Polarization modulation instability in a Manakov fiber system

The Manakov model is the simplest multicomponent model of nonlinear wave theory: It describes elementary stable soliton propagation and multisoliton solutions, and it applies to nonlinear optics, hydrodynamics, and Bose-Einstein condensates. It is also of fundamental interest as an asymptotic model in the context of the widely used wavelength-division-multiplexed optical fiber transmission systems. However, although its physical relevance was confirmed by the experimental observation of Manakov (vector) solitons in a planar waveguide in 1996, there have in fact been no quantitative experiments confirming its validity for nonlinear dynamics other than soliton formation. Here, we report experiments in optical fiber that provide evidence of passband and baseband polarization modulation instabilities in a defocusing Manakov system. In the spontaneous regime, we also reveal a unique saturation effect as the pump power increases. We anticipate that such observations may impact the application of this minimal model to describe and understand more complicated phenomena in nature, such as the formation of extreme waves in multicomponent systems.

Figure 1

(a) PMI gain vs sideband detuning for total pump powers in the range $0.2P_0–50P_0$. (b) PMI peak gain vs power (the blue dashed line represents the saturation level of the peak gain). (c) OMF vs total pump power. The black line gives the results obtained from the linear stability analysis [dispersion relation (3)], whereas the red dash-dotted line is obtained via the phase-matching condition (5). The blue dashed line represents the saturation limit. (d) Intensities of the MI sidebands obtained from the eigenvectors of the system vs total pump power. The blue solid (green dashed) line corresponds to the primary (secondary) sidebands.

Figure 2

(a) Experimental setup: red and green lines depict the two wavelength-division-multiplexed and orthogonally polarized pumps. ECL: external-cavity diode laser; 50/50 and 90/10: fiber couplers; EDFA: erbium-doped fiber amplifier; IM: intensity modulator; PC: polarization controller; PM: phase modulator; PBS: polarization beam splitter; PRBS: pseudorandom binary sequence generator; PwM: power-meter; OPF: optical programmable filter; OSA: optical spectrum analyzer. (b) Impact of the input polarization states of the two-pump system with 200 GHz frequency spacing on the observation of PMI. (Left: input spectra. Right: output spectra.)

Figure 3

Output spectra vs input pump power on $u$ and $v$ axis. (a,b) numerical simulation of the CNLSEs (1) with loss; (c,d) experiments.

Figure 4

Dependence of cumulated PMI gain (primary and secondary sidebands) on input total pump power.

Figure 5

Variation of output spectra as a function of the pump frequency spacing. (a,b): numerical simulation of the CNLSEs (1) with loss; (c,d): experiments. The emergence of the mirror image of the MI spectrum is revealed in subfigure (a) as the broad pedestal indicated by blue dashed arrow around the pump spectrum (red arrow). The primary MI sideband is highlighted by the red dashed circle.

Figure 6

Comparison between analytical predictions and numerical or experimental results for the variation of cumulated MI gain as a function of the frequency spacing among the pumps.