Hybrid Photonic Ring Modulator
By using a hybrid photon ring modulator in a photonic integrated circuit, the p-i-n diode structure of compound semiconductor materials and the refractive index modulation of the ring waveguide is solved, and the existing optical modulators are high in area and high in power consumption are achieved, achieving high efficiency and low Optical modulation effect of power consumption.
Patent Information
- Application Number
- CN202011590790.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Priority Date
- 2020-10-07
- Filing Date
- 2020-12-29
- Publication Date
- 2024-12-31
- Estimated Expiration
- 2040-12-29
AI Technical Summary
The optical modulators in existing photonic integrated circuits have large area and high power consumption, making it difficult to meet the power and area requirements of high-channel counting photonic transceivers.
Using a hybrid photon ring modulator, a ring resonator structure is formed on the silicon bus waveguide, and a refractive index modulation of the ring waveguide is achieved using the p-i-n diode structure of the compound semiconductor material, and efficient optical modulation is achieved through vertical coupling and voltage modulation.
Higher tuning efficiency and smaller footprint are achieved, reducing the power consumption of photonic circuits and improving device density.
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Figure CN114296260B_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates to optical modulators for use in photonic integrated circuits (PICs), and to associated methods of manufacture, calibration, and operation. Background Art
[0002] Many PICs employ integrated optical (or synonymously, photonic) modulators to convert electrical signals into optical signals. For example, a photonic transceiver may use an optical modulator to transfer high-speed digital data onto a laser carrier signal for transmission via a fiber-optic cable. In silicon photonics, an optical modulator may be implemented directly in a silicon device layer (e.g., of a silicon-on-insulator (SOI) substrate) as a Mach-Zehnder modulator, where an electro-optically or thermo-optically induced phase shift in one of the interferometer arms of a Mach-Zehnder interferometer achieves amplitude modulation of the optical signal. Alternatively, in a hybrid material platform comprising a compound semiconductor (e.g., III-V) layer above the silicon device layer, light may be coupled between the silicon device layer and a compound semiconductor electro-absorption modulator that achieves optical amplitude modulation by wavelength-shifting the absorption edge. Two of these common optical modulator implementations occupy the active area of the chip and consume a large amount of power to tune the phase or absorption for signal modulation. Optical modulators with higher tuning efficiency and smaller footprint are desired to reduce overall power consumption and increase device density in photonic circuits, especially in higher-lane-count photonic transceivers where power and area requirements increase rapidly. Summary of the invention
[0003] According to some embodiments, a hybrid photonic ring modulator is disclosed, comprising: a silicon bus waveguide formed in a silicon device layer of a silicon-on-insulator (SOI) substrate; and a ring resonator structure formed above the silicon device layer, the ring resonator structure comprising a pin diode structure of a semiconductor compound material and associated electrodes, the active region of the pin diode structure forming a ring waveguide that laterally overlaps with the bus waveguide, the ring waveguide and the silicon bus waveguide together forming a vertically oriented coupler in the overlapping region.
[0004] According to some embodiments, a photonic integrated circuit (PIC) is disclosed, comprising: a laser; and a hybrid photonic ring modulator, the hybrid photonic ring modulator comprising: a silicon bus waveguide vertically coupled to a ring-shaped active region of a pin diode structure formed of a compound semiconductor material, an optical input of the silicon bus waveguide coupled to an output of the laser, and an optical output of the silicon bus waveguide coupled to an output port of the PIC.
[0005] According to some embodiments, a method of modulating light guided in a silicon waveguide is disclosed, the method comprising: vertically coupling light from the silicon waveguide into an optically active ring waveguide of a compound semiconductor pin diode structure formed above the silicon waveguide; and applying a swing voltage across the pin diode structure to thereby modulate a refractive index in the ring waveguide. BRIEF DESCRIPTION OF THE DRAWINGS
[0006] Figure 1A and Figure 1B are a cross-sectional side view and a top view, respectively, of an example hybrid photonic ring modulator according to various embodiments, and Figure 1C to Figure 1E Along various horizontal lines from Figure 1A Cut cross-section view.
[0007] FIG. 2A to FIG. 2F is a top view of an example heater configuration according to various embodiments for use in Figure 1A and Figure 1B The hybrid photonic ring modulator shown.
[0008] Figures 3A to 3G According to various embodiments Figures 1A to 1E A cross-sectional side view of a semiconductor photonic structure showing various stages during fabrication of a hybrid photonic ring modulator is shown.
[0009] Figure 4 is a schematic block diagram of an example photonic transceiver system including a hybrid photonic ring modulator according to various embodiments.
[0010] Figure 5A and Figure 5B Example spectral modulator responses of a hybrid photonic ring modulator at various bias voltage levels without absorption and with absorption at higher bias voltages, respectively, according to various embodiments.
[0011] Figure 6 is a graph showing example optical amplitude modulation and eye crossing of a hybrid photonic ring modulator according to various embodiments as a function of heater power.
[0012] Figure 7 is a flow chart of a method of calibrating a hybrid photonic ring modulator with an integrated heater according to various embodiments.
[0013] Figure 8 is a flow chart of a method of operating a hybrid photonic ring modulator with an integrated heater according to various embodiments. DETAILED DESCRIPTION
[0014] A hybrid photonic ring modulator formed of a silicon bus waveguide vertically coupled to a compound semiconductor ring waveguide that acts as a ring resonator and has high-speed electrode connections to facilitate changing the refractive index in the ring waveguide, thereby shifting the resonance, is described herein. In various embodiments, the ring waveguide is formed of an annular optically active region of a vertically layered pin diode structure of compound semiconductor material, and the refractive index change is achieved by applying a voltage across the pin diode structure based on the (linear and / or quadratic) electro-optic effect.
