Daulet Askarov

Effect of Mode Coupling on Signal Processing Complexity in Mode-Division Multiplexing

Mode-division multiplexing systems employ multi-input multi-output (MIMO) equalization to compensate for chromatic dispersion (CD), modal dispersion (MD) and modal crosstalk. The computational complexity of MIMO equalization depends on the number of modes and on the group delay (GD) spread arising from CD and MD. Assuming the strong-coupling regime, in which the total system length far exceeds the correlation length of modal fields, we quantify the GD spread arising from MD, showing that it can be reduced significantly by mode coupling. We evaluate the computational complexity of various MIMO single-carrier equalizers, considering separate or combined equalization of CD and MD, in the time or frequency domain. We present numerical examples for the optimally designed graded-index depressed-cladding fibers supporting D=6, 12, 20 or 30 modes in two polarizations. Assuming a 2000-km system length, a 1-km correlation length, and a combined CD+MD frequency-domain equalizer, the complexity (in complex multiplications per two-dimensional symbol) is a factor 1.4, 1.7, 2.2, 2.8 times higher for D=6, 12, 20, 30 than for polarization-multiplexed systems in standard single-mode fiber (D=2).

Adaptive Frequency-Domain Equalization in Mode-Division Multiplexing Systems

Long-haul mode-division multiplexing (MDM) employs adaptive multi-input multi-output (MIMO) equalization to compensate for modal crosstalk and modal dispersion. MDM systems must typically use MIMO frequency-domain equalization (FDE) to minimize computational complexity, in contrast to polarization-division-multiplexed systems in single-mode fiber, where time-domain equalization (TDE) has low complexity and is often employed to compensate for polarization effects. We study two adaptive algorithms for MIMO FDE: least mean squares (LMS) and recursive least squares (RLS). We analyze tradeoffs between computational complexity, cyclic prefix efficiency, adaptation time and output symbol-error ratio (SER), and the impact of channel group delay spread and fast Fourier transform (FFT) block length on these. Using FDE, computational complexity increases sublinearly with the number of modes, in contrast to TDE. Adaptation to an initially unknown fiber can be achieved in ~3-5 μs using RLS or ~15-25 μs using LMS in fibers supporting 6-30 modes. As compared to LMS, RLS achieves faster adaptation, higher cyclic prefix efficiency, lower SER, and greater tolerance to mode-dependent loss, but at the cost of higher complexity per FFT block. To ensure low computational complexity and fast adaptation in an MDM system, a low overall group delay spread is required. This is achieved here by a family of graded-index graded depressed-cladding fibers in which the uncoupled group delay spread decreases with an increasing number of modes, in concert with strong mode coupling.

Adaptive control of input field to achieve desired output intensity profile in multimode fiber with random mode coupling

We develop a method for synthesis of a desired intensity profile at the output of a multimode fiber (MMF) with random mode coupling by controlling the input field distribution using a spatial light modulator (SLM) whose complex reflectance is piecewise constant over a set of disjoint blocks. Depending on the application, the desired intensity profile may be known or unknown a priori. We pose the problem as optimization of an objective function quantifying, and derive a theoretical lower bound on the achievable objective function. We present an adaptive sequential coordinate ascent (SCA) algorithm for controlling the SLM, which does not require characterizing the full transfer characteristic of the MMF, and which converges to near the lower bound after one pass over the SLM blocks. This algorithm is faster than optimizations based on genetic algorithms or random assignment of SLM phases. We present simulated and experimental results applying the algorithm to forming spots of light at a MMF output, and describe how the algorithm can be applied to imaging.

Design of Transmission Fibers and Doped Fiber Amplifiers for Mode-Division Multiplexing

Transmission fibers and erbium-doped fiber amplifiers (EDFAs) for 12 signal modes (including spatial and polarization degrees of freedom) are studied. Modal fields are computed numerically and their effective areas, group delays (GDs), and chromatic dispersion coefficients are determined. Multimode rate equations are solved numerically to calculate mode-dependent gains (MDGs) and pump power requirements in multimode EDFAs. Results are compared for various numerical apertures (NAs), index profiles, and doping profiles. Graded-index depressed-cladding fibers offer an attractive combination of low GD spread in transmission fibers (583 ps/km rms with 0.15 NA) and low MDG in EDFAs (0.14 dB rms at 25-dB mode averaged gain with 0.15 NA). Optimized erbium doping profiles are comprised of a uniform cylindrical region plus an extra annulus.

