Transverse-magnetic polarization silicon-photonic modulator

Abstract

To provide a novel electro-optic modulator in silicon photonics which can achieve a higher bandwidth and / or a lower drive voltage.SOLUTION: A silicon-photonic optical modulator includes at least one optical input, and at least one optical waveguide that is connected to the at least one optical input. The at least one optical waveguide is configured to propagate quasi-transverse-magnetic (quasi-TM) polarized light, where each of the at least one optical waveguide is configured as a rib waveguide that includes a rib arranged on a slab. The silicon-photonic optical modulator also includes at least one electrode configured to apply at least one electric field to the quasi-TM polarized light in the at least one optical waveguide. In some implementations, a height of the rib waveguide is greater than 0.85 λ / n, where λ is a free-space wavelength of light and n is a refractive index of silicon in the silicon-photonic optical modulator, and a width of the rib waveguide is greater than a thickness of the slab.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] FIELD OF THE DISCLOSURE This disclosure relates generally to electro-optic modulators in silicon photonics. [Background technology]

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

[0003] SUMMARY OF THE INVENTION Embodiments of the present disclosure are generally directed to electro-optic modulators in silicon photonics.

[0004] One general aspect includes a silicon photonic optical modulator including at least one optical input and at least one optical waveguide connected to the at least one optical input. The at least one optical waveguide is configured to propagate quasi-transverse magnetic (quasi-TM) polarized light, each of the at least one optical waveguides being configured as a rib waveguide including ribs disposed on a slab. The silicon photonic optical modulator also includes at least one electrode configured to apply at least one electric field to the quasi-TM polarized light in the at least one optical waveguide.

[0005] Embodiments may include one or more of the following features: A silicon photonic optical modulator, wherein at least one optical waveguide is configured as a silicon photonic depletion modulator including at least one semiconductor junction diode; A silicon photonic optical modulator, wherein at least one electrode is configured to apply at least one electric field to quasi-TM polarized light in the at least one semiconductor junction diode; A silicon photonic optical modulator, wherein an effective refractive index of a TM-polarized two-dimensional (2D) guided mode in the rib waveguide is greater than an effective refractive index of a transverse electric (TE) polarized one-dimensional (1D) guided mode in the slab; A silicon photonic optical modulator, wherein a doping concentration in a first portion of the slab that is within 100 nm of the nearest sidewall of the rib is greater than an effective refractive index of a transverse electric (TE) polarized one-dimensional (1D) guided mode in the slab that ... 3 10 per 17 A silicon photonic optical modulator, wherein the doping concentration is increased by more than 1 cm in a first portion of the slab that is within 50 nm to 500 nm of the nearest sidewall of the rib, compared to a second portion of the slab that is further away from the nearest sidewall of the rib. 3 5x10 17 ~1×10 19a silicon photonic optical modulator, wherein the active dopant is increased by a value within the range of 1 / 2 to 1 / 4. a silicon photonic optical modulator further comprising a Mach-Zehnder interferometer including at least one optical waveguide, the at least one optical waveguide 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 silicon photonic optical modulator further comprising a semiconductor region connecting the first semiconductor junction diode and the second semiconductor junction diode; a silicon photonic optical modulator, wherein the distance between the first optical waveguide and the second optical waveguide is less than 500 nm along at least a portion of the longitudinal direction of the silicon photonic optical modulator; a silicon photonic optical modulator, wherein the first semiconductor junction diode includes a first p-doped region and a first n-doped region; and a silicon photonic optical modulator, wherein the second semiconductor junction diode includes a second p-doped region and a second n-doped region. 1. A silicon photonic optical modulator, wherein the first p-doped region is connected to the second p-doped region through a third p-doped region within the semiconductor region connecting the first semiconductor junction diode and the second semiconductor junction diode, the third p-doped region being configured with no external voltage connection and having an impedance of less than 100 ohms.

[0006] Another general aspect includes a silicon photonic optical modulator including at least one optical input and at least one optical waveguide. The at least one optical waveguide is configured to receive light from the at least one optical input, and each of the at least one optical waveguides is configured as a rib waveguide including ribs disposed on a slab. The silicon photonic optical modulator also includes at least one electrode configured to apply at least one electric field to light in the at least one optical waveguide. The silicon photonic optical modulator includes a height of the rib waveguide greater than 0.85λ / n (where λ is the free-space wavelength of light and n is the refractive index of silicon in the silicon photonic optical modulator). The silicon photonic optical modulator includes a width of the rib waveguide greater than the thickness of the slab.

[0007] Embodiments may include one or more of the following features. A silicon photonic optical modulator, wherein the height of the rib waveguide is greater than the width of the rib waveguide. A silicon photonic optical modulator, wherein the height of the rib waveguide is in the range of 320 nm to 500 nm. A silicon photonic optical modulator, wherein the width of the rib waveguide is in the range of 150 nm to 270 nm. A silicon photonic optical modulator, wherein the thickness of the slab is in the range of 50 nm to 140 nm. A silicon photonic optical modulator, wherein the height of the rib waveguide is in the range of 330 nm to 370 nm when the free-space wavelength of light is equal to 1310 nm. A silicon photonic optical modulator, wherein the width of the rib waveguide is in the range of 200 nm to 240 nm. A silicon photonic optical modulator, wherein the thickness of the slab is in the range of 70 nm to 110 nm. A silicon photonic optical modulator, wherein the at least one optical waveguide includes a first rib waveguide and a second rib waveguide. A silicon photonic optical modulator, wherein the distance between the first rib waveguide and the second rib waveguide is less than 500 nm. A silicon photonic optical modulator, wherein the height of the first rib waveguide is greater than the height of the second rib waveguide in at least a portion of the silicon photonic optical modulator. A silicon photonic optical modulator, wherein the height of the first rib waveguide is greater than the height of the second rib waveguide by at least 40 nm in a first portion of the silicon photonic optical modulator. A silicon photonic optical modulator, wherein the height of the second rib waveguide is greater than the height of the first rib waveguide by at least 40 nm in a second portion of the silicon photonic optical modulator. A silicon photonic optical modulator, wherein the doping concentration in a first portion of the slab that is within 100 nm of the nearest sidewall of the rib is greater than the doping concentration in a second portion of the slab that is more than 100 nm away from the nearest sidewall of the rib. 3 10 per 17 Silicon photonic optical modulators, where the active dopant is increased by a factor of 10.

