Patent ID: 12222627

DETAILED DESCRIPTION

Systems and techniques are disclosed herein that provide a novel differential electro-optic modulator which can achieve a significantly higher modulation bandwidth and/or efficiency. This is accomplished by novel implementations which enable significant reduction in the physical distance between waveguides of the modulator. In some implementations, the reduced physical distance between the waveguides is achieved by removing a bias voltage connection between semiconductor junction diodes of waveguides of the modulator, while maintaining finite depletion regions in the semiconductor junction diodes. The reduced physical distance between the diodes, in turn, enables significantly reduced electrical resistance between the diodes, which increases the modulation bandwidth and/or efficiency of the modulator. In some implementations, to mitigate detrimental optical coupling that may occur between the closely-spaced waveguides, the waveguides have widths that vary in an alternating manner along the length of the modulator.

FIG.1illustrates an example of a top view of a differential modulator100which implements a bias voltage connection between the waveguides. This example is provided for comparison with modulators according to implementations of the present disclosure which are described further below with reference toFIGS.5-14.

The modulator100is based on a Mach-Zehnder interferometer (MZI) implementation, in which optical signals propagate along the length of the modulator100(e.g., from left to right inFIG.1) along two optical transmission paths102and104. At the input of modulator100, optical splitter106splits an input light into the two optical transmission paths102and104. At the output of the modulator100, the optical combiner108combines light output from the two optical transmission paths102and104. The optical splitter106and the optical combiner108may be implemented in various ways, for example, using symmetric, asymmetric, or tunable optical intensity couplers. The optical transmission paths102and104can be implemented by waveguides formed in a semiconducting structure116, as described in further detail with reference toFIG.2, below. In some implementations, the optical cores of the waveguides, and/or the optical splitter106, and/or the optical combiner108can include silicon ribs.

The modulator100uses a travelling wave configuration in which voltages applied at terminals110and112create an electrical signal that propagates along a radio frequency (RF) transmission line114, which is terminated at an RF termination resistance. The electrical signal in RF transmission line114travels at the same speed as and induces electro-optic modulation in the light that propagates along the two optical transmission paths102and104. In particular, the RF transmission line114is connected to the semiconducting structure116via electrodes (described in further detail with reference toFIG.2, below), that apply respective voltages, and resulting electric fields, across one or both of the optical transmission paths102and104. The applied voltage(s) induce a phase shift in the light that propagates in one or both of the optical transmission paths102and104. In some implementations, the phase shift is differential in that the phase shift magnitude is equal and the phase shift sign is opposite between the optical transmission paths102and104.

Electro-optic modulation is achieved by varying the voltage at one or both of the terminals110and112to modulate the differential phase shift between the phase of light in the first optical transmission path102and the phase of light in the second optical transmission path104. For example, if the terminal voltages are controlled such that the differential phase shift causes destructive interference at the optical combiner108, then this corresponds to an “off” or logic “0” state of the modulator100. By contrast, if the terminal voltages are controlled such that the differential phase shift between the two optical transmission paths102and104causes constructive interference at the optical combiner108, then this corresponds to the “on” or logic “1” state of the modulator100.

The differential phase shift between the two optical transmission paths102and104can also be influenced by other factors. For example, the physical lengths of the optical transmission paths102and104can be the same to provide zero inherent differential phase shift, or can be different lengths to provide non-zero inherent differential phase shift. Furthermore, in some implementations, direct current (DC) phase shifters122and124(e.g., thermo-optic phase-shifters, such as optical waveguide heaters), may be implemented near the ends of the optical transmission paths102and104to control the relative phases of the two light signals before being combining in the optical combiner108.

In some implementations, the phase modulation can be performed by a “push-pull” mechanism, in which the phases of light in both of optical transmission paths102and104are modulated, to control the relative phase shift between the two paths. In push-pull operation, the voltage V+ at terminal110is increased and voltage V− at terminal112is decreased (or vice versa), resulting in corresponding phase shifts of light in each of the optical transmission paths102and104. Push-pull modulation can provide various advantages over non-push-pull modulation, such as achieving smaller average energy consumption and reduced chirp in the modulated signal.

In some scenarios, a direct current (DC) bias connection118can be connected between the two optical transmission paths102and104. The DC bias connection118is implemented such that semiconductor junction diodes in each of the optical transmission paths102and104remain reverse biased, even when data signals applied at the terminals110and112vary between logical 1 and logical 0. Further details of the DC bias connection118and the semiconductor junction diodes are provided with reference toFIG.2, below.

