Chirp-compensating transmitter and method

A method for laser chirp precompensation includes modulating an amplitude of an optical signal, in response to an amplitude of one of (i) a chirp-compensated signal generated via distortion of an original modulated signal according to an inverse of a chirp-response function of a laser and (ii) a first signal derived from the chirp-compensated signal, to yield an amplitude-modulated optical signal. The method also includes modulating a phase of the amplitude-modulated optical signal in response to a phase of one of (i) the chirp-compensated signal and (ii) a second signal derived from the chirp-compensated signal to yield a chirp-compensated optical signal.

BACKGROUND

Communication network traffic continues to grow, such as due to emergence of new services with high bandwidth demand, including data center interconnection services, fifth generation (5G) wireless broadband services, and virtual reality services. Optical communication networks, which use fiber-optic cable to transmit data between network nodes, are increasingly being used for data transmission, due to their inherent capability to support high bandwidth and to transport data over long distances.

In an optical communication network, data is modulated onto an optical carrier generated by a laser to yield a modulated optical signal. One modulation scheme is direct modulation, in which the current driving the laser is modulated according to the content of the transmitted data. Direct modulation changes the refractive index of the material forming the laser's cavity, which results in a distortion of the modulated optical signal known is laser chirp.

SUMMARY OF THE EMBODIMENTS

In a first aspect, a method for laser chirp precompensation is disclosed. The method includes modulating an amplitude of an optical signal, in response to an amplitude of one of (i) a chirp-compensated signal generated via distortion of an original modulated signal according to an inverse of a chirp-response function of a laser and (ii) a first signal derived from the chirp-compensated signal, to yield an amplitude-modulated optical signal. The method also includes modulating a phase of the amplitude-modulated optical signal in response to a phase of one of (i) the chirp-compensated signal and (ii) a second signal derived from the chirp-compensated signal to yield a chirp-compensated optical signal.

In a second aspect, a method of determining a chirp-response function of a laser is disclosed. The method includes the following steps (a)-(e). Step (a) includes modulating the laser with a real-valued double-side-band orthogonal frequency-domain multiplexed (OFDM) signal to yield a characterization optical signal that includes a plurality of subcarriers each including a respective transmitted amplitude and a respective transmitted phase. Step (b) includes transmitting the characterization optical signal to a coherent receiver via a fiber-optic cable. Step (c) includes receiving, at the coherent receiver, the characterization optical signal as a chirped-modulated optical signal. Step (d) includes demodulating the chirped-modulated optical signal to obtain, for each subcarrier of the plurality of subcarriers, a respective received amplitude and a respective received phase. Step (e) includes for each subcarrier of the plurality of subcarriers, (i) determining a respective chirp-response amplitude of a plurality chirp-response amplitudes of the chirp-response function as a ratio of the respective received amplitude to the respective transmitted amplitude, and (ii) determining a respective chirp-response phase of a plurality chirp-response phases of the chirp-response function as a difference between the respective received phase to the respective transmitted phase.

In a third aspect, chirp-compensating transmitter includes a signal generator, a laser, and a phase modulator. The signal generator is configured to distort an original modulated signal according to an inverse of a chirp-response function of a laser, to yield a chirp-compensated signal. The laser is configured to modulate an amplitude of an optical signal in response to an amplitude of one of (i) the chirp-compensated signal and (ii) a first signal derived therefrom, to yield an amplitude-modulated optical signal. The phase modulator is disposed downstream of the laser with respect to the optical signal, and is configured to modulate a phase of the amplitude-modulated optical signal in response to a phase of one of (i) the chirp-compensated signal and (ii) a second signal derived therefrom.

DETAILED DESCRIPTION OF THE EMBODIMENTS

One promising communication network architecture for meeting growing data transmission needs is an optical communication network including single-polarized direct-detected (DD) high speed transceivers and implementing wavelength division multiplexing. This communication network architecture is relatively simple and economical compared to other optical communication network architectures, which makes it a strong candidate for many communication network applications.

However, conventional long-distance communication networks including DD high speed transceivers suffer from chromatic dispersion (CD) induced power fading, which significantly limits bandwidth and maximum fiber-optic cable distance. Chromatic dispersion is a phenomenon where different wavelengths of light traveling through a fiber-optic cable arrive at a common destination at different times. To help understand the effects of chromatic dispersion on an optical communication network, considerFIGS.1-5, which are based on a simulated optical communication network using DD transceivers and implementing four levels of pulse-amplitude-modulation (PAM4).FIG.1is a graph100of power versus time of a transmitting laser of the simulated optical communication network, illustrating that the laser has four possible power output levels, P1, P2, P3, and P4. Each output power level is offset from an adjacent power level by a difference in power of ΔP.FIG.2is a graph200of power versus frequency of a signal of the simulated optical communication network, after transmission of the signal via a fiber-optic cable and detection of the signal by a receiver. As evident fromFIG.2, the received signal does not have a flat response but instead has notches at several frequencies. The notches are caused by chromatic dispersion of the signal when traveling through the fiber-optic cable.

The received signal in the simulated communication network has a complex value which can be represented by a graph300ofFIG.3, which illustrates possible distributions of the received signal in an in-phase (I) plane and a quadrature (Q) plane. The received signal can be located at any position on any one of four rings302, depending on its amplitude and phase. Only one instance of ring302is labeled inFIG.3for illustrative clarity. It should be noted that while adjacent power outputs of the laser are offset by a uniform difference in power of ΔP, as illustrated inFIG.1, adjacent amplitude levels are offset by non-uniform differences in amplitude, as illustrated inFIG.3by separation of adjacent rings302in a radial direction304being non-uniform. This non-uniformity of radial separation of rings302results from the relationship between signal power and amplitude, where signal amplitude is the square root of signal power.

FIG.4is a graph400of optical field amplitude, andFIG.5is a graph500of optical field phase in arbitrary units (a. u.), of a signal in the simulated optical communication network after transmission through the network. A curve402ofFIG.4illustrates that the amplitude is flat, i.e., that the amplitude of the transmitted signal does not materially vary with frequency. A curve502ofFIG.5, in contrast, illustrates that phase of the transmitted signal varies significantly with frequency, due to chromatic dispersion in the fiber-optic cable. Accordingly, chromatic dispersion causes the fiber-optic cable to behave like an all-pass filter, which does not directly affect signal amplitude but significantly affects signal phase, as illustrated inFIGS.4and5. While the distortion in phase caused by chromatic distortion does not directly affect signal amplitude, the distortion in phase affects signal power, as illustrated inFIG.2.