[0015] Typically, light entering the bus waveguide at its input is partially transmitted to the output of the bus waveguide and partially evanescently coupled into the ring waveguide and, after a round trip, returns to the bus waveguide where it interferes with the directly transmitted portion of the light. The total transmitted power obtained at the output (as a fraction of the input power) is a function of the coupling coefficient between the bus waveguide and the ring waveguide, the absorption in the ring waveguide, and the phase shift induced in the ring waveguide during the round trip. If the round trip phase is an integer multiple of 2π, or equivalently, the round trip optical path length is an integer multiple of the wavelength of the light, the ring waveguide is in resonance and the transmission at the modulator output is minimum; therefore, the ring modulator acts as a spectral filter. The transmission minimum can be conceptually understood as the destructive interference between the directly transmitted light and the light coupled back into the bus waveguide from the ring waveguide, which has undergone a coupling-induced π phase shift. Further, for any given round-trip phase, the transmission is minimum when the intensity of the directly transmitted light is equal to the intensity of the light in the ring waveguide after completing one round trip (subject to any absorption in the ring waveguide), which is called the "critical coupling" condition. If the intensity of the directly transmitted light after one round trip is greater than the intensity in the ring waveguide, the modulator is "overcoupled"; if the intensity of the light after one round trip through the ring waveguide is greater, the modulator is "undercoupled". If both the resonance condition and the critical coupling condition are met, the transmitted power at the transmission minimum is zero.
[0016] By modulating the refractive index (and hence the optical phase) in the ring waveguide via an applied voltage, the transmitted power can be modulated. The optical modulation amplitude (OMA), defined as the difference between the maximum and minimum transmitted optical powers during an RF voltage swing, depends on the refractive index change over the RF swing and the relative optical intensities of the interference components of the light (corresponding to whether the modulator is undercoupled, critically coupled, or supercooled). The refractive index modulation in turn depends on the wavelength shift of the modulator response per volt, referred to herein as the "tuning efficiency." The maximum OMA occurs in the case of high tuning efficiency and slight undercoupling.
[0017] Ring modulators provide a resonant enhancement to the OMA achieved with a given refractive index modulation, and therefore, are much more compact in design compared to non-resonant modulators such as Mach-Zehnder modulators and electro-absorption modulators. In various embodiments, the diameter of the ring waveguide is, for example, between 5 μm and 50 μm. For comparison, the length of a typical Mach-Zehnder interferometer is in the range of 1 mm to 5 mm, and the length of a typical electro-absorption modulator is about 150 μm or more. These savings in chip area allow for denser photonic circuits and lower wafer area costs.
[0018] In addition, the compound semiconductor materials used for the disclosed ring modulators are subject to a strong electro-optic effect, which means that under applied voltage, they undergo a large refractive index change and, therefore, the tuning efficiency is high. As a result, the maximum achievable OMA per applied voltage swing (referred to herein as "modulation efficiency") of a hybrid photonic ring modulator according to this generally exceeds not only a conventional Mach-Zehnder modulator or an electro-absorption modulator, but also a pure silicon ring modulator (e.g., a silicon diode ring modulator formed by a silicon ring waveguide horizontally coupled to a silicon bus waveguide). In various embodiments, the hybrid photonic ring modulator achieves a 40% or greater reduction in voltage swing for a given OMA compared to an electro-absorption modulator or a silicon diode ring modulator. This reduction in voltage swing significantly reduces the power consumption of a photonic transceiver, where the modulator drive typically consumes more than 10% of the total transceiver power. To provide a specific example: an output OMA of 7dBm at an input optical power of 10dBm (where dBm represents power in decibels relative to one milliwatt) may employ a peak-to-peak voltage swing of 1V in the case of a compound semiconductor modulator, but 1.75V in the case of an electro-absorption modulator. This drive swing reduction corresponds to a power saving of 130mW per channel at 100Gbps PAM4 modulation, or equivalently, 0.5W for a 4-channel transceiver and 4.2W for a 32-channel transceiver.
[0019] According to various embodiments, a direct current (DC) bias voltage across the diode is used to optimize the modulation efficiency of the photonic ring modulator to achieve a high refractive index change for each applied voltage swing. The refractive index shift in the ring waveguide is usually caused by a combination of the linear electro-optic (LEO) effect and the secondary electro-optic (QEO) effect, as well as free carrier absorption and the effect of the QEO effect, which is expected to dominate because it reduces the voltage swing of a given OMA and increases with increasing bias. Therefore, a higher voltage bias can improve the tuning efficiency. However, a higher bias voltage will also enhance absorption via the quantum confined Stark effect (QCSE). Therefore, in operation, the bias voltage is set to a level that provides a high QEO effect without being so high as to cause significant QCSE absorption. For a given ring modulator configuration, the bias voltage level will also determine the spectral position of the modulator response and its resonance. In applications using tunable lasers, the laser wavelength can then be adjusted to track the modulator response. However, in many applications, the operating wavelength of the laser will be fixed. In this case, to enable the modulator response to track the laser wavelength, the ring modulator can be equipped with a heater placed inside or outside the ring waveguide, which provides an independent mechanism for changing the refractive index in the ring waveguide. The laser wavelength or the heater power (if applicable) can be used to position the modulator response at the optimal offset from the laser wavelength to optimize the OMA. The heater also provides a degree of freedom to compensate for the difference between the designed nominal resonant wavelength and the actual resonant wavelength at a set bias voltage and the wavelength shift caused by temperature in any manufactured ring modulator. In some embodiments, the values of the bias voltage and heater power level are determined by calibration for a temperature range and stored in a memory for lookup during operation of the ring modulator.
[0020] As mentioned, hybrid photonic ring modulators offer advantages over non-resonant modulators and pure silicon ring modulators in terms of footprint and power requirements. In addition, the hybrid ring modulators described herein offer advantages for integration with silicon circuit devices and manufacturability compared to ring modulators implemented entirely with compound semiconductor materials. One challenge of a compound semiconductor ring modulator that includes a compound semiconductor bus waveguide that is laterally coupled to a compound semiconductor ring waveguide in the same layer is that the outer sidewalls of the ring waveguide need to be kept smooth to prevent optical losses due to scattering, and deeply etched to prevent radiation losses and leakage of light out of the ring. Deep etching around the outside of the ring reduces evanescent coupling laterally, and the deeper the etching, the closer the coupling waveguides need to be placed. Therefore, deep etching limits the lateral coupling efficiency, and manufacturing techniques are required to photolithographically define and etch small dimensions without affecting the smoothness of the ring sidewalls. As used herein, compound semiconductor ring waveguides are integrated with silicon circuits including bus waveguides in a hybrid photonic platform to circumvent this problem by coupling light between the bus waveguide and the ring waveguide vertically rather than laterally. This vertical coupling does not affect the deep and smooth etching outside the ring. In addition, since the vertical coupling distance is defined via material deposition rather than lithography and etching, the vertical coupling structure can be manufactured with a coupling distance much smaller than the coupling distance achievable by lateral coupling. For example, the vertical coupling distance between the center of the mode guided in the compound semiconductor ring waveguide and the center of the mode guided in the silicon bus waveguide can directly reach about 0.5μm or less, while the lateral coupling distance is typically greater than 0.5μm, such as in the range between about 0.6μm and 2μm (for compound semiconductor modulators only and pure silicon ring modulators). Although hybrid integration adds some process complexity, hybrid material platforms are already in use, for example for implementing lasers and photodetectors in photonic transceivers (or electro-absorption modulators, which can be replaced by ring modulators accordingly), allowing the disclosed hybrid ring modulator to be implemented simply by adapting existing hybrid processes.