[0008] Another general aspect includes a method for modulating quasi-transverse magnetic (TM) polarized light, the method including inputting input quasi-TM polarized light into at least one optical waveguide and applying at least one electric field to the quasi-TM polarized light in the at least one optical waveguide.

[0009] Embodiments may include one or more of the following features. The method may further include splitting input quasi-TM polarized light into a first optical waveguide and a second optical waveguide. The method may also include modulating a phase difference between the quasi-TM polarized light in the first optical waveguide and the quasi-TM polarized light in the second optical waveguide through an impedance of less than 100 Ω between the first optical waveguide and the second optical waveguide without applying a bias voltage. The method may also include combining the quasi-TM polarized light output from the first optical waveguide and the quasi-TM polarized light output from the second optical waveguide. The method may include modulating a phase difference between the quasi-TM polarized light in the first optical waveguide and the quasi-TM polarized light in the second optical waveguide while maintaining finite depletion regions of the semiconductor junction diodes of each of the first optical waveguide and the second optical waveguide.

[0010] The details of one or more embodiments of the presently disclosed subject matter 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 detailed description, the drawings, and the claims. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram illustrating an example of a top view of a modulator in which embodiments of the present disclosure may be used.

[0012] [Figure 2] FIG. 2 is a diagram illustrating an example of a cross section of a modulator according to an embodiment of the present disclosure.

[0013] [Figure 3] FIG. 3 is a diagram illustrating an example of an equivalent circuit along a cross section of a modulator according to an embodiment of the present disclosure.

[0014] [Figure 4] 4A and 4B are diagrams illustrating detailed cross-sectional examples of a single waveguide of a modulator according to an embodiment of the present disclosure.

[0015] [Figure 5]5A and 5B are diagrams showing examples of TE and TM modes, respectively, in a silicon rib waveguide.

[0016] [Figure 6] FIG. 6 is a diagram illustrating an example of a top view of a modulator according to an embodiment of the present disclosure.

[0017] [Figure 7] FIG. 7 is a diagram illustrating another example of a top view of a modulator according to an embodiment of the present disclosure.

[0018] [Figure 8] FIG. 8 is a diagram illustrating an example of a cross section of a modulator according to an embodiment of the present disclosure.

[0019] [Figure 9] FIG. 9 is a diagram illustrating an example of an equivalent circuit along a cross section of a modulator according to an embodiment of the present disclosure.

[0020] [Figure 10] FIG. 10 is a flowchart illustrating an example of modulating a TM polarization optical signal according to an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0021] Disclosed herein are systems and techniques that provide novel electro-optic modulators in silicon photonics that can achieve higher bandwidths and / or lower drive voltages compared to conventional electro-optic modulators. This is achieved through novel embodiments that reduce the amount of light leaking into the slab portion of the modulator's optical waveguide. This allows for higher doping within the slab for the same optical loss, thereby enabling higher bandwidth modulators without increasing optical loss. These technical advantages are realized through a modulator structure that allows for the use of transverse magnetic (TM) polarization instead of transverse electric (TE) polarization within the modulator. In some embodiments, this is made possible by a rib waveguide structure in which the waveguide height is greater than the waveguide width. This results in TM light having a higher effective refractive index within the rib waveguide than TE light.

[0022] FIG. 1 illustrates an example of a top view of a differential modulator 100 in which embodiments of the present disclosure may be utilized. In this example, the modulator 100 is based on a Mach-Zehnder interferometer (MZI) implementation, and 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 light output from the two optical transmission lines 102 and 104. The optical splitter 106 and the optical combiner 108 may be implemented in various ways, for example, using symmetric, asymmetric, or tunable optical intensity couplers. The optical transmission lines 102 and 104 may be implemented by waveguides formed in a semiconductor structure 116, as described in further detail with reference to FIG. 2 below. In some embodiments, the waveguides and / or the optical cores of the optical splitter 106 and / or the optical combiner 108 may include silicon ribs. In some embodiments, an optical phase rotator may be implemented between the input of the modulator 100 and the optical transmission lines 102 and 104 to rotate the phase of the input light such that quasi-TM light propagates through the optical transmission lines 102 and 104.

[0023] 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 RF transmission line 114 propagates at the same speed as the light propagating along the two optical transmission lines 102 and 104, inducing electro-optic modulation. In particular, RF transmission line 114 is connected to semiconductor structure 116 via electrodes (described in further detail with reference to FIG. 2 below) that apply respective voltages and resulting electric fields across one or both of optical transmission lines 102 and 104. The applied voltages induce a phase shift in the light propagating through one or both of optical transmission lines 102 and 104. In some embodiments, the phase shift is differential in that the magnitude of the phase shift is equal and the signs of the phase shift are opposite between optical transmission lines 102 and 104.

[0024] 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 light in the first optical transmission line 102 and the phase of the light in the second optical transmission line 104. For example, if the terminal voltages are controlled so that the differential phase shift causes destructive interference at the optical combiner 108, this corresponds to the “off” or logic “0” state of the modulator 100. In contrast, if the terminal voltages are controlled so that the differential phase shift between the two optical transmission lines 102 and 104 causes positive interference at the optical combiner 108, this corresponds to the “on” or logic “1” state of the modulator 100.

[0025] 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 zero inherent differential phase shift, or may be different lengths to provide a non-zero inherent differential phase shift. Furthermore, in some embodiments, 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.

[0026] In some embodiments, phase modulation may be performed by a "push-pull" mechanism in which the phase of light in both optical transmission lines 102 and 104 is modulated to control the relative phase shift between the two paths. 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 light in each of optical transmission lines 102 and 104. Push-pull modulation may offer various advantages over non-push-pull modulation, such as lower average power consumption and reduced chirp in the modulated signal.

