Phase-constant amplitude modulation including examples of QAM optical transceivers

Abstract

In one aspect, a method described herein can be used for laser carrier recovery in optical coherent communication systems utilizing quadrature amplitude modulation (QAM) at a receiver. The method includes receiving, at the receiver, a transmitted signal modulated using QAM and a local oscillator (LO) signal. The method includes detecting, at the receiver, a phase offset between the transmitted signal and the LO signal. The method includes compensating, at the receiver, by generating an error signal based on the average power and / or voltage difference between the In-phase (I) and Quadrature-phase (Q) paths of the received signal at the receiver, where the error signal compensates for the phase offset between the transmitted signal and the LO signal.

Description

PHASE-CONSTANT AMPLITUDE MODULATION INCLUDING EXAMPLES OF QAM OPTICAL TRANSCEIVERSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit under 35 U.S.C. § 119(e) of the earlier filing date of U.S. Provisional Application No. 63 / 554,868, filed February 16, 2024, the entire contents of which are hereby incorporated by reference in their entirety for any purpose.STATEMENT OF FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

[0002] This invention was made with government support under Grant No. 2142996, awarded by the National Science Foundation. The government has certain rights in the invention.BACKGROUND

[0003] As artificial intelligence and / or machine learning (AI / ML) accelerators, graphics processing units (GPUs) and / or network switches can demand high data rated (e.g., tens of Tb / s) of off-package input / output (IO) bandwidths. Consequently, the adoption of copackaged optics (CPO) can be beneficial. Wavelength and / or polarization division multiplexing (WDM / PDM) have been proposed for CPO to increase data rates per fiber. These techniques, however, can provide limited scalabilities due to various limitations, such as limited available laser lines for WDM.

[0004] Achieving energy-efficient higher data rates will require more advanced and / or coherent modulations. For example, currently, some CPO use amplitude modulation, such as pulse amplitude modulation (PAM), non-return-to-zero (NRZ) PAM, PAM-4, etc. Increasing the data rate with the current amplitude modulation schemes may be not feasible because the electronic control and / or driving circuitry will consume immense power at higher frequencies and / or increased noise power at higher bandwidths.

[0005] Coherent modulations provide some advantages, such as higher receiver gain and / or noise suppression. While coherent optics using quadrature amplitude modulation (QAM) have been used for long haul (e.g., 10 kilometers (km) or higher distances) applications withMach-Zehnder Interferometer (MZI)-based transmitters, the large footprint of these devices (e.g., multi-millimeters squared (mm2) footprint) makes the MZI-based transmitter for meeting the necessary shoreline and aerial bandwidth densities for CPO.

[0006] For example, the optical transceivers may advantageously be co-packaged (e.g., “surround”) with the device that is generating the data they send to / receive from (e.g., a central processing unit (CPU) or GPU, referred to herein as an “XPU”). The XPU may have a fixed perimeter, and all the optical transmitters used for sending away data generated by the XPU need to fit roughly on that perimeter. The radio frequency (RF) loss of modulation signal for MZIs at high baud rates (e.g., 200 Gbaud / s or more) is another limiting factor to realize practical QAM optical transmitters.

[0007] Microring modulators (MRMs) (or MZIs) have shown promise for CPO due to their small footprint. The MRMs have been adopted to perform pulse amplitude modulation. Unfortunately, this solution can be challenging due to the coupled nature of MRMs’ phase and amplitude outputs. One proposed solution is to bias the resonance and laser such that an MRM acts as a pure phase shifter by inducing a n phase shift, while keeping the amplitude constant. However, the limited wavelength shift of the p-type / n-type (PN) junctions gives these single-MRM BPSK modulator approaches a high insertion loss (IL) (e.g., IL greater than 10 decibels (dB)). Also, MRMs have limited capability to handle large optical powers inside the cavity due to nonlinear effects such as free carrier absorption (FC A) and thermal sensitivity. This has resulted in distorted constellations using this type of circuit.BRIEF SUMMARY

[0008] Examples of methods are disclosed herein. In an embodiment, an example method for laser carrier recovery in optical coherent communication systems may include utilizing quadrature amplitude modulation (QAM) at a receiver. The method may include receiving, at the receiver, a transmitted signal. The method may include receiving, at the receiver, a local oscillator (LO) signal. The method may include detecting, at the receiver, a phase offset between the transmitted signal and the LO signal. The method may include compensating, at the receiver, for the phase offset between the transmitted signal and the LO signal based on the detected phase offset, wherein the compensation accounts for a movement of a constellation center and a rotation of the constellation due to the phase offset. The compensation may include detecting an average power and / or voltage difference between In- phase (I) and Quadrature-phase (Q) paths of the received signal at the receiver. The compensation may include generating an error signal based on the average power and / orvoltage difference between the In-phase (I) and Quadrature-phase (Q) paths of the received signal at the receiver, wherein the error signal compensates for the phase offset between the transmitted signal and the LO signal.

[0009] Additionally, or alternatively, the method may include forwarding a transmit laser signal from a transmitter to the receiver; and tuning a phase using at least one phase shifter.

[0010] Additionally, or alternatively, the at least one phase shifter may include a first phase shifter and a second phase shifter. The method further may include performing a coarse phase tuning using the first phase shifter, where the first phase shifter has a wider bandwidth operation than the second phase shifter. The method may further include performing a finer phase tuning, compared to the coarse phase tuning, using the second phase shifter.

[0011] Additionally, or alternatively, the first phase shifter may include an electro-optical phase shifter.

[0012] Additionally, or alternatively, the second phase shifter may include a thermal phase shifter.

[0013] Additionally, or alternatively, the method may further include maintaining a single polarity of the error signal, where the single polarity aids the receiver maintain stability of the error signal.

[0014] Additionally, or alternatively, the method may further include locking, at the receiver, a receiver laser to a phase of the transmitted signal.

[0015] Additionally, or alternatively, the method may further include differentially coding the transmitted signal; responsive to the coding, adding redundancy to the transmitted signal; and determining, at the receiver, phase polarities of In-phase (I) and Quadrature-phase (Q) signals.

[0016] Additionally, or alternatively, the compensation may further include filtering the received signal using a low-pass filter to retain only an average voltage of the signal; and subtracting the output of the low-pass filter in the In-phase (I) and Quadrature-phase (Q) paths to generate the error signal.

[0017] Additionally, or alternatively, the error signal may be equal to a constant direct current (de) offset of In-phase (I) and Quadrature-phase (Q) signals multiplied by a sine or sinusoid of the phase offset.

[0018] Additionally, or alternatively, the compensation may further include processing the received signal through a Costas loop technique; and utilizing the Costas loop technique to generate an error signal based on the average signals in the In-phase (I) and Quadrature-phase (Q) paths after processing through a Sign (SGN) block and a mixer.

[0019] Example apparatuses are described herein. In an embodiment, an example apparatus may include a beam splitter configured to receive optical energy having a wavelength. The beam splitter may be configured to provide a first split beam and a second split beam. The example apparatus may include a first resonant modulator having a first input, where the first resonant modulator may be configured to modulate an amplitude and a phase of the first split beam. Based on the first input, the first resonant modulator may be configured to provide a first modulated beam. The example apparatus may include a second resonant modulator having a second input, where the second resonant modulator may be configured to modulate an amplitude and a phase of the second split beam. Based on the second input, the second resonant modulator may be configured to provide a second modulated beam.

[0020] Additionally, or alternatively, the apparatus may include a phase shifter positioned to receive the second modulated beam and provide a phase-shifted modulated beam. The apparatus may include a combiner configured to combine the phase-shifted modulated beam and the first modulated beam to provide an output signal. The resonant frequencies of the first and second resonant modulators are such that, responsive to particular first and second tuning signals applied at the first and second resonant modulators, the output signal may be configured to be a phase-constant amplitude-modulated signal.

[0021] Additionally, or alternatively, the changes in the first and second modulation signals may be configured to provide equal changes to the amplitude modulation provided by the first and second resonant modulators.

[0022] Additionally, or alternatively, the changes in first and second input signals applied to the first and second resonant modulators may be configured to provide equal and opposite changes to the phase modulation provided by the first and second resonant modulators, respectively.

[0023] Examples of other methods are disclosed herein. In an embodiment, an example method may include applying tuning signals to phase-amplitude modulators of an interferometer such that the interferometer may be configured to provide phase-constant amplitude modulation. The example method may include applying data signals to the phaseamplitude modulators to provide phase-constant amplitude-modulated output signals based on the data signals.

[0024] Additionally, or alternatively, the phase-amplitude modulators may be resonant modulators, where the tuning signals may be selected to provide the phase-constant amplitude modulation of the interferometer.

[0025] Additionally, or alternatively, the tuning signals vary resonances of the phaseamplitude modulators.

[0026] Examples of transceivers are disclosed herein. In an embodiment, an example transceiver may include a transmitter and a receiver. The transmitter may include a first and a second phase-constant amplitude modulator (PCAM). The transmitter may include a laser configured to: provide optical energy to the first and the second PCAMs; and provide a local oscillator (LO) signal; where the transmitter may be configured to transmit a signal modulated with quadrature amplitude modulation (QAM). The receiver may include: an optical filter configured to receive the modulated signal. The receiver may include at least one phase shifter configured to receive the LO signal. The receiver may include a carrier phase recovery (CPR) circuitry. The CPR circuitry may be configured to: detect an average power and / or voltage difference between In-phase (I) and Quadrature-phase (Q) paths of the modulated signal; and generate an error signal based on the average power and / or voltage difference between the In-phase (I) and Quadrature-phase (Q) paths of the modulated signal, where the error signal may compensate for a phase offset between the LO signal and the modulated signal.

[0027] Additionally, or alternatively, the transceiver may include a laser-forwarded coherent optical link, where a frequency of the laser may be configured to provide a same frequency to the transmitter and the receiver.

[0028] Additionally, or alternatively, the at least one phase shifter may include a first phase shifter and a second phase shifter. The first phase shifter may be configured to perform a coarse phase tuning, where the first phase shifter may have a wider bandwidth operation than the second phase shifter; and the second phase shifter may be configured to perform a finer phase tuning compared to the coarse phase tuning.

[0029] Additionally, or alternatively, the modulated signal beats with the LO signal in the optical filter to demodulate the In-phase (I) and Quadrature-phase (Q) paths of the modulated signal.BRIEF DESCRIPTION OF THE DRAWINGS

[0030] FIG. 1 shows a block diagram of a QAM transmitter that includes two PCAMs, in accordance with examples described herein.

[0031] FIG. 2A shows a block diagram of a monolithic integrated circuit that may be used in the context of FIG. 1, in accordance with examples described herein.

[0032] FIG. 2B shows a block diagram of heterogeneous integrated circuits that may be used in the context of FIG. 1, in accordance with examples described herein.

[0033] FIG. 3 shows another block diagram of another QAM transmitter that includes two PCAMs, in accordance with examples described herein.

[0034] FIG. 4 shows a block diagram of a PCAM, in accordance with examples described herein.

[0035] FIG. 5 shows a method of biasing and modulating amplitude-phase modulators in a RAMZI to achieve phase-constant amplitude modulation, where the method is shown at least in reference to two graphs, in accordance with examples described herein.

[0036] FIG. 6 show an offset-QAM-4 constellation and an offset-QAM-16 constellation, in accordance with examples described herein.

[0037] FIG. 7 shows a non-offset-QAM-16 constellation, in accordance with examples described herein.

[0038] FIG. 8A shows a block diagram of a laser-locked coherent optical link between a transmitter and a receiver, in accordance with examples described herein.

[0039] FIG. 8B shows a block diagram of a laser-forwarded coherent optical link between a transmitter and a receiver, the laser-forwarded coherent optical link uses a carrier phase recovery, in accordance with examples described herein.

[0040] FIG. 9A shows a constellation diagram for a conventional QAM-4 or QPSK with and without phase error between Rx and LO paths, in accordance with examples described herein.

[0041] FIG. 9B shows a constellation diagram for an offset-QAM-4 with and without phase error between the Rx and LO paths, in accordance with examples described herein.