Effects of chromatic dispersion on a transmitted signal may make it difficult, or even essentially impossible, to recover information, such as a payload, from the signal. Single-side band (SSB) modulation may be used to mitigate effects of chromatic dispersion, and use of SSB modulation may therefore extend maximum transmission distance of an optical communication network. Nevertheless, single-side band modulation does not eliminate power fading caused by chromatic dispersion, and single-side band modulation leads to signal-to-signal beating interference, which degrades signal quality. Additionally, single-side band modulation reduces receiving sensitivity from loss of power associated with eliminating one side band. Chromatic dispersion can also be mitigated by pre-compensation at a transmitter-side IQ-modulator, but this pre-compensation scheme induces high insertion loss and requires complex and costly bias control.

Disclosed herein systems and methods for chromatic dispersion pre-compensation (CDPC) which at least partially overcome drawbacks of conventional techniques for mitigating chromatic dispersion. Certain embodiments include a phase modulator (PM) cascaded with a laser that is a directly-modulated laser (DML), such as a directly-modulated coherent-optical-injection locked (COIL) laser or OFFT, to realize full-field light modulation. The new systems and methods achieve chromatic pre-compensation by a combination of intensity and phase modulations, thereby potentially significantly extending maximum communication system transmission distance, while achieving significant advantages. For example, use of a phase modulator to achieve phase modulation, instead of an IQ-modulator, relaxes bias control requirements and reduces insertion losses. Additionally, a low-cost, intensity-modulated distributed feedback (DFB) laser can be used as a light source in the new systems. Accordingly, the new systems and methods may be more economical and more efficient than conventional systems and methods. Additionally, the new systems and methods are compatible with optical injection locking subsystems. Moreover, the new systems and methods may extend usable transmission light wavelengths when used in passive optical network (PON) applications. Specifically, a PON is typically configured such that uplink transmission light wavelength is limited to the O band (1260 nm-1360 nm), to avoid chromatic dispersion penalties. Use of the new systems and methods in a PON, however, may sufficiently mitigate chromatic dispersion such that additional bands, such as the C band, can be used, thereby significantly expanding PON capacity and/or flexibility.

FIG.6is a block diagram of an optical communication network600including a dispersion-compensating transmitter602configured to implement chromatic dispersion pre-compensation, as well as a fiber-optic cable604, a receiver606, a post-processor608, and an optional non-linear equalizer609. Fiber-optic cable604communicatively couples dispersion-compensating transmitter602and receiver606, and post-processor608is communicatively coupled to an output of receiver606. Optical non-linear equalizer609, when present, is communicatively coupled to an output of post-processor608. Fiber-optic cable604may be replaced with a free-space optical transmission system without departing from the scope hereof.

Dispersion-compensating transmitter602includes a preprocessor612, a signal generator610, a laser616, a phase modulator618, and, in embodiments, a tunable delay line620. Although the elements of dispersion-compensating transmitter602are illustrated as being separate elements, two or more of these elements could be at least partially combined without departing from the scope hereof. For example, in some embodiments, preprocessor612and signal generator610are embodied by a common processor executing instructions in the form of software and/or firmware. Additionally, all elements of dispersion-compensating transmitter602need not be disposed in the same location. For example, preprocessor612and signal generator610could be remote from laser616and phase modulator618. Signal generator610may be a digital signal generator.

Preprocessor612is configured to modulate a carrier signal622by an input signal624to be transmitted by optical communication network600to generate an original modulated signal s(t). For example, some embodiments of preprocessor612are configured to modulate solely amplitude of carrier signal622, such as by using a non-return-to-zero (NRZ) modulation format or a PAM4 modulation format. As another example, some embodiments of preprocessor612are configured to modulate both amplitude and phase of carrier signal622, such as by using a quadrature phase shift keying (QPSK) modulation format or a 16-order quadrature amplitude modulation (16-QAM) modulation format. Signal generator610is configured to distort original modulated signal s(t) according to an inverse of a transmission function Hof optical communication network600, to generate a compensated signal p(t), which has an amplitude Q(t) and a phase θ(t). Transmission function H includes effects of chromatic dispersion by fiber-optic cable604. Therefore, distorting original modulated signal s(t) according to an inverse of transmission function H advantageously at least substantially compensates for the chromatic dispersion, such that a signal received by receiver606will be at least substantially free of chromatic dispersion artifacts. Such intentional distortion of original modulated signal s(t) to compensate for chromatic dispersion in fiber-optic cable604may be referred to a “pre-compensation,” since signals are compensated for chromatic dispersion before being transmitted through fiber-optic cable604. In some embodiments, transmission function H may be determined from length and material of fiber-optic cable604, such that transmission function His static. In some other embodiments, transmission function His determined in real time, or on a periodic basis, such that transmission function His dynamic. Several possible embodiments of signal generator610are discussed below with respect toFIGS.7-9.

Signal generator610provides amplitude Q(t) of compensated signal p(t) to laser616, and signal generator610provides phase θ(t) of compensated signal p(t) to phase modulator618. Laser616is configured to generate an optical signal626and modulate amplitude of optical signal626in response to amplitude Q(t) of compensated signal p(t), such that laser616is controlled by amplitude Q(t). Accordingly, optical signal626, as outputted by laser616, includes amplitude information, but the optical signal does not include phase information. In some embodiments, laser616a directly-modulated laser (DML), such as a directly modulated coherent-optical injection-locked (COIL) laser or OFFT.

Phase modulator618is located downstream of laser616with respect to optical signal626, and phase modulator618is configured to modulate a phase of optical signal626in response to a phase θ(t) of compensated signal p(t), to generate an optical signal628for transmission by fiber-optic cable604to receiver606. Optical signal628includes both amplitude and phase information. It may be necessary for respective clocks of laser616and phase modulator618to be synchronized, or in other words, for the two clocks to match. Accordingly, some embodiments of dispersion-compensating transmitter602include tunable delay line620configured to synchronize the clock of phase modulator618with the clock of laser616, by adding a delay to phase θ(t) of compensated signal p(t), before phase modulator618modulates phase of optical signal626according to phase θ(t).