[0027] 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 of each of the optical transmission lines 102 and 104 remain reverse biased even when the data signals applied to the terminals 110 and 112 vary between logic 1 and logic 0. Further details are provided with reference to FIG. 2 below.

[0028] FIG. 2 is a diagram illustrating an example cross section of a modulator 200 (eg, cross section 126 of modulator 100 of FIG. 1).

[0029] A cross section of modulator 200 shows details of the MZI structure. The MZI includes a first optical waveguide 202 and a second optical waveguide 204. In some embodiments, modulator 200 includes 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 that includes optical waveguides 202 and 204).

[0030] Optical waveguides 202 and 204 may be implemented, for example, as silicon ribbed waveguides on slabs. In the example of Figure 2, optical waveguide 202 includes ribs 203 disposed on slab 205. Similarly, optical waveguide 204 includes ribs 207 on slab 209. Ribs 203, 207 and slabs 205, 209 are all part of semiconductor structure 210. Further details of ribbed waveguide structures are described below with reference to Figures 4A and 4B.

[0031] Each of the optical waveguides 202 and 204 includes a semiconductor junction. The semiconductor junction diodes can 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, 204, forming a diode within each waveguide. These diodes are shown as a first semiconductor junction diode 212 and a second semiconductor junction diode 214.

[0032] Modulator 200 also includes electrodes 216 and 218 (e.g., metal electrodes) in physical contact with silicon layer 210. In some embodiments, electrodes 216 and 218 are in physical contact with P-doped contact regions 220 and 222 of silicon layer 210. Electrodes 216 and 218 may be formed, for example, by etching insulating layer 208 and forming metal (e.g., tungsten, copper, and / or aluminum) contacts. In some embodiments, in modulator 200, the P-doped regions may instead be N-doped regions, or vice versa (e.g., so that contact regions 220 and 222 are N-doped rather than P-doped).

[0033] Modulator 200 may also include metal layers 224 and 226 over electrodes 216 and 218. In some embodiments, metal layers 224 and 226 may form segments of an RF transmission line (e.g., RF transmission line 114 of FIG. 1).

[0034] 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 push-pull mode 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+) on the first electrode 216 increases and the voltage (e.g., V−) on the second electrode 218 decreases, the width of the depletion region in the first optical waveguide 202 decreases, but the width of the depletion region in the second optical waveguide 204 increases (and vice versa). As the depletion width changes, this changes the effective refractive index experienced by light traveling along each of the optical waveguides 202 and 204, resulting in a corresponding phase shift of the light. As a result, push-pull modulation can be achieved in the modulator 200.

[0035] In the example modulator 200, a DC bias connection 228 is applied to the cathodes 230 and 232 (N-doped regions) of the semiconductor junction diodes 212 and 214, and 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 at the DC bias connection 228 is very low (or non-existent), this could result in activation of the first semiconductor junction diode 212 (e.g., a forward bias of about 0.6 V or more relative to silicon) due to a significant number of carriers injected into the depletion region of the first semiconductor junction diode 212, 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.

[0036] FIG. 3 is a diagram illustrating an exemplary equivalent circuit 300 along a cross section of a modulator (eg, cross section 126 of modulator 100 of FIG. 1).

[0037] In the example of FIG. 3, the electrical series 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 R p (e.g., expressed in mΩ-m). The electrical series 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 also expressed as R p (However, in some embodiments, the actual values ​​of electrical series resistances 340 and 342 may differ.) The electrical series resistance 338 between semiconductor junction diodes 312 and 314 (e.g., corresponding to semiconductor region 238 in FIG. 2) is expressed as 2*R n (The series resistance between each of the semiconductor junction diodes 312 and 314 and the DC bias voltage connection 328 is R n (Let us say that.)

[0038] In the equivalent circuit of the phase modulator shown in Figure 3, the resistor R n and R p The loss mainly comes from the slab and is the main limitation on the modulator bandwidth. Increasing the doping of the slab decreases the resistance and increases the bandwidth, but also increases the optical loss because doped silicon is absorptive.

[0039] 4A and 4B are diagrams illustrating detailed cross-sectional examples of a single waveguide of a silicon photonic depletion phase modulator (e.g., a waveguide in one of transmission lines 102 or 104 of modulator 100, or one of waveguides 202 or 204 of FIG. 2). In particular, FIG. 4A illustrates an exemplary waveguide 400 configured for TE polarization, and FIG. 4B illustrates an exemplary waveguide 420 configured for TM polarization, which may be implemented in some systems according to embodiments of the present disclosure.

[0040] In both Figures 4A and 4B, the waveguide 400 (and waveguide 420) are implemented using a rib waveguide structure with ribs 402 (422) on top of a slab 404 (424). Light is guided along the ribs 402 (422) and propagates along the length of the modulator (perpendicular to the cross-section shown in Figures 4A and 4B) due to total internal reflection within the ribs 402 (422). The rib structure allows for optical modes to be confined within the ribs 402 (422) while still allowing electrical connection to the ribs 402 (422) through regions on either side of the slab 404 (424). As described above with reference to Figure 2, phase modulation of light within the ribs 402 (422) is achieved by modulating the voltage difference between the n-doped and p-doped regions of the waveguide 400 (420). For example, increasing the voltage difference between the n-doped and p-doped regions widens the depletion width, thereby increasing the effective refractive index of the optical mode and enabling phase modulation of light within rib 402 (rib 422).

[0041] Waveguides 400 and 420 in FIGS. 4A and 4B differ in several respects. Most notably, waveguides 400 and 420 differ in dimensions: waveguide 400 (configured for TE polarization) is wide and short, while waveguide 420 (configured for TM polarization) is narrow and tall. The narrow and tall configuration of waveguide 420 in FIG. 4B reduces the portion of the optical mode residing in slab 424, allowing for higher doping in slab 424 for the same optical loss compared to waveguide 400 in FIG. 4A. The higher doping in slab 424, in turn, allows for higher bandwidth in modulator 420 without increasing optical loss compared to modulator 400. This is achieved by using transverse magnetic (TM) polarization instead of transverse electric (TE) polarization in modulator 420. In practical implementations, the guided optical modes of modulators 400 and 420 are actually quasi-TE or quasi-TM modes, since guided 2D modes are rarely pure TE or TM modes. In a quasi-TM mode, the dominant polarization component of the light is aligned along the y-axis. In a quasi-TE mode, the dominant polarization component of the light is aligned along the x-axis. For simplicity, the word "quasi" may be omitted when discussing the polarization of guided optical modes in this disclosure.