[0042] FIG. 10A shows another constellation diagram for a conventional QAM-4 or QPSK with and without phase error between Rx and LO paths, in accordance with examples described herein.

[0043] FIG. 10B shows a constellation diagram for another offset-QAM-4 with and without phase error between the Rx and LO paths, in accordance with examples described herein.

[0044] FIG. 11 A shows a block diagram of an example architecture of an offset-QAM coherent receiver, where the receiver may implement a first method for laser phase recovery, in accordance with examples described herein.

[0045] FIG. 11B shows a block diagram of another example architecture of an QAM coherent receiver, where the receiver may implement a second method for laser phase recovery, in accordance with examples described herein.

[0046] FIG. 12A shows a block diagram of another example architecture of an QAM coherent receiver, where the receiver may implement the first method for laser phase recovery, in accordance with examples described herein.

[0047] FIG. 12B shows a block diagram of another example architecture of an QAM coherent receiver, where the receiver may implement the second method for laser phase recovery, in accordance with examples described herein.

[0048] FIG. 13 shows aspects of the first method of FIG. 11A and / or FIG. 12A and the second method of FIG. 11B and / or FIG. 12B, where these methods are used to generate an error signal, and where the error signal is used for laser phase recovery, in accordance with examples described herein.

[0049] FIG. 14A shows simulation results of a QAM constellation, in accordance with examples described herein.

[0050] FIG. 14B shows simulation results of an offset-QAM constellation, in accordance with examples described herein.

[0051] FIG. 15 A shows simulation results of an error signal over time, in accordance with examples described herein.

[0052] FIG. 15B shows simulation results of an LO phase over time, in accordance with examples described herein.

[0053] FIG. 16 shows a list of equations and / or mathematical expressions used in the context with examples described herein.

[0054] FIG. 17A shows an example operation of a PCAM utilized for non-offset-QAM, where the example operation is shown at least in reference to two graphs, in accordance with examples described herein.

[0055] FIG. 17B shows another example operation of the PCAM utilized for offset-QAM, where the example operation is shown at least in reference to two graphs, in accordance with examples described herein.

[0056] FIG. 17C shows yet another example operation of the PCAM utilized for offset- QAM, where the example operation is shown at least in reference to two graphs, in accordance with examples described herein.DETAILED DESCRIPTION

[0057] Examples described herein include an offset-QAM-4 transmitter architecture using a Ring-Assisted MZI (RAMZI) structure(s). RAMZIs can be or include phase-constantamplitude modulators (PCAMs), which are the building blocks of example offset-QAM transmitters.

[0058] While amplitude-phase modulators (e.g., MRMs) are described herein, in other examples other optical device modulators may be used. Example optical device modulators generally may be used for modulating both amplitude and phase. Generally, an amplitudephase modulator and an MRM may be described interchangeably herein. An MRM may be one example implementation of an amplitude-phase modulator.

[0059] Examples of transmitter (Tx) designs can also be used for applications other than CPO that utilize compact and efficient phase-constant amplitude modulation, including but not limited to optical machine learning accelerators.

[0060] Overall, higher data-rate coherent transmitters can use offset-QAM modulation for higher data rates per polarization and / or wavelength. Examples of receivers (Rx) to recover the laser carrier for offset-QAM using a closed-loop system may be described.

[0061] Examples described herein may include laser-forwarded carrier phase recovery systems for QAM modulation. Systems, methods, and / or techniques described herein may implement QAM to be power-efficient and / or area-efficient optical input / output (I / O) interrack and / or intra-rack communication at high data rates. These systems, methods, and / or techniques may be implemented with little or minimal circuit area and / or power overhead, eliminating the need for an additional local oscillator (LO), for example, at the receiver. For example, the LO may be implemented with a laser at a transmitter. These laser-forwarded carrier phase recovery systems may rely little, or may not rely, on digital signal processing (DSP). Therefore, in some embodiments, examples described herein may be or include DSP- free laser-forwarded carrier phase recovery systems.

[0062] FIG. 1 shows a block diagram 100 schematic illustration of a QAM transmitter that includes two phase-constant optical amplitude modulators (PCAMs), in accordance with examples described herein. The block diagram 100 may also be or include an offset-QAM-4 (or -16, or -64, etc.) transmitter architecture using a RAMZI structure(s).

[0063] In some embodiments, the block diagram 100 may include a PCAM-based QAM transmitter 102; an optical input 104 to the PCAM-based QAM transmitter 102; an optical output 106 out of the PCAM-based QAM transmitter 102; an optical splitter 108 (e.g., a beam splitter); a PCAM 110 (e.g., a first PCAM); a PCAM 112 (e.g., a second PCAM); an optical signal input 114 to the PCAM 110; an optical signal input 116 to the PCAM 112; a top modulator 118 (e.g., a first modulator) of the PCAM 110; a bottom modulator 120 (e.g., a second modulator) of the PCAM 110; a top modulator 122 (e.g., a first modulator) of thePCAM 112; a bottom modulator 124 (e.g., a second modulator) of the PCAM 112; an electrical input for I 126 to the PCAM 110; an electrical input for 1 128 to the PCAM 110; an electrical input for I 130 to the PCAM 110; an electrical input for 1 132 to the PCAM 110; an electrical input for Q 134 to the PCAM 112; an electrical input for Q 136 to the PCAM 112; an electrical input for Q 138 to the PCAM 112; an electrical input for Q 140 to the PCAM 112; I data 142; Q data 144; a 90-degree phase shifter 146; and an optical combiner 148. The block diagram 100 is an example schematic, and the block diagram 100 may include other components, additional components, or fewer components. In some examples, the QAM transmitter 102 may be an offset-QAM transmitter.

[0064] Note that, in examples described herein, QAM transmitters and / or QAM techniques are described. QAM techniques and / or transmitters generally utilize In-phase and Quadrature components (e.g., a constellation). These components may be centered around zero, or may be centered around a non-zero value. In examples where the components are centered around a non-zero value, the techniques may be referred to as offset-QAM and / or offset-QAM transmitters. Accordingly, examples of QAM transmitters and / or QAM techniques can include examples of offset QAM and non-offset QAM.

[0065] In some embodiments, each of the PCAMs 110 and 112 of FIG. 1 may generally be implemented using components designed to generate amplitude modulation, which varies with input, but apply a constant phase modulation across inputs, such as across all inputs and / or across a particular input range during normal operation. The PCAM 110 may be positioned to generate an in-phase (I) data component, while the PCAM 112 may be positioned to generate a quadrature (Q) data component. In some examples, PCAMs described herein, such as PCAMs 110 and 112 may be implemented using one or more microring modulators, such as one or more ring-assisted Mach-Zehnder interferometer (RAMZI).

[0066] Each phase-constant modulator (e.g., PCAMs 110 and 112) may receive an optical input beam. A coherent source of light may be split then input (e.g., optical input 104) into the PCAMs 110 and 112. Each of the PCAMs 110 and 112 modulates the data from electronic inputs (e.g., the electrical inputs for I 126-132, the electrical inputs for Q 134-140) onto this light. The data may be represented in the intensity of the optical signal outputted (e.g., the I data 142, the Q data 144, and / or the optical output 106) from the PCAMs. This intensity can have multiple levels, meaning that the PCAMs can encode multiple bits of information at a time, not just a 1 or a 0, although a binary output is present in some examples. The incoming data (e.g., the I data 142, the Q data 144, and / or the optical output 106) can be in an analog or digital form.

[0067] In some embodiments, the optical input 104 may be generated with a laser. The optical splitter 108 (e.g., a beam splitter) is configured to provide the optical signal inputs 114 and 116 (e.g., a first beam split and a second beam split) into the two PCAMs 110 and 112. In some embodiments, the optical splitter 108 may divide the power of the optical input 104 evenly or near-evenly into two outputs to provide the optical signal input 114 and the optical signal input 116. Other splits may be possible (e.g., 60 percent / 40 percent, etc.).

[0068] In some embodiments, the outputs of the PCAM 110 and the PCAM 112 are combined after the output of the PCAM 112 passes through the 90-degree phase shifter 146, which makes the two data streams (e.g., In-phase (I) and Quadrature-phase (Q) signals, the I data 142 and the Q data 144) orthogonal, as is illustrated in FIG. 1.

[0069] Generally, the optical splitter 108 or beam splitter may be a device that divides an incoming light beam (e.g., optical input 104, laser, etc.) into at least two separate beams, such as the optical signal input 114 and the optical signal input 11 . The optical splitter 108 may be implemented in various forms, such as a cube beam splitter, a plate beam splitter, a fiber optic beam splitter, and so forth. Beam splitters may sometimes be characterized by their splitting ratio, which defines the percentage of light that is transmitted versus reflected. The beam splitter may be used in various applications, such as interferometry, telecommunications, optical instruments, etc.

[0070] Each of the PCAMs 110 and 112 may be implemented using one or more modulators, such as one or more modulators described herein. Generally, phase-constant modulators may be used such that amplitude modulation is applied by the modulators, but input phase is preserved in the output. Accordingly, optical signal input 114 may have its amplitude modulated by PCAM 110, however the phase at the output may remain unchanged (e.g., not significantly changed) from the optical signal input 114. In an analogous manner, optical signal input 116 may have its amplitude modulated by PCAM 112, however the phase at the output of PCAM 112 may remain unchanged (e.g., not significantly changed) from the optical signal input 116. By constant phase herein is meant that the phase may not be acted upon by the modulator. In some examples, the phase is altered less than 5%, less than 3 % in some examples, less than 2 % in some examples, less than 1% in some examples, and not at all in some examples. Phase modification made by phase-constant modulators described herein may be incidental.

[0071] Electrical inputs to phase-constant modulators described herein may be used to control the modulation and / or configuration or tuning of the modulators. PCAM 110 may include a first modulator 118. The first modulator 118 may receive a control signal 126 whichmay control modulation applied by the first modulator 118. The first modulator 118 may receive a control signal 128 which may tune a performance of the first modulator 118. The second modulator 120 may receive a control signal 130 which may control modulation applied by the second modulator 120. The second modulator 120 may receive a control signal 132 which may tune a performance of the second modulator 120. The tuning control signals 128 and 132 may be applied such that the PCAM 110 provides phase-constant modulation. The control signals 126 and 130 may represent data to be encoded in the optical input signal, and may be referred to as data signals. Accordingly, an optical output signal from the transmitter of FIG. 1 may represent an optical signal modulated with the data provided at the control signal inputs including inputs 126 and 130.

[0072] PCAM 12 may include a first modulator 122. The first modulator 122 may receive a control signal 134 which may control modulation applied by the first modulator 122. The first modulator 122 may receive a control signal 136 which may tune a performance of the first modulator 122. The second modulator 124 may receive a control signal 138 which may control modulation applied by the second modulator 124. The second modulator 124 may receive a control signal 140 which may tune a performance of the second modulator 124. The tuning control signals 136 and 140 may be applied such that the PCAM 110 provides phaseconstant modulation. The control signals 134 and 138 may represent data to be encoded in the optical input signal. Accordingly, an optical output signal from the transmitter of FIG. 1 may represent an optical signal modulated with the data provided at the control signal inputs including inputs 134 and 138.

[0073] The control signals may be generated using one or more control components (not depicted in FIG. 1).

[0074] Designers and / or manufacturers can use various chip-level architectures for sending the appropriate electrical control and / or driver signals to the PCAM-based QAM transmitter (e.g., the PCAM-based QAM transmitter 102), as is described and / or illustrated herein.

[0075] FIG. 2A shows a block diagram 200 of a monolithic integrated circuit 204 that can be used in the context of FIG. 1, in accordance with examples described herein. The block diagram 200 is an example block diagram, and the block diagram 200 may include other components, additional components, or fewer components than what is illustrated in FIG. 2A.

[0076] In some embodiments, the block diagram 200 of the monolithic integrated circuit 204 may include a PCAM-based QAM transmitter 206; an optical input 208 to the PCAM-based QAM transmitter 206; an optical output 210 (e.g., a modulated optical output) out of the PCAM-based QAM transmitter 206; and an electrical driver and / or control circuitry 212 usedwith the PCAM-based QAM transmitter 206. In some examples, the QAM transmitter 206 may be an offset-QAM transmitter.