Fiber-optic cable604is configured to transmit optical signal628from phase modulator618to receiver606, and receiver606is configured to convert optical signal628into an electrical signal630. Post-processor608is configured to recover input signal624from electrical signal630and thereby generate an output signal632, such as by performing a demodulation technique appropriate for modulation performed by preprocessor612. In the event that there is non-linear distortion on output signal632, such as caused by pre-compensation performed by dispersion-compensating transmitter602, optional non-linear equalizer609may be used to perform non-linear equalization of output signal632to generate a corrected output signal634.

Possible applications of optical communication network600including transmitting data over a short distance, a medium distance, or a long distance. For example, optical communication network600could be used to transmit data within a data center, within a building, or even within a single networking appliance. As another example, optical communication network600could be part of an access network, including but not limited to, a PON. As yet another example, optical communication network600could be part of a long-distance data transmission network.

FIG.7is a block diagram of a signal generator710, which is one possible embodiment of signal generator610ofFIG.6, although it is understood that signal generator610is not limited to theFIG.7embodiment. Signal generator710includes a processor702, a memory704, and a communication bus706communicatively coupling processor702and memory704. Memory704includes distortion instructions708in the form of software and/or firmware. Memory704also holds a copy of each of original modulated signal s(t), an inverse H−1of the network transmission function H, and compensated signal p(t). Processor702is configured to execute instructions708to generate compensated signal p(t) from original modulated signal s(t) and inverse H−1of the network transmission function H In some embodiments, instructions708are configured such that processor702generates compensated signal p(t) according to a method illustrated inFIG.8or a method illustrated inFIGS.9A-9F(discussed below). Processor702may be configured to perform additional functions without departing from the scope hereof. For example, in some embodiments, memory704includes additional instructions (not shown) for processor702to generate original modulated signal s(t), such that signal generator710embodies preprocessor612as well as signal generator610.

FIG.8is a block diagram800illustrating a method performed by some embodiments of signal generator610to generate compensated signal p(t). In the method illustrated inFIG.8, signal generator610determines a time domain filter function c(t) by converting the inverse H−1of the network transmission function H from the frequency domain to the time domain, such as by using an inverse fast Fourier transform (IFFT). Signal generator610then convolves, using a convolution operation802, original modulated signal s(t) with time domain filter function c(t) to generate compensated signal p(t). The method illustrated inFIG.8may be practical to implement in applications where a required number of taps in time domain filter function c(t) is less than 20, which is common in applications where fiber-optic cable604is relatively short, such as less than or equal to 40 Kilometers (Km). However, theFIG.8method may not be practical to implement in applications requiring a larger number of taps, due to large memory requirements and high computation complexity associated with convolution operation802.

FIGS.9A-9Fare block diagrams collectively illustrating a method performed by some other embodiments of signal generator610to generate compensated signal p(t). The method begins with signal generator610dividing original modulated signal s(t) into N blocks sk(t), as illustrated inFIG.9A, where N is an integer greater than one and k is an index ranging from 1 to N. Signal generator610then adds leading zeros ZLand trailing zeros ZTto each block sk(t), as illustrated inFIG.9B. Signal generator610next converts each block sk(t) from a time domain to a frequency domain, such as by using a fast Fourier transform (FFT) technique, to generate frequency domain blocks Sk(ω), as illustrated inFIG.9C. Signal generator610subsequently multiplies each frequency domain block Sk(ω) by the inverse H1(ω) of the network transmission function H to obtain frequency domain filtered blocks Sk(ω)H−1(ω), as illustrated inFIG.9D. Each frequency domain filtered block Sk(ω)H−1(ω) is subsequently converted to the time domain by signal generator610to yield time domain filtered blocks pk(t), as illustrated inFIG.9E, such as by using an inverse fast Fourier transform technique.

Each time domain filtered blocks pk(t) includes a respective damping tail at the beginning and end of the block, caused by pulse expansion from the chromatic dispersion pre-compensation process. The leading and trailing zeros discussed above help mitigate effects of the damping tails, such that each damping tail is at least substantially encompassed by leading zeros or trailing zeros. Time domain filtered blocks pk(t) are labeled inFIG.9Eto show portions902associated with leading zeros and portions904associated with trailing zeros. In this document, specific instances of an item may be referred to by use of a numeral in parentheses (e.g. portion902(1)) while numerals without parentheses refer to any such item (e.g. portions902). Signal generator610subsequently partially overlaps and sums time domain filtered blocks pk(t) to obtain compensated signal p(t), as illustrated inFIG.9F. Signal generator610overlaps time domain filtered blocks pk(t) such that for each pair of immediately adjacent time domain filtered blocks pk(t), a portion904of a first block of the pair associated with trailing zeros overlaps a portion902of a second block of the pair associated with leading zeros. For example, in pair of immediately adjacent time domain filtered blocks p1(t) and p2(t), portion of904(1) of block p1(t) associated with trailing zeros overlaps portion902(2) of block p2(t) associated with leading zeros.

The method illustrated inFIGS.9A-9Fmay be more computationally efficient than the method illustrated inFIG.8, and the method ofFIGS.9A-9Fmay therefore be particularly suitable for embodiments of communication network600where length of fiber-optic cable604is relatively long, such as greater than 40 Km. However, the method ofFIGS.9A-9Fis more susceptible to data frame desynchronization than theFIG.8method, due to the block-wise signal processing techniques used in theFIGS.9A-9Fmethod.

FIG.10is a block diagram of a non-linear equalizer1000, which is one possible embodiment of non-linear equalizer609ofFIG.6. Non-linear equalizer1000has a Volterra non-linear equalizer architecture and includes a plurality of delay taps1002, a nonlinear combiner1004, a plurality of tap weight modules1006, and an addition module1008. Tap weight modules1006are optionally adjusted to minimize a mean-square error between transmitted symbols and received symbols after digital filtering. In some embodiments, the elements of non-linear equalizer1000are embodied by a processor (not shown) executing instructions in the form of software and/or firmware stored in a memory (not shown).