FIG.2illustrates an example cross section of a modulator200which implements a bias voltage connection between the waveguides (e.g., the modulator100ofFIG.1). This example is provided for comparison with modulators according to implementations of the present disclosure which are described further below with reference toFIGS.5-14.

The cross-section of modulator200shows details of the MZI structure. The MZI includes a first optical waveguide202and a second optical waveguide204. The optical waveguides202and204can be implemented, for example, as silicon ribbed waveguides on top of a slab. In some implementations, the modulator200includes a substrate206(e.g., a silicon substrate) an insulating structure208(e.g., a dielectric, such as an oxide), and a semiconducting structure210(e.g., a silicon layer which includes optical waveguides202and204).

Each of the optical waveguides202and204includes a semiconductor junction. The semiconductor junction diodes can be implemented, for example, by a PIN (P-type/intrinsic/N-type) junction diode or a P/N junction diode. In modulator200, a P/N junction is implanted into each of the optical waveguides202and204, forming a diode in each waveguide. These diodes are shown as first semiconductor junction diode212and second semiconductor junction diode214.

The modulator200also includes electrodes216and218(e.g., metal electrodes) which are in physical contact with the silicon layer210. In some implementations, the electrodes216and218are in physical contact with P-doped contact regions220and222of the silicon layer210. The electrodes216and218may be formed, for example, by etching the insulator layer208and forming metal (e.g., tungsten, copper, and/or aluminum) contacts.

The modulator200may also include metal layers224and226on top of the electrodes216and218. In some implementations, the metal layers224and226may form segments of an RF transmission line (e.g., RF transmission line114inFIG.1).

In some scenarios, a DC bias connection228is implemented between the two optical waveguides202and204. The DC bias connection228ensures that the semiconductor junction diodes212and214remain reverse biased during modulation. For example, in a push-pull mode of modulation, a differential voltage (e.g., V+ and V−) is applied at the metal layers224and226(and hence at electrodes216and218). If the voltage (e.g., V+) at first electrode216is increased while the voltage (e.g., V−) at the second electrode218is decreased, then a width of the depletion region in the first optical waveguide202decreases while a width of the depletion region in the second optical waveguide204increases (and vice versa). As the depletion widths change, this changes the effective refractive index experienced by the light traveling along each of the optical waveguides202and204, resulting in corresponding phase shifts of the light. As a result, push-pull modulation can be achieved in the modulator200.

In the example of modulator200, the DC bias connection228is applied at the cathodes230and232(N-doped regions) of the semiconductor junction diodes212and214, while the varying voltages V+ and V− are applied at the anodes234and236(P-doped regions) of the semiconductor junction diodes212and214. The DC bias connection228ensures that the semiconductor junction diodes212and214remain reverse biased. For example, in the example of modulator200, if the bias voltage applied at the DC bias connection228is very low (or non-existent), then this may result in activation of the first semiconductor junction diode212(e.g., forward bias above 0.6 V for silicon) with a significant number of carriers injected into the depletion region of the first semiconductor junction diode212, resulting in forward bias and slower operation. Implementing the DC bias connection228with a sufficiently large bias voltage ensures that the semiconductor junction diodes212and214remain reverse biased under modulation.

However, the structure of modulator200results in various limitations on modulation performance. In particular, the structure of modulator200results in significant electrical series resistance in various regions of the modulator200.

In particular, the presence of DC bias connection228increases the physical distance of the semiconducting (e.g., silicon) region238between the semiconductor junction diodes212and214. This results in significant electrical series resistance in the semiconducting region238that connects the semiconductor junction diodes212and214. Furthermore, typical techniques to reduce such electrical series resistance, such as increasing the silicon doping of the semiconducting structure, can have other negative consequences such as increasing optical absorption.

Furthermore, the semiconducting regions240and242(which connect each of semiconductor junction diodes212and214with their respective electrodes216and218) are P-doped semiconducting material, which has higher resistance than N-doped semiconducting material (for the same optical absorption). This results in significant electrical series resistance in the semiconducting regions240and242between electrodes216and218and the semiconductor junction diodes212and214.

Consequently, the total electrical series resistance between electrodes216and218can significantly attenuate the voltage along the modulator200due to charging and discharging of the diode capacitance. Furthermore, this attenuation typically increases as modulation frequency increases. The resulting RF loss along the modulator200can detrimentally impact the bandwidth of the modulator200.