[0077] In some embodiments, the PCAM-based QAM transmitter 206 of FIG. 2A may be an example implementation of the PCAM-based QAM transmitter 102 of FIG. 1.

[0078] In some embodiments, the outputs of the electrical driver and / or control circuitry 212 of FIG. 2A may be, provide, and / or include the electrical input for Is 126-132 and / or the electrical input for Qs 134-140 of FIG. 1.

[0079] In some embodiments, the block diagram 200 of FIG. 2A shows that the electrical control signals can be generated on the same integrated circuit (e.g., a monolithic integrated circuit 204). The integrated circuit 204 can be manufactured using various semiconductor fabrication processes that integrate photonics and electronics, monolithically, such as the Global Foundries 45 nm CLO.

[0080] The electrical driver and / or control circuitry 212 may be used to provide the control signals including control signals 126, 138, 130, 132, 134, 136, 138, and 140 of FIG. 1. The electrical driver and / or control circuitry 212 may be implemented using, for example, one or more application specific integrated circuits (ASICs), filed programmable gate arrays (FPGAs), central processing unit (CPU), graphics processing unit (GPU), microcontroller, or other circuitry.

[0081] In the example of FIG. 2A, the electrical driver and / or control circuitry 212 is accordingly implemented in a same substrate as the transmitter 206. For example, both the control circuitry 212 and the transmitter 206 may be supported by and / or integrated into a substrate, such as a silicon substrate. Conductive traces may be supported by the silicon substrate and used to electrically couple the control circuitry 212 and the transmitter 206.

[0082] FIG. 2B shows a block diagram 202 of heterogeneous integrated circuits that can be used in the context of FIG. 1, in accordance with examples described herein. The block diagram 202 is an example block diagram, and the block diagram 202 may include other components, additional components, or fewer components than what is illustrated in FIG. 2B.

[0083] The block diagram 202 illustrates a photonic integrated circuit 214 and an electronic integrated circuit 216. Therefore, the block diagram 202 shows a heterogeneous integration of an electronic integrated circuit (e.g., the electronic integrated circuit 216) and a photonic integrated circuit (e.g., the photonic integrated circuit 214). For example, the electronic integrated circuit 216 may be a complementary metal -oxide-semiconductor (CMOS) electronic circuit, a CMOS-based electronic device. As another example, the photonic integrated circuit 214 may utilize indium phosphide (InP): silicon photonics; silicon nitride(S13N4); gallium arsenide (GaAs); lithium niobate (LiNbO3); and / or other technologies that may offer benefits, such as the integration with electronics, wavelength range, required functionality, etc.

[0084] In some embodiments, the photonic integrated circuit 214 of FIG. 2B may include a PCAM-based QAM transmitter 220; an optical input 222 to the PCAM-based QAM transmitter 220; and an optical output 224 out of the PCAM-based QAM transmitter 220.

[0085] In some embodiments, the electronic integrated circuit 216 may include an electrical driver and / or control circuitry 218. The electrical driver and / or control circuitry 218 may be used to provide the control signals including control signals 126, 138, 130, 132, 134, 136, 138, and 140 of FIG. 1. The electrical driver and / or control circuitry 218 may be implemented using, for example, one or more application specific integrated circuits (ASICs), filed programmable gate arrays (FPGAs), central processing unit (CPU), graphics processing unit (GPU), microcontroller, or other circuitry.

[0086] In some embodiments, the outputs of the electrical driver and / or control circuitry 218 of FIG. 2B may be, provide, and / or include the electrical input for Is 126-132 and / or the electrical input for Qs 134-140 of FIG. 1 The PCCAM-based QAM transmitter 220 may be used to implement and / or may be implemented by the transmitter 102 of FIG. 1.

[0087] In this manner, the control circuitry 218 may be supported by and / or integrated with one substrate (e.g., a silicon substrate) while the transmitter 220 may be supported by and / or integrated with another substrate (e.g., an InP substrate). In some examples, the substrates may be co-packaged. Conductive leads may be connected to electrical contacts on both substrates to electrically couple the control circuitry 218 and the transmitter 220.

[0088] FIG. 3 shows a block diagram 300 of an QAM transmitter that includes two PC AMs, in accordance with examples described herein. The block diagram 300 may also be or include an QAM transmitter architecture using a RAMZI structure(s).

[0089] The block diagram 300 of FIG. 3 may share some similarities with the block diagram 100 of FIG. 1. However, in some embodiments, the photonic circuit portion of the block diagram 300 of FIG. 3 may be built using discrete photonic devices connected by, for example, waveguides. The electronic circuits of block diagram 300 may be built from silicon or a variety of other materials suitable for building photonic and / or CMOS-based devices. Accordingly, the transmitter 302 may be formed on a different substrate than the circuitry 304 in some examples.

[0090] In some embodiments, the block diagram 300 may include a PCAM-based QAM transmitter 302 and an electronic integrated circuit 304, where the PCAM-based QAMtransmitter 302 and the electronic integrated circuit 304 may be heterogeneously integrated, as is shown in FIG. 3.

[0091] In some embodiments, the block diagram 300 may include an optical input 306 to the PCAM-based QAM transmitter 302; an optical output 308 out of the PCAM-based QAM transmitter 302; an optical splitter 310; a PCAM 312 (e.g., a first PCAM) of the PCAM-based QAM transmitter 302; a PCAM 314 (e.g., a second PCAM) of the PCAM-based QAM transmitter 302; an optical signal input 316 to the PCAM 312; an optical signal input 318 to the PCAM 314; an I data 320; a Q data 322; a 90-degree phase shifter 324; and an optical combiner 326. The block diagram 300 is an example schematic, and the block diagram 300 may include other components, additional components, or fewer components, where the components may be discrete components. For example, in some embodiments, one, some, or each of the PCAM-based QAM transmitter 302, the optical splitter 310, the PCAM 312, the PCAM 314, the 90-degree phase shifter 324, and / or the optical combiner 326 may include discrete components, where these discrete components may be connected and / or coupled by, for example, waveguides.

[0092] In some embodiments, the electronic integrated circuit 304 may include an electrical driver and / or control circuitry 328, where the electrical driver and / or control circuitry 328 of FIG. 2A may provide inputs the same as, similar to, or equivalent to the electrical input for Is 126-132 and / or the electrical input for Qs 134-140 of FIG. 1.

[0093] FIG. 4 shows a block diagram 400 of a PCAM 402, in accordance with examples described herein. In some embodiments, the PCAM 402 may be used to implement and / or may be implemented by PCAMs described herein, such as PCAM 110 and / or 112 of FIG. 1, and / or PCAMs shown and described with reference to FIG. 2 A, FIG. 2B, and FIG. 3.

[0094] In some embodiments, the block diagram 400 of the PCAM 402 may include an optical input 404 to the PCAM 402; an optical output 406 out of the PCAM 402; an optical splitter 408 (or a beam splitter); an amplitude-phase modulator 410 (e.g., a first amplitudephase modulator, a top amplitude-phase modulator, a first resonant modulator); an amplitudephase modulator 412 (e.g., a second amplitude-phase modulator, a bottom amplitude-phase modulator, a second resonant modulator); an optical signal input 414 (e.g., a split beam, a first split beam) to the amplitude-phase modulator 410; an optical signal input 416 (e.g., another split beam, a second split beam) to the amplitude-phase modulator 412; a modulation control signal 418 to the amplitude-phase modulator 410; a configuration and / or tuning control signal 420 to the amplitude-phase modulator 410; a modulation control signal 422 to the amplitude-phase modulator 412; a configuration and / or tuning control signal 424 to theamplitude-phase modulator 412; an I data 426; a Q data 428; a phase shifter 430; and an optical combiner 432 of the I data 426 and Q data 428 to provide the optical output 406.

[0095] In some embodiments, the phase shifter 430 of FIG. 4 may be tuned to have a fixed phase shift.

[0096] In some embodiments, one, some, or each of the modulation control signals 418 and / or configuration and / or tuning control signals 420 may be provided to the amplitudephase modulator 410 (e.g., the top amplitude-phase modulator of FIG. 4) using one or more number (e.g., count) of wires and / or traces. Similarly, in some embodiments, one, some, or each of the modulation control signals 422 and / or configuration and / or tuning control signals 424 may be provided to the amplitude-phase modulator 412 (e.g., the bottom amplitude-phase modulator of FIG. 4) using one or more number (e.g., count) of wires and / or traces.

[0097] In some embodiments, the amplitude-phase modulator 410 and the amplitude-phase modulator 412 of the PCAM 402 may be two optical modulators and / or two resonant modulators. These modulators can be controlled using the modulation control signal 418 and the modulation control signal 422 such that they modulate the amplitude of the input light (e.g., optical signal input 414, optical signal input 416) identically, or near-identically, while providing opposite phase shifts to the input light. Light input into the device (e.g., the PCAM 402) may be split into two branches, where each of the branches has one of the modulators (e.g., the amplitude-phase modulator 410 or the amplitude-phase modulator 412). The output from the bottom device (e.g., the amplitude-phase modulator 412, the bottom amplitude-phase modulator, the bottom resonant modulator) may be sent to the phase shifter 430. The phase shifter 430 may be programmable (e.g., with electrical input, not illustrated in FIG. 4), but may maintain a fixed phase shift during operation. Meanwhile, the two beams of light (e.g., the I data 426, the Q data 428) may be combined in the optical combiner 432.

[0098] In some embodiments, the two optical modulators (e.g., the amplitude-phase modulator 410 and the amplitude-phase modulator 412, two resonant modulators) have equal (or near equal) amplitudes and opposite phase shifts, while the output phase is constant. In some embodiments, one or each of the optical modulators may utilize two electronic control signals: a first signal (e.g., configuration and / or tuning control signal 420, configuration and / or tuning control signal 424) to configure the device to be in the correct operation regime, and a second signal (e.g., modulation control signal 418, modulation control signal 422) to control modulation of the optical input (e.g., optical input 404, optical signal input 414).

[0099] In some embodiments, a PCAM described herein may be implemented using an amplitude- phase modulator(s), an MRM(s), an MZI(s), and / or a RAMZI(s).

[0100] An example RAMZI photonic circuit may include two amplitude-phase modulators (e.g., MRMs) on either arm of an MZI. For example, referring to FIG. 1, the PCAM 110 may include an MRM used to implement the first amplitude-phase modulator and an MRM used to implement the second amplitude-phase modulator. The PCAM 112 may include an MRM used to implement the first amplitude-phase modulator and an MRM used to implement the second amplitude-phase modulator. The PCAM operation may utilize the fact that as the MRM moves away from resonance, its amplitude changes identically in either direction, while its phase changes in an opposite manner in either direction. Each MRM’s resonance wavelength may be thermally tuned such that their resonances lie equal distances from the laser wavelength, but on opposite sides. Accordingly, tuning control signals described herein may be used to adjust resonance wavelengths of modulators described herein. Referring again to FIG. 1, the tuning control signals 128 and 132, for example, may be used to set resonance wavelengths of the modulators 118 and 120 to be equal distances from the laser wavelengths on opposite sides. For example, the tuning control signal 128 may cause an MRM used to implement modulator 118 to have a resonance wavelength that is a predetermined amount greater than a wavelength of the optical input 104 and / or 114. The tuning control signal 132 may accordingly cause an MRM used to implement modulator 120 to have a resonance wavelength that is the same predetermined amount less than a wavelength of the optical input 104 and / or 116.

[0101] In some embodiments, differential (e.g., push-pull) driving voltages may be applied to simultaneously modulate the resonance frequency of the amplitude-phase modulators (e.g., MRMs) in opposite directions towards or away from the laser wavelength, as is shown in FIG. 5. Accordingly, each amplitude-phase modulator of a PCAM (e.g., each MRM) may apply an identical amplitude change to an incoming optical signal and an opposite phase shift, which modulates the RAMZFs output amplitude while holding output phase constant. For example, referring to FIG. 1, the modulator 118 may provide an amplitude shift to an incoming optical signal, and may shift the phase of the optical signal by an amount. The modulator 120 may provide an additive amplitude shift (e.g., the same amplitude shift), and may shift the phase of the optical signal by an opposite amount. Accordingly, an optical signal applied to the modulator 118 and the modulator 120 may have an amplitude shift as output but no phase shift relative to the input.