Example Simulation Results

Discussed below with respect toFIGS.11-13are simulation results of several embodiments of communication network600. It is appreciated, though, that communication network600need not necessarily perform as indicated in these simulation results. To the contrary, performance of communication network600will vary depending on the specific configuration and operating conditions of the communication network.

FIG.11is a graph1100of simulated signal power magnitude versus frequency of original modulated signal s(t), andFIG.12is a graph1200of simulated signal power magnitude versus frequency of output electrical signal630from receiver606. In these simulations, preprocessor612is configured to modulate carrier signal622at a rate of 40 Giga Baud (GBaud) per second, fiber-optic cable604is a five-kilometer long single-mode fiber fiber-optic cable, and (c) signal generator610is configured to implement the method illustrated inFIGS.9A-9F. It should be appreciated that the response ofFIG.12has a similar shape to that ofFIG.11, thereby showing that this embodiment of communication network600compensates for chromatic distortion. The performance of communication network600can be further appreciated by comparingFIG.12toFIG.2, where the response ofFIG.12does not include the notches from chromatic dispersion that are present in theFIG.2response.

FIG.13is a graph1300of simulated bit error rate (BER) versus optical signal to noise ratio (OSNR) of two communication networks. The first communication network, corresponding to the curve labeled “w/CDPC”, is an embodiment of communication network600where (a) preprocessor612is configured to modulate carrier signal622at a rate of 40 GBaud per second using PAM4 and (b) fiber-optic cable604is five-kilometer long single-mode fiber fiber-optic cable. The second communication network, corresponding to the curve labeled “w/o CDPC” is like the embodiment of communication network600described immediately above but with without CDPC capability.FIG.13also includes lines respectively representing BER thresholds of 2×10−2and 4.5×10−3. It can be determined fromFIG.13that a OSNR penalty is improved by 1 dB and 1.5 dB, respectively, by the CDPC capabilities of communication network600.

Further Examples

Discussed below with respect toFIG.14are additional examples of operation of communication network600. It is appreciated however, that communication network600is not limited to operating according to these examples.

FIG.14is a flow chart of a method1400for chromatic dispersion pre-compensation in an optical communication network. In a block1402of method1400, an original modulated signal is distorted according to an inverse of a transmission function of the optical communication network to generate a compensated signal. In one example block1402, signal generator610distorts original modulated signal s(t) according to an inverse of transmission function H to generated compensated signal p(t). In a block1404of method1400, a magnitude of an optical signal is modulated using an intensity modulator, in response to magnitude of the compensated signal. In one example of block1404, laser616modulates a magnitude of optical signal626in response to a magnitude Q(t) of compensated signal p(t). In a block1406of method1400, a phase of the optical signal is modulated using a phase modulator, in response to a phase of the compensated signal, after modulating magnitude of the optical signal. In one example of block1406, phase modulator618modulates phase of optical signal628in response to phase θ(t) of compensated signal p(t).

Laser Chirp Compensation

Continuously increased demands on broadband access networks, 5G mobile backhaul, and virtual-reality entertainment impose a stricter requirement on capacity for future optical access and transport networks. Meanwhile, the high cost of coherent optical transceivers remains to be a limitation. Embodiments thus far disclosed include integrating a cascaded directly modulated laser (DML) and phase modulator (PM) as an optical full-field transmitter (OFFT) to replace the traditional laser-plus-external-modulator platform in coherent optical transmitter site. Compared to the later scheme, an OFFT could significantly reduce the cost and insertion loss of the system, which makes it a promising solution for future low-cost high-speed coherent optical transmitter.

Embodiments disclosed above describe a technique to pre-compensate the fiber chromatic dispersion in an OFFT, which increases the transmission distance of the optical signal sent out by an OFFT. However, the impacts from laser chirp are not considered. Laser chirp degrades the transmitted signal quality from two aspects: firstly, the laser response is distorted, and modulation bandwidth is narrowed; and secondly the phase response of the chirp will interact with chromatic dispersion and further reduce the transmission distance, which adds to a fundamental limitation to DML for long-distance transmission. Embodiments disclosed herein include methods based on coherent orthogonal frequency division multiplexing (OFDM) for laser chirp estimation and pre-compensation. These methods improve the operation bandwidth and transmission distance of optical communication systems incorporating directly modulated lasers, e. g., an OFFT, a coherent-optical-injection locked (COIL) laser, and intensity modulation and direct detection (IM-DD).

Introduction of Coherent OFDM

Conceptual diagrams of OFDM and single-carrier (SC) modulation are shown inFIG.15, which include an optical spectrum1510of carrier signals of an OFDM-modulated signal, an optical spectrum1550of a single-carrier modulated signal.FIG.15also depicts constellation diagrams1512,1514, and1516of modulation schemes that are simultaneously compatible with the OFDM-modulated signal, and a constellation diagram1552of a modulation scheme compatible with the single-carrier modulated signal.

The signal generation of SC is simple and straightforward. The digital signal processing (DSP) including carrier frequency offset (CFO) estimation, phase noise compensation, and channel equalization can be accomplished based on blind algorithms. As such, meaning that, the signal can be recovered based on the statistical property of them without utilizing training or pilots. SC is also featured by lower peak-to-average-power ratio (PAPR), thus showing higher resistance against nonlinear distortions from the electrical amplifiers.

Yet, SC modulation has drawbacks. Firstly, it suffers seriously from skew and timing offset among multiple data streams in coherent optical systems. Secondly, the complexity of the DSP is high, especially for CFO and carrier phase noise estimation. If high-order modulation formats beyond 16-ary quadrature amplitude modulation (QAM) are used, the blind DSP complexity becomes nearly intolerable. By contrast, as a multi-carrier modulation format, OFDM is distinguished by its higher spectral efficiency and flexibility, e. g., to load different modulation formats and power levels at different subcarriers.

When combining with pilots or training symbols, the DSP for eliminating CFO and phase noise becomes simpler and more effective. However, one of the major drawback of OFDM lies in its high PAPR, which requires a high-power electrical driver with a large dynamic range, thus reducing its power efficiency. However, this reduced efficiency could be mitigated through some DSP techniques, such as frequency-spread OFDM. The multi-carrier feature empowers OFDM as a good candidate for measuring system frequency-domain response. When adopting an appropriate subcarrier spacing, the frequency transmission curve can be measured and plotted with higher accuracy. In embodiments, by tracking the intensity and phase of each subcarrier, OFDM plus optical coherent detection is used to measure the chirp response of a DML.