FIG.3illustrates an example equivalent circuit300along a cross-section of a modulator which implements a bias voltage connection between the waveguides (e.g., the cross section of modulator200ofFIG.2). This example is provided for comparison with modulators according to implementations of the present disclosure which are described further below with reference toFIGS.5-14.

In the example ofFIG.3, the electrical series resistance340between first electrode316and first semiconductor junction diode312(e.g., corresponding to semiconducting region240inFIG.2) is 7.2 mΩ-m. The electrical series resistance342between second electrode318and second semiconductor junction diode314(e.g., corresponding to semiconducting region242inFIG.2) is 7.2 mΩ-m. The electrical series resistance338between semiconductor junction diodes312and314(e.g., corresponding to semiconducting region238inFIG.2) is 7.4 mΩ-m (with 3.7 mΩ-m of series resistance between each of semiconductor junction diodes312and314and DC bias voltage connection328).

FIG.4illustrates another example of a cross section of a modulator400which implements a bias voltage connection between the waveguides (e.g., another example of a cross section of modulator100ofFIG.1). This example is provided for comparison with modulators according to implementations of the present disclosure which are described further below with reference toFIGS.5-14.

The structure of modulator400is referred to as a silicon-insulator-silicon capacitor (SISCAP) modulator structure. As compared with modulator200ofFIG.2, the modulator400implements thin oxide layers444and446in the semiconductor junction diodes412and414of optical waveguides402and404. Furthermore, in modulator400, the DC bias connection428applies a bias voltage at the anodes434and436(P-doped regions) of semiconductor junction diodes412and414, while the electrodes416and418apply varying voltages at the cathodes430and432(N-doped regions) of semiconductor junction diodes412and414. The DC bias connection428ensures that the semiconductor junction diodes412and414remain reverse biased.

FIGS.5-14relate to modulators according to implementations of the present disclosure. In contrast with the modulators ofFIGS.1-4, the modulators ofFIGS.5-14do not implement any bias voltage connection between the waveguides, resulting in significantly smaller series resistance between electrodes, and thus higher bandwidth of modulation. Furthermore, inFIGS.5-14, the modulators implement waveguide structures that vary in width so as to mitigate detrimental optical coupling between the closely-spaced waveguides.

FIG.5illustrates an example of a top view of a modulator500according to implementations of the present disclosure.

The modulator500is based on an MZI implementation which includes two optical transmission paths502and504, optical splitter506, and optical combiner508. The modulator500further includes terminals, such as terminal510and terminal512, through which voltages can be applied. The voltages travel along RF transmission line514, which is connected to semiconducting structure516via electrodes that apply respective voltages, and resulting electric fields, across one or both of the optical transmission paths502and504.

In contrast to the modulator100ofFIG.1, the modulator500does not implement any DC bias connection between the two optical transmission paths502and504. This enables the two optical transmission paths502and504to be more closely-spaced together, thus reducing electrical series resistance therebetween. For example, in some implementations, the distance between the waveguides of the two optical transmission paths502and504is less than 0.5 μm for at least a portion of the longitudinal direction of the optical transmission paths502and504. In some implementations, the distance between the waveguides is less than 2.0 μm for at least a portion of the longitudinal direction of the optical transmission paths502and504. In some implementations, the distance between the waveguides is within a range of 0.1 μm to 2.0 μm for at least a portion of the longitudinal direction of the optical transmission paths502and504. In some implementations, the distance between the waveguides is defined as the distance between the inner sidewalls of the two waveguides, at a given point along a longitudinal direction of the modulator500(e.g., at a point505inFIG.5).

However, because the two optical transmission paths502and504are more closely spaced, there is risk of more significant detrimental optical coupling between light in optical transmission path502and light in optical transmission path504. To mitigate such optical coupling, in some implementations, the waveguide of one of the optical transmission paths (502or504) is designed to have a larger width than the other path, at the same distance along the length of the modulator500. This helps ensure that the light traveling in the waveguides of optical transmission paths502and504are not phase matched, thus mitigating 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 paths502and504. If the waveguides have equal widths, then the lowest order eigenmode is the even eigenmode, and the second lowest eigenmode is the odd eigenmode. In such a scenario, no differential modulation can occur. However, if one waveguide is sufficiently wider than the other, then the lowest order eigenmode consists of light that is predominantly in the wider waveguide, and the second lowest eigenmode is predominantly in the narrower waveguide. This enables differential modulation to occur despite the closely-spaced waveguides. For example, in some implementations, the waveguide of the one of the optical transmission paths702or704is wider by at least 0.04 μm than the waveguide of the other optical transmission path. In some implementations, the waveguide width difference is within a range of 0.04 μm to 0.4 μm.