[0021] Referring now to the accompanying drawings, Figure 1A and Figure 1B are cross-sectional side and top views, respectively, of an example hybrid photonic ring modulator 100 according to various embodiments, and Figure 1C to Figure 1E Along various horizontal lines from Figure 1Asectional view taken. The ring modulator 100 includes a silicon bus waveguide 102 (also referred to herein as a "silicon waveguide") and a ring resonator structure 104, which includes a compound semiconductor structure with associated electrical connections. The silicon bus waveguide 102 is formed in a silicon device layer 106 of an SOI substrate 108 (also including a silicon handle 110 and a buried oxide (BOX) or other insulating layer 112 between the silicon handle 110 and the silicon device layer 106). The compound semiconductor structure is formed in a layered stack of compound semiconductor materials disposed above the substrate 108 and includes a ring waveguide 114 that acts as a resonator. In various embodiments, the compound semiconductor material is a III-V material, such as, for example, indium phosphide (InP), indium arsenide (InAs), gallium arsenide (GaAs), gallium nitride (GaN), or indium antimonide (InSb). However, in some embodiments, II-VI or other compound semiconductor materials may also be used. As shown, the compound semiconductor material may be bonded directly to the silicon device layer 106, or may be separated from the silicon device layer 106 by a thin layer of dielectric material 116. The ring modulator 100 may also include a heater 118 in the form of a metal filament that is resistively heated and associated electrical connections. As shown, the heater 118 may be disposed within the ring resonator structure 104, specifically within the ring waveguide 114 and / or the ring layer above the ring waveguide 114. Alternatively, the heater 118 may at least partially surround the ring waveguide 114 and / or the ring layer above. (See below for various example heater configurations.) FIG. 2A to FIG. 2F . ) The ring resonator structure 104 and the heater 118 (including associated electrical connections) can be embedded in the dielectric cladding 119.
[0022] In the depicted embodiment, the silicon waveguide 102 is a rib waveguide defined between channels 120 created by etching through a portion of the silicon device layer 106, leaving a thin sheet of silicon underneath. The compound semiconductor structure is a cylindrically symmetrical pin diode structure 121, which includes an n-type layer 122, for example in the form of a disk, and an annular mesa including an active layer (or "active region") is disposed above the n-type layer 122, the annular mesa forming a ring waveguide 114 and a p-type layer 124 disposed above the ring waveguide 114, the p-type layer 124 optionally covered by a thin p-contact layer 126. The heater 118 may be disposed at the level of the ring waveguide 114 or the p-type layer 124. To facilitate placing the heater 118 at the same vertical level as the ring waveguide 114, the n-type layer 122 may be etched below the heater 118 to form a ring structure. The active layer constituting the ring waveguide 114 may be generally formed of quantum wells, quantum dots, quantum dashes, or bulk compound semiconductor (e.g., III-V) materials. In certain advantageous embodiments, multiple quantum wells are used for the active layer. The refractive index variation in the active region occurs primarily in the quantum wells, and therefore, the use of multiple wells may be used to increase the overlap between the optical mode in the ring waveguide 114 and the refractive index variation region. In order to reduce light absorption in the active region due to the QCSE, the quantum wells may be designed such that their photoluminescence wavelength is substantially detuned (e.g., by at least 100 nm) from the expected operating wavelength (e.g., laser wavelength) of the light to be modulated.
[0023] The electrical connections to the pin diode structure 121 include an n-contact ring electrode 128 disposed on top of the n-type layer 122, surrounding the annular mesa, and a p-contact ring electrode 130 disposed on top of the p-contact layer 126 (or, in embodiments that do not include a p-contact layer, directly on top of the p-type layer 124). In addition, the electrical connections include metal wiring layers and vias for connecting the electrodes 128, 130 to electrical terminals of electronic drive circuitry associated with the pin diode structure 121 and used to operate the pin diode structure 121, and for connecting the heater 118 to a heater power supply. A first metal wiring layer disposed at a level directly above the p-contact ring electrode 130 includes a closed metal ring 132 directly on top of the p-contact ring electrode 130, and a broken metal ring 134 (with associated laterally extending metal traces 136, 137) above the n-contact ring electrode 128. The broken metal ring 134 extends along a larger portion of the circumference of the n-contact ring electrode 128 and is connected to the n-contact ring electrode 128 by one or more metal vias 138, which may be placed at different angles along the ring 134. A second metal wiring layer disposed at a level above the first wiring layer includes a broken metal ring 140 above the closed metal ring 132, the broken metal ring 140 being connected to the closed metal ring 132 by a metal via (or a single, e.g., annular via) 142, and having an associated laterally extending metal trace 144. The metal trace 144 is located above a break in the ring 134 of the first metal wiring layer; the break is used to avoid an increase in capacitance between the first metal wiring layer and the second metal wiring layer, which may otherwise have a negative impact on the achievable signal modulation speed. The break in the metal ring 140 is used to accommodate metal traces 146, 147 in the second metal wiring layer to the via 148, which vertically connects the traces 146, 147 to the heater 118. In embodiments where the heater 118 is arranged around the ring waveguide 114 and in embodiments without the heater 118, the metal ring in the second metal wiring layer can be closed. The configuration of the metal wiring layer and the via is designed to achieve continuous circular contact with the p-type layer and the n-type layer, as established by the ring electrodes 128, 130. The via 138 connecting the first metal layer and the second metal layer allows the p-side electrical interface to be wired on the n-side electrical interface without creating a break in the n-contact electrode. Similarly, the heater electrical interface can be wired on the p-side electrical interface and the n-side electrical interface without causing a break in their contact electrodes.
