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Mode-dependent loss and gain (MDL and MDG) of multimode components are fundamental impairments that reduce the capacity of mode-division-multiplexed (MDM) systems. MDL of components is commonly quantified either in terms of the root mean square (rms) or peak-to-peak (P-P) gain and loss variations. It is incorrect to specify only the P-PMDL of components if they are to be used in an MDM system with nonnegligible mode coupling, because the system's overall coupled gains are random variables whose statistics cannot be determined from the P-P MDL values. On the other hand, measurements of the rms MDL of components are sufficient to determine the rms value of the system's overall coupled MDL, regardless of whether the system has weak or strong coupling. We propose novel algorithms based on convex optimization, which can efficiently measure all modal gains of any multimode component using low-cost direct-detection hardware. In particular, we propose an efficient algorithm that produces accurate measurements of all modal gains by estimating a high-dimensional MDL ellipse using a sequence of power measurements.

Multi-input multi-output (MIMO) digital signal processing (DSP) for mode-division multiplexing (MDM) may have high complexity, owing to a plurality of modes and a potentially long group delay (GD) spread in multimode fiber (MMF). This paper addresses the management of GD in MMF and its implications for the complexity and performance of MIMO DSP. First, we review the generalized Jones and Stokes representations for modeling propagation in MMF, and describe key GD properties derived using the two representations. Then, we describe three approaches for GD management: 1) optimized fiber design, 2) mode coupling, and 3) GD compensation. For approach 1), we explain design principles for minimizing the GD spread. We review experimental results to date, showing that fabrication nonidealities significantly increase the GD spread, and this approach alone may not achieve sufficiently low GD spread. For approach 2), we describe mechanisms for inducing intragroup and intergroup coupling. We describe mode scrambler designs based on photonic lanterns or long-period fiber gratings, both of which can ensure strong intergroup coupling. For approach 3), we review GD-compensated system design principles and show that GD compensation is only partially effective in the presence of random intragroup or intergroup coupling. Finally, we provide an overview of adaptive MIMO frequency-domain equalization algorithms. Considering tradeoffs between complexity, performance, and adaptation time, we show that the GD spread is a key factor determining the feasibility of MIMO DSP, and its feasibility requires judicious GD management.

Reduction of the group delay (GD) spread is crucial for minimizing signal processing complexity in mode-division multiplexing. Strong mode coupling and GD compensation (concatenating different fibers with opposing GD ordering) are two approaches for reducing the end-to-end GD spread. In this paper, we study the GD behavior in systems where mode coupling and GD compensation are both present. Using a propagation model in generalized Stokes space, we describe the evolution of the GD variance by coupled differential equations. By integration of these equations, we evaluate the GD variance in GD compensated systems with different mode coupling lengths and GD compensation lengths. When the mode coupling length is much longer than the GD compensation length, a low GD variance can be obtained as a result of GD compensation. By contrast, when the mode coupling length is much shorter than the GD compensation length, GD compensation becomes ineffective, but a low GD variance can be obtained as a result of strong mode coupling. The largest GD variance is obtained when the mode coupling length is comparable to the GD compensation length.

In this paper, we review linear propagation effects in a multimode fiber (MMF) and their impact on performance and complexity in long-haul mode-division multiplexing (MDM) systems. We highlight the many similarities to wireless multi-input multioutput (MIMO) systems. Mode-dependent loss and gain (MDL), analogous to multipath fading, can reduce average channel capacity and cause outage in narrowband systems. Modal dispersion (MD), analogous to multipath delay spread, affects the complexity of MIMO equalization, but has no fundamental effect on performance. Optimal MIMO transmission uses a basis of the Schmidt modes, which may be obtained by a singular value decomposition of the MIMO channel. In the special case of a unitary channel (no MDL), an optimal basis is the set of principal modes, which are eigenvectors of a group delay operator, and are free of signal distortion to first order. We present a concatenation rule for the accumulation of MD along a multisection link. We review mode coupling in MMF, including physical origins, models, and regimes of weak and strong coupling. Strong mode coupling is a key to overcoming challenges in MDM systems. Strong coupling reduces the group delay spread from MD, minimizing the complexity of MIMO signal processing. Likewise, it reduces the variations of loss and gain from MDL, maximizing channel capacity. In the strong-coupling regime, the statistics of MD and MDL depend only on the number of modes and the variance of accumulated group delay or loss/gain, and can be derived from the eigenvalue distributions of certain Gaussian random matrices.