[0042] 4A is a diagram illustrating a cross section of an exemplary waveguide 400 configured for TE polarization. The modulator 400 has ribs 402 on top of a slab 404. The ribs have a height 406 (h core ) and width 408 (w core As shown, a typical implementation of a waveguide 400 configured for TE polarization has a rib height 406 (h core ) is rib width 408 (w core ) which ensures that the effective index of the TE 2D waveguide modes in the ribs 402 is higher than the effective index of the TM 1D slab modes, and therefore the guided TE modes leak less into the slab 404 compared to the guided TM modes.

[0043] There are a variety of reasons why silicon photonic modulators such as modulator 400 are configured for TE polarization.

[0044] First, in a modulator using a rib waveguide, the TM 2-D rib mode index is typically significantly lower than the TE 1-D slab mode index. Rib waveguides require a special condition, not typically met, to guide transverse magnetic (TM) light: the effective index of the TM 2-D rib mode must be larger than that of the TE 1-D slab mode. The slab mode refers to the 1-D mode that would be guided if the ribs 402 were absent and the slab 404 were infinitely wide. Otherwise, the TM rib mode would be phase-matched with the TE slab mode propagating at a certain angle relative to the ribs 402. In this case, even small perturbations can cause TM-mode light to leak into the slab 404.

[0045] Second, TE polarization has stronger vertical confinement within the ribs 402 compared to TM polarization, reducing losses due to the underlying substrate and layers above. For example, in some embodiments, there is a metal wiring layer above the silicon, and the metal layer can be brought much closer to the silicon before causing greater optical loss for TE polarization than for TM polarization.

[0046] Third, in most silicon photonic modulators, the waveguide height 406 is smaller than the waveguide width 408, resulting in a higher effective refractive index for TE polarization than for TM polarization, which allows for smaller bending radii and therefore smaller silicon photonic device sizes.

[0047] Fourth, most silicon photonic modulators use TE polarization because most other elements in silicon photonic circuits are designed for TE polarization. For example, most grating couplers are designed for TE polarization.

[0048] Fifth, in many scenarios, it is usually easier to fabricate waveguide structures that are wider than they are tall, for example, because shallow etching depths simplify the lithography process.

[0049] However, TM polarization has distinct advantages. For example, TM polarization has the advantage of reducing the amount of light in the slab 424 compared to TE polarization. To understand why TM polarization reduces the amount of light in the slab 424 compared to TE polarization, we can consider the boundary conditions for the electric field of light given by Maxwell's equations: In a non-magnetic material such as silicon, the transverse electric field E ∥ is continuous across the boundary, while the longitudinal electric field multiplied by the permittivity (E ⊥ )(ε) is continuous across the boundary. Because the dielectric constant of silicon is about 5.8 times that of oxide, when the electric field is perpendicular to a thin piece of silicon surrounded by oxide, the electric field inside the silicon is about 5.8 times lower than in the surrounding oxide. Therefore, TM-polarized light has almost no electric field inside the silicon slab 424.

[0050] This can be visually seen in Figures 5A and 5B, which show the TE and TM modes, respectively, in a silicon rib waveguide. Figure 5A shows an example of calculated modes for a conventional silicon phase modulator using TE polarization. In particular, Figure 5A shows the magnitude of the x-component of the electric field. Figure 5B shows an example of calculated modes for a silicon phase modulator using TM polarization according to an embodiment of the present disclosure. In particular, Figure 5B shows the magnitude of the y-component of the electric field.

[0051] As can be seen, there is significant light in the slab in Figure 5A, but very little light in the slab in Figure 5B. Thus, the slab in Figure 5B can have significantly higher doping near the ribs, and therefore significantly lower series resistance.

[0052] Additionally, the waveguide rib dimensions are different in the examples of Figures 5A and 5B. In both cases, the slab thickness is 90 nm. However, in Figure 5A, the waveguide rib height and rib width are 220 nm and 420 nm, respectively, while in Figure 5B, the waveguide rib height and rib width are 400 nm and 220 nm, respectively. The waveguide in Figure 5A is a typical modulator waveguide configured for TE polarization. As mentioned above, in such a configuration, the effective refractive index of the TM 2D rib mode is lower than that of the TE 1D slab mode, resulting in leakage of the guided TM mode into the slab (see Table 1 below).

[0053] In contrast, the waveguide in Figure 5B, with its taller and narrower waveguide ribs, is able to guide the TM mode without leakage into the slab. As shown in Table 1, increasing the waveguide rib height increases the effective refractive index of the TM 2D guided mode above that of the TE 1D slab mode. This occurs when the waveguide rib height is greater than a threshold of approximately 0.85λ / n and when the waveguide rib width is greater than the slab height. Here, λ is the free-space wavelength of light and n is the refractive index of silicon. This ensures that, for TM polarization, the electric field drops to low values ​​at the top and bottom of the waveguide, ensuring that boundary conditions do not create large electric fields outside the waveguide. For example, for a wavelength of λ = 1310 nm, the threshold is 0.85λ / n = 320 nm. Therefore, in this example, the waveguide rib height must be greater than 320 nm and the waveguide rib width must be greater than 90 nm.