[0024] The ring waveguide 114 is positioned so that a portion of its circumference laterally overlaps the silicon bus waveguide 102, thereby enabling light to be coupled vertically between the silicon bus waveguide 102 and the ring waveguide 114 in the overlapping region or "coupling region", as shown in FIG. Figure 1B, as indicated by the optical modes 150, 152 in the ring waveguide 114. In other words, the silicon bus waveguide 102 and the ring waveguide 114 form a vertical coupler in the coupling region. As shown, the silicon waveguide 102 can be straight and of uniform width. In alternative embodiments, the silicon waveguide 102 can be curved, for example to follow a portion of the contour of the ring waveguide 114, and / or taper downward and backward in the overlapping region to improve coupling efficiency. In order to reduce optical losses in the ring waveguide 114 due to coupling to the silicon device layer 106 below, silicon can be etched and oxide-filled (or filled with some other dielectric) in an annular channel 153 extending below the ring waveguide 114 and merged with one of the channels 120 defining the bus waveguide 102 to one side of the ring waveguide 114. Figures 1B to 1E The direction of light propagation in the silicon bus waveguide 102 from the optical input (generally indicated at 154) to the optical output (generally indicated at 156) and in the ring waveguide 114 (counterclockwise in the depicted case) are illustrated by arrows.
[0025] The structure of the hybrid ring modulator 100 may be modified in various ways without departing from the general design principles. For example, a pin diode may be formed with a p-type (rather than n-type) disk at the bottom and an annular n-type (rather than p-type) layer at the top. Also, the relative widths and thicknesses of the various rings and layers and other dimensions may be different from those depicted. (In general, it is to be understood that Figures 1A to 1E ) are not drawn to scale and are intended only to schematically depict the structural configuration of the ring modulator. ) Further, the electrodes and metal traces and vias that collectively form the electrical interface with the n-type and p-type layers and (where applicable) with the heater 118 can be configured in many different ways (including, for example, with fewer or more metal wiring layers), although some implementations are more desirable than others (e.g., in terms of contact efficiency, manufacturing complexity, and other criteria). Additionally, in certain embodiments, such as where the ring modulator is used in conjunction with a tunable laser input, the heater 118 can be omitted.
[0026] Now go to FIG. 2A to FIG. 2F , shown in top view for Figures 1A to 1E An example heater configuration according to various embodiments of the hybrid ring modulator 100 is shown. Figure 2A and Figure 2B The heaters 200, 202 are shown for placement inside the ring waveguide 114 (if projected into the plane of the substrate, i.e., neglecting any vertical displacement), implemented as serpentine metal filaments that differ from one another in the orientation of the serpentine tubes relative to the metal traces 146, 147 connected to the terminal points of the respective heaters 200, 202 by vertical vias 148. Figure 2A as well as Figure 1AIn the illustrated serpentine heater 200, the serpentine tubes are oriented perpendicular to the metal traces 146, 147 wired to the heater 200. Figure 2B In the serpentine heater 202 , the serpentine tube is oriented parallel to the metal traces 146 , 147 , and the terminal points (and vias 148 ) are on the same side of the heater 202 as the metal traces 146 , 147 .
[0027] Figure 2B and Figure 2C Heaters 210, 212 are also illustrated for placement within the ring waveguide 114, implemented as arcuate (substantially circular) and square metal filaments extending along a portion of the circumference of the ring waveguide 114. Other convex heater shapes (e.g., formed from hexagonal or rectangular filaments, etc.) are also possible. The heaters 210, 212 extend almost all the way around the ring waveguide 114, leaving small openings separating the terminal points that will be connected to the metal traces 146, 147. In general, these and similar convex heaters can cover an angle of at least 270° around the center of the ring resonator structure.
[0028] Figure 2E and Figure 2F An example of heaters 214, 216 placed outside of the ring waveguide 114 is provided, both extending partially around the ring waveguide 114 (e.g., enclosing an angle of at least 180° around the center of the ring waveguide 114). Figure 2E In the embodiment, the heater 214 is in the form of a single wider metal filament extending in an arc around the ring waveguide 114, with the terminal points on both sides of the heater and the associated metal traces 218, 219 coming from different directions. Figure 2F , the heater 216 is an arcuate serpentine filament that extends back and forth along a portion of the circumference of the ring waveguide 114, with terminal points and metal traces 146, 147 on the same side of the heater 216. As will be appreciated by one of ordinary skill in the art, the various heater configurations depicted are merely examples, and other shapes and configurations may alternatively be used. Typically, the heater 118 is configured to be close enough to the ring waveguide 114 to effectively heat the ring waveguide 114.
[0029] Figures 3A to 3G According to various embodiments Figures 1A to 1E The cross-sectional side view of the semiconductor photonic structure of the hybrid ring modulator 100 at various stages during the manufacturing is shown. The ring modulator 100 is formed on an SOI substrate 108, which includes a silicon carrier 110, a BOX (e.g., a silicon oxide layer) 112, and a silicon device layer 106, such as Figure 3AFabrication begins by photolithographically patterning and etching the silicon device layer 106 to form the silicon bus waveguide 102 and the channel to extend underneath the ring waveguide 114, along with any other waveguide and silicon device structures of a larger photonic circuit in which the ring modulator 100 is integrated, as shown. Figure 3B As shown. The silicon bus waveguide 102 can be formed as ribs defined between channels 120 created in the silicon device layer 106 by partial etching. After such patterning of the silicon device layer 106, a dielectric (e.g., silicon oxide) layer 116 is coated on the silicon device layer 106 to fill the channels 120 (and other etched features) and planarize the patterned substrate 108, as shown. Figure 3C shown.
[0030] The creation of the compound semiconductor structure of the ring modulator begins by bonding a compound semiconductor die 300 having a suitable layer structure to the dielectric layer 116, laterally overlapping the silicon bus waveguide 102 formed in the silicon device layer 106, as shown. Figure 3D As shown. Bonding can be achieved, for example, using plasma activation of the bonding surfaces, followed by annealing or vacuum assisted wafer bonding, or using other bonding techniques known to those of ordinary skill in the art. In various embodiments, the die 300 is made of III-V materials and includes appropriately doped layers and intrinsic layers, which will serve as n-type layers, active layers, p-type layers, and p-contact layers of the pin diode structure 121. The diode structure 121 is created in the die 300 by a series of alternating photolithographic patterning and etching steps to form a bottom disk and annular mesa thereon, and the bottom n-type layer 122 and the top p-contact layer 126 are subsequently metallized to create an n-contact ring electrode 128 and a p-contact ring electrode 130, as shown. Figure 3E shown.