[0102] In some embodiments, a bias thermal phase shifter may be included in one arm of the RAMZI. For example, the transmitter 102 of FIG. 1 may include phase shifter 146 coupled to an output of the PCAM 112. The phase shifter may be tuned so that the individual MRM outputs (e.g., an output of the PCAM 110 and the PCAM 116) interfere constructively in thehigh transmission and destructively in the low transmission state. In doing so, the RAMZI pay provide an amplitude contrast which may generally be superior to that of a single MRM by taking advantage of both amplitude and phase modulation in the MRM.

[0103] Since the amplitude-phase modulators (e.g., MRMs) may be packaged closely to a large and / or variable source of heat, in some implementations, a feedback loop may be implemented so the thermal tuning maintains the correct bias point for each MRM. In some embodiments, a small portion of the power in the MRM may be measured, for example, using a drop port and photodiode, and comparing the power (either in the high transmission state, low transmission state, or a combination of both) to an expected value. For example, referring to FIG. 1, a sensor (e.g., a photodiode) may be positioned to measure power consumed by all or portions of the PCAM 110, such as by the modulator 118 and / or the modulator 120. The photodiode may communicate with a controller (e.g., control circuitry described herein). The controller may compare the power indicated by the photodiode with a predetermined and / or threshold value. The predetermined and / or threshold value may be stored in memory or other storage devices accessible to the controller. Based on the comparison, one or more tuning signals to the PCAM may be adjusted. Adjustment of the tuning signals may occur to maintain a bias point (e.g., resonant frequency) of the modulator.

[0104] Examples of systems described herein may utilize one or more PCAMs, which may be or utilize phase-constant optical amplitude modulators. Generally, the phase-constant optical amplitude modulators may modulate an amplitude in accordance with an input signal to generate an output signal, while a phase of the output signal may remain constant over a range of input signals.

[0105] In some embodiments, for example, as is shown in FIG. 4, a beam splitter (e.g., optical splitter 408) may be provided with an optical input (e.g., optical input 404). The beam splitter may receive optical energy from an optical energy source, such as a laser. The optical energy may have or include energy at a particular wavelength and / or frequency. The beam splitter may output a first split beam (e.g., optical signal input 414) and a second split beam (e.g., optical signal input 416). The first split beam and the second split beam may be referred to as two ‘arms’ of the modulator (e.g., PCAM 402). In some examples, the incoming optical energy may be split evenly into the first and second split beams. However, other split ratios may be used in other examples.

[0106] In some embodiments, a first split beam (e.g., optical signal input 414) from the optical splitter (e.g., the optical splitter 408) may be provided to a first amplitude-phase modulator (e.g., amplitude-phase modulator 410, a top amplitude-phase modulator). Theamplitude-phase modulator may also be referred to as a resonant modulator. Generally, the amplitude-phase modulator may be implemented using an optical modulator, which modulates both an amplitude and frequency of an input optical beam in accordance with an input to the modulator. Similarly, a second split beam (e.g., optical signal input 416) may be provided to a second amplitude-phase modulator (e.g., amplitude-phase modulator 412, bottom amplitude-phase modulator).

[0107] In some embodiments, the top amplitude-phase modulator may accordingly output a first modulated beam. The bottom amplitude-phase modulator may accordingly output a second modulated beam. The second modulated beam may be provided to a phase shifter (e.g., phase shifter 430), and the phase shifter may output a phase-shifted modulated beam (e.g., Q data 428).

[0108] In some embodiments, an optical combiner (e.g., optical combiner 432) may be provided to combine the phase-shifted modulated beam and the first modulated beam to provide an output signal (e.g., optical output 406).

[0109] In some embodiments, the operation of the top and the bottom amplitude-phase modulators may be controlled such that the optical output of the PCAM (e.g., PCAM 402) is a phase-constant amplitude modulated signal. In some examples, configuration and / or tuning control inputs (e.g., configuration and / or tuning control signal 420, configuration and / or tuning control signal 424) to each of the amplitude-phase modulators may be used. In some examples, the tuning control inputs may receive tuning control signals, which may control a resonant frequency of the amplitude-phase modulator(s). Generally, tuning control signals may be used which may adjust a resonant frequency of top amplitude-phase modulator (e.g., amplitude-phase modulator 410, a first amplitude-phase modulator) to be on an opposite side of the input optical energy frequency than the resonant frequency of the bottom amplitudephase modulator (e.g., amplitude-phase modulator 412, a second amplitude-phase modulator). Accordingly, a resonant frequency of the top amplitude-phase modulator may be greater than a frequency of the optical input. A resonant frequency of the bottom amplitude-phase modulator may be less than a frequency of the optical input. In some examples, the resonant frequency of the top amplitude-phase modulator may be greater than the frequency of the optical input by the same amount that the resonant frequency of the bottom amplitude-phase modulator is less than the frequency of the optical input.

[0110] Generally, tuning control inputs are used which cause the top amplitude phase modulator to provide an opposite phase shift to the bottom amplitude-phase modulator. In some examples, the two modulators provide equal and opposite phase shifts. The tuningcontrol inputs further cause the top and bottom amplitude phase modulators to provide a same (or same sign) amplitude modulation.

[0111] Generally, modulation control signals (e.g., modulation control signal 418, modulation control signal 422) may be applied to modulation control inputs of the top and bottom amplitude-phase modulators. The modulation control signals may represent data to be output from the PCAM (e.g., PCAM 402), for example. Changes in modulation signals may result in providing equal and opposite changes to the phase modulation provided by the top and bottom resonant modulators, respectively. In some examples, changes in the modulation signals are configured to provide equal changes to the amplitude modulation provided by the top and bottom resonant modulators.

[0112] In some embodiments, during operation, tuning signals may be applied to phaseamplitude modulators of an interferometer such that the interferometer is configured to provide phase-constant amplitude modulation. Data signals may be applied to the phaseamplitude modulators to provide phase-constant amplitude-modulated output signals based on the data signals. The data signals may be applied, for example, at the modulation control inputs of the amplitude-phase modulators.

[0113] By modulating the amplitude, PC AMs described herein may provide any number of output states. Generally, any number of output states may be provided, such as between two (2) and sixteen (16) output states. An output state typically refers to an output amplitude that may be distinguished and / or distinguishable from other amplitudes of other states.

[0114] FIG. 5 shows a method 500 of biasing and modulating amplitude-phase modulators (e.g., MRMs) in a RAMZI to achieve phase-constant amplitude modulation, where the method 500 is shown at least in reference to two graphs, in accordance with examples described herein. The graphs include graph 502 and graph 504.

[0115] In some embodiments, graph 502 and graph 504 share a same wavelength 506 (or lambda) axis, where this axis is expressed in nanometers (nm). The lambda axis may refer to the wavelength of the light supplied to the system (e.g., PCAM 402 of FIG. 4) by the laser (e.g., optical input 404 of FIG. 4).

[0116] In some embodiments, graph 502 plots a normalized output power 508 versus wavelength 506 (e.g., lambda in nm). Note that the normalized output power is typically unitless. This is because the normalized output power normally represents the ratio of the output power of the amplitude-phase modulator (e.g., MRM) to a reference power level, thereby creating a dimensionless quantity. In some embodiments, the reference power may, generally, be the input power or the maximum possible output power.

[0117] In some embodiments, graph 504 plots output phase 510 (expressed in degrees) versus wavelength 506 expressed in nanometers.

[0118] In some embodiments, graphs 502 and 504 show the outputs of the amplitude-phase modulators, such as the output of the amplitude-phase modulator 410 (e.g., I data 426) and / or the output of the amplitude-phase modulator 412 (e.g., before entering the phase shifter 430 to generate the Q data 428) of FIG. 4.

[0119] In some embodiments, the states illustrated in FIG. 5 may refer to the different behaviors and / or operations of the system (e.g., PCAM 402 of FIG. 4) that may be controlled by modulation control signals (e.g., the modulation control signal 418 and / or the modulation control signal 422 of FIG. 4) to the amplitude-phase modulators (e.g., MRMs). For example, the PCAM 402 of FIG. 4 may be configured to provide different electrical field amplitudes of the optical output 406 in different states, while holding the phase of the optical output 406 constant or near-constant. As another example, the PCAM 402 of FIG. 4 may be in state “1” of FIG. 5 when the top amplitude-phase modulator 410 (e.g., top MRM) has a higher applied voltage, and the bottom amplitude-phase modulator 412 (e.g., bottom MRM) has a lower applied voltage. As yet another example, the PCAM 402 may be in the state “0” when the top amplitude-phase modulator 410 (e g., top MRM) has a lower applied voltage, and the bottom amplitude-phase modulator 412 (e.g., bottom MRM) has a higher applied voltage.

[0120] FIG. 6 show an offset-QAM-4 constellation 600 and an offset-QAM-16 constellation 602, in accordance with examples described herein. Note that each of these constellations is plotted as Q versus I. The offset-QAM-4 constellation 600 includes four (4) combinations of I and Q values, and the offset-QAM-16 constellation 602 includes sixteen (16) combinations of I and Q values.

[0121] In some embodiments, the offset-QAM-4 constellation 600 and the offset-QAM-16 constellation 602 may be produced using the same PCAM-based offset-QAM transmitter 604, as is shown in FIG. 6 with, for example, more finely spaced electrical inputs. Generally, any PCAM-based QAM transmitters described herein may generate the constellations shown in FIG.6, such as the transmitter shown and described with reference to FIG. 1.

[0122] In some embodiments, I, Q bits 608 may be used to generate the offset-QAM-4 constellation 600 of FIG. 6, and I, Q bits 610 may be used to generate the offset-QAM-16 constellation 602 of FIG. 6.

[0123] In some embodiments, Equations 1, 2, and 3 of FIG. 16 may be used to mathematically describe the RAMZI operation.

[0124] In Equation 1 of FIG. 16, ([lout may represent an output phase; <[>PS may represent a phase shift of a thermal phase shifter; AT may represent an amplitude of a top ring modulator, a top resonant modulator, and / or a top amplitude-phase modulator; AB may represent an amplitude of a bottom ring modulator, a bottom resonant modulator, and / or a bottom amplitude-phase modulator; (|>T may represent a phase of the top ring modulator, the top resonant modulator, and / or the top amplitude-phase modulator; (|)B may represent a phase of the bottom ring modulator, the bottom resonant modulator, and / or the bottom amplitude-phase modulator. Continuing with Equation 1 of FIG. 16, since these rings, resonant modulators, and / or amplitude-phase modulators have opposite phases and equal amplitudes, (|)T may be represented as (|)x, and <|)B may be represented as -(|>x; AT and AB may be represented as Ax.

[0125] In Equation 2 of FIG. 16, Pout may represent an output power (e.g., a normalized output power to the input power); <|)ps may represent the phase shift of the thermal phase shifter; AT may represent the amplitude of the top ring modulator, the top resonant modulator, and / or the top amplitude-phase modulator; AB may represent the amplitude of the bottom ring modulator, the bottom resonant modulator, and / or the bottom amplitude-phase modulator; (|)T may represent the phase of the top ring modulator, the top resonant modulator, and / or the top amplitude-phase modulator; (|)B may represent the phase of the bottom ring modulator, the bottom resonant modulator, and / or the bottom amplitude-phase modulator. Similarly, since these rings, resonant modulators, and / or amplitude-phase modulators have opposite phases and equal amplitudes, (|>T may be represented as x, and (|)B may be represented as -(|>x; AT and AB may be represented as Ax.

[0126] In some embodiments, as is shown by observing Equation 1 of FIG. 16, the output phase of the RAMZI is constant.