When an electronic equalizer is used to compensate the modal dispersion in a mode-division multiplexed system, receiver phase noise induces interference to the multi-input- multi-output (MIMO) receiver. Based on the statistics of the modal dispersion in the strong coupling regime, the interference variance is evaluated analytically based on an exact model, a semicircle asymptotic for large number of modes, and a first-order approximation.

In the strong mode coupling regime, the delay spread of multimode fiber is statistically the same as the difference between the maximum and minimum eigenvalues of a Gaussian unitary ensemble. We study the delay-spread distribution using three methods: 1) numerical evaluation of the Fredholm determinant; 2) numerical integration based on the Andreief identity; and 3) approximation based on the Tracy-Widom distribution. Results obtained using the Fredholm determinant and the Andreief identity are virtually indistinguishable. The approximation based on the Tracy-Widom distribution is sufficiently accurate for most engineering purposes when the number of modes is at least 12. In a digital equalizer, a memory length of four to five times the group-delay standard deviation is sufficient to ensure that the delay spread will exceed the equalizer memory length with a probability of less than 10-4-10-6 .

The exact error probability of quadriphase shift keying (QPSK) signals with homodyne crosstalk is derived analytically. With respect to the signal, homodyne crosstalk may be from the same, the worst, or random polarization. Valid for many interferers, Gaussian model overestimates the SNR penalty for homodyne crosstalk from a single interferer. For 1-dB SNR penalty, QPSK signal may tolerate up to a crosstalk ratio of -16.3 dB from a single interferer from the worst polarization alignment.

Optical duobinary signal has narrow spectrum, tolerance to chromatic dispersion, and resistance to filter distortion. With many early patents from different organizations, optical duobinary modulation was actually invented earlier and described in a thesis by L. C. Blank. The later development of optical duobinary modulation is reviewed, including its applications for retrofitting 40-Gb/s signal into existing 10-Gb/s fiber networks.

The phase and amplitude responses of a narrow-band optical filter are measured simultaneously using a microwave network analyzer. The measurement is based on an interferometric arrangement to split light into two paths and then combine them. In one of the two paths, a Mach-Zehnder modulator generates two tones without carrier and the narrow-band optical filter just passes through one of the tones. The temperature and environmental variations are removed by separated phase and amplitude averaging. The amplitude and phase responses of the optical filter are measured to the resolution and accuracy of the network analyzer.

A miniature-size erbium doped fibre amplifier (MS-EDFA) is constructed with a saturation power of 17.0 dBm and low noise figure of 5.2 dB using an uncooled pump laser. The MS-EDFA has achieved low polarization dependent gain, large signal gain and small signal gain of 0.05 dB, 15 dB (at Pin = +2 dBm) and 42 dB (at Pin = −30 dBm), respectively, with negligible temperature dependent gain. The dimension of MS-EDFA is only twice than a typical credit card.

In highly dispersive return-to-zero differential phase-shift keying (RZ-DPSK) transmission systems, the overlap of optical pulses gives a nonperiodic optical intensity that induces nonperiodic phase modulation to adjacent channels through cross-phase modulation (XPM). The variance of the differential phase induced by XPM and pulse overlap is derived analytically. The impact of pulse overlap is smaller for a system using short RZ optical pulses. For two adjacent channels without spectral overlap, the standard deviation (STD) of XPM-induced phase shift is approximately inversely proportional to the channel separation.

When a differential-phase-shift-keying (DPSK) signal is directly detected using an asymmetric interferometer and balanced receiver, the exact error probability of the signal with homodyne crosstalk is derived analytically. Homodyne crosstalk from many interferers is Gaussian distributed, but the Gaussian model overestimates the signal-to-noise ratio (SNR) penalty for homodyne crosstalk from a single interferer. For the DPSK signal, the crosstalk ratio for a 1-dB SNR penalty must be less than -16.5 dB. For the same crosstalk ratio, the SNR penalty for a DPSK signal is far smaller than that for an ON-OFF keying (OOK) signal.

Regardless of the number of constellation points, all quadrature-amplitude modulation (QAM) signals can be generated using a single dual-drive Mach-Zehnder modulator. When the general method is applied to quadrature-phase-shift-keying (QPSK) signals, three different QPSK transmitters are shown with drive signals having four, three, or two levels. The usage of only one dual-drive modulator greatly simplifies the design of QAM and QPSK transmitters.