[0031] The heater 118 and metal rings 132, 134 and associated traces of the first metal wiring layer and associated vias 138 are then created by planarizing the dielectric cladding 119, patterning and etching the dielectric cladding 119, and filling the etched structures with metal and polishing back in multiple steps. Figure 3F The resulting structure is illustrated. A second metal wiring layer and associated vias 142 are then created in a similar process by planarizing with more dielectric cladding 119, etching and filling vias 142, 148 connecting the second metal wiring layer to the first wiring layer and heater 118, and coating the second metal wiring layer (including metal ring 140 and associated traces 144 and metal traces 146, 147 for heater 118). Figure 3G The resulting final structure of the ring modulator 100 is shown.
[0032] The hybrid ring modulator 100 described above can generally be used in any photonic system implemented in a hybrid material platform, including, for example, in a photonic transmitter or transceiver. The small footprint and high tuning efficiency provided by the hybrid ring modulator 100 are particularly advantageous compared to conventional optical modulators such as electro-absorption modulators or Mach-Zehnder modulators to facilitate high channel counts (e.g., greater than sixteen) in a transmitter or transceiver.
[0033] Figure 4 is a hybrid ring modulator 402 (eg, as provided by Figures 1A to 1E Schematic block diagram of an example photonic transceiver system 400 implemented with the ring modulator 100 shown in FIG. 1 . For simplicity, only a single channel is shown. However, it is to be understood that the components depicted can be directly replicated to implement a multi-channel transceiver embodiment. The photonic transceiver system 400 includes a PIC 404 interfaced with an electronic circuit device 406, which provides control and data processing functions.
[0034] The PIC 404 includes a laser 408 that generates an optical carrier signal, a ring modulator 402, and a transmitter output port 410 that amplitude modulates the optical carrier signal output by the laser 408 according to an applied electrical signal. The laser 408, the ring modulator 402, and the transmitter output port 410 are optically coupled via a transmitter path waveguide 412, a portion of which forms a bus waveguide of the ring modulator 402. The PIC 404 also includes a data photodiode 414 for converting a modulated (data-carrying) optical signal received from a receiver input port 418 via a receiver path waveguide 416 into an electrical signal. The transmitter output port 410 and the receiver input port 418 may, for example, be implemented as optical couplers that couple light between the transceiver waveguides 412, 416 and an optical fiber of an optical communication network. Like the ring modulator 402, the laser 408 and the photodiode 414 may be implemented using III-V (or other compound semiconductor) materials for their respective optically active regions.
[0035] As shown, the PIC 404 may also include taps 420 in the transmitter path waveguide 412 before and after the ring modulator 402. The taps 420 split a fixed small portion of the laser light (e.g., 5% of the intensity) in the transmitter path waveguide 412 and direct that portion to a corresponding monitor photodiode 422 (e.g., also implemented using III-V materials). Monitoring the optical intensity before and after the ring modulator 402 can provide feedback to adjust modulator settings, such as DC voltage and heater power level, to achieve a target insertion loss both during calibration and in mission mode operation; see below for more information. Figure 7 and Figure 8Provide details of this feedback control.
[0036] The electronic circuit device 406 communicates with the various optical components of the PIC via electronic power / control and data lines (indicated by dashed lines). For example, the electronic circuit device includes a modulator driver 424 that applies an electrical swing voltage (e.g., under RF conditions) across the pin diode of the ring modulator 402, and optionally applies a DC bias voltage. Further, in the ring modulator embodiment including a heater, the electronic circuit device 406 includes a digital-to-analog converter (DAC) circuit 426 that provides power to the modulator heater at a level set by the digital input signal to the DAC circuit 426. An analog-to-digital converter (ADC) circuit 428 is used to read out the monitor photodiode 422. Moreover, in order to process the optical signal received by the PIC receiver, the electronic circuit device 406 includes an amplifier, an equalizer, and a high-speed ADC circuit 430 for data readout from the receiver's data photodiode 414. The modulator driver 424, the DAC circuit 426 for the modulator ring heater, the ADC circuit for the monitor photodiode 422, and the high speed ADC circuit 430 for reading out the data photodiode 414 can all communicate with a microprocessor 432, which in turn can include or access an integrated memory 434 (e.g., flash memory) that stores, for example, voltage and power settings associated with the ring modulator 402.
[0037] To implement a multi-channel transceiver system, various optical and electronic components can be replicated. In a multi-channel transceiver system, each channel has its own ring modulator 402 and an associated modulator drive 424 and DAC circuit 426 for a heater (if applicable) and its own data photodiode 414. Further, each channel can include its own laser 408, although alternatively, the output of the laser can also be split between multiple channels before modulation. Similarly, each channel can have its own transmitter output port 410 and receiver input port 418, or alternatively, modulated signals of different wavelengths from different channels can be multiplexed and transmitted via a shared output port 410, and the multiplexed incoming signals received via a shared receive port 416 can be demultiplexed between multiple associated channels before distribution. In various embodiments, the hybrid photonic ring modulator discussed herein can facilitate photonic transceiver systems with higher channel counts due to its power efficiency and small footprint compared to other types of optical modulators.
[0038] Now to address the modulation performance, Figure 5A and Figure 5BExample spectral modulator responses of a hybrid photonic ring modulator at various bias voltage levels without absorption and with absorption at higher bias voltages, respectively, according to various embodiments. All modulator responses (or "transmission curves") show the transmission of the ring modulator, i.e., the optical power at the output of the bus waveguide (measured in decibels relative to the input optical power), as a function of the laser wavelength in the range from 1299.9 nm to 1300.5 nm.
[0039] In the absence of any voltage-dependent changes in the absorption in the ring waveguide (e.g. due to the quantum well photoluminescence wavelength being sufficiently detuned from the laser operating wavelength), as Figure 5A As shown, the minimum transmitted power (corresponding to the spectral peak of each transmission curve) is independent of the bias voltage level; in the depicted example, this minimum has a value of slightly less than -20 dB, corresponding to an output power of less than 1% of the input power, and therefore an insertion loss of more than 99% of the input. It can be seen that the modulator response, including its resonant wavelength (i.e., the wavelength associated with the peak), shifts to longer wavelengths with increasing voltage, reflecting an increase in the refractive index or an increase in the optical phase at a given operating wavelength. This effect can be exploited to modulate the transmission by superimposing a swing voltage on the bias voltage. A monotonic increase or decrease in transmitted power according to the swing voltage can be achieved by tuning the spectral position of the modulator response relative to the operating wavelength of the modulated light so that the operating wavelength falls to the left or right of the (shifted) peak, respectively, during the entire swing. From Figure 5A It can also be seen that in a series of transmission curves for equally spaced bias voltages of 0 V, 1 V, 2 V, 3 V, 4 V and 5 V with a larger spread between adjacent curves for higher voltages, the wavelength shift reflected for each voltage increment or wavelength gradient increases with increasing voltage. This increase in wavelength gradient is a result of the increasingly dominant QEO effect at higher voltages and corresponds to an increase in tuning efficiency.