Furthermore, in such implementations, the width variation of the two waveguides may be exchanged along the modulator500, to help ensure that the total length of the wider portions in each waveguide are equal, and also that the total length of the narrower portions in each waveguide are equal. In the example ofFIG.5, moving from the left to right, the waveguide of first optical transmission path502is wider than the waveguide of the second optical transmission path504, and then becomes narrower than the waveguide of the second optical transmission path504(alternatively, the first optical transmission path502may start narrower and become wider). The example ofFIG.5shows one width swap in the middle of modulator500, but in some implementations, additional width swaps can be included. Further details of the width variations of the waveguides will be discussed in reference toFIG.7, below.

Although the description ofFIG.5, above, provided an example of a modulator500with variable-width waveguides in the two optical transmission paths502and504, in other implementations, the waveguides may have constant width along the length of the modulator500.

Furthermore, although the description ofFIG.5provided an example of a modulator500without a physical DC bias connection, in some implementations, a DC bias connection may be implemented between the two optical transmission paths502and504, but through a high impedance. For example, in some implementations, the high impedance is achieved with an impedance greater than 1 kohm. As another example, in some implementations, the high impedance is achieved with an impedance greater than 100 ohm. In such scenarios 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 be between the optical transmission paths502and504if there were no applied external voltage. This generated current would be less than the diode leakage current plus any photo-generated current in the diodes, and thus the circuit would act primarily as if there were no applied external DC bias voltage (e.g., similar to a true floating voltage). Therefore, it should be appreciated that implementations of the present disclosure, such as those shown inFIGS.5-10in which there is no physical DC bias connection, can also be implemented with a DC bias connection but through a high impedance.

The modulator500implements an example of a continuous traveling-wave structure, in which the RF transmission line514is continuously connected to the semiconducting structure516. Alternatively, a segmented traveling-wave structure can be implemented, as described with reference toFIG.6, below.

FIG.6illustrates another example of a top view of a modulator600according to implementations of the present disclosure. The modulator600is an example of an implementation of a segmented traveling-wave structure.

The modulator600is also based on an MZI implementation which includes two optical transmission paths602and604, optical splitter606, and optical combiner608. The modulator600further includes terminals, such as terminal610and terminal612, through which voltages can be applied. The voltages travel along RF transmission line614, which is connected to a semiconducting structure616via electrodes that apply respective voltages, and resulting electric fields, across one or both of the optical transmission paths602and604. The modulator600also does not implement any DC bias connection between the two optical transmission paths602and604, which reduces the distance therebetween. For example, in some implementations, the distance between the waveguides of the two optical transmission paths602and604is less than 0.5 μm for at least a portion of the longitudinal direction of the optical transmission paths602and604. In some implementations, the distance between the waveguides is less than 2.0 μm for at least a portion of the longitudinal direction of the optical transmission paths602and604. In some implementations, the distance between the waveguides is within a range of 0.1 μm to 2.0 μm for at least a portion of the longitudinal direction of the optical transmission paths602and604. In some implementations, the distance between the waveguides is defined as the distance between the inner sidewalls of the two waveguides, at a given point along a longitudinal direction of the modulator600(e.g., at a point605inFIG.6).

The differences between modulator500ofFIG.5and modulator600ofFIG.6arise from the configuration of the semiconducting structure (516,616) and the manner in which the RF transmission line (514,614) is connected to the semiconducting structure (516,616). Modulator500ofFIG.5implements a continuous traveling wave structure in which RF transmission line514is continuously directly connected to the semiconducting structure516. By contrast, modulator600ofFIG.6implements a segmented traveling wave structure in which RF transmission line614is intermittently connected to segments of the semiconducting structure616, with intermittent regions620along the optical transmission paths602and604in which there is no semiconducting structure. This structure of modulator600can also be referred to as a capacitively loaded traveling wave structure, and has an advantage of providing an additional degree of freedom in implementing the RF transmission614, e.g., of the average capacitance per unit length of the RF transmission line614. A lumped-element modulator can also benefit from the techniques disclosed herein.

Furthermore, in modulator600, the waveguides of optical transmission paths602and604have different widths in different sections of the modulator600, similar to the configuration of the waveguides in modulator500ofFIG.5. Further details of the width variation of the waveguides are provided with reference toFIG.7, below.