FIG.16is a schematic of a coherent OFDM system1600, which includes a transmitter site1608and a receiver1650. Transmitter1608includes a signal generator1610, a digital-to-analog converter (DAC)1614, and coherent transmitter1616. In embodiments, coherent transmitter1616is or includes at least one of an IQ modulator, a coherent-optical-injection-locked (COIL) transmitter, and an OFFT. Signal generator1610an example of signal generator610. DAC1614may be part of signal generator1610.

In an example mode of operation, at transmitter1608, the first step is symbol generation and, to simplify the complexity in this system, QPSK format is applied. Then the symbols are mapped onto subcarriers. After applying an inverse fast Fourier transform (IFFT) and adding a cyclic prefix, the samples in parallel are converted into a waveform in serial and sent to DAC1614. Electrical signals from DAC1614are modulated onto the light through coherent transmitter1616to yield a modulated optical signal1620.

Receiver site1650includes an optical local oscillator1652, coherent receiver1654, and a digital-to-analog converter1656. Modulated optical signal1620arrives at receiver1650as a modulated optical signal1630, which is modulated optical signal1620with the addition of distortion caused by chirp and, in embodiments, also by chromatic dispersion. At receiver1650, after modulated optical signal1630enters coherent receiver1654, modulated optical signal1620light beats with optical local oscillator1652first, which projects the optical signal into four dimensions with two orthogonal phases and two polarizations, from which coherent receiver generates four streams of electrical signals, which ADC 1656 samples. The samples are converted from serial to parallel data blocks. The cyclic prefix is removed for each data block and an FFT is applied. After that, DSP techniques are applied to estimate the CFO, compensate the carrier phase noise, and equalize the channel response before making the final decisions to each symbol. It is worth noting that, because of the adoption of cyclic prefix, if the clock timing offset among the four data streams are within the cyclic prefix protection window, the timing offset may be totally compensated within each data block. Thus, the clock recovery of OFDM is much simpler than traditional single-carrier modulation at an expense of slightly increased overhead.

One of the key DSP techniques in optical OFDM is to estimate the CFO and phase noise. In embodiments, pilot tone-based carrier recovery is used for CFO and phase-noise compensation.FIG.17includes optical signals1710,1720, and1730, and is a schematic illustration of pilot configuration of a coherent OFDM signal (optical signal1710); a coherent optical OFDM signal under the influence of CFO and phase noise (optical signal1720); and DSP for estimating and compensating for the CFO and phase noise (optical signal1730).FIG.17also depicts signal processing steps1750, which are examples of digital signal processing steps of associated with receiver1650,FIG.16.

In optical signal1710, a direct-current (DC) component is introduced at the center of the OFDM signal in its spectrum. Between the DC component and the loaded subcarriers at the two side bands, some guard subcarriers remain unloaded to protect the central pilot tone from loaded subcarriers' interference. Optical signal1710includes a pilot tone1712.

After transmission pilot tone1712along an optical link and exposure of pilot tone1710to the CFO and phase noise, the bandwidth of pilot tone1712is slightly broadened because random sideband components are introduced by the phase noise, as shown by optical signal1720. Optical signal1720is also slightly deviated from the DC because of the CFO. The procedures for CFO and phase noise compensation are shown in processing steps1750, which are based on the DSP flows of a coherent OFDM receiver of receiver1650inFIG.16.

Optical signal1730includes a central pilot tone1735. After transforming optical signal1730into frequency domain through an FFT, for each data block, the position of the central pilot is located through peak search and a low-pass digital filter is applied to filter out central pilot tone1735along with the phase-noise side bands surrounding itself. Then an IFFT is executed to inversely convert central pilot tone1735into time domain, which contains the CFO and phase-noise information in time domain. After taking the conjugate of the time-domain pilot component and multiplying it back to the corresponding buffered data block before FFT, the CFO and phase noise are cancelled, and, after FFT, the signal may be processed for channel response equalization and decisioning.

FIG.18is a schematic of a laser-chirp measurement system1800, which includes a signal generator1810, a test laser1860, fiber-optic cable604, a coherent receiver1850, a local oscillator1852, and a signal processor1870. In embodiments, system1800also includes a bias-tee1820. Signal generator1810is an example of signal generator610, and may include bias-tee1820.

In an example mode of operation, signal generator1810produces a real-valued double-sideband OFDM signal1812. Since test laser1860only converts the electrical signal to the intensity fluctuations of the light, only the real-part of OFDM signal1812is sent to an alternating-current (AC) port of bias-tee1820. It is worth noting that, after the offline signal generation, there is no DC component for the signal. However, when test laser1860is biased at the linear operation region, after modulating onto the light, a DC component will be automatically introduced at the center of the signal in frequency domain, which is equivalent to a pilot tone added offline. In an OFDM signal recovery process, this central pilot subcarrier may be located and filtered out to compensate the CFO and phase noise based on the algorithms described in herein.

Test laser1860has a chirp response1864, which laser-chirp measurement system1800estimates as a chirp-response function1878. Laser-chirp measurement system1800is described in further detail below as part of a description of a method2300for measuring a chirp-response of a laser.