[0127] In some embodiments, since coherent optical receivers may detect power proportional to the transmitted electric field strength, Equation 3 of FIG. 16 may be used to calculate an effective optical modulation amplitude (OMAE). Equation 3 shows that the phase shift of the thermal phase (e.g., 4>PS) may be tuned such that ring outputs (or outputs of a PCAM(s), outputs of resonant modulator(s), outputs of amplitude modulator(s)) may interfere constructively when amplitudes are high (Aout,ni), and may interfere destructively when amplitudes are low (Aout,Lo). Therefore, in addition to a constant output phase shown in Equation 1, Equation 3 shows that the RAMZI can provide an enhanced optical modulation amplitude (OMA) compared to, for example, a single amplitude-phase modulator (e.g., instead of two amplitude-phase modulators or MRMs).

[0128] In some embodiments, PCAM-based QAM transmitters described herein may perform a coherent modulation similar to the one shown in the offset-QAM-4 constellation 600 of FIG. 6. However, PCAM-based QAM transmitters described herein may perform higher-order coherent modulations, such as a QAM-16 (e.g., as is shown in example of offset- QAM-16 constellation 602). FIG. 6 shows a modulation performed in an ‘offset’ manner. However, the modulation can be performed in a ‘non-offset’ manner (e.g., in a manner where the offset is zero (0)).

[0129] FIG. 7 shows a non-offset-QAM-16 constellation 700, in accordance with examples described herein. Note that each of the non-offset-QAM-16 constellation 700 is plotted as Q versus I. The non-offset-QAM-1 constellation 700 includes sixteen (16) combinations of I and Q values. As is shown in FIG. 7, the non-offset-QAM-16 constellation 700 differs from the offset-QAM-16 constellation 602 of FIG. 6, since the non-offset-QAM-16 constellation 700 modulation is generated in a non-offset manner.

[0130] In some embodiments, the non-offset-QAM-16 constellation 700 is generated using a PCAM-based non-offset-QAM transmitter 702, a phase shifter 704, an electrical driving and / or control circuitry 706, an electrical driving and / or control circuitry 708, and a set of I, Q bits 710.

[0131] In some embodiments, the phase shifter 704 may be placed and / or coupled after the PCAM-based non-offset-QAM transmitter 702. The phase shifter 704 may be an electro- optical phase shifter, a PN-junction phase shifter, or another technology.

[0132] In some embodiments, a portion (e.g., two I bits, two In-phase bits) of the I, Q bits 710 may be fed to the electrical driving and / or control circuitry 706 that drives and / or controls the PCAM-based non-offset-QAM transmitter 702; and another portion (e.g., two Q bits, two quadrature bits) of the I, Q bits 710 may be fed to electrical driving and / or control circuitry 708 that drives and / or controls the phase shifter 704.

[0133] Generally, an offset-QAM modulation scheme (e.g., the offset-QAM-4 constellation 600, the offset-QAM-16 constellation 602 of FIG. 6) and / or a non-offset-QAM modulation scheme (e.g., non-offset-QAM-16 constellation 700 of FIG. 7) can be used. A difference between these modulation schemes may be the way and / or manner the signals are transmitted and / or timed, and their impact on a spectral efficiency and / or a system(s) (e.g., RAMZI(s), PCAM(s)) performance(s).

[0134] For example, when using an offset-QAM modulation scheme, the in-phase (I) and quadrature (Q) components of the signal are transmitted simultaneously. This can result in both components changing at the same time.

[0135] As another example, an offset-QAM modulation scheme may introduce a timing offset between the I and Q components, for example, by delaying one of the components by a portion of the symbol's duration (e.g., T / 2, T / 3, n / 3, TC / 2, or another delay and / or offset). In some embodiments, the offset can reduce signal peaks by, for example, changing both components at the same time.

[0136] As another example, when using a non-offset-QAM modulation scheme, a system may experience a more pronounced signal envelope fluctuation(s) compared when using an offset-QAM modulation scheme due to the simultaneous changes in both components. This may sometime lead to higher out-of-band emissions and potentially more stringent power amplifier requirements.

[0137] As another example, when using an offset-QAM modulation scheme, by staggering the changes in the I and Q components, the system (e.g., RAMZI, PCAM) can offer reduced peak-to-average power ratio (PAPR) and, for example, the system may improve the performance of the power amplifiers and / or reduce channel interference (e.g., adjacent channel interference).

[0138] As yet another example, offset-QAM modulation schemes may provide some advantages in terms of power amplifier efficiency and / or channel interference reduction. Non-offset-QAM modulation schemes, however, may maintain simplicity in implementation by, for example, reducing the complexity of the system by reducing or eliminating components that provide timing offsets. A non-offset-QAM modulation scheme may be considered an offset-QAM modulation scheme, where the offset is zero (0).

[0139] In some embodiments, phase compensation for offset-QAM can happen in a variety of ways. For example, an receive laser at a receiver may be locked to the phase of the signal. In some examples, a transmit laser beam may be forwarded to the receiver, and a phase shifter may tune the phase. FIG. 8A and FIG. 8B shows both of these example approaches.

[0140] FIG. 8A shows a block diagram 800 of a laser-locked coherent optical link between a transmitter (Tx) and a receiver (Rx), in accordance with examples described herein. The block diagram 800 may represent a diagram of a transceiver that includes a Tx 804 and a Rx 806.

[0141] In some embodiments, the block diagram 800 of the laser-locked optical link may include a Tx 804 (e.g., a transmitter); a Rx 806 (e.g., a receiver); a Tx laser 808 of the Tx 804; an QAM modulator 810 of the Tx 804; an optical input 812 (e.g., a first optical input) to the QAM modulator 810, where the optical input 812 is generated by the Tx laser 808; atransmitted signal 814 (e.g., ETX) generated by the QAM modulator 810 and / or the Tx 804; a QAM Rx 816 of the Rx 806, where the transmitted signal 814 is an input to the QAM Rx 816; an I 818 out of the Rx 806; a Q 820 out of the Rx 806; an error signal 822 generated by the QAM Rx 816; a Rx laser 824 of the Rx 806, where the error signal 822 may be an input to the Rx laser 824; a laser output 826 (e.g., a second optical input) to the QAM Rx 816, where the laser output 826 is generated by the Rx laser 824. Note that block diagram 800 includes two lasers: the Tx laser 808 and the Rx laser 824. In some embodiments, the frequencies of these two lasers may not be matched. In some examples, the QAM Rx 816 may be an offset- QAM.

[0142] The block diagram 800 is an example schematic of a laser-locked coherent optical link between a transmitter and a receiver, and the block diagram 800 may include other components, additional components, or fewer components. The block diagram 800 is illustrated as a monolithic device and / or system. It is to be understood that, in some embodiments, the transmitter and / or the receiver may be heterogeneously designed and / or manufactured. The QAM modulator 810 may be implemented by QAM transmitters described herein, such as that shown and described with reference to FIG. 1. In some examples, the QAM modulator 810 may be an offset-QAM modulator.

[0143] FIG. 8B shows a block diagram 802 of a laser-forwarded coherent optical link, in accordance with examples described herein. In some embodiments, the block diagram 802 is an example of a transceiver that uses the same laser for a transmitter and a receiver of the transceiver. By so doing, the transmitter and the receiver of FIG. 8B are frequency matched.

[0144] In some embodiments, the block diagram 802 of the laser-forwarded coherent optical link may include a Tx 828 (e.g., a transmitter); a Rx 830 (e.g., a receiver); a Tx laser 832 of the Tx 828; a QAM modulator 834 of the Tx 828; an optical input 836 (e.g., a first optical input) to the QAM modulator 834, where the optical input 836 is generated by the Tx laser 832; a transmitted signal 838 (e.g., ETX) generated by the QAM modulator 834 and / or the Tx 828; a QAM Rx 840 of the Rx 830, where the transmitted signal 838 is an input to the QAM Rx 840; an I 842 out of the QAM Rx 840; a Q 844 out of the QAM Rx 840; an error signal 846 generated by the QAM Rx 840; a Rx phase shifter 848, where the error signal 846 is an input to the Rx phase shifter 848; an optical input 852 to the QAM Rx 840, where the optical input 852 is generated by the Rx phase shifter 848; and a LO signal 850 (e.g., ELO) generated by the Tx laser 832 of the 828, where the LO signal 850 is an input to the Rx phase shifter 848. In some examples, the QAM Rx 840 may be an offset-QAM Rx.

[0145] The block diagram 802 is an example schematic of a laser-forwarded coherent optical link between a transmitter and a receiver, and the block diagram 802 may include other components, additional components, or fewer components. The block diagram 802 is illustrated as a monolithic device and / or system. It is to be understood that, in some embodiments, the transmitter and / or the receiver may be heterogeneously designed and / or manufactured. The QAM modulator 834 may be implemented by QAM transmitters described herein, such as that shown and described with reference to FIG. 1.

[0146] In some embodiments, an optical coherent communication may rely on the precise frequency and the phase locking and / or tracking of the received signal and the local oscillator (LO) (e g., laser). Any phase error between the two paths (A ) may cause I / Q crosstalk and / or may reduce the detected signal power at the receiver, significantly degrading the bit error rate (BER) and / or the symbol error rate (SER).

[0147] FIG. 9A shows a constellation diagram 900 for a conventional QAM-4 or quadrature phase shift keying (QPSK) with (A(|) = 0) and without (A<|) = 0) phase error (or phase offset) between the Rx and LO paths, in accordance with examples described herein.

[0148] FIG. 9B shows a constellation diagram 902 for an offset-QAM-4 with (A(|) 0) and without (A(|) = 0) phase error between the Rx and LO paths, in accordance with examples described herein.

[0149] The constellation diagram 900 and the constellation diagram 902 illustrate the effect of phase offset between the Rx and LO signals. In the constellation diagram 900 of the QAM- 4, a A(|) phase offset may cause the entire constellation to rotate around the origin, and a Costas loop technique may be utilized to calculate the phase offset (A<|)). However, as is shown in the constellation diagram 902 of the offset-QAM, the rotation not only affects amplitudes but also shifts the center of the constellation, making the conventional Costas loop at times less effective, or difficult to implement.

[0150] Generally, the Costas loop may be a phase-locked loop (PLL) used for carrier phase recovery in communication systems, such as for demodulating suppressed-carrier amplitude- modulated signals, such as a QPSK. The Costas loop may be designed to lock onto the phase of an incoming carrier signal and to maintain synchronization with it. The Costas loop may include components, such as a phase detector(s); a loop filter(s); a voltage-controlled oscillator (VCO); a quadrature mixer to split the incoming signal into two components that are mixed with the LO signal to produce I (In-phase) and Q (Quadrature-phase) components, where these I and Q components may be compared to reduce and / or eliminate phase ambiguity; other components; fewer components; and / or additional components.

[0151] In some embodiments, technique(s) and / or method(s) described herein may be used to perform, calculate, and / or determine a phase error detection based, in part, on measuring the average amplitudes of I and Q symbols for QAM carrier phase recovery systems, such as offset-QAM carrier phase recovery (CPR) systems. Some of the systems, technique(s), and / or methods described herein may not rely on the Costas loop in some examples. Other technique(s) and / or method(s) described herein may rely on the Costas loop in some examples. Yet other techniques(s) and / or methods described herein may be similar to the Costas loop in some examples.

[0152] In some embodiments, an architecture of the laser-forwarded coherent optical link (e.g., block diagram 802 of FIG. 8B) may be used for correcting and / or aligning the phase of the Rx signal and LO signal using a tunable phase shifter (e.g., Rx phase shifter 848 of FIG. 8B) in the LO path.

[0153] In some embodiments, the I and Q signals before a phase error compensation may be described using the Equations 4 and 5 of FIG. 16. In Equations 4 and 5 of FIG. 16, Ao may denote a constant value due to an QAM modulation and / or offset-QAM modulation; I(t) / Q(t) may be approximately or equal to ±AOMA / 2; and Ac|) may denote a phase error.

[0154] In some embodiments, the high portions of I’(t) and Q’(t) may be filtered using low- pass filters, retaining an average voltage of the I (I avg) and Q (Q av ) signals, as is shown using Equations 6 and 7 of FIG. 16.

[0155] FIG. 10A shows constellation diagram 1000 for a conventional QAM-4 or QPSK with (A(|) #= 0) and without ( A(|J = 0) phase error between Rx and LO paths, in accordance with examples described herein. FIG. 10A is illustrated and / or described in the context of FIG. 9A.