[0054] Table 1 Effective modal refractive index at wavelength λ = 1310 nm [Table 1]

[0055] Implementations of modulators according to the present disclosure configured for TM polarization can provide various technical advantages (compared to typical modulators configured for TE polarization). For example, the doping within the slab can be significantly increased and / or higher doping can be located closer to the rib. In some embodiments, the doping concentration can be higher in a first portion of the slab that is within 50 nm to 500 nm (e.g., 100 nm) of the nearest sidewall of the rib than in a second portion of the slab that is more than 100 nm from the nearest sidewall of the rib. 3 5x10 17 ~1×10 19 can be increased with the active dopant to a value in the range of (e.g., 1×10 18 ~1×10 19 (Increases in the range of . Some implementations of the present disclosure can provide approximately 3.5 times lower series resistance compared to typical modulators configured for TE polarization. Another advantage is that the phase modulation efficiency can be increased for a given voltage and a given modulator length. This is because TM polarization is more horizontally confined within the waveguide ribs perpendicular to the depletion region, resulting in a larger change in the effective refractive index for a given voltage change.

[0056] Modulator implementations according to the present disclosure can also be configured to mitigate potential technical challenges. For example, in modulators configured for TM polarization, the waveguide ribs are configured tall and thin (compared to those of typical modulators designed for TE polarization), which can increase series resistance along the vertical edges of the ribs that connect to the top of the waveguide. To mitigate such resistance, preferred embodiments configure the waveguide ribs slightly above threshold, increasing the effective refractive index of the TM 2D ribs above that of the TE 1D slab. For example, in some embodiments, the waveguide rib height is 350 nm, the waveguide rib width is 220 nm, and the slab is 90 nm thick at a wavelength of 1310 nm.

[0057] Another challenge is the potential increase in capacitance of the waveguide pn junctions (e.g., semiconductor junction diodes 212 and 214 in Figure 2) as a result of the higher depletion region. However, in these structures, fringing fields contribute significantly to the capacitance, resulting in a sublinear increase in capacitance with increasing height. Therefore, doubling the waveguide rib height only increases the capacitance by about 1.5 times.

[0058] Figures 6-9 relate to modulators according to other embodiments of the present disclosure. In contrast to the modulators of Figures 1-3, the modulators of Figures 6-9 do not implement any bias voltage connections between the waveguides, which significantly reduces the series resistance between the electrodes and further increases the modulation bandwidth. Furthermore, in Figures 6-9, the modulators implement a variable height waveguide structure to mitigate detrimental optical coupling between closely spaced waveguides.

[0059] The features described with reference to Figures 6-9 can be useful in improving the modulator structures of Figures 1-3 in various ways. For example, the presence of DC bias connection 228 in Figure 2 increases the physical distance of semiconductor (e.g., silicon) region 238 between semiconductor junction diodes 212 and 214. This results in a large electrical series resistance in semiconductor region 238 connecting semiconductor junction diodes 212 and 214. Common techniques for reducing this electrical series resistance, such as increasing the silicon doping of the semiconductor structure, can have adverse effects, such as increased optical absorption.

[0060] 2 (connecting semiconductor junction diodes 212 and 214, respectively, with their respective electrodes 216 and 218) are P-doped semiconductor material, which has a higher resistivity (for the same optical absorption) than N-doped semiconductor material, resulting in a large electrical series resistance in semiconductor regions 240 and 242 between electrodes 216 and 218 and semiconductor junction diodes 212 and 214.

[0061] As a result, the total electrical series resistance between electrodes 216 and 218 in Figure 2 can significantly attenuate the voltage along modulator 200 due to the charging and discharging of the diode capacitance. Furthermore, this attenuation typically increases as the modulation frequency increases. RF losses along modulator 200 can adversely affect the bandwidth of modulator 200.

[0062] FIG. 6 illustrates an example top view of a modulator 600 according to an embodiment of the present disclosure.

[0063] Modulator 600 is based on an MZI implementation that includes two optical transmission lines 602 and 604, an optical splitter 606, and an optical combiner 608. Modulator 600 further includes terminals, such as terminal 610 and terminal 612, to which a voltage can be applied. The voltage propagates along an RF transmission line 614 connected to a semiconductor structure 616 via respective voltage-applying electrodes, creating an electric field across one or both of optical transmission lines 602 and 604. In some embodiments, an optical phase rotator may be implemented between the input of modulator 600 and optical transmission lines 602 and 604 that rotates the phase of the input light such that quasi-TM light propagates through optical transmission lines 602 and 604.

[0064] In contrast to modulator 100 of FIG. 1 , modulator 600 does not implement any DC bias connection between the two optical transmission lines 602 and 604. This allows the two optical transmission lines 602 and 604 to be placed closer to each other, reducing the electrical series resistance between them. For example, in some embodiments, 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 embodiments, 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 embodiments, 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 embodiments, the distance between the waveguides is defined as the distance between the inner sidewalls of two waveguides at a given point along the length of the modulator 600 (eg, point 605 in FIG. 6).

[0065] However, because the two optical transmission lines 602 and 604 are positioned closer together, there is a greater risk of detrimental optical coupling between the light in optical transmission line 602 and the light in optical transmission line 604. To mitigate such optical coupling, in some embodiments, one of the waveguides in the optical transmission lines (602 or 604) is designed to have a greater height than the other waveguide at the same distance along the length of the modulator 600. This prevents the light traveling in the waveguides of optical transmission lines 602 and 604 from phase matching, thereby mitigating optical coupling between the two waveguides. Another way to understand the importance of using different waveguide heights is to look at the two eigenmodes of the coupled waveguides of optical transmission lines 602 and 604. If the waveguide heights are equal, 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 sufficiently higher than the other, the lowest eigenmode will consist of light that resides primarily in the higher waveguide, and the second lowest eigenmode will reside primarily in the lower waveguide. This allows for differential modulation despite the proximity of the waveguides. For example, in some embodiments, the waveguide in one of the optical transmission lines 702 or 704 is at least 40 nm higher than the waveguide in the other optical transmission line. In some embodiments, the difference in height of the waveguides is in the range of 40 nm to 120 nm.

[0066] Furthermore, in such embodiments, the height changes of the two waveguides may be swapped along the modulator 600 so that the total length of the high portion of each waveguide is equal and the total length of the low portion of each waveguide is equal. In the example of FIG. 6, moving from left to right, the waveguide of the first optical transmission line 602 becomes higher than the waveguide of the second optical transmission line 604 and then becomes lower than the waveguide of the second optical transmission line 604 (alternatively, the first optical transmission line 602 may start lower and then become higher). While one such swap of relative heights may be located in the center of the modulator 600, in some embodiments, additional height swaps may be included, as long as, for example, the distance between the height swaps is significantly longer than the beat length (typically 10 μm) between the two eigenmodes in the two waveguides. This can reduce optical coupling between the two waveguides. In some embodiments, an odd number of swaps is preferred, as this ensures that the start and end transitions cancel each other out.

