction of the optical modulator.

2. The first semiconductor junction diode includes a first anode and a first cathode, The second semiconductor junction diode includes a second anode and a second cathode, and The optical modulator according to claim 1, wherein the first anode is connected to the second anode through the semiconductor region spanning the distance between the first optical waveguide and the second optical waveguide.

3. The optical modulator according to claim 2, wherein the semiconductor region between the first anode and the second anode is configured without any external voltage connection having an impedance of less than 100 Ω.

4. A first electrode connected to the first cathode and configured to apply a first electric field to the first optical waveguide; and The optical modulator according to claim 2, further comprising a second electrode connected to the second cathode and configured to apply a second electric field to the second optical waveguide.

5. The optical modulator according to claim 2, further comprising a radio frequency (RF) transmission line configured to (i) apply a first voltage to the first cathode through the first electrode and (ii) apply a second voltage to the second cathode through the second electrode.

6. The first optical waveguide includes a plurality of first semiconductor junction diodes, The second optical waveguide includes a plurality of second semiconductor junction diodes, and The RF transmission line is configured to: (i) apply the first voltage to the plurality of first semiconductor junction diodes via a plurality of first electrodes, and (ii) apply the second voltage to the plurality of second semiconductor junction diodes via a plurality of second electrodes. The optical modulator according to claim 5.

7. In a first portion of the optical modulator, the first optical waveguide is at least 0.04 μm wider than the second optical waveguide, and In a second portion of the optical modulator, the second optical waveguide is at least 0.04 μm wider than the first optical waveguide. The optical modulator according to claim 1.

8. In at least a part of the optical modulator: The width of the first optical waveguide increases along the longitudinal direction of the optical modulator, and The width of the second optical waveguide decreases along the longitudinal direction of the optical modulator. The optical modulator according to claim 1.

9. The first semiconductor junction diode includes a first p-doped region and a first n-doped region, and The second semiconductor junction diode includes a second p-doped region and a second n-doped region. The optical modulator according to claim 1.

10. The first p-doped region is connected to the second p-doped region via a third p-doped region of the semiconductor region connecting the first semiconductor junction diode to the second semiconductor junction diode, The third p-doped region is configured without any external voltage connection having an impedance of less than 100 Ω. The optical modulator according to claim 9.

11. The first semiconductor junction diode further includes a first oxide layer between the first p-doped region and the first n-doped region, and The second semiconductor junction diode further includes a second oxide layer between the second p-doped region and the second n-doped region. The optical modulator according to claim 9.

12. The Mach-Zehnder interferometer being: An optical splitter configured to receive an input light and split the input light into the first optical waveguide and the second optical waveguide; and Further comprising an optical combiner configured to receive a first output light from the first optical waveguide and a second output light from the second optical waveguide and combine the first output light and the second output light, the optical modulator according to claim 1.

13. An optical splitter configured to split an input light into a first optical transmission path and a second optical transmission path; Means for modulating a phase difference between the light in the first optical transmission path and the light in the second optical transmission path without applying a bias voltage via an impedance of less than 100 Ω between the first optical transmission path and the second optical transmission path; and An optical modulator comprising an optical combiner configured to combine the light output from the first optical transmission path and the light output from the second optical transmission path.

14. Further comprising a radio frequency (RF) transmission line configured to apply (i) a first voltage to the first optical transmission path via a first electrode and (ii) a second voltage to the second optical transmission path via a second electrode, the optical modulator according to claim 13.

15. The first optical transmission path comprising a first semiconductor junction diode, The second optical transmission path comprising a second semiconductor junction diode, and During modulation, the first semiconductor junction diode is at a voltage slightly lower than when it is turned on, while the second semiconductor junction diode is at a maximum reverse voltage, the optical modulator according to claim 13.

16. The phase difference between the light in the first optical transmission path and the light in the second optical transmission path is modulated in a push-pull mode by applying a first electric field to the first optical transmission path and a second electric field to the second optical transmission path, the optical modulator according to claim 13.

17. The optical modulator according to claim 13, wherein a phase difference between the light in the first optical transmission path and the light in the second optical transmission path is modulated while maintaining a finite depletion region of the semiconductor junction diode in each of the first optical transmission path and the second optical transmission path.