Methods of Laser Chirp Estimation

When driven by an external small electrical signal, the frequency chirp response HF(ƒ) for the cavity of a semiconductor laser may be determined by the rate equation description of the modulation dynamics, which per reference [1] can be written as

HF(f)=Z(j⁢2⁢π⁢f)2+j⁢2⁢π⁢fY+Z(1)y=g0⁢S_1+ε⁢S_+1τn-Γ⁢g0(N_-Nt)⁢1(1+ε⁢S_)2+1τp(2)Z=g0⁢S_(1+ε⁢S_)⁢1τp+(β-1)⁢Γ⁢g0(N_-Nt)τn⁢1(1+ε⁢S_)2+1τn⁢τp,(3)
whereNis the steady-state value of carrier density,Sis the steady-state value of photon density, ƒ is the frequency of the modulation signal, ϵ is the gain compression factor, τpis the photon life time, τnis the electron life time, ϑ0is the gain slope constant, and Γ is the mode confinement. In the following simulation, the values of Y and Z are set to be 55.87×109s−1and 55.52×1020Hz2, respectively. The curves of the simulated laser chirp amplitude and phase responses are shown in power-response plot1910and phase-response plot1920ofFIG.19respectively. The effective bandwidth is around 15 GHz. However, it is observed that except from the distortions in the intensity, the phase rotations are also different for different frequency component. After long-distance fiber transmission, the phase differences will jointly work together with chromatic dispersion and thus further distorting the channel response. Because of the phase rotations, such distortion induced by laser-chirp dynamics cannot be eliminated through intensity compensation only. Nevertheless, a cascaded DML plus phase modulator structure in an OFFT enables mitigation of the chirp degradations via manipulation and pre-distortion of the signal's phase and pre-compensation of the signal's shape in intensity.

FIG.20depicts measured intensity responses2010and measured phase responses2020of laser chirp as measured by laser-chirp measurement system1800,FIG.18, in which the transmitter device under test—an example of test laser1860, is a Fabry-Perot laser under coherent injection-locking in a COIL system. For each bias voltage ofFIG.20, the combination of the corresponding measured intensity response2010and the corresponding measured phase response2020is an example of chirp-response function1878determined by laser-chirp measurement system1800.

In the example ofFIG.20, the operation wavelength is around 1561 nm and the injecting power is fixed at around 2-dBm. As shown by measured intensity responses2010, the operation bandwidth in intensity domain is enlarged with a higher bias voltage. The estimated modulation bandwidths are around 12 GHz and 16 GHz under bias voltages of 1.11 V and 1.45 V respectively. It can be found that the general trends of the curve basically match the tendency shown in power-response plot1910,FIG.19. By contrast, measured phase responses2020, each under different voltages, are basically overlapped, which proves that the phase response is not sensitive towards changes of bias voltage.

Joint Chirp and Chromatic Dispersion Compensation

FIGS.6-14describe DSP techniques in an OFFT site to pre-compensate the chromatic dispersion after long-distance-fiber transmission. However, when a direct-modulated laser is used in the system, the chromatic dispersion will interact with the chirp of the laser, which further degrades the signal quality. A single-stage chromatic dispersion pre-compensation cannot totally mitigate the transmission distortions because the chirp is not considered.

With embodiments of the coherent optical OFDM technique to measure the chirp response of the laser under modulation shown inFIGS.18-20, the distortion precompensation ofFIGS.6-14can be extended to jointly compensate for chirp and chromatic dispersion.FIG.21is a schematic diagram of a chirp-compensating transmitter2100that transmits a chirp-compensated optical signal2128to a receiver unit2190. Chirp-compensating transmitter2100includes signal generator2110, DAC1614, a laser2160, and phase modulator618. In embodiments, laser2160is a directly-modulated laser, and may also be a coherent-optical-injection locked laser.

Laser2160has a chirp response2164. In embodiments of laser-chirp measurement system1800, test laser1860is identical to laser2160such that chirp-response2164has been measured by laser-chirp measurement system1800, which outputs chirp-response function1878. Measured intensity responses2010and measured phase responses2020,FIG.20are example measurements of chirp-response2164.

As shown inFIG.21, after modelling of the chirp and chromatic-dispersion responses, they are inversed and multiplied, by signal generator2110, to the corresponding data block subsequently in frequency domain. After the signal generation process, the compensated signal, represented by p(t), is decomposed into an intensity component P(t) and a phase component θ(t), which will be modulated onto laser2160and phase modulator618respectively, which will cooperate to cancel both chirp induced by direct modulation and phase distortion induced by fiber-optic cable604. In the frequency domain, the compensated signal P(ω) equals Hc−1(ω)S(ω), where Hc(ω) is a transfer function that includes distortion effects of chirp and, in embodiments, also chromatic dispersion. S(ω) is a frequency-domain representation of a modulated signal without precompensation. Transfer function Hc(ω) is an example of transfer function H(ω), the inverse of which is stored in embodiments of memory704of signal generator710. Transfer function Hc(ω) is also an example of chirp-response function1878.

Embodiments disclosed herein describe the use of a coherent optical OFDM signal to measure the chirp response in a DML, such a directly modulated laser of a COIL transmitter or an OFFT. An efficient DSP technique to estimate and mitigate the CFO and phase noise in coherent optical OFDM is also applied. The experimental results of measured chirp responses are basically matched with the existing theoretical studies. With the tool for chirp measurement and estimation, it is enabled to further extend the embodiments ofFIGS.6-14to jointly pre-compensate the penalties brought by the interactions between chromatic dispersion and chirp, which further improves the signal quality after fiber transmission in an IM-DD, COIL, or an OFFT system.

FIG.22is a schematic of a chirp-compensating transmitter2200, which is an embodiment of dispersion-compensating transmitter602,FIG.6. Chirp-compensating transmitter2200includes a signal generator2210, laser2160, and a phase modulator2218, which are respective examples of signal generator610, laser616, and phase modulator618of dispersion-compensating transmitter602,FIG.6. In embodiments, chirp-compensating transmitter2200also includes tunable delay line620.

Signal generator2210is configured to distort original modulated signal s(t) according to an inverse of chirp-response function2178, to yield a chirp-compensated signal pc(t), which has an amplitude Qc(t) and a phase θc(t). In embodiments, signal generator2210is also configured to distort original modulated signal s(t) by an inverse of a chromatic dispersion response function2279, of which H(ω) is an example. Chirp-compensated signal pc(t), herein also referred to a chirp-compensated signal2280, as an example of chirp-compensated optical signal2128.

Chirp-response function2178is an estimate of chirp response2164of laser2160, and is an example of chirp-response function1878, produced by laser-chirp measurement system1800. In embodiments, signal generator2210generates original modulated signal s(t). In other embodiments, chirp-compensating transmitter2200, includes preprocessor612, from which signal generator2210receives original modulated signal s(t).