FIG.7illustrates an example of a top view of a width-exchange region of modulator700showing width variations of optical waveguides, according to implementations of the present disclosure (e.g., modulator500ofFIG.5or modulator600ofFIG.6). In some implementations, the width-exchange region is implemented between the semiconducting regions616ofFIG.6.

The modulator700includes two optical transmission paths702and704, which can be implemented by silicon ribbed waveguides. Furthermore, as discussed with reference toFIGS.5and6, above, modulator700does not implement any DC bias connection, thus enabling the two optical transmission paths702and704to be more closely-spaced together, thus reducing electrical series resistance therebetween.

To mitigate detrimental optical coupling between the more closely-spaced waveguides of the optical transmission paths702and704, one of the optical transmission paths702or704has a waveguide of a larger width than the waveguide the other optical transmission path. This helps ensure that light traveling in the waveguides of optical transmission paths702and704are not phase matched, thus mitigating optical coupling between the two waveguides. For example, in some implementations, the waveguide of one of the optical transmission path702or704is wider by at least 0.04 μm than the waveguide of the other optical transmission path.

Furthermore, the width variation of the two waveguides may be exchanged along the modulator700. For example, inFIG.7, in portion722of modulator500, the waveguide of second optical transmission path704is wider than the waveguide of the first optical transmission path702. Then, in portion724of modulator700, the waveguide of the first optical transmission path702is wider than the waveguide of the second optical transmission path704. In some implementations, the difference in waveguide width is at least 0.04 μm. In some implementations, the waveguide width difference is within a range of 0.04 μm to 0.4 μm.

The example ofFIG.7shows one width exchange in the middle of modulator700, but in some implementations, additional width exchanges can be included, e.g., as long as the distance between width exchanges is significantly longer than the beat length between the two eigenmodes in the two waveguides, which is typically 10 μm. This helps mitigate optical coupling between the two waveguides. In some implementations, an odd number of exchanges is preferred, since this will help ensure that the beginning and end transitions cancel each other out.

A potential complication that arises from varying the widths of waveguides in optical transmission paths702and704is that wider waveguides have higher effective refractive index than narrower waveguides. As a result, the phase of light in the waveguide is affected differently in wider portions of the waveguide as compared to narrower portions of the waveguide. As such, if the two optical transmission paths702and704have different lengths of wider portions (e.g., if the length of portion722is greater than the length of portion724, or vice versa), then this could result in different inherent phase shifts of light in the two waveguides, e.g., due to wavelength or temperature differences, or different speeds of light in the two waveguides.

To mitigate such complications, the exchanging of widths of the two waveguides can be implemented to ensure that the total length of the wider portions in each waveguide are equal, and also that the total length of the narrower portions in each waveguide are equal. This helps ensure that the total effective path length of optical transmission path702is the same as that of optical transmission path704. As a result, this can help ensure non-zero inherent differential phase shift between light propagating along the two optical transmission paths702and704.

In some implementations, the width-exchanging transition can be implemented in a gradual manner. For example, from left to right inFIG.7, the distance between the waveguides of the two optical transmission paths702and704is gradually increased. This helps ensure that light in the two optical transmission paths702and704remains largely uncoupled. With this increased separation, the widths of each waveguide is changed, such that the wider waveguide becomes narrower and the narrower waveguide becomes wider. Once the waveguides have exchanged widths, then the two waveguides are gradually brought closer together again.

In some implementations, the distance between the waveguides of the two optical transmission paths702and704is less than 0.5 μm for at least a portion of the longitudinal direction of the optical transmission paths702and704. In some implementations, the distance between the waveguides is less than 2.0 μm for at least a portion of the longitudinal direction of the optical transmission paths702and704. In some implementations, the distance between the waveguides is within a range of 0.1 μm to 2.0 μm for at least a portion of the longitudinal direction of the optical transmission paths702and704. In some implementations, the distance between the waveguides is defined as the distance between the inner sidewalls of the two waveguides, at a given point along a longitudinal direction of the modulator700(e.g., at a point705inFIG.7).

FIG.8illustrates an example of a cross section of a modulator800according to implementations of the present disclosure (e.g., a cross section at point505of modulator500ofFIG.5or a cross at point605of modulator600ofFIG.6).

The cross-section of modulator800shows details of the MZI structure. The MZI includes a first optical waveguide802and a second optical waveguide804. The optical waveguides802and804can be implemented, for example, as silicon ribbed waveguides on top of a slab. In some implementations, the modulator800includes a substrate806(e.g., a silicon substrate) an insulating structure808(e.g., a dielectric, such as an oxide), and a semiconducting structure810(e.g., a silicon layer which includes optical waveguides802and804).