[0156] FIG. 10B shows a constellation diagram for another offset-QAM-4 with (A(|) 0) and without (A(|) = 0) phase error between the Rx and LO paths, in accordance with examples described herein. FIG. 10B is illustrated and / or described in the context of FIG. 9B.

[0157] In some embodiments, DSP-free carrier phase recovery system may be tailored for offset-QAM. Offset-QAM may be created by leaking a portion of an LO signal with an QAM signal at the transmitter, similar to what is shown in FIG. 10B. For example, offset-QAM may be generated using Mach-Zehnder Modulators (MZMs), where the MZMs may operate with an offset from a transmission null. As another example, offset-QAM may be generated using amplitude-phase modulators, such as micro-ring modulators (MRMs).

[0158] In some embodiments, when using an offset-QAM signaling, an Rx may detect the phase offset between the Rx and LO paths based on the average power and / or voltagedifference between the in-phase (I) and quadrature (Q) signals. The difference may then be used as an error signal to compensate for the phase error using a phase shifter in the LO path for a laser-forwarded link.

[0159] In some embodiments, a carrier phase recovery (CPR) block may support offsetfl AM modulation levels, such as 4, 16, or 256, without or with little architectural changes. Therefore, the systems, techniques, and / or methods described herein may communicate with high-order modulation schemes. Additionally, or alternatively, unlike the Costas loop, some receivers described herein may not suffer from a phase ambiguity (e.g., u / 2 phase ambiguity).

[0160] FIG. 11A shows a block diagram of an example architecture of a QAM coherent receiver or Rx 1100, where the Rx 1100 may implement a first method (may be referred herein as "method 1") for laser phase recovery, in accordance with examples described herein. The Rx 1100 of FIG. 11A is an example schematic and / or architecture, and the Rx 1100 may include other components, additional components, or fewer components.

[0161] FIG. 11B shows a block diagram of another example architecture a QAM coherent receiver or Rx 1150, where the Rx 1150 may implement a second method (may be referred herein as "method 2") for laser phase recovery, in accordance with examples described herein. The Rx 1150 of FIG. 11B is an example schematic and / or architecture, and the Rx 1150 may include other components, additional components, or fewer components.

[0162] In some embodiments, the Rx 1100 of FIG. 11A and / or the Rx 1150 of FIG. 11B may be described and / or illustrated in the context of Rx 830 of the block diagram 802 of FIG. 8B. For example, the Rx 1100 of FIG. 11A and / or the Rx 1150 of FIG. 11B may be an implementation of the Rx 830 of FIG. 8B. Note that the block diagrams of FIG. 11 A and FIG. 11B do not show transmitters.

[0163] Regarding FIG. 11A and FIG. 1 IB, some of the description may refer to the Rx 1100 of FIG. 11A and / or the Rx 1150 of FIG. 11B, depending on the components of these architectures. For example, the Rx 1100 and the Rx 1150 share some, but not all, components and / or operations. For the sake of brevity, some of the shared components and / or operations may be described in the context of the Rx 1100 of FIG. HA and the Rx 1150 of FIG. 11B.

[0164] The Rx 1100 of FIG. HA includes and / or utilizes a carrier phase recovery (CPR) circuitry that is different from that utilized by the Rx 1150 of FIG. 1 IB. Specifically, the CPR circuitry 1128 helps the Rx HOO of FIG. HA to implement the first method (or “method 1”) for laser phase recovery described herein. The CPR circuitry 1178 helps the Rx 1150 of FIG. 11B to implement the second method (or “method 2”) for laser phase recovery described herein.

[0165] In some embodiments, the Rx 1100 of FIG. HA may include a received signal 1102; an LO signal 1104; a 90-degree optical filter 1106 (e.g., a 90-degree hybrid optical filter); a photodetector 1108; a photodetector 1110; a photodetector 1112; a photodetector 1114; an AFE 1116 (AFE denotes an analog front end); an AFE 1118; a comparator 1120; a comparator 1122; an I 1124; a Q 1126; a CPR circuitry 1128; and a phase shifter 1130.

[0166] In some embodiments, the CPR circuitry 1128 of the Rx 1100 of FIG. HA may include a low-pass filter 1132; a low-pass filter 1134; an adder 1136; a subtractor 1138; an SGN(x) 1140; a mixer 1142; an error signal 1144; a loop filter 1146; and a gain component 1148.

[0167] In some embodiments, CPR circuitry 1128 of the Rx 1100 of FIG. 11 A may generate the error signal 1144. The error signal 1144 can then be fed to the phase shifter 1130 to compensate for the phase offset between the received signal 1102 and the LO signal 1104.

[0168] In some embodiments, the Rx 1150 of FIG. 1 IB may include a received signal 1152; an LO signal 1154; a 90-degree optical filter 1156 (e.g., a 90-degree hybrid optical filter); a photodiode 1158; a photodiode 1160; a photodiode 1162; a photodiode 1164; an AFE 1166; an AFE 1168; a comparator 1170; a comparator 1172; an I 1174; a Q 1176; a CPR circuitry 1178; and a phase shifter 1180.

[0169] In some embodiments, the CPR circuitry 1178 of the Rx 1150 of FIG. 1 IB may include a low-pass filter 1182; a low-pass filter 1184; an SGN(x) 1186; an SGN(x) 1188; a mixer 1190; a mixer 1192; a subtractor 1194; an error signal 1196; a loop filter 1198; and a gain component 11-100.

[0170] In some embodiments, referencing the receivers in FIG. 11 A and FIG. 11B, photodetectors 1108 to 1114 of Rx 1100 and / or the photodiodes 1158 to 1164 of Rx 1150 may be balanced photodetectors and may convert the optical signals into the electrical domain.

[0171] In some embodiments, referencing the receivers in FIG. HA and FIG. 1 IB, the AFE(s) (e.g., AFE(s) 1116, 1118, 1166, and / or 1168) may include a trans-impedance amplifier (TIA) that may be followed by, for example, by a continuous time linear equalizer (CTLE).

[0172] In some embodiments, in a CPR circuitry, the In-phase (I) and Quadrature-phase (Q) paths may be differenced in current mode using a subtractor to generate an error signal proportional to sin (A(|>). The subtractor may be followed by (e.g., coupled to) a capacitor. In some embodiments, the CPR circuitry may use an adder, followed by a comparator, to select only the negative slope of the error signal to maintain loop stability. In some embodiments, the comparator may be implemented using a non-clocked strong-arm latchcomparator followed by inverters, with the first stage setting the bias point of the comparator. In some embodiments, the CPR circuitry may include an operational amplifier (may be referred herein an “opamp”) with capacitive feedback to create a second-order loop filter to maintain a zero or near-zero remaining phase error between the LO and Rx signals. In some embodiments, the CPR circuitry may include a driver to continuously adjust the phase shifter’s phase in the LO path with the error signal (yerr) until the loop is locked and the I and Q averages become equal. In some embodiments, the error signal is equal to a constant direct current (de) offset of In-phase (I) and Quadrature-phase (Q) signals multiplied by a sine or sinusoid of the phase offset. In some examples, the de offset may be zero (0).

[0173] In some embodiments, a laser output (e.g., an output of the Tx laser 832 of FIG. 8B) of a transmitter (not illustrated in FIG. 11 A and FIG. 1 IB) may be divided into two paths (or may be split into two beams). For example, a first path from the laser output of the transmitter may result and / or be received as the received signal 1102 to the Rx 1100 of FIG. HA and / or the received signal 1152 of the Rx 1150 of FIG. 11B. As another example, a second path may generate the LO signal 1104 of Rx 1100 of FIG. 11 A and / or the LO signal 1154 of the Rx 1150 of FIG. 1 IB. The transmitter (not illustrate in FIG. 11A and / or FIG. 1 IB) generates a QAM signal using I and Q data from, for example, pseudo-random binary sequence (PRBS) generators.

[0174] In some embodiments, an optical transmitter may be implemented using amplitude modulators and thermal phase shifters. The modulated signal (e.g., transmitted signal 838 of FIG. 8B, received signal 1102 of FIG. 11 A, received signal 1152 of FIG. 1 IB) along with the LO signal (e.g., LO signal 850 of FIG. 8B, the LO signal 1104 of FIG. HA, the LO signal 1154 of FIG. 1 IB), is transmitted to the receiver (e.g., the Rx 1100 of FIG. 11 A, the Rx 1150 of FIG. 1 IB) through fibers. At the receiver (e.g., the Rx 1100 of FIG. 11A, the Rx 1150 of FIG. 1 IB), the received signal (e.g., received signal 1102, received signal 1152) beats with the LO signal (e.g., LO signal 1104, LO signal 1154) in the 90-degree optical filter 1106 of the Rx 1100 of FIG. HA and / or the 90-degree optical filter 1156 of the Rx 1150 of FIG. 11B to demodulate I and Q signals.

[0175] FIG. 12A shows a block diagram of an example architecture of an QAM coherent receiver or Rx 1200, where the Rx 1200 may implement a first method (may be referred herein as "method 1") for laser phase recovery, in accordance with examples described herein. The Rx 1200 of FIG. 12A is an example schematic and / or architecture, and the Rx 1200 may include other components, additional components, or fewer components.

[0176] FIG. 12B shows a block diagram of another example architecture an of QAM coherent receiver or Rx 1258, where the Rx 1258 may implement a second method (may be referred herein as "method 2") for laser phase recovery, in accordance with examples described herein. The Rx 1258 of FIG. 12B is an example schematic and / or architecture, and the Rx 1258 may include other components, additional components, or fewer components.

[0177] In some embodiments, the Rx 1200 of FIG. 12A may be described and / or illustrated in the context of Rx 830 of FIG. 8B and / or of the Rx 1100 of FIG. 11 A. Note that the block diagram of FIG. 12A does not show a transmitter. A difference between the Rx 1200 of FIG. 12A and the Rx 1100 of FIG. 11A is the use of two (2) phase shifters in the Rx 1200 of FIG. 12A instead of one phase shifter in the Rx 1100 of FIG. 11 A.

[0178] In some embodiments, the Rx 1258 of FIG. 12B may be described and / or illustrated in the context of Rx 830 of FIG. 8B and / or of the Rx 1150 of FIG. 1 IB. Note that the block diagram of FIG. 12B does not show a transmitter. Some differences between the Rx 1258 of FIG. 12B and the Rx 1150 of FIG. 1 IB is the use of two (2) phase shifters in the Rx 1258 of FIG. 12B instead of one phase shifter in the Rx 1150 of FIG. 1 IB.

[0179] Regarding FIG. 12A and FIG. 12B, some of the description may refer to the Rx 1200 of FIG. 12A and / or the Rx 1258 of FIG. 12B, depending on the components of these architectures. For example, the Rx 1200 and the Rx 1258 share some, but not all, components and / or operations. For the sake of brevity, some of the shared components and / or operations may be described in the context of the Rx 1200 of FIG. 12A and the Rx 1258 of FIG. 12B.

[0180] The Rx 1200 of FIG. 12A includes and / or utilizes a carrier phase recovery (CPR) circuitry that is different from that utilized by the Rx 1258 of FIG. 12B. Specifically, the CPR circuitry 1228 helps the Rx 1200 of FIG. 12A to implement the first method (or “method 1”) for laser phase recovery described herein. The CPR circuitry 1286 helps the Rx 1258 of FIG. 12B to implement the second method (or “method 2”) for laser phase recovery described herein.

[0181] In some embodiments, the Rx 1200 of FIG. 12A may include a received signal 1202; a LO signal 1204; a 90-degree optical filter 1206 (e.g., a 90-degree hybrid optical filter); a photodetector 1208; a photodetector 1210; a photodetector 1212; a photodetector 1214; an AFE 1216 (e.g., an analog front end, a high-speed analog front end); an AFE 1218; a comparator 1220; a comparator 1222; an I 1224; a Q 1226; a CPR circuitry 1228; a phase shifter 1230; and a phase shifter 1230.