[0040] In practice, the absorption in the ring waveguide increases at least slightly at higher biases due to the QCSE, although, as mentioned, this effect can be reduced by moving the absorption wavelength of the ring waveguide away from the operating wavelength (via appropriate design of the quantum wells). Figure 5B The figure shows that the absorption increases significantly between the bias voltages of 0V and 5V (due to the Figure 5AThe detuning of quantum well photoluminescence is only about 100nm compared to 150nm or more of the bus waveguide). In the depicted example, the ring modulator is critically coupled at a bias voltage of about 2V, undercoupled at 0V, and overcoupled at 4V and 5V. In the undercoupled case, the optical power after one round trip in the ring waveguide (which is coupled back into the bus waveguide) exceeds the optical power transmitted directly from the input to the output along the bus waveguide. In the overcoupled case, due to the high absorption in the ring waveguide, the directly transmitted power exceeds the power after one round trip through the ring waveguide. At high undercoupling or high overcoupling, modulation efficiency decreases; maximum modulation efficiency occurs when the modulator is only slightly undercoupled, close to critical coupling.
[0041] To balance the improvement in tuning efficiency obtained by the QEO effect with the reduction in modulation efficiency caused by QCSE-based optical absorption, it is generally desirable that the operating wavelength falls near the peak of the modulator response associated with a bias voltage that is high but not too high (e.g., in the example shown, the bias voltage is between Figure 5A About 5V or Figure 5B Alignment of the operating wavelength with the modulator response for a desired bias voltage can be achieved by tuning the operating wavelength itself, or if the operating wavelength is fixed, by heating the ring modulator. Like an increase in bias voltage, heat will shift the modulator response to longer wavelengths. Over a typical range of heater power levels, the modulator response may shift over multiple free spectral ranges (FSRs) associated with multiple corresponding resonances of the modulator (where adjacent spectral ranges differ in accumulated optical phase in the ring waveguide by 2π), allowing the heater to effectively select a FSR of the modulator that is aligned with the laser wavelength at a desired point along the modulator response.
[0042] Figure 66 is a graph showing example OMA and eye crossing of a hybrid ring modulator according to various embodiments as a function of heater power. In this example, the ring modulator is a III-V ring modulator on silicon with negligible absorption at higher bias voltages. A 1V (peak-to-peak) voltage swing is applied at a fixed bias voltage level, and the laser is held at a fixed operating wavelength. As the heater power is increased, the transmission curve of the modulator for the selected bias voltage shifts to longer wavelengths, and the operating point along the transmission curve, which is determined by the laser wavelength and corresponds to the center of the voltage swing (e.g., zero volts for a swing from -0.5V to +0.5V), thus moves relative to the transmission curve in a direction toward lower wavelengths. As shown in the OMA curves 600, 602, starting from an operating point on the longer wavelength or "red" edge of the transmission curve, the OMA (curve 600) initially increases as the heater power is increased and the operating point moves toward the resonant peak (transmission minimum) of the curve, but then reaches a maximum value (in 604) and rapidly decreases as the swing voltage moves across the transmission minimum. As the heater power is further increased, the operating point moves to the shorter wavelength or "blue" edge of the transmission curve, and the OMA (now along curve 602) increases again, reaches a peak (in 606), and gradually decreases thereafter. It can be seen that for a non-absorbing modulator, the OMA is symmetric about the resonant peak of the modulator.
[0043] In addition to achieving high tuning efficiency, i.e., high OMA, over a given voltage swing, it is also desirable that the optical modulation be symmetric about the midpoint of the voltage swing, as reflected by the 50% eye crossing (the midpoint between the maximum and minimum optical amplitudes coincides with the 0V midpoint of the swing voltage). Figure 8 , eye crossing is plotted as a function of heater power at the red and blue edges of the modulator transfer curve (curves 608, 610, respectively). Intuitively, as the swing voltage passes back and forth between the resonant peaks of the modulator, the optical modulation becomes highly asymmetric, as shown by the very low and very high eye crossing levels in curves 608, 610. The 50% eye crossing level is achieved on both edges near the OMA peaks 604, 606 but not exactly at the OMA peaks.
[0044] Figure 7 is calibrated according to various embodiments with an integrated heater (e.g. Figures 1A to 1EFlowchart of a method 700 for tuning a hybrid photonic ring modulator (e.g., ring modulator 100) of a ring modulator 100 of FIG. 1 . The method 700 is performed with a laser set at a fixed mission mode power at a target operating wavelength (action 702). The power of a heater (e.g., heater 118 of the ring modulator 100) is initially tuned until the ring modulator reaches its transmission minimum (maximum insertion loss), which corresponds to the alignment of the modulator resonance with the laser wavelength (action 704). The DC bias voltage on the modulator pin diode is then stepped across a range of voltages, and the heater power is simultaneously adjusted to keep the modulator at maximum insertion loss (action 706). At each step, the tuning efficiency (e.g., in nm / V) and the maximum insertion loss of the ring modulator are determined and recorded. Then, within the tested DC bias voltage range, the bias level that maintains the RF voltage swing at the highest tuning efficiency while still keeping the maximum insertion loss above a specified loss cutoff level (e.g., 20 dB) is selected as the target DC bias voltage (action 708). The loss cutoff level is typically optimized for a specific device based on maximum OMA. As mentioned, as the ring modulator becomes increasingly overcoupled, the absorption in the ring waveguide will increase and the maximum insertion loss decreases accordingly. The loss cutoff level is set to avoid this high absorption condition.