In some implementations, as discussed in regards toFIGS.5-7, above, one of the optical waveguides802and804is wider than the other optical waveguide. For example, inFIG.8, the second optical waveguide804is wider by at least 0.04 μm than the first optical waveguide802. In some implementations, the waveguide width difference is within a range of 0.04 μm to 0.4 μm.

Each of the optical waveguides802and804includes a semiconductor junction. The semiconductor junction diodes can be implemented, for example, by a PIN (P-type/intrinsic/N-type) junction diode or a P/N junction diode. In modulator800, a P/N junction is implanted into each of the optical waveguides802and804, forming a diode in each waveguide. These diodes are shown as first semiconductor junction diode812and second semiconductor junction diode814.

The modulator800also includes electrodes816and818(e.g., metal electrodes) which are in physical contact with the silicon layer810. In some implementations, the electrodes816and818are in physical contact with N-doped contact regions820and822of the silicon layer810. The electrodes816and818may be formed, for example, by etching the insulator layer808and forming metal (e.g., tungsten, copper, and/or aluminum) contacts. The modulator800may also include metal layers824and826on top of the electrodes816and818. In some implementations, the metal layers824and826may form segments of an RF transmission line (e.g., RF transmission line114inFIG.1).

There are numerous differences between modulator800and modulator200ofFIG.2. Most notably, modulator800does not implement any DC bias voltage connection between semiconductor junction diodes812and814(as compared to modulator200which implements DC bias connection228). Instead, the semiconductor junction diodes812and814are connected in series with opposite polarity (with anodes834and836connected together). This ensures that a continuous current can never flow through the semiconductor junction diodes812and814. This configuration enables the voltages across the two semiconductor junction diodes812and814to naturally self-adjust to ensure that the diodes812and814remain reverse-biased, despite variations in modulation voltages (e.g., V+ and V−) that may be applied at electrodes816and818. Implementing a floating voltage between the semiconductor junction diodes812and814automatically biases the diodes812and814at the most efficient point of the modulator in terms of phase shift per volt, which is where the diodes812and814are just below turn-on. In some implementations, this phase shift per volt is the “gain” of the modulator.

Another difference between modulator800and modulator200ofFIG.2is that the polarities of semiconductor junction diodes812and814are flipped, as compared with modulator200. In particular, semiconductor junction diodes812and814have their respective (P-doped) anodes834and836closer to the center of modulator800, and their respective (N-doped) cathodes830and832closer to the edges of modulator800. As such, the semiconducting region838between the semiconductor junction diodes812and814is P-doped, while semiconducting regions840and842(connecting each of semiconductor junction diodes812and814with their respective electrodes816and818) are N-doped.

These aforementioned differences provide numerous technical advantages for modulator800, as compared to modulator200ofFIG.2. One advantage is that the absence of a DC bias voltage connection in modulator800enables the two optical waveguides802and804to be implemented significantly closer to each other, as compared to modulator200ofFIG.2. This enables significant reduction in the size of semiconducting region838connecting semiconductor junction diodes812and814, which significantly reduces the electrical series resistance between semiconductor junction diodes812and814. For example, in some implementations, the distance (denoted as805inFIG.8) between the two optical waveguides802and804is less than 0.5 μm. In some implementations, the distance805between the two optical waveguides802and804is less than 2.0 μm. In some implementations, the distance805between the two optical waveguides802and804is within a range of 0.1 μm to 2.0 μm. In some implementations, the distance805between waveguides may be defined as the distance between the inner sidewalls of the two waveguides, at a given point along the longitudinal direction of the modulator800(e.g., measured at a cross section of the modulator800as shown inFIG.8).

Another advantage is that, since P-doped silicon has a higher resistivity than N-doped silicon (for the same optical absorption), higher-resistivity P-doped material is used in the smaller semiconducting region838(between semiconductor junction diodes812and814), and lower-resistivity N-doped material is used in the larger semiconducting regions840and842(connecting semiconductor junction diodes812and814with electrodes816and818). Alternatively, in some implementations, N-doped material can be used in the smaller semiconducting region838, and P-doped material can be used in the larger semiconducting regions840and842.

As a result, the total series resistance between the electrodes816and818is significantly reduced, thus significantly improving bandwidth and speed of the modulation.