The nonlinear phase noise, often called the Gordon–Mollenauer effect, is correlated with the intensity of the optical signal. With a single linear compensator, the optimal location is not preceding the receiver but located at about 2/3 of the fiber link. When N compensators are approximately optimally placed, the standard deviation of nonlinear phase noise is reduced by a factor of 2 N + 1. The optimal compensation factors are all approximately equal to each other.

The error probability is derived analytically for differential phase-shift keying (DPSK) signals contaminated by both self- and cross-phase modulation (SPM and XPM)-induced nonlinear phase noise. XPM-induced nonlinear phase noise is modeled as Gaussian distributed phase noise. When fiber dispersion is compensated perfectly in each fiber span, XPM-induced nonlinear phase is summed coherently span after span and is the dominant nonlinear phase noise for typical wavelength-division-multiplexed (WDM) DPSK systems. For systems without or with XPM-suppressed dispersion compensation, SPM-induced nonlinear phase noise is usually the dominant nonlinear phase noise. With longer walkoff length, for the same mean nonlinear phase shift, 10-Gb/s systems are more sensitive to XPM-induced nonlinear phase noise than 40-Gb/s systems.

Information-theoretic limits to spectral efficiency in dense wavelength-division-multiplexed (DWDM) transmission systems are reviewed, considering various modulation techniques (unconstrained, constant-intensity, binary), detection techniques (coherent, direct), and propagation regimes (linear, nonlinear). Spontaneous emission from inline optical amplifiers is assumed to be the dominant noise source in all cases. Coherent detection allows use of two degrees of freedom per polarization, and its spectral efficiency limits are several b/s/Hz in typical terrestrial systems, even considering nonlinear effects. Using either constant-intensity modulation or direct detection, only one degree of freedom per polarization can be used, significantly reducing spectral efficiency. Using binary modulation, regardless of detection technique, spectral efficiency cannot exceed 1 b/s/Hz per polarization. When the number of signal and/or noise photons is small, the particle nature of photons must be considered. The quantum-limited spectral efficiency for coherent detection is slightly smaller than the classical capacity, but that for direct detection is 0.3 b/s/Hz higher than its classical counterpart. Various binary and nonbinary modulation techniques, in conjunction with appropriate detection techniques, are compared in terms of their spectral efficiencies and signal-to-noise ratio requirements, assuming amplified spontaneous emission is the dominant noise source. These include a) pulse-amplitude modulation with direct detection, b) differential phase-shift keying with interferometric detection, c) phase-shift keying with coherent detection, and d) quadrature-amplitude modulation with coherent detection.

The optical power spectrum of a signal externally modulated using a Mach-Zehnder modulator is calculated analytically. Optical power spectra are calculated for binary signals for which the drive signal has either raised-cosine or Bessel-filtered pulse shape as well as for duobinary signals created by Bessel filtering. While the optical power spectrum is often approximated by the electrical power spectrum of the drive signal, this approximation usually underestimates the spectral spreading of the optical signal. Differences between the optical spectrum and the drive-signal electrical spectrum are most significant for drive signals having longer rise and fall times. Modulator chirp also broadens the optical spectrum. Chirp-induced spectral broadening is more significant for drive signals having longer rise and fall times.

The nonlinear phase noise, often called the Gordon–Mollenauer effect, is correlated with the received intensity. The optimal compensator is the minimum mean-square error (MMSE) compensator to estimate the nonlinear phase noise using the received intensity. The MMSE compensator is derived analytically and approximated by subtracting a correction term proportional to the received intensity.

Polarization control is used in a tri-directional wavelength-reused system to reduce the power penalty caused by coherent mixing of the signal with Rayleigh backscattering noise. For a 25 + 25 km, 10 Gb/s tri-directional transmission system, the power penalty is 4.0 dB under the worst polarization control and could be reduced to 0.4 dB under optimal polarization control. The experimental results show that reusing the same wavelength is an efficient and promising method for tri-directional lightwave systems.