[0182] In some embodiments, the CPR circuitry 1228 of the Rx 1200 of FIG. 12A may include a low-pass filter 1234; a low-pass filter 1236; an adder 1238; a subtractor 1240; anSGN(x) 1242; a mixer 1244; a loop filter 1246 (e.g., a first loop filter); a loop filter 1248 (e.g., a second loop filter); a gain component 1250 (e.g., a first gain component) coupled to the loop filter 1246; a gain component 1252 (e.g., a second gain component) coupled to the loop filter 1248; an error signal 1254; and an error signal 1256. Both of the CPR circuitry 1228 of FIG. 12A and CPR circuitry 1128 of FIG. 11A are configured to help their respective receiver implement the first method (or “method 1”) of laser phase recovery. However, the CPR circuitry 1228 of FIG. 12A may generate two error signals, while the CPR circuitry 1128 of FIG. 11A may generate one error signal, as is illustrated and / or described herein.

[0183] In some embodiments, the Rx 1258 of FIG. 12B may include a received signal 1260; a LO signal 1262; a 90-degree optical filter 1264 (e.g., a 90-degree hybrid optical filter); a photodiode 1266; a photodiode 1268; a photodiode 1270; a photodiode 1272; an AFE 1274; an AFE 1276; a comparator 1278; a comparator 1280; an I 1282; a Q 1284; a CPR circuitry 1286; a phase shifter 1288; and a phase shifter 1290.

[0184] In some embodiments, the CPR circuitry 1286 of the Rx 1258 of FIG. 12B may include a low-pass filter 1292; a low-pass filter 1294; an SGN(x) 1296; an SGN(x) 1298; a mixer 12-100; a mixer 12-102; a subtractor 12-104; a loop filter 12-106 (e.g., a first loop filter); a gain component 12-108 coupled to the loop filter 12-106; a loop filter 12-110; a gain component 12-112 coupled to the loop filter 12-110; an error signal 12-114; and an error signal 12-116.

[0185] In some embodiments, the phase shifter 1232 of FIG. 12A and / or the phase shifter 1290 of FIG. 12B may be an electro-optical phase shifter, a PN-junction phase shifter, or another type of phase shifter. Electro-optical phase shifters, for example, offer several advantages, such as faster switching speeds due to the inherent quick response time of the electro-optical effect, which is beneficial in high-speed communication systems; linearity, which may benefit applications requiring precise phase control without distortion; lower power consumption than, for example, PN junction phase shifters; lower optical losses; and / or wider bandwidth operation compared to some other types of phase shifters.

[0186] In some embodiments, the phase shifter 1230 of FIG. 12A and / or the phase shifter 1288 of FIG. 12B may be a thermal phase shifter.

[0187] In some embodiments, the phase shifter 1232 of FIG. 12A and / or the phase shifter 1290 of FIG. 12B (e.g., electro-optical phase shifters) may perform a coarse phase tuning; and the phase shifter 1230 of FIG. 12A and the phase shifter 1288 FIG. 12B (e.g., thermal phase shifters) may perform a finer tuning, compared to the coarse phase tuning. Note that an electro-optical phase shifter generally has a wider bandwidth operation compared to athermal phase shifter, among other operational differences between these types of phase shifters. By using these two (2) phase shifters, each of the Rx 1200 of FIG. 12A and / or the Rx 1258 of FIG. 12B can achieve a faster integration feedback path and / or a faster phase locking compared to using only one (1) phase shifter, such as the case(s) of the Rx 1100 FIG. 11A and / or the Rx 1150 of FIG. 11B.

[0188] In some embodiments, this course tuning followed by the finer tuning helps Rx 1200 of FIG. 12A and / or the Rx 1258 of FIG. 12B may aid the Rx to provide fast and integration feedback path for fast locking of the LO signal.

[0189] In some embodiments, a laser output (e.g., an output of the Tx laser 832 of FIG. 8B) of a transmitter (not illustrated in FIG. 12A and FIG. 12B) may be divided into two paths. For example, a first path from the laser output of the transmitter may result and / or be received as the received signal 1202 to the Rx 1200 of FIG. 12A and / or the received signal 1260 of the Rx 1258 of FIG. 12B. As another example, a second path may generate the LO signal 1204 of Rx 1200 of FIG. 12A and / or the LO signal 1262 of the Rx 1258 of FIG. 12B. The transmitter (not illustrate in FIG. 12A and / or FIG. 12B) generates an QAM signal using I and Q data from, for example, pseudo-random binary' sequence (PRBS) generators.

[0190] FIG. 13 shows a first method (may be described and / or illustrated as “method 1”) and a second method (may be described and / or illustrated as “method 2”) for generating an error signal, in accordance with examples described herein. Specifically, FIG. 13 shows plots of error signal 1300 (verr, which may be expressed in Volts (V)) versus a phase shift 1302 (e.g., in radians (rad)). In FIG. 13, a first plot includes a first method 1304 for generating the error signal 1300 as a function of the phase shift 1302; a second plot includes a second method 1306 for generating the error signal 1300 as a function of the phase shift 1302; and a third plot includes a sinusoid graph 1308 as a function of the phase shift 1302, specifically, the plot of 2Ao-sin(A(|)).

[0191] FIG. 13 may be illustrated and / or described in the context of the FIG. HA, FIG. 11B, FIG. 12A, and / or FIG. 12B. For example, the plot of the first method 1304 of FIG. 13 may reference operations of the Rx 1100 of FIG. HA and / or the Rx 1200 of FIG. 12A, where the plot of the first method 1304 may represent the error signal 1144 of the Rx 1100, the error signal 1254 of the Rx 1200, and / or the error signal 1256 of the Rx 1200. As another example, the plot of the second method 1306 may reference operations of the Rx 1150 of FIG. 11B and / or the Rx 1258 of FIG. 12B, where the plot of the second method 1306 may represent the error signal 1196 of the Rx 1150, the error signal 12-116 of the Rx 1258, and / or the error signal 12-114 of the Rx 1258.

[0192] In some embodiments, for example, to generate an error signal 1300 same as, or similar to, the first method 1304 of FIG. 13, the outputs of low-pass filters in the I and Q paths may be subtracted, generating an error signal 1300 approximately or equal to 2Ao-sin(At|)), as is depicted in FIG. 13. However, if the error signal is in the region where the slope of the error signal has a positive sign, the loop of the receiver may have positive feedback and may become unstable. To maintain loop stability, the negative slope of the error signal may be used in some examples. For example, a summation of Lvg and Qavg (2A<rcos (A(|))) may be used as a select signal that may be selected between 2Ao-sin(A(|)) (e.g., positive 2Ao>sin(A(|))) and -2Ao>sin(A(|)) (e.g., negative 2Ao>sin(A(|))). Consequently, as is shown in FIG. 13, the error signal may be approximately or equal to 2Ao-sin (A4>) for n-ji / 2 < A<|) < (n + 2)'7i / 2, where “n” denotes an integer.

[0193] In some embodiments, the CPR circuitry 1128 of FIG. 11 A that may include the low- pass filter 1132, low-pass filter 1134, adder 1136, subtractor 1138, SGN(x) 1140, and / or mixer 1142 of the Rx 1100 of FIG. 11 A may generate the error signal 1144 (e.g., one error signal) of the Rx 1100 of FIG. 11A that may be represented in the first method 1304 of FIG. 13. As is shown in FIG. 13, the error signal generated by the CPR circuitry 1128 and / or the Rx 1100 of FIG. 11A includes only a negative slope that is similar to the negative slope of the sinusoid graph 1308.

[0194] Similarly, the CPR circuitry 1228 of FIG. 12A that may include the low-pass filter 1234, low-pass filter 1236, adder 1238, subtractor 1240, SGN(x) 1242, and / or mixer 1244 may generate the error signal 1254 and / or the error signal 1256 (e.g., two error signals) of the Rx 1200 of FIG. 12A that is represented in the first method 1304 of FIG. 13. As is shown in FIG. 13, the error signal generated by the CPR circuitry 1228 and / or the Rx 1200 of FIG. 12A includes only a negative slope that is similar to the negative slope of the sinusoid graph 1308.

[0195] As is illustrated in FIG. 13, the Rx 1100 of FIG. 11 A and / or the Rx 1200 of FIG. 12A maintain a single polarity (e.g., instead of two polarities) of the error signal(s) in the closed- loop system(s) of the receiver (e.g., Rx 1100 of FIG. 11A, Rx 1200 of FIG. 12A). By so doing, the receiver avoids positive feedback and / or becoming unstable. Instead, the receivers Rx 1100 of FIG. HA and / or Rx 1200 of FIG. 12A maintain stability (e.g., loop stability).

[0196] In some embodiments, for example, to generate an error signal 1300 same as, or similar to, the second method 1306 (or may be referred to as "method 2”) of FIG. 13, the Lvg and Qavg can be sent to limiting amplifiers, for example, using SGN(s)) and mixers, as is shown in Rx 1150 of FIG. 11B and / or Rx 1258 of FIG. 12B. The outputs of the mixers can then be subtracted, generating an error signal (e.g., error signal 12-116 of FIG. 12B, errorsignal 12-114 of FIG. 12B, and / or error signal 1196 of FIG. 11B) approximately, or equal to, V2Ao / 2-sin (A<|>) for n-n / 4 < A(|> < (n + 2)-n / 4, where “n” denotes an integer. As is shown in FIG. 13, the second method 1306, the CPR circuitry 1178 of Rx 1150 of FIG. 11 B, the CPR circuitry 1286 of Rx 1258 of FIG. 12B may generate and / or produce a ‘sawtooth-shaped’ error signal that may provide a constant gain over the range (e.g., the entire range), where the slope of the amplitude of the error signal may be constant or near constant. This error signal, however, may have a periodicity of JI / 2, with zero values at n-ji / 2 and n-7i, causing a 90-degree phase ambiguity between the I and Q signals at the receiver.

[0197] In some embodiments, differential coding during transmission and / or differential decoding after demodulation may overcome the 90-degree phase ambiguity between the I and Q signals, when using the second method 1306 (or “method 2”), the CPR circuitry 1178 of Rx 1150 of FIG. 1 IB, and / or the CPR circuitry 1286 of Rx 1258 of FIG. 12B. For the sake of clarity, the first method 1304 (or “method 1”) does not cause a 90-degree phase ambiguity between the I and Q signals at the receiver.

[0198] Continuing with the second method 1306 of FIG. 13, in some embodiments, differential coding during transmission may transmit information based on the difference between successive symbols, rather than on the absolute phase values. This approach ensures that phase shifts such as ±90 degrees, which do not alter the relative differences between successive symbols, may not affect the interpretability of the received signal at the receiver (e.g., the Rx 1150 of FIG. 11B, the Rx 1258 of FIG. 11B). For example, in some embodiments, differential coding during transmission may add redundancy to the transmitted data, ensuring that even with phase shifts, the receiver can still correctly interpret the transmitted information. Unfortunately, this redundancy may take up part of the bandwidth that could otherwise be used for transmitting additional data, as some bandwidth is now dedicated to preserving the information reliability amidst phase ambiguity, when using the second method 1306 of FIG. 13.

[0199] FIG. 14A shows simulation results of a QAM constellation, in accordance with examples described herein. FIG. 14B shows simulation results of an offset-QAM constellation, in accordance with examples described herein. FIG. 14A and FIG. 14B show the effect of a phase offset between a transmitter (Tx) and a local oscillator (LO) signal in the QAM and the offset-QAM, respectively.

[0200] In some embodiments, optical coherent communication may rely on precise frequency and phase locking and / or tracking of a transmitted signal(s) (e.g., from a transmitter) and a local oscillator (LO) signal (e.g., laser). In some examples, this phaseoffset may cause I / Q crosstalk and / or lower detection signal power at a receiver, significantly degrading the bit error rate (BER) and / or the symbol error rate (SER). The effect of phase difference in QAM and offset-QAM, and alternatively, the compensation forthat, is different.

[0201] Simulation data (e.g., using MATLAB SIMULINK) show example simulation results in FIG. 14A and FIG. 14B. Note the different scales of the Q and I axis of FIG. 14A and FIG. 14B. Each of these constellations are shown with (e.g., JC / 3) and without (e.g., 0) the phase offset between the receiver (Rx) and the LO signals. As can be seen, in offset-QAM (e.g., FIG. 14B), not only does the constellation rotate, but also the center of the constellation moves. This movement makes the phase error detection and compensation used for QAM generally disadvantageous for offset-QAM.