Although the lack of a DC bias voltage connection in modulator800takes away a degree of freedom in the ability to adjust the amount of reverse bias in semiconductor junction diodes812and814, such limitations are, in some scenarios, outweighed by the significant benefits offered by the configuration of modulator800, such as improved bandwidth and speed of modulation.

FIG.9illustrates an example equivalent circuit900along a cross-section of a modulator according to implementations of the present disclosure (e.g., the cross section of modulator800ofFIG.8).

In the example ofFIG.9, the electrical series resistance940between first electrode916and first semiconductor junction diode912(e.g., corresponding to semiconducting region840inFIG.8) is 3.7 mΩ-m. The electrical series resistance942between second electrode918and second semiconductor junction diode914(e.g., corresponding to semiconducting region842inFIG.8) is 3.7 mΩ-m. The electrical series resistance938between semiconductor junction diodes912and914(e.g., corresponding to semiconducting region838inFIG.8) is 4.6 mΩ-m (without any DC bias voltage connection between the diodes).

As seen in this example, the total series resistance between electrodes916and918is reduced by about a factor of two, as compared with the equivalent circuit300ofFIG.3. This reduction in total series resistance can significantly improve modulator performance. For example, the modulation bandwidth is increased, by reducing the RF loss along the modulator. Alternatively, modulator efficiency can be improved. For example, a thinner slab can be utilized, which increases total series resistance but also increases optical confinement in the optical waveguides802and804, thus improving modulator efficiency. Alternatively, a thicker waveguide can be utilized, which increases capacitance but also increases optical confinement.

FIG.10illustrates another example of a cross section of a modulator1000according to implementations of the present disclosure (e.g., another example of a cross section of modulator500ofFIG.5or modulator600ofFIG.6).

The structure of modulator1000is a silicon-insulator-silicon capacitor (SISCAP) modulator structure. As compared with modulator800ofFIG.8, the modulator1000implements thin oxide layers1044and1046in the semiconductor junction diodes1012and1014of optical waveguides1002and1004. Furthermore, as in modulator800ofFIG.8, the anodes1034and1036(P-doped regions) of semiconductor junction diodes1012and1014are connected together (without a DC bias connection therebetween), and the electrodes1016and1018apply varying voltages at the cathodes1030and1032(N-doped regions) of semiconductor junction diodes1012and1014.

These features provide numerous technical advantages for modulator1000, as compared to modulator200ofFIG.2. One advantage is that the absence of a DC bias voltage connection in modulator1000enables the two optical waveguides1002and1004to be implemented significantly closer to each other, as compared to modulator200ofFIG.2. This enables significant reduction in the size of semiconducting region1038connecting semiconductor junction diodes1012and1014, which significantly reduces the electrical series resistance between semiconductor junction diodes1012and1014. Another advantage is that higher-resistivity P-doped material is used in the smaller semiconducting region1038(between semiconductor junction diodes1012and1014), and lower-resistivity N-doped material is used in the larger semiconducting regions1040and1042(connecting semiconductor junction diodes1012and1014with electrodes1016and1018). As a result, the total series resistance between the electrodes1016and1018is significantly reduced, thus significantly improving bandwidth and speed of the modulation. For example, in some implementations, the distance (denoted as1005inFIG.10) between the two optical waveguides1002and1004is less than 0.5 μm. In some implementations, the distance1005between the two optical waveguides1002and1004is less than 2.0 μm. In some implementations, the distance1005between the two optical waveguides1002and1004is within a range of 0.1 μm to 2.0 μm. In some implementations, the distance1005between waveguides may be defined as the distance between the inner sidewalls of the two waveguides, at a given point along the longitudinal direction of the modulator1000(e.g., measured at a cross section of the modulator1000as shown inFIG.10).

Furthermore, in some implementations, as discussed in regards toFIGS.5-8, above, one of the optical waveguides1002and1004is wider than the other optical waveguide. For example, inFIG.10, the second optical waveguide1004is wider by at least 0.04 μm than the first optical waveguide1002. In some implementations, the waveguide width difference is within a range of 0.04 μm to 0.4 μm.

The 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 to generate intensity-modulated direct-detection (IM-DD) formats such as non-return-to-zero (NRZ) or pulse amplitude modulation (PAM). Another application is to use the modulator in conjunction with a second modulator with a 90-degree relative phase shift as part of a larger interferometer 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 by an in-phase/quadrature (IQ) modulator structure that includes nested modulators, with each of the two branches of a modulator (the outer modulator) implementing another modulator (the inner modulators). In some implementations, phase shifters can be implemented that set 180-degree and 90-degree phase differences for the inner and outer modulators, respectively. Each modulator in such a nested modulator structure can be implemented as described in the present disclosure (e.g., implemented as a modulator described with reference toFIGS.5-10).