Adaptive Modal Gain Equalization Techniques in Multi-Mode Erbium-Doped Fiber Amplifiers

We demonstrate two adaptive methods to equalize mode-dependent gain (MDG) in multi-mode erbium-doped fiber amplifiers (MM-EDFAs). The first method uses a spatial light modulator (SLM) in line with the amplifier pump beam to control the modal powers in the pump. The second method uses an SLM immediately after the MM-EDFA to directly control the modal powers in the signal. We compare the performance of the two methods applied to a MM-EDFA with a uniform erbium doping profile, supporting 12 signal modes in two polarizations. We show that root-mean-squared MDGs lower than 0.5 and 1 dB can be achieved in systems having frequency diversity orders of 1 and 100, respectively, while causing less than a 2.6-dB loss of mode-averaged gain.

Long-Period Fiber Gratings for Mode Coupling in Mode-Division-Multiplexing Systems

In mode-division-multiplexing systems, multi-input multi-output (MIMO) equalization is used to compensate for linear impairments, including modal dispersion (MD) and modal crosstalk. The MIMO equalizer memory length depends on the group delay (GD) spread arising from MD. The GD spread arising from MD can be significantly reduced by introducing strong mode coupling via mode scramblers. We study the design of such mode scramblers implemented as long-period multimode fiber gratings for systems using D = 12 modes (six spatial modes). By optimizing the grating chirp function, we minimize the mode-dependent loss (MDL) of the grating while ensuring full intergroup mode coupling. We find a design yielding MDL and mode-averaged loss in the C band not exceeding 0.36 and 0.45 dB, respectively. We also verify the effect of such mode scramblers on the GD scaling of a long-haul system, demonstrating that the scramblers reduce the scaling of GD spread with length from a linear to a square-root dependence, as expected in the strong coupling regime.

Design of multi-mode erbium-doped fiber amplifiers for low mode-dependent gain

Erbium-doped fiber amplifiers for 12 signal modes (six spatial modes in two polarizations) are studied by numerically solving multi-mode rate equations. Mode-dependent gains are compared for different numerical apertures, index profiles and doping profiles.

MIMO signal processing in mode-division multiplexing systems

We present the fundamentals of multi-input multi-output (MIMO) signal processing for mode-division multiplexing (MDM) in multi-mode fiber. We review group delay management techniques that minimize adaptation time and complexity in MIMO signal processing. We describe long-period fiber grating (LPFG) devices for introducing strong mode coupling, which represent a promising practical approach for group delay management. We analyze MIMO equalization complexity, adaptation time and throughput efficiency for MDM systems employing LPFG devices.

Adaptive control of mode-dependent gain in multi-mode erbium-doped fiber amplifiers

We demonstrate adaptive control of mode-dependent gain in a multi-mode erbium-doped fiber amplifier by placing a spatial light modulator in line with the pump laser.

Frequency-Derivative Measurement Technique for Dispersive Effects in Single-Mode Fiber Systems

An optical dispersion analysis and measurement technique based on frequency derivatives of the Jones matrix is presented. This approach enables measurement of all scalar and polarization-dependent phase and amplitude dispersion effects over a broad wavelength range in a single sweep. Owing to its differential nature, it can be more accurate than techniques that calculate dispersion by comparing phase and amplitude measurements from adjacent wavelengths in a sweep. The method involves measuring eight elementary parameters related to the frequency derivative of the Jones matrix. An experimental setup and data analysis methods for measuring the elementary parameters are presented. Three optical devices exhibiting various dispersive effects are tested, and the ability to measure all the elementary parameters is demonstrated. Elementary parameter estimation error is 1-2 ps in this proof-of-concept experiment.