In chirp-compensating transmitter2200, laser2160is configured to modulate an amplitude of an optical signal2262in response to an amplitude of one of (i) chirp-compensated signal pc(t) and (ii) a signal derived therefrom, to yield an amplitude-modulated signal2226. Phase modulator2218is disposed downstream of laser2160with respect to optical signal2262. Phase modulator2218is configured to modulate a phase of amplitude-modulated signal2226in response to (i) one of phase θc(t) of chirp-compensated signal2280(pc(t)) and (ii) a phase of a signal derived from chirp-compensated signal2280(pc(t)).

In embodiments, original modulated signal s(t) is modulated over a range of modulation frequencies, and at least one an amplitude and a phase of chirp-response2164varies over the range of modulation frequencies. An example range of modulation frequencies is between one and sixteen GHz, or a subrange therein.

Signal generator2210may be a digital signal generator. For example, in embodiments, signal generator2210includes a processor2212and a memory2214. Memory2214may be transitory and/or non-transitory and may include one or both of volatile memory (e.g., SRAM, DRAM, computational RAM, other volatile memory, or any combination thereof) and non-volatile memory (e.g., FLASH, ROM, magnetic media, optical media, other non-volatile memory, or any combination thereof). Part or all of memory2214may be integrated into processor2212. Memory2214stores machine readable instructions, shown as software2216. When executed by processor2212, software2216controls processor2212to generate chirp-compensated signal pc(t) by distorting original modulated signal s(t) according to the inverse of chirp-response2164. In embodiments, memory2214stores estimated chirp-response function2178, which may be calculated values, as inFIG.19, measured values, as inFIG.20, or a combination thereof.

In embodiments, chirp-response function2178is an analytical expression that is a function of a modulation frequency of the original modulation signal and one or more characteristics of laser2160. The characteristics include at least one of: a steady-state value of carrier density, a steady-state value of photon density, a gain compression factor, a characteristic photon life time, a characteristic electron life time, a gain slope constant, and a mode confinement parameter. An example of the analytical expression is frequency chirp response HF(ƒ) of equation (1).

Step2310includes modulating the laser with a real-valued double-side-band orthogonal frequency-domain multiplexed (OFDM) signal to yield a characterization optical signal that includes a plurality of subcarriers each including a respective transmitted amplitude and a respective transmitted phase. In an example of step2310, signal generator1810modulates test laser1860with signal1812to yield a characterization signal1814.

Step2320includes transmitting the characterization optical signal to a coherent receiver via a fiber-optic cable. In an example of step2320, signal1812is transmitted to coherent receiver1850via fiber-optic cable604.

Step2330includes receiving, at the coherent receiver, the characterization optical signal as a chirped-modulated optical signal. In an example of step2330, coherent receiver1850receives a chirp-modulated signal1816.

Step2340includes demodulating the chirped-modulated optical signal to obtain, for each subcarrier of the plurality of subcarriers, a respective received amplitude and a respective received phase. In an example of step2340, coherent receiver demodulates chirp-modulated signal1816to obtain, or each subcarrier of the plurality of subcarriers of signal1812, a respective received amplitude and a respective received phase.

Step2350includes, for each subcarrier of the plurality of subcarriers, (i) determining a respective chirp-response amplitude of a plurality chirp-response amplitudes of the chirp-response function as a ratio of the respective received amplitude to the respective transmitted amplitude, and (ii) determining a respective chirp-response phase of a plurality chirp-response phases of the chirp-response function as a difference between the respective received phase to the respective transmitted phase. In an example of step2350, signal processor1870determines chirp-response function1878. In embodiments, chirp-response function1878includes a plurality chirp-response amplitudes of measured intensity responses2010and a plurality chirp-response phases of measured phase responses2020,FIG.20.

FIG.24is a flowchart illustrating a method2400for laser chirp precompensation. Method2400includes steps2450and2460. In embodiments, method2400also includes at least one of steps2410,2420,2430,2440, and2470. Method2400may be implemented by chirp-compensating transmitter2200.

Step2410includes determining a chirp-response function by executing method2300. In an example of step2410, laser-chirp measurement system1800outputs chirp-response function2178.

Step2420includes distorting an original modulated signal according to the inverse of the chirp-response function to yield a chirp-compensated signal. In an example of step2420, signal generator2210distorts original modulated signal s(t) according to an inverse of chirp-response function2178to yield chirp-compensated signal2280.

Step2430includes distorting the chirp-compensated signal, according to an inverse of a chromatic-dispersion response function of a fiber-optic cable, to generate a twice-compensated signal. In an example of step2430, signal generator2210distorts chirp-compensated signal2280according to chromatic dispersion-response function2279, which yields a twice-compensated signal2282that is precompensated for both chirp and chromatic dispersion. In embodiments, the chirp-precompensation of step2420precedes the chromatic dispersion precompensation of step2430, while in other embodiments, step2430precedes step2420, or steps2420and2430are executed in a single step. When method2400includes step2430, pc(t) represents twice-compensated signal2282.

Step2440includes producing an optical signal with the laser. In an example of step2440, laser2160produces optical signal2262.

Step2450includes modulating an amplitude of an optical signal, in response to an amplitude of one of (i) a chirp-compensated signal generated via distortion of an original modulated signal according to an inverse of a chirp-response function of a laser and (ii) a first signal derived from the chirp-compensated signal, to yield an amplitude-modulated optical signal. Step2450may include directly modulating the laser, e.g., signal generator2210may directly modulate laser2160.

In a first example of step2450, signal generator2210modulates an amplitude of optical signal2262according to an amplitude of chirp-compensated signal2280to yield amplitude-modulated signal2226. In a second example of step2450, applicable when method2400includes step2430, signal generator2210modulates an amplitude of optical signal2262according to an amplitude of twice-compensated signal2282to yield amplitude-modulated signal2226.

Step2460includes modulating a phase of the amplitude-modulated optical signal in response to a phase of one of (i) the chirp-compensated signal and (ii) a second signal derived from the chirp-compensated signal. In a first example of step2460, phase modulator2218modulates a phase of amplitude-modulated signal2226according to a phase of chirp-compensated signal2280to yield chirp-compensated optical signal2128. In a second example of step2450, applicable when method2400includes step2430, phase modulator2218modulates a phase of amplitude-modulated signal2226according to a phase of twice-compensated signal2282to yield chirp-compensated optical signal2128.