FIG.11illustrates an example of the performances of different modulators, in terms of conductance per unit length between the V+ and V− terminals as a function of distance between the waveguides.

The plots shown inFIG.11compare the performance of a modulator with a DC bias connection (e.g., modulator100ofFIG.1) with the performance of a modulator with a floating anode implementation (e.g., the modulators ofFIGS.5-10), and a modulator with a floating cathode implementation, for typical semiconductor doping levels. As shown inFIG.11, if the distance between the waveguides is 0.1 μm, then the floating anode implementation doubles the conductance, as compared to the DC bias connection implementation. The floating cathode implementation also provides an improvement over the DC bias connection implementation, although significantly smaller due to the predominance of the P-doped regions in the semiconducting structure of the modulator.

FIG.12illustrates an example of the performances of different modulators, in terms of voltage across each semiconductor junction diode as a function of applied differential voltage ΔV across the two terminals of the modulator, where ΔV=V+−V−, which is the voltage across the two diodes in series inFIGS.3and9.

The curves with dotted lines represent the voltages across each of the two diodes of a modulator with a DC bias connection (e.g., modulator100ofFIG.1), and the curves with solid lines represent the voltages across each of the two diodes of a modulator with a floating anode implementation (e.g., the modulators ofFIGS.5-10).

For the curves with dotted lines (a modulator with a DC bias connection, e.g., modulator100ofFIG.1), the bias voltage is adjusted so that the diodes remain below the diode turn-on voltage. For these curves, the voltage across each diode is approximately linear with a magnitude of slope equal to approximately ½ (i.e., +½ and −½ for the two dotted-line curves).

For the curves with solid lines (a modulator with a floating anode implementation, e.g., the modulators ofFIGS.5-10), when the differential applied voltage ΔV is equal to zero, the voltage across each diode is also zero, such that curves for the two diodes intersect at point (0, 0) of the graph. If the applied differential voltage ΔV is large, then one diode is just below turn-on, and the other diode has a large reverse voltage. This allows the modulator to operate at the highest possible gain automatically, despite environmental or fabrication process changes. The solid-line curves for both diodes initially transition with slopes of magnitude 1 (i.e., +1 and −1 for the sloped portions of the two solid-line curves). The overall result is a nonlinear behavior of voltage across each diode as a function of applied differential voltage ΔV. The difference of the voltages across the two diodes is strictly proportional to the applied differential voltage ΔV in both cases, but the MZI configuration of the modulator is no longer driven with equal and opposite sign in each optical transmission path. This will introduce a small nonlinear chirp on the resulting optical signal that is output from the optical combiner, which may impact transmission in the presence of chromatic dispersion. However, this effect should be very small.

FIG.13illustrates an example of the performances of modulators according to implementations of the present disclosure (e.g., the modulators ofFIGS.5-10), in terms of normalized differential refractive index change between the two waveguides of the modulator, as a function of distance between the waveguides, for various waveguide widths.

In the example ofFIG.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 ofFIG.13were generated by simulating a depletion zone in the center of each waveguide, with the size of the depletion zone having width 0.2 μm and height 0.22 μm. The depletion zone is increased in refractive index by 3×10−4in one waveguide and decreased in refractive index by 3×10−4in the other waveguide, and the refractive indices of the two waveguide modes are calculated. The sign of the refractive index change is changed, and the refractive indices of the two waveguide modes are 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 yield the differential index in the plots ofFIG.13.

FIG.14is a flowchart illustrating an example method1400of modulating an optical signal, according to implementations of the present disclosure. The method1400may be performed by using a modulator as disclosed herein (e.g., a modulator as described with reference toFIGS.5-10).

The method1400includes splitting input light into a first optical transmission path and a second optical transmission path (1402).

The method1400further includes 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 between the first optical transmission path and the second optical transmission path (1404). In some implementations, the phase difference between the light in the first optical transmission path and the light in the second optical transmission path is modulated while maintaining finite depletion regions in semiconductor junction diodes in each of the first optical transmission path and the second optical transmission path. For example, this modulation can be performed using the floating anode structure of modulators discussed above with reference toFIGS.5-10.

The method1400further includes combining light that is output from the first optical transmission path and light that is output from the second optical transmission path (1406).

While this disclosure contains many specific implementation details, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular implementations of particular inventions. Certain features that are described in this disclosure in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results.