As the bit rates of routed data streams exceed the throughput of single wavelength-division multiplexing channels, spectral and spatial traffic aggregation become essential for optical network scaling. These aggregation techniques reduce network routing complexity by increasing spectral efficiency to decrease the number of fibers, and by increasing switching granularity to decrease the number of switching components. Spectral aggregation yields a modest decrease in the number of fibers but a substantial decrease in the number of switching components. Spatial aggregation yields a substantial decrease in both the number of fibers and the number of switching components. To quantify routing complexity reduction, we analyze the number of multi-cast and wavelength-selective switches required in a colorless, directionless and contentionless reconfigurable optical add-drop multiplexer architecture. Traffic aggregation has two potential drawbacks: reduced routing power and increased switching component size.

As the bit rates of routed data streams exceed the throughput of single wavelength-division multiplexing channels, spectral and spatial traffic aggregation become essential for optical network scaling. These aggregation techniques reduce network routing complexity by increasing spectral efficiency to decrease the number of fibers, and by increasing switching granularity to decrease the number of switching components. Spectral aggregation yields a modest decrease in the number of fibers but a substantial decrease in the number of switching components. Spatial aggregation yields a substantial decrease in both the number of fibers and the number of switching components. To quantify routing complexity reduction, we analyze the number of multi-cast and wavelength-selective switches required in a colorless, directionless and contentionless reconfigurable optical add-drop multiplexer architecture. Traffic aggregation has two potential drawbacks: reduced routing power and increased switching component size.

The crosstalk variance of stimulated Raman crosstalk in wavelength-division-multiplexing (WDM) systems is derived analytically in a closed-form formula for all systems with different walkoff length. The probability density function (pdf) of stimulated Raman crosstalk is found to be lognormal distribution (Gaussian distribution in decibel scale). Both power penalty and power limit induced by Raman crosstalk are evaluated and can be applied to single- and multispan WDM systems.

A close-form analytical expression is obtained for the performance study of a bit-rate limiter (BRL). Both bit-error rate (BER) and power penalty are derived for different BRL modulation signals and modulation formats using a random signal model. We also present ways to improve the BRL performance and to eliminate the BRL-induced crosstalk, by using an optimal BRL modulation index and a specific BRL modulation signal, respectively. The analytical expression is found to match well with the experimental measurements.

The usable bandwidth of an optical filter is not only limited by signal attenuation, but also the waveform distortion when optical signal is passed through the edge of the filter. The waveform distortion due to optical filtering is investigated with the assumption of linearly chirped Gaussian pulse. While the first-order optical filtering (linear slope in dB) does not induce waveform distortion, second-order optical filtering induces pulse distortion similar to fiber dispersion.

Two reconfigurable wavelength add/drop multiplexer (WADM) and optical cross-connect (OXC) devices based on strain-tunable fiber Bragg gratings (ST-FBGs) are proposed. The feasibility of WADM is verified by measuring the bit-error-rate performance of the dropped (cross-connect) and pass-through (no cross-connect) channels over a 50- and 100-km standard single-mode fiber for a 2.5 Gb/s system. Compared to back-to-back transmission, a negligible power penalty of only 0.2 dB is observed.

The power spectral density is derived analytically for the phase noise generated by cross-phase modulation from a randomly modulated signal to a continuous-wave probe signal. The autocorrelation function of the probe signal is first derived and the power spectral density is then evaluated by Fourier transform. The power spectral density may be asymmetric with some discrete tones.

We proposed and experimentally demonstrated two power-equalized erbium-doped fiber amplifier (EDFA) modules using fiber Bragg gratings (FBGs) with various reflectivities for individual channels. The transmission type power-equalized EDFA module is low-cost for its simple design, while the reflection type power-equalized EDFA module can suppress most of the amplified spontaneous emission noise. Both consist of a bidirectional EDFA, a set of FBG chains with suitable reflectivities, and an optical isolator/optical circulator. They can find potential applications in wavelength division multiplexing lightwave transmission systems.

A reconfigurable wavelength-division-multiplexing (WDM) add/drop multiplexer (WADM) is constructed using optical switches (OSWS) and fibre Bragg gratings (FBGs). Selected one or two channel(s) can be added/dropped at the same multiplexer by properly controlling the optical switch pair and fibre Bragg grating arrangement. A␣four-channel system is experimentally demonstrated for a data rate of 2.5 Gb s−1 and a single-mode fibre (SMF) distance of 100km. A negligible maximum power penalty of only 0.3dB is observed when compared with back-to-back transmission.