Step2470includes transmitting the chirp-compensated optical signal to a receiver via a fiber-optic cable. In an example of step2470, chirp-compensating transmitter transmits chirp-compensated optical signal2128to receiver unit2190via fiber-optic cable604.

Combinations of Features

Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following enumerated examples illustrate some possible, non-limiting combinations.

(A1) A method of determining a chirp-response function of a laser includes the following steps (a)-(e). Step (a) includes modulating the laser with a real-valued double-side-band orthogonal frequency-domain multiplexed (OFDM) signal to yield a characterization optical signal that includes a plurality of subcarriers each including a respective transmitted amplitude and a respective transmitted phase. Step (b) includes transmitting the characterization optical signal to a coherent receiver via a fiber-optic cable. Step (c) includes receiving, at the coherent receiver, the characterization optical signal as a chirped-modulated optical signal. Step (d) includes demodulating the chirped-modulated optical signal to obtain, for each subcarrier of the plurality of sub carriers, a respective received amplitude and a respective received phase. Step (e) includes for each subcarrier of the plurality of subcarriers, (i) determining a respective chirp-response amplitude of a plurality chirp-response amplitudes of the chirp-response function as a ratio of the respective received amplitude to the respective transmitted amplitude, and (ii) determining a respective chirp-response phase of a plurality chirp-response phases of the chirp-response function as a difference between the respective received phase to the respective transmitted phase.

(B1) A method for laser chirp precompensation includes modulating an amplitude of an optical signal, in response to an amplitude of one of (i) a chirp-compensated signal generated via distortion of an original modulated signal according to an inverse of a chirp-response function of a laser and (ii) a first signal derived from the chirp-compensated signal, to yield an amplitude-modulated optical signal. The method also includes modulating a phase of the amplitude-modulated optical signal in response to a phase of one of (i) the chirp-compensated signal and (ii) a second signal derived from the chirp-compensated signal to yield a chirp-compensated optical signal.

(B2) In embodiments, method (B1) includes distorting the original modulated signal according to the inverse of the chirp-response function to yield the chirp-compensated signal.

(B3) In embodiments of either of methods (B1) and (B2), at least one of an amplitude and a phase of the chirp-response function varies over a range of modulation frequencies of the original modulated signal.

(B4) In embodiments of any one of methods (B1)-(B3), chirp-response function is an analytical expression that is a function of a modulation frequency of the original modulation signal and a number of characteristics of the laser that includes at least one of: a steady-state value of carrier density, a steady-state value of photon density, a gain compression factor, a characteristic photon life time, a characteristic electron life time, a gain slope constant, and a mode confinement parameter.

(B5) In embodiments of any one of methods (B1)-(B4), distorting includes one of (i) multiplying a frequency-domain representation of the original modulated signal by a frequency-domain representation of the chirp-response function, and (ii) convolving a time-domain representation of the original modulated signal by a time-domain representation of the chirp-response function.

(B6) Embodiments of any one of methods (B1)-(B5) further include transmitting the chirp-compensated optical signal to a receiver via a fiber-optic cable.

(B7) In embodiments of any one of methods (B1)-(B6), the original modulated signal being a non-optical signal.

(B8) Embodiments of any one of methods (B1)-(B7) further include producing the optical signal with the laser.

(B9) In embodiments of method (B8), modulating the amplitude of the optical signal includes directly modulating the laser.

(B10) Embodiments of any one of methods (B1)-(B9) further include distorting the chirp-compensated signal, according to an inverse of a chromatic-dispersion response function of a fiber-optic cable, to generate a twice-compensated signal. Said modulating the amplitude of the optical signal includes modulating the amplitude of the optical signal in response to an amplitude of the twice-compensated signal. Said modulating the phase of the amplitude-modulated optical signal comprising modulating the phase of the amplitude-modulated optical signal in response to a phase of the twice-compensated signal.

(B11) Embodiments of method (B10) further includes, when modulating the phase of the amplitude-modulated optical signal yields an as-transmitted optical signal, transmitting the as-transmitted optical signal to a receiver via the fiber-optic cable.

(B12) Embodiments of any one of methods (B1)-(B10) further include determining the chirp-response function via method (A1).

(C1) A chirp-compensating transmitter includes a signal generator, a laser, and a phase modulator. The signal generator is configured to distort an original modulated signal according to an inverse of a chirp-response function of a laser, to yield a chirp-compensated signal. The laser is configured to modulate an amplitude of an optical signal in response to an amplitude of one of (i) the chirp-compensated signal and (ii) a first signal derived therefrom, to yield an amplitude-modulated optical signal. The phase modulator is disposed downstream of the laser with respect to the optical signal, and is configured to modulate a phase of the amplitude-modulated optical signal in response to a phase of one of (i) the chirp-compensated signal and (ii) a second signal derived therefrom.

(C2) In embodiments of transmitter (C1) the original modulated signal being modulated over a range of modulation frequencies, at least one an amplitude and a phase of the chirp-response function varying over the range of modulation frequencies.

(C3) In embodiments of either of transmitters (C1) and (C2), the laser is a directly-modulated laser.

(C4) In embodiments of any one of transmitters (C1)-(C3), the laser is a coherent-optical-injection locked laser.

(C5) In embodiments of any one of transmitters (C1)-(C4), the signal generator is a digital signal generator.

(C6) In embodiments of any one of transmitters (C1)-(C5), the signal generator includes a processor and a memory. The memory stores machine readable instructions that when executed by the processor, control the processor to generate the chirp-compensated signal by distorting the original modulated signal according to the inverse of the chirp-response function.

(C7) In embodiments of any one of transmitter (C6), the chirp-response function is an analytical expression that is a function of a modulation frequency of the original modulation signal and one or more characteristics of the laser. The characteristics includes at least one of: a steady-state value of carrier density, a steady-state value of photon density, a gain compression factor, a characteristic photon life time, a characteristic electron life time, a gain slope constant, and a mode confinement parameter. The memory stores the analytical expression and the characteristics of the laser.

Changes may be made in the above methods and systems without departing from the scope of the present embodiments. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. Herein, and unless otherwise indicated the phrase “in embodiments” is equivalent to the phrase “in certain embodiments,” and does not refer to all embodiments. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.

REFERENCES