Optimization of Multi-Soliton Joint Phase Modulation for Reducing the Time-Bandwidth Product

Multi-soliton pulses are potential candidates for fiber optical transmission where the information is modulated and recovered in the so-called nonlinear frequency domain. While this is an elegant technique to account for the channel nonlinearity, the obtained spectral efficiency, so far, is not competitive with the classic Nyquist-based schemes. This is especially because of soliton pulses generally having a large time-bandwidth product. We consider the phase modulation of spectral amplitudes in the nonlinear spectrum for multi-solitons with purely imaginary eigenvalues. Each eigenvalue carries an M-PSK constellation for modulation of its corresponding spectral phase. We study the variation of the soliton's pulse duration and bandwidth due to modulation and transmission along an ideal optical fiber. The receiver is placed at multiples of the soliton period. For this scenario, we give a suitable defintion for the time-bandwidth product. By joint modulation of a subset of the spectral phases and optimization of the soliton parameters, we maximize the ideal spectral efficiency for the considered scenario. We quantify the improvement achieved when compared to first order pulses.