[0067] While the description of FIG. 6 above illustrates an example of a modulator 600 having waveguides of varying heights for the two optical transmission paths 602 and 604, in other embodiments the waveguides may have a constant height along the length of the modulator 600.

[0068] Furthermore, while the description of FIG. 6 shows an example of modulator 600 without a physical DC bias connection, in some embodiments, a DC bias connection may be implemented between the two optical transmission lines 602 and 604, albeit through a high impedance. For example, in some embodiments, the high impedance is achieved with an impedance greater than 1 kohm. As another example, in some embodiments, the high impedance is achieved with an impedance greater than 100 ohms. In such a scenario of a DC bias connection through a high impedance, a current would be generated by the voltage difference between (i) the external voltage and (ii) the voltage that would exist between the optical transmission lines 602 and 604 if no external voltage was applied. This generated current is less than the diode leakage current plus the photo-generated current in the diode, and thus the circuit operates primarily as if no external DC bias voltage was applied (e.g., similar to a true floating voltage). Therefore, it should be understood that embodiments of the present disclosure, such as those shown in FIGS. 6-9 without a physical DC bias connection, can also be implemented with a DC bias connection, albeit through a high impedance.

[0069] Modulator 600 implements an example of a continuous traveling wave structure, in which RF transmission line 614 is continuously connected to semiconductor structure 616. Alternatively, a segmented traveling wave structure may be implemented, as described below with reference to FIG.

[0070] 7 is a diagram illustrating another example of a top view of a modulator 700 according to an embodiment of the present disclosure. Modulator 700 is an example of an implementation of a segmented traveling wave structure.

[0071] The modulator 700 is also based on an MZI implementation, including two optical transmission lines 702 and 704, an optical splitter 706, and an optical combiner 708. The modulator 700 further includes terminals, such as terminal 710 and terminal 712, to which a voltage can be applied. The voltage propagates along an RF transmission line 714 connected to a semiconductor structure 716 via respective voltage-applying electrodes, generating an electric field across one or both of the optical transmission lines 702 and 704. The modulator 700 also does not implement any DC bias connection between the two optical transmission lines 702 and 704, thereby reducing the distance between them. For example, in some embodiments, 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 embodiments, 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 embodiments, the distance between the waveguides is in the range of 0.1 μm to 2.0 μm for at least a portion of the length of optical transmission lines 702 and 704. In some embodiments, the distance between the waveguides is defined as the distance between the inner sidewalls of the two waveguides at a given point along the length of modulator 700 (e.g., point 705 in FIG. 7).

[0072] The differences between the modulator 600 of FIG. 6 and the modulator 700 of FIG. 7 arise from the configuration of the semiconductor structures (616, 716) and the manner in which the RF transmission lines (614, 714) are connected to the semiconductor structures (616, 716). The modulator 600 of FIG. 6 implements a continuous traveling-wave structure, in which the RF transmission line 614 is continuously and directly connected to the semiconductor structure 616. In contrast, the modulator 700 of FIG. 7 implements a segmented traveling-wave structure, in which the RF transmission line 714 is intermittently connected to segments of the semiconductor structure 716, with intermittent regions 720 along the optical transmission paths 702 and 704 where no semiconductor structure is present. This structure of the modulator 700 can be referred to as a capacitively loaded traveling-wave structure and has the advantage of providing additional degrees of freedom in the implementation of the RF transmission line 714, for example, the average capacitance per unit length of the RF transmission line 714. Lumped-element modulators can also benefit from the techniques disclosed herein.

[0073] Additionally, in modulator 700, the waveguides of optical transmission lines 702 and 704 have different widths in different sections of modulator 700, similar to the configuration of the waveguides in modulator 600 of Figure 6. Further details of the variation in waveguide width are provided further below.

[0074] 8 illustrates an example cross-section of a modulator 800 according to an embodiment of the present disclosure (e.g., a cross-section of modulator 600 of FIG. 6 at point 605 or a cross-section of modulator 700 of FIG. 7 at point 705). In particular, modulator 800 of FIG. 8 is an example of a differential proximity design, in which one waveguide is higher than the other.

[0075] A cross section of modulator 800 shows details of the MZI structure. The MZI includes 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 embodiments, modulator 800 includes 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 including the optical waveguides 802 and 804).

[0076] In some embodiments, one of the optical waveguides 802 and 804 is taller than the other optical waveguide, as described above with respect to Figures 6 and 7. For example, in Figure 8, the second optical waveguide 804 is at least 40 nm taller than the first optical waveguide 802. In some embodiments, the difference in height of the waveguides is in the range of 40 nm to 120 nm.

[0077] Each of the optical waveguides 802 and 804 includes a semiconductor junction. The semiconductor junction diodes can 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, 804, forming a diode within each waveguide. These diodes are shown as a first semiconductor junction diode 812 and a second semiconductor junction diode 814.

[0078] Modulator 800 also includes electrodes 816 and 818 (e.g., metal electrodes) in physical contact with silicon layer 810. In some embodiments, 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 embodiments, metal layers 824 and 826 may form segments of RF transmission lines (e.g., RF transmission line 114 of FIG. 1). In some embodiments, in modulator 800, P-doped regions may instead be N-doped regions, or vice versa (e.g., so that contact regions 820 and 822 are N-doped instead of P-doped).

[0079] 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 connected together). This prevents continuous current from flowing through semiconductor junction diodes 812 and 814. This configuration ensures that the voltage across the two semiconductor junction diodes 812 and 814 naturally self-regulates, maintaining diodes 812 and 814 reverse bias, despite variations in modulation voltages (e.g., V+ and V−) that may be applied to electrodes 816 and 818. Implementing a floating voltage between semiconductor junction diodes 812 and 814 automatically biases diodes 812 and 814 at the modulator's most efficient point in terms of phase shift per volt. This is where diodes 812 and 814 are less than turned on. In some embodiments, this phase shift per volt becomes the "gain" of the modulator.