18. A method for modulating an optical signal, comprising: splitting input light into a first optical transmission path and a second optical transmission path; modulating a phase difference between the light in the first optical transmission path and the light in the second optical transmission path without applying a bias voltage through an impedance of less than 100 Ω between the first optical transmission path and the second optical transmission path; and combining the light output from the first optical transmission path and the light output from the second optical transmission path.

19. The method according to claim 18, wherein a phase difference between the light in the first optical transmission path and the light in the second optical transmission path is modulated while maintaining a finite depletion region of the semiconductor junction diode in each of the first optical transmission path and the second optical transmission path.

20. A Mach-Zehnder interferometer comprising (i) a first optical waveguide having a first semiconductor junction diode and (ii) a second optical waveguide having a second semiconductor junction diode; and a semiconductor region connecting a terminal of the first semiconductor junction diode to a terminal of the second semiconductor junction diode, wherein the terminal of the first semiconductor junction diode and the terminal of the second semiconductor junction diode are both p-doped anodes or both n-doped cathodes, and the semiconductor region is not connected to other circuit elements through an impedance of less than 100 Ω.

21. including a high-impedance direct current (DC) bias connected between the first semiconductor junction diode and the second semiconductor junction diode, The optical modulator according to claim 20, wherein the high-impedance DC bias is connected to an impedance exceeding 100 Ω.

22. The optical modulator according to claim 21, wherein the high-impedance DC bias is configured to maintain a reverse bias during modulation of a data signal by the first semiconductor junction diode and the second semiconductor junction diode via the optical modulator.

23. A first electrode connected to the first semiconductor junction diode and configured to apply a first electric field to the first optical waveguide; and The optical modulator according to claim 20, further comprising a second electrode connected to the second semiconductor junction diode and configured to apply a second electric field to the second optical waveguide.

24. The optical modulator according to claim 23, further comprising a radio frequency (RF) transmission line configured to (i) apply a first voltage to the first semiconductor junction diode via the first electrode and (ii) apply a second voltage to the second semiconductor junction diode via the second electrode.

25. The first optical waveguide includes a plurality of first semiconductor junction diodes, The second optical waveguide includes a plurality of second semiconductor junction diodes, and The optical modulator according to claim 24, wherein the RF transmission line is configured to (i) apply the first voltage to the plurality of first semiconductor junction diodes via a plurality of first electrodes and (ii) apply the second voltage to the plurality of second semiconductor junction diodes via a plurality of second electrodes.

26. The optical modulator according to claim 20, wherein a distance between the first optical waveguide and the second optical waveguide is less than 2.0 μm in at least a part of a longitudinal direction of the optical modulator.

27. In a first portion of the optical modulator, the first optical waveguide is at least 0.04 μm wider than the second optical waveguide, and In the second part of the optical modulator, the second optical waveguide has a width that is at least 0.04 μm wider than that of the first optical waveguide, the optical modulator according to claim 20. **Claim 28** An optical modulator comprising: (i) a first optical waveguide having a first semiconductor junction diode, and (ii) a Mach-Zehnder interferometer comprising a second optical waveguide having a second semiconductor junction diode, The optical modulator, wherein the first optical waveguide has a width that is wider than that of the second optical waveguide at the same first distance along the lengths of the first optical waveguide and the second optical waveguide. **Claim 29** The first semiconductor junction diode comprises a first anode and a first cathode, The second semiconductor junction diode comprises a second anode and a second cathode, and The optical modulator according to claim 28, wherein the first anode is connected to the second anode via a semiconductor region connecting the first semiconductor junction diode to the second semiconductor junction diode. **Claim 30** The optical modulator according to claim 29, wherein the semiconductor region between the first anode and the second anode is configured without any external voltage connection having an impedance of less than 100 Ω. **Claim 31** The optical modulator according to claim 28, wherein the first optical waveguide has a width that is at least 0.04 μm wider than that of the second optical waveguide at the same first distance along the lengths of the first optical waveguide and the second optical waveguide. **Claim 32** The optical modulator according to claim 28, wherein the second optical waveguide has a width that is wider than that of the first optical waveguide at the same second distance along the lengths of the first optical waveguide and the second optical waveguide. **Claim 33** The optical modulator according to claim 32, wherein the width of the first optical waveguide at the same first distance matches the width of the second optical waveguide at the same second distance. **Claim 34** The optical modulator according to claim 33, wherein the width of the first optical waveguide at the same second distance matches the width of the second optical waveguide at the same first distance.

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