[0045] Once the target DC bias voltage has been determined, the heater power is adjusted to locate the red or blue (as required) edge of the modulator response to align it with the operating wavelength (act 710). More specifically, with the laser set to a fixed mission mode power at the target wavelength and the DC bias voltage set to a target level, an RF voltage at the mission mode swing level is applied. The heater power is tuned (e.g., gradually increased from zero heating) and the resulting modulator insertion loss (or transmission) is measured to find the expected edge of the modulator response. For the red edge, the insertion loss increases (transmission decreases) with heater power (so that electrical data = "1" corresponds to optical data = "1"), and for the blue edge, the insertion loss decreases (transmission increases) with heater power (so that electrical data = "1" corresponds to optical data = "0"). Next, the heater power is adjusted stepwise, and the eye crossing and insertion loss are measured at each step (e.g., before and after the ring modulator 402, 100 using the tap 420 and monitor photodiode 422) to find the target eye crossing point (e.g., 50%) (act 712). The determined value of the DC voltage bias, the value of the heater power, and the value of the target insertion loss of the ring modulator (corresponding to a 50% eye crossing) are then stored to an integrated memory (e.g., memory 434, such as flash memory in microprocessor 432) (act 714). The calibration may be repeated at multiple temperatures (changing the temperature in act 716, such as by placing the PIC including the ring modulator in a controlled temperature environment) to create a lookup table of target values for the DC voltage bias, heater power, and target insertion loss over a range of temperatures.
[0046] Figure 8 is a hybrid photonic ring modulator (eg, Figures 1A to 1E 8. Flowchart of method 800 for initializing a ring modulator 100 of the type shown in FIG. 8. When the ring modulator is initialized in mission mode, the temperature of the modulator is read (e.g., using a temperature sensor integrated in the PIC) (act 802). The DC bias voltage and heater power are then set based on a lookup table value for the measured temperature (act 804). Next, the heater power is fine-tuned based on a measurement of the modulator insertion loss (e.g., using tap 420 and monitor photodiode 422 before and after the ring modulator 402, 100) to achieve a target insertion loss read from the lookup table for the initially measured temperature (act 806). During operation of the ring modulator, the heater power may be continuously adjusted in a control loop 808 to compensate for any temperature changes due, for example, to data-dependent self-heating (act 808).
[0047] In embodiments where a heater is not included in the ring modulator, the laser wavelength is tuned instead of the heater tuning in the calibration and operation methods 700, 800. In this case, the lookup table lists target values for DC voltage bias, laser wavelength, and modulator insertion loss over a temperature range.
[0048] Having described the structure and operating principles of the hybrid photonic ring modulator in conjunction with the example embodiments depicted in the accompanying drawings, the following numbered examples also define various illustrative embodiments.
[0049] 1. A hybrid photonic ring modulator, comprising: a silicon bus waveguide formed in a silicon device layer of a silicon-on-insulator (SOI) substrate; and a ring resonator structure formed above the silicon device layer, the ring resonator structure comprising a pin diode structure of a semiconductor compound material and associated electrodes, an active region of the pin diode structure forming a ring waveguide that laterally overlaps with the bus waveguide, the ring waveguide and the silicon bus waveguide together forming a vertical coupler in the overlapping region.
[0050] 2. The hybrid photonic ring modulator of Example 1, wherein a diameter of the ring waveguide is between about 5 μm and about 50 μm.
[0051] 3. The hybrid photonic ring modulator of Example 1 or Example 2, wherein the semiconductor compound material is a III-V material.
[0052] 4. The hybrid photonic ring modulator of any one of examples 1 to 3, wherein the active region comprises a quantum well, the photoluminescence wavelength of the quantum well being detuned by at least 100 nm from an operating wavelength of light to be modulated by the hybrid photonic ring modulator.
[0053] 5. The hybrid photonic ring modulator of any one of Examples 1 to 4, further comprising a heater positioned above the silicon device layer proximate to the pin diode structure, the heater operative to adjust the resonant wavelength of the ring waveguide.
[0054] 6. The hybrid photonic ring modulator of Example 5, wherein the heater is placed inside the ring resonator structure.
[0055] 7. The hybrid photonic ring modulator of example 6, wherein the heater comprises a serpentine metal filament or a metal filament extending along the ring resonator structure over an angle of at least 270° around the center of the ring resonator structure.
[0056] 8. The hybrid photonic ring modulator of Example 5, wherein the heater is placed outside the ring resonator structure.
[0057] 9. The hybrid photonic ring modulator of example 8, wherein the heater extends along the ring resonator structure over an angle of at least 180° around the center of the ring resonator structure.
[0058] 10. The hybrid photonic ring modulator of any one of Examples 5 to 9, further comprising an electronic drive circuit device electrically connected to the electrode for applying a reverse bias voltage and a radio frequency (RF) voltage swing across the pin diode structure.
[0059] 11. The hybrid photonic ring modulator of Example 10, further comprising a memory storing a value of a reverse bias voltage and a value of a power of a heater.
[0060] 12. A photonic integrated circuit (PCI) comprising: a laser; and a hybrid photonic ring modulator, the hybrid photonic ring modulator comprising: a silicon bus waveguide vertically coupled to a ring-shaped active region of a pin diode structure formed of a compound semiconductor material, an optical input of the silicon bus waveguide coupled to an output of the laser, and an optical output of the silicon bus waveguide coupled to an output port of the PIC.
[0061] 13. The PIC of Example 12, further comprising optical taps in the silicon bus waveguide before and after the optical ring modulator, and photodiodes at the outputs of the optical taps.
[0062] 14. The PIC of example 12 or example 13, wherein the annular active region comprises a plurality of quantum wells, the photoluminescence wavelengths of the quantum wells being detuned by at least 100 nm from the operating wavelength of the laser.
[0063] 15. The PIC of any of Examples 12 to 14, wherein the diameter of the annular active area is between about 5 μm and about 50 μm.
[0064] 16. The PIC of any one of Examples 12 to 15, wherein the hybrid photonic ring modulator further comprises a heater operative to tune a resonant wavelength of the ring-shaped active region.
[0065] 17. The PIC of any one of Examples 12 to 16, wherein the PIC implements a multi-channel photonic transceiver, the hybrid photonic ring modulator and the output port are included in a first transceiver channel, and the PIC further includes one or more additional channels, each of the one or more additional channels including an additional hybrid photonic ring modulator having an optical output coupled to an additional output port.
[0066] 18. A method of modulating light guided in a silicon waveguide, the method comprising: vertically coupling light from the silicon waveguide into an optically active ring waveguide of a compound semiconductor pin diode structure formed above the silicon waveguide; and applying a swing voltage across the pin diode structure to thereby modulate the refractive index in the ring waveguide.