[0080] 2 is that the polarity of semiconductor junction diodes 812 and 814 is reversed compared to modulator 200. In particular, 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 ends of modulator 800. Thus, semiconductor region 838 between semiconductor junction diodes 812 and 814 is P-doped, and semiconductor regions 840 and 842 (connecting semiconductor junction diodes 812 and 814, respectively, to respective electrodes 816 and 818) are N-doped.

[0081] These aforementioned differences provide modulator 800 with numerous technical advantages over modulator 200 of FIG. 2. One advantage is that the absence of a DC bias voltage connection in modulator 800 allows the two optical waveguides 802 and 804 to be mounted much closer to each other than in modulator 200 of FIG. 2. This allows the size of semiconductor region 838 connecting semiconductor junction diodes 812 and 814 to be significantly reduced, significantly reducing the electrical series resistance between semiconductor junction diodes 812 and 814. For example, in some embodiments, the distance between the two optical waveguides 802 and 804 (labeled 805 in FIG. 8) is less than 0.5 μm. In some embodiments, the distance 805 between the two optical waveguides 802 and 804 is less than 2.0 μm. In some embodiments, 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 embodiments, the distance 805 between the waveguides may be defined as the distance between the inner sidewalls 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 as shown in FIG. 8).

[0082] Another advantage is that P-doped silicon has a higher resistivity than N-doped silicon (for the same optical absorption), so a more resistive P-doped material can be used for the small semiconductor region 838 (between semiconductor junction diodes 812 and 814) and a less resistive N-doped material can be used for the larger semiconductor regions 840 and 842 (connecting semiconductor junction diodes 812 and 814 to electrodes 816 and 818). Alternatively, in some embodiments, an N-doped material can be used for the smaller semiconductor region 838 and a P-doped material can be used for the larger semiconductor regions 840 and 842.

[0083] As a result, the total series resistance between electrodes 816 and 818 is significantly reduced, significantly improving the bandwidth and speed of modulation.

[0084] Although the lack of a DC bias voltage connection in modulator 800 removes a degree of freedom in the ability to adjust the amount of reverse bias in semiconductor junction diodes 812 and 814, in some scenarios the significant benefits provided by the configuration of modulator 800, such as improved modulation bandwidth and speed, outweigh such limitations.

[0085] FIG. 9 illustrates an exemplary equivalent circuit 900 along a cross section of a modulator (eg, a cross section of modulator 800 of FIG. 8) according to an embodiment of the present disclosure.

[0086] 9, the electrical series 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 electrical series 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 electrical series resistance 938 between the semiconductor junction diodes 912 and 914 (e.g., corresponding to semiconductor region 838 in FIG. 8) is 4.6 mΩ-m (when there is no DC bias voltage connection between the diodes).

[0087] 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 the equivalent circuit 300 in Figure 3. This reduction in total series resistance can significantly improve modulator performance. For example, the modulation bandwidth can be increased by reducing RF losses along the modulator. Alternatively, the modulator efficiency can be improved. For example, a thinner slab can be utilized, which increases the total series resistance but also increases the optical confinement within optical waveguides 802 and 804, thus improving modulator efficiency. Alternatively, a thicker waveguide can be utilized, which increases the capacitance but also increases the optical confinement.

[0088] Modulators according to embodiments of the present disclosure can be used in many applications. For example, one application is as a high-speed optical intensity modulator for generating Intensity Modulated Direct Detection (IM-DD) formats such as Non-Return-to-Zero (NRZ) and Pulse Amplitude Modulation (PAM). Another application is to use the modulator as part of a larger interferometer in combination with a second modulator with a 90-degree relative phase difference to generate more complex modulation formats for coherent detection, such as Quadrature Phase Shift Keying (QPSK) modulation or Quadrature Amplitude Modulation (QAM). For example, this can be achieved using an in-phase / quadrature (IQ) modulator structure with nested modulators, where each of the two branches of a modulator (outer modulator) implements another modulator (inner modulator). In some embodiments, phase shifters can be implemented to set the phase differences of 180 degrees and 90 degrees for the inner and outer modulators, respectively. Each modulator in such a nested modulator structure can be implemented as described in this disclosure.

[0089] 10 is a flowchart illustrating an exemplary method 1000 for modulating a quasi-TM polarized optical signal, according to an embodiment of the present disclosure. The method 1000 may be performed by using a modulator as disclosed herein.

[0090] The method 1000 includes splitting 1002 the quasi-TM polarized light into a first optical transmission path and a second optical transmission path. In some embodiments, an optical phase rotator may be implemented at the input of the modulator to rotate the phase of the input light such that the quasi-TM light propagates through the optical transmission path.

[0091] The method 1000 further includes modulating the phase difference between the quasi-TM polarized light in the first optical transmission line and the quasi-TM polarized light in the second optical transmission line (1004) without applying a bias voltage between the first optical transmission line and the second optical transmission line. In some embodiments, the phase difference between the quasi-TM polarized light in the first optical transmission line and the quasi-TM polarized light in the second optical transmission line is modulated while maintaining finite depletion regions in the semiconductor junction diodes of 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.

[0092] The method 1000 further includes combining the quasi-TM polarized light output from the first optical transmission path with the quasi-TM polarized light output from the second optical transmission path (1006).

[0093] While this disclosure contains many specific implementation details, these should not be construed as limitations on the scope of the invention or the claims, but rather as descriptions of features specific to particular implementations of a particular invention. Certain features described in this disclosure in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Furthermore, while features may be described above as working in a particular combination, and even initially claimed as such, one or more features from a claimed combination may, in some cases, be deleted from the combination, such that the claimed combination is directed to a subcombination or variations of the subcombination.

[0094] Similarly, although the figures depict operations in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown, or sequentially, or that all of the illustrated operations be performed, to achieve desirable results.

