On time-bandwidth product of multi-soliton pulses

Multi-soliton pulses are potential candidates for fiber optical transmission where the information is modulated and recovered in the so-called nonlinear Fourier 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. In this paper, we study the evolution of the time-bandwidth product of multi-solitons as they propagate along the optical fiber. For second and third order soliton pulses, we numerically optimize the pulse shapes to achieve the smallest time-bandwidth product when the phase of the spectral amplitudes is used for modulation. Moreover, we analytically estimate the pulse-duration and bandwidth of multi-solitons in some practically important cases. Those estimations enable us to approximate the time-bandwidth product for higher order solitons.