[0067] 19. The method of Example 18 further includes applying a direct current (DC) bias voltage across the pin diode structure, the value of the DC bias voltage being set to a stored value calibrated to maximize modulator tuning efficiency while exceeding a specified loss cutoff level for maximum modulator insertion loss.
[0068] 20. The method of example 19, further comprising heating the ring waveguide, the heater power being set to a stored value calibrated to achieve a target crossover point.
[0069] Although the inventive subject matter has been described with reference to specific example embodiments, it will be evident that various modifications and changes may be made to these embodiments without departing from the broader scope of the inventive subject matter.Accordingly, the specification and drawings are to be regarded in an illustrative rather than a restrictive sense.
Claims
1. A hybrid photonic ring modulator for modulating light at a target operating wavelength, the photonic ring modulator comprising: a silicon bus waveguide formed in a silicon device layer of a silicon-on-insulator (SOI) substrate; as well as a ring resonator structure formed above the silicon device layer, the ring resonator structure comprising a pin diode structure of a compound semiconductor material and associated electrodes, the active region of the pin diode structure forming a ring waveguide that laterally overlaps the silicon bus waveguide, the ring waveguide and the silicon bus waveguide together forming a vertically oriented coupler in the overlapping region; a heater disposed above the silicon device layer proximate to the pin diode structure; an electronic drive circuit device electrically connected to the electrodes for applying a voltage across the pin diode structure, the voltage comprising a reverse bias voltage and a radio frequency (RF) voltage swing; as well as a memory storing a target value of the reverse bias voltage and a target value of the power of the heater; wherein the target value of the reverse bias voltage maximizes the tuning efficiency of the shift by varying the applied voltage, the spectral position of the modulator response, while exceeding a specified loss cutoff level for maximum modulator insertion loss at a resonant wavelength of a modulator response of the photonic ring modulator; as well as wherein the target value of the power to the heater optimizes a shift in the modulator response between the resonant wavelength at the target value of the reverse bias voltage and the target operating wavelength to achieve a target insertion loss at the target operating wavelength.
2. The hybrid photonic ring modulator of claim 1, wherein the diameter of the ring waveguide is between 5 μm and 50 μm.
3. The hybrid photonic ring modulator of claim 1, wherein the compound semiconductor material is a III-V material.
4. The hybrid photonic ring modulator of claim 1, wherein the active region comprises quantum wells having a photoluminescence wavelength that is detuned by at least 100 nm from the target operating wavelength.
5. The hybrid photonic ring modulator of claim 1, wherein the heater is placed inside the ring resonator structure.
6. The hybrid photonic ring modulator of claim 5, wherein the heater comprises a serpentine metal filament or a metal filament extending along the ring resonator structure over an angle of at least 270° around the center of the ring resonator structure.
7. The hybrid photonic ring modulator of claim 1, wherein the heater is placed outside the ring resonator structure.
8. The hybrid photonic ring modulator of claim 7, wherein the heater extends along the ring resonator structure over an angle of at least 180° around the center of the ring resonator structure.
9. The hybrid photonic ring modulator of claim 1, wherein the memory stores a plurality of target values of the power of the heater and the reverse bias voltage, the plurality of target values being associated with a plurality of corresponding temperatures.
10. A photonic integrated circuit (PIC), comprising: a laser for emitting light at an operating wavelength; as well as a hybrid photonic ring modulator, the hybrid photonic ring modulator comprising: a silicon bus waveguide formed in a silicon device layer and vertically coupled to a ring-shaped active region of a pin diode structure formed of a compound semiconductor material, an optical input of the silicon bus waveguide being coupled to an output of the laser, and an optical output of the silicon bus waveguide being coupled to an output port of the photonic integrated circuit; a heater disposed above the silicon device layer proximate to the pin diode structure; electrodes and associated electronic drive circuitry configured to apply a voltage across the pin diode structure, the voltage comprising a reverse bias voltage and a radio frequency (RF) voltage swing; and a memory storing a target value of the reverse bias voltage and a target value of the power of the heater; wherein the target value of the reverse bias voltage maximizes the tuning efficiency of the shift by varying the applied voltage, the spectral position of the modulator response, while exceeding a specified loss cutoff level for maximum modulator insertion loss at a resonant wavelength of a modulator response of the photonic ring modulator; wherein the target value of the power to the heater optimizes a shift between the operating wavelength and the resonant wavelength of the modulator response at the target value of the reverse bias voltage to achieve a target insertion loss at the operating wavelength.
11. The photonic integrated circuit of claim 10, further comprising optical taps in the silicon bus waveguide before and after the hybrid photonic ring modulator, and photodiodes at outputs of the optical taps.
12. The photonic integrated circuit of claim 10, wherein the annular active region comprises a plurality of quantum wells, the photoluminescence wavelengths of the quantum wells being detuned by at least 100 nm from the operating wavelength of the laser.
13. The photonic integrated circuit of claim 10, wherein the diameter of the annular active region is between 5 μm and 50 μm.
14. The photonic integrated circuit of claim 10, wherein the photonic integrated circuit implements a multi-channel photonic transceiver, the hybrid photonic ring modulator and the output port are included in a first transceiver channel, the photonic integrated circuit further comprising one or more additional channels, each of the one or more additional channels comprising an additional hybrid photonic ring modulator having an optical output coupled to an additional output port.
15. A method of modulating light guided in a silicon waveguide, the method comprising: vertically coupling the light at an operating wavelength from the silicon waveguide into an optically active ring waveguide of a compound semiconductor pin diode structure formed above the silicon waveguide, the ring waveguide having an associated resonant wavelength; applying a voltage across the pin diode structure to thereby modulate a refractive index in the ring waveguide, the voltage comprising a direct current (DC) reverse bias voltage and a swing voltage; as well as heating the pin diode structure, wherein the DC reverse bias voltage is set to a stored value that maximizes the shifted modulator tuning efficiency by applying an applied voltage, a change in the resonant wavelength, in the event of exceeding a specified loss cutoff level of a maximum modulator insertion loss associated with the resonant wavelength; as well as The power of the heater used to heat the pin diode structure is set to a value that optimizes the shift between the operating wavelength and the resonant wavelength at the set value of the DC reverse bias voltage to achieve a target insertion loss at the operating wavelength. The method of claim 15 , wherein the target insertion loss is associated with a target cross-point.