[0202] FIG. 15 A shows simulation results 1500 of an error signal 1502 over time 1504, in accordance with examples described herein. FIG. 15B shows simulation results 1506 of aLO phase 1508 over time 1510, in accordance with examples described herein.

[0203] To evaluate the performance of the systems, methods, and / or techniques described herein, the simulation results 1500 and the simulation results 1506 modeled the laser- forwarded technique, for example, described in the context of FIG. 8B, FIG. 11 A, FIG. 11B, FIG. 12 A, FIG. 12B, etc. These simulation results were generated using MATLAB SIMULINK, and the simulation was run for Acp = JC / 3. It is to be understood that other simulation tools and / or simulation times may be used to achieve similar results.

[0204] FIG. 15A and FIG. 15B show the error signal 1502 and the LO phase 1508 (e.g., after a phase shifter of the Rx) when the loop of the receiver is locked, confirming and / or showing the functionality, efficiency, and / or effectiveness of the laser-forwarded technique. As is shown in FIG. 15 A, the error signal 1502 goes to zero, confirming that the average power and / or voltage of the I and Q paths became the same or equal during the run simulation time. As is shown in FIG. 15B, the phase error between the Rx and LO phase 1508 becomes zero during the run simulation time. Therefore, simulation results show that the loop of the receiver does not have positive feedback and is not unstable. On the contrary, the error signal 1502 reaches and / or approaches zero (e.g., 0 V) and maintains that value in a relatively short time; and the LO phase 1508 reaches and / or approaches n / 3 radians (rad) and maintains that value.

[0205] FIG. 16 shows a list of equations and / or mathematical expressions, in accordance with examples described herein.

[0206] FIG. 17A shows an example operation 1702 of a PCAM (e.g., PCAM 402 of FIG. 4) performing a non-offset-QAM, where the example operation 1702 is shown in reference tograph 1704 and graph 1706, in accordance with examples described herein. The graph 1704 and the graph 1706 show the normalized output power 1710 and the output phase 1712, respectively, versus the wavelength 1708. Note that FIG. 17 A illustrates an output power versus wavelength relationship for Top MRM State 1. The relationship for output power versus wavelength for Bottom MRM State 1 is also shown. In an analogous manner, in the graph of phase versus wavelength, the relationship for Top MRM State 1 is shown, while the relationship for Bottom MRM State 1 is also shown. Note that, in FIG. 17A, the lines for Top MRM State 1 also represent bottom MRM State 0. Similarly, the lines for Bottom MRM state 1 also represent top MRM state 0 in FIG. 17A.

[0207] FIG. 17B shows an example operation 1714 of the PCAM (e.g., PCAM 402 of FIG. 4) performing an offset-QAM (e.g., a first offset-QAM), where the example operation 1714 is shown in reference to graph 1716 and graph 1718, in accordance with examples described herein. The graph 1716 and the graph 1718 show the normalized output power 1716 and the output phase 1718, respectively, versus the wavelength 1720.

[0208] FIG. 17C shows an example operation 1726 of the PCAM (e.g., PCAM 402 of FIG. 4) generating another offset-QAM (e.g., a second offset-QAM), where the example operation 1726 is shown in reference to graph 1728 and 1730, in accordance with examples described herein. The graph 1730 and the graph 1728 show the normalized output power 1736 and output phase 1734, respectively, versus the wavelength 1732.

[0209] In the examples shown in FIG. 17A, FIG. 17B, and FIG. 17C, the laser (e.g., optical input 404 of FIG. 4) may have a wavelength of approximately 1310 nm, and the PCAM (e.g., PCAM 402 of FIG. 4) may use this laser wavelength to perform the example operation 1702 of FIG. 17A, the example operation 1714 of FIG. 17B, and / or the example operation 1726 of FIG. 17C. It is to be understood that other laser wavelengths may be used in other examples.

[0210] In some embodiments, the PCAM may include and / or utilize two amplitude-phase modulators (e.g., two MRMs, a top MRM, a bottom MRM) to perform a non-offset-QAM (e.g., in a manner where the offset is zero (0)), as is shown in FIG. 17A; perform an offset- QAM (e.g., a first offset-QAM, a first level offset-QAM), as is shown in FIG. 17B; and / or perform another offset-QAM (e.g., a second offset-QAM, a second level offset-QAM), as is shown in FIG. 17C. Therefore, in some embodiments, the PC AMs described herein may be selectively configured to perform offset-QAMs of various offset levels, including, for example, an offset of zero (0) or a non-offset-QAM.

[0211] FIGs. 17A, 17B, and / or 17C may illustrate operation of the transmitters described herein, or portions thereof, such as those shown and described with reference to FIGs. 4, 5,6, and / or 7, for example. For the sake brevity, the various “1” and / or “0” states of the top and / or bottom MRMs of the PC AM may operate similarly as is described in relation to FIG. 5.

[0212] From the foregoing it will be appreciated that, although specific embodiments have been described herein for purposes of illustration, various modifications may be made while remaining within the scope of the claimed technology. Examples described herein may refer to various components as “coupled” or signals as being “provided to” or “received from” certain components or nodes. It is to be understood that in some examples, the components are directly coupled one to another, while in other examples, the components are coupled with intervening components disposed between them.

[0213] Similarly, signals or communications may be provided directly to and / or received directly from the recited components without intervening components, but also may be provided to and / or received from the certain components through intervening components.

Claims

CLAIMSWhat is claimed is:

1. A method for laser carrier recovery in optical coherent communication systems utilizing quadrature amplitude modulation (QAM) at a receiver, the method comprising: receiving, at the receiver, a transmitted signal; receiving, at the receiver, a local oscillator (LO) signal; detecting, at the receiver, a phase offset between the transmitted signal and the LO signal; and compensating, at the receiver, for the phase offset between the transmitted signal and the LO signal based on the detected phase offset, wherein the compensation accounts for a movement of a constellation center and a rotation of the constellation due to the phase offset, wherein the compensation comprises: detecting an average power and / or voltage difference between In-phase (I) and Quadrature-phase (Q) paths of the received signal at the receiver; and generating an error signal based on the average power and / or voltage difference between the In-phase (I) and Quadrature-phase (Q) paths of the received signal at the receiver, wherein the error signal compensates for the phase offset between the transmitted signal and the LO signal.

2. The method of claim 1 further comprising: forwarding a transmit laser signal from a transmitter to the receiver; and tuning a phase using at least one phase shifter.

3. The method of claim 2, wherein the at least one phase shifter comprises a first phase shifter and a second phase shifter, and wherein the method further comprises: performing a coarse phase tuning using the first phase shifter, the first phase shifter having a wider bandwidth operation than the second phase shifter; and performing a finer phase tuning, compared to the coarse phase tuning, using the second phase shifter.

4. The method of claim 3, wherein the first phase shifter comprises an electro-optical phase shifter.

5. The method of claim 3, wherein the second phase shifter comprises athermal phase shifter.

6. The method of claim 3 further comprises maintaining a single polarity of the error signal, wherein the single polarity aids the receiver maintain stability of the error signal.

7. The method of claim 1 further comprises locking, at the receiver, a receiver laser to a phase of the transmitted signal.

8. The method of claim 7 further comprises: differentially coding the transmitted signal; responsive to the coding, adding redundancy to the transmitted signal; and determining, at the receiver, phase polarities of In-phase (I) and Quadrature-phase (Q) signals.

9. The method of claim 1, wherein the compensation further comprises: filtering the received signal using a low-pass filter to retain only an average voltage of the signal; and subtracting the output of the low-pass filter in the In-phase (I) and Quadrature-phase (Q) paths to generate the error signal.

10. The method of claim 9, wherein the error signal is equal to a constant direct current (de) offset of In-phase (I) and Quadrature-phase (Q) signals multiplied by a sine or sinusoid of the phase offset.

11. The method of claim 1, wherein the compensation further comprises: processing the received signal through a Costas loop technique; and utilizing the Costas loop technique to generate an error signal based on the average signals in the In-phase (I) and Quadrature-phase (Q) paths after processing through a Sign (SGN) block and a mixer.

12. An apparatus comprising: a beam splitter (408) configured to receive optical energy (404) having a wavelength, the beam splitter (408) configured to provide a first split beam (414) and a second split beam (416); a first resonant modulator (410) having a first input (418), the first resonant modulator (410) configured to modulate an amplitude and a phase of the first split beam (414), based on the first input (418), to provide a first modulated beam (426);a second resonant modulator (412) having a second input (422), the second resonant modulator (412) configured to modulate an amplitude and a phase of the second split beam (416), based on the second input (422), to provide a second modulated beam; a phase shifter (430) positioned to receive the second modulated beam and provide a phase-shifted modulated beam (428); and a combiner (432) configured to combine the phase-shifted modulated beam (428) and the first modulated beam (426) to provide an output signal (406); wherein resonant frequencies of the first (410) and second (412) resonant modulators are such that, responsive to particular first (420) and second (424) tuning signals applied at the first (410) and second (412) resonant modulators, the output signal (406) is configured to be a phase-constant amplitude-modulated signal.

13. The apparatus of claim 12, wherein changes in the first and second modulation signals are configured to provide equal changes to the amplitude modulation provided by the first and second resonant modulators.

14. The apparatus of claim 12, wherein changes in first and second input signals applied to the first and second resonant modulators are configured to provide equal and opposite changes to the phase modulation provided by the first and second resonant modulators, respectively.

15. A method comprising: applying tuning signals to phase-amplitude modulators of an interferometer such that the interferometer is configured to provide phase-constant amplitude modulation; and applying data signals to the phase-amplitude modulators to provide phase-constant amplitude-modulated output signals based on the data signals.

16. The method of claim 15, wherein the phase-amplitude modulators are resonant modulators, and wherein the tuning signals are selected to provide the phase-constant amplitude modulation of the interferometer.

17. The method of claim 16, wherein the tuning signals vary resonances of the phaseamplitude modulators.

18. A transceiver (802) comprising: a transmitter (828) comprising: a first (110) and a second (112) phase-constant amplitude modulator (PCAM); and a laser (832) configured to:provide optical energy to the first (110) and the second (112) PCAMs; and provide a local oscillator (LO) signal (850, 1104, 1154, 1204, 1262); and wherein the transmitter (828) is configured to transmit a signal (838, 1102, 1152, 1202, 1260) modulated with quadrature amplitude modulation (QAM); and a receiver (830, 1100, 1150, 1200, 1258) comprising: an optical filter (1106, 1156, 1206, 1264) configured to receive the modulated signal (838, 1102, 1152, 1202, 1260); at least one phase shifter (848, 1130, 1180, 1230, 1232, 1290, 1288) configured to receive the LO signal; and carrier phase recovery (CPR) circuitry (1128, 1178, 1228, 1286) configured to: detect an average power and / or voltage difference between In-phase (I) (842, 1124, 1174, 1224, 1282) and Quadrature-phase (Q) (846, 1126, 1176, 1226, 1284) paths of the modulated signal; and generate an error signal (846, 1144, 1196, 1254, 1256, 12-114, 12-116) based on the average power and / or voltage difference between the In-phase (I) and Quadrature-phase (Q) paths of the modulated signal, wherein the error signal compensates for a phase offset between the LO signal and the modulated signal.

19. The transceiver of claim 18 comprises a laser-forwarded coherent optical link, wherein a frequency of the laser is configured to provide a same frequency to the transmitter and the receiver.

20. The transceiver of claim 18, wherein the at least one phase shifter comprises a first phase shifter and a second phase shifter, and wherein: the first phase shifter is configured to perform a coarse phase tuning, the first phase shifter having a wider bandwidth operation than the second phase shifter; and the second phase shifter is configured to perform a finer phase tuning compared to the coarse phase tuning.

21. The transceiver of claim 18, wherein the modulated signal beats with the LO signal in the optical filter to demodulate the In-phase (I) and Quadrature-phase (Q) paths of the modulated signal.

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