Claims

1. at least one optical input; at least one optical waveguide connected to the at least one optical input and configured to propagate quasi-transverse magnetic (quasi-TM) polarized light, each of the at least one optical waveguide configured as a rib waveguide including ribs disposed on a slab; and at least one electrode configured to apply at least one electric field to the quasi-TM polarized light in the at least one optical waveguide.

2. 10. The silicon photonic optical modulator of claim 1, configured as a silicon photonic depletion modulator, wherein the at least one optical waveguide comprises at least one semiconductor junction diode; the at least one electrode is configured to apply the at least one electric field to the quasi-TM polarized light within the at least one semiconductor junction diode;

3. 2. The silicon photonic optical modulator of claim 1, wherein the effective refractive index of a TM-polarized two-dimensional (2D) guided mode in the rib waveguide is greater than the effective refractive index of a transverse electric (TE)-polarized one-dimensional (1D) guided mode in the slab.

4. a doping concentration in a first portion of the slab that is within 100 nm of the nearest sidewall of the rib is greater than 1 cm compared to a second portion of the slab that is more than 100 nm away from the nearest sidewall of the rib; 3 10 per 17 10. The silicon photonic optical modulator of claim 1, wherein the active dopant is increased by more than 100%.

5. In the first portion of the slab that is within 50 nm to 500 nm from the nearest sidewall of the rib, the doping concentration is 1 cm 3 5x10 17 ~1×10 19 5. The silicon photonic optical modulator of claim 4, wherein the active dopant is increased by a value in the range of .

6. 10. The silicon photonic optical modulator of claim 1, comprising a Mach-Zehnder interferometer having the at least one optical waveguide, the at least one optical waveguide 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 The silicon photonic optical modulator further comprises a semiconductor region connecting the first semiconductor junction diode and the second semiconductor junction diode.

7. 7. The silicon photonic optical modulator of claim 6, wherein the distance between the first optical waveguide and the second optical waveguide is less than 500 nm along at least a portion of the longitudinal direction of the silicon photonic optical modulator.

8. the first semiconductor junction diode has a first p-doped region and a first n-doped region; and 7. The silicon photonic optical modulator of claim 6, wherein the second semiconductor junction diode has a second p-doped region and a second n-doped region.

9. the first p-doped region is connected to the second p-doped region through a third p-doped region in the semiconductor region connecting the first semiconductor junction diode and the second semiconductor junction diode; and 10. The silicon photonic optical modulator of claim 8, wherein the third p-doped region is configured without an external voltage connection with an impedance of less than 100 ohms.

10. at least one optical input; at least one optical waveguide configured to receive light from the at least one optical input, each of the at least one optical waveguide configured as a rib waveguide including ribs disposed on a slab; and at least one electrode configured to apply at least one electric field to light in the at least one optical waveguide; the height of the rib waveguide is greater than 0.85λ / n, where λ is the free-space wavelength of light and n is the refractive index of silicon in the silicon photonic optical modulator; and The silicon photonic optical modulator, wherein the width of the rib waveguide is greater than the thickness of the slab.

11. The silicon photonic optical modulator of claim 10 , wherein the height of the rib waveguide is greater than the width of the rib waveguide.

12. the height of the rib waveguide is in the range of 320 nm to 500 nm; The width of the rib waveguide is in the range of 150 nm to 270 nm; and The silicon photonic optical modulator of claim 11, wherein the thickness of the slab is in the range of 50 nm to 140 nm.

13. If the free space wavelength of said light is equal to 1310 nm, the height of the rib waveguide is in the range of 330 nm to 370 nm; The width of the rib waveguide is in the range of 200 nm to 240 nm; and The silicon photonic optical modulator of claim 12, wherein the thickness of the slab is in the range of 70 nm to 110 nm.

14. the at least one optical waveguide comprises a first rib waveguide and a second rib waveguide; and 11. The silicon photonic optical modulator of claim 10, wherein the distance between the first rib waveguide and the second rib waveguide is less than 500 nm.

15. 15. The silicon photonic optical modulator of claim 14, wherein a height of the first rib waveguide is greater than a height of the second rib waveguide in at least a portion of the silicon photonic optical modulator.

16. In the first portion of the silicon photonic optical modulator, a height of the first rib waveguide is at least 40 nm greater than a height of the second rib waveguide; 16. The silicon photonic optical modulator of claim 15, wherein in the second portion of the silicon photonic optical modulator, the height of the second rib waveguide is at least 40 nm greater than the height of the first rib waveguide.

17. a doping concentration in a first portion of the slab that is within 100 nm of the nearest sidewall of the rib is greater than 1 cm compared to a second portion of the slab that is more than 100 nm away from the nearest sidewall of the rib; 3 10 per 17 11. The silicon photonic optical modulator of claim 10, wherein the active dopant content is increased by more than 100%.

18. 1. A method for modulating quasi-transverse magnetic (TM) polarized light, comprising: inputting input quasi-TM polarized light into at least one optical waveguide; and applying at least one electric field to quasi-TM polarized light in the at least one optical waveguide.

19. splitting the input quasi-TM polarized light into a first optical waveguide and a second optical waveguide; modulating a phase difference between the quasi-TM polarized light in the first optical waveguide and the quasi-TM polarized light in the second optical waveguide without applying a bias voltage across an impedance of less than 100 ohms between the first optical waveguide and the second optical waveguide; and 19. The method of claim 18, further comprising: combining the quasi-TM polarized light output from the first optical waveguide with the quasi-TM polarized light output from the second optical waveguide.

20. 20. The method of claim 19, wherein a phase difference between the quasi-TM polarized light in the first optical waveguide and the quasi-TM polarized light in the second optical waveguide is modulated while maintaining finite depletion regions of semiconductor junction diodes in each of the first optical waveguide and the second optical waveguide.

21. 10. The silicon photonic optical modulator of claim 1, further comprising a polarization rotator between the at least one optical input and a first optical waveguide of the at least one optical waveguide, the polarization rotator configured to rotate the polarization of input light from the at least one optical input to produce quasi-TM polarization in the first optical waveguide.

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