Multichannel soliton transmission and pulse shepherding in bit-parallel-wavelength optical fiber links

Abstract

We study basic principles of the bit-parallel-wavelength (BPW) pulse transmission in multichannel single-mode optical fiber links for high-performance computer networks. We develop a theory of the pulse shepherding effect that allows simultaneous propagation of pulses in parallel bit slots by binding them into a multicomponent BPW soliton. We describe families of the BPW solitons and bifurcation cascades in a system of incoherently coupled nonlinear Schrödinger equations that model the multichannel multiwavelength transmission in a single-mode optical fiber. We demonstrate high robustness of the composite BPW solitons, due to their underlying linear stability, to a moderate pulse walkoff.

Polarization interactions in multi-component defocusing media

“…The term proportional to q o in equation (1) makes q  independent of time but can be removed by a simple gauge transformation. Importantly, multicomponent VNLS equations such as equation (1) also arise in nonlinear optical media [11][12][13]. Therefore, the results of this work are applicable to both physical contexts.…”

“…One then expresses the non-analytic Jost eigenfunctions in equations (13) in terms of the columns of c  via equations ( 9) and (10) and uses the Schwarz reflection principle to lift the resulting relations off the real axis. In particular, wherever the eigenfunctions are analytic…”

Dark-bright soliton solutions with nontrivial polarization interactions for the three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions

“…Mathematically, these systems have been the subject of intense study for over 40 years, and renewed interest is motivated by recent experiments in multi-component BECs, which have highlighted a variety of dark-dark and dark-bright soliton solutions. 4,10,11 Moreover, multicomponent VNLS equations also arise in nonlinear optics, 16,19,21 and the same kind of dark and dark-bright soliton solutions appears in optical media with Kerr nonlinearity and normal dispersion. 13,18,20,24,25 To model dark-bright soliton interactions, one must consider solutions with non-zero boundary conditions (NZBC).…”

Soliton-guided phase shifter and beam splitter

“…As in [1] we adopt the formulation in [2,[7][8][9]: two coupled wave equations. The large-signal pump, P (z, t), is described by the standard cubic nonlinear Schrödinger equation; the probe signal, u(z, t), which is assumed to be very much smaller than the pump, is described by a linear wave equation; and the pump determines the potential seen by the probe:…”