Self-polarization effect in the middle point of an optical fiber

In this paper, we report both numerically and experimentally an unexpected phenomenon of self-polarization occurring in the middle point of an isotropic optical fiber when two uncorrelated partially polarized waves are simultaneously injected at the ends of the fiber. More precisely, we demonstrate that two counterpropagating waves of equal intensity exhibit a spontaneous organization of their polarization states around two pools of attraction just in the middle point of propagation, and then both recover a partially polarized state at their respective fiber outputs. The self-polarization effect then remains hidden within the optical fiber in the sense that no apparent sign of this process is detected at the fiber outputs. A geometric definition of the degree of polarization is used to measure the efficiency of the polarization phenomenon.

Figure 1

Numerical simulations of the spatiotemporal system on the Poincaré sphere. The red (gray), green (light gray), and blue (dark gray) dots denote, respectively, the input, middle, and output SOPs of the signal (${\displaystyle \vec{S}}$, upper panels) and of the pump (${\displaystyle \vec{J}}$, lower panels).

Figure 2

(a) Evolution of the DOP as a function of the position ${\displaystyle \xi }$ for ${\displaystyle {\tau }_c=24\mu \mathrm{s}}$ (blue dotted line), ${\displaystyle {\tau }_c=60\mu \mathrm{s}}$ (red dashed line), and ${\displaystyle {\tau }_c=120\mu \mathrm{s}}$ (green solid line). (b) DOP of the forward beam at ${\displaystyle \xi =0}$ (black line), ${\displaystyle \xi =L/2}$ (blue line), and ${\displaystyle \xi =L}$ (red circle). The same fiber parameters as in Fig. 1 are used.

Figure 3

(a)–(c) Evolution of the PDF of the three components (${\displaystyle S_x,S_y,S_z}$) of the SOP of the forward beam as a function of the position ${\displaystyle \xi }$. The PDFs have been computed from the results displayed in Fig. 1. The coherence time is set to ${\displaystyle 60\mu \mathrm{s}}$. Panel (d) is a zoom of panel (c).

Figure 4

Stationary solutions ${\displaystyle S_z\left(\xi \right)}$ along the fiber [the coordinate ${\displaystyle J_z\left(\xi \right)}$ has exactly the same evolution in the stationary regime]. The trajectories attracted towards the north and the south poles are, respectively, plotted in red (gray) and in blue (dark gray). The corresponding trajectories on the doubly pinched torus are schematically represented. The positions of the two hyperbolic fixed points are indicated by a black dot.

Figure 5

Experimental setup. ASE, amplified spontaneous emission; Pol, polarizer; OBPF, optical bandpass filter; IM, intensity modulator; AWG, arbitrary waveform generator; EDFA, erbium doped fiber amplifier; PS, polarization scrambler.

Figure 6

Experimental Poincaré spheres recorded for ${\displaystyle S}$ and ${\displaystyle J}$ at the input (red or gray dots), at the output (blue or dark gray dots), and in the middle of the fiber (green or light gray dots). The power of each wave is set to 4.5 W and the number of points is 256.

Figure 7

Experimental probability density function of the Stokes parameters for the ${\displaystyle S}$ wave recorded at the input (blue or dark gray line) and in the middle of the fiber (green or light gray line). The power of each wave is set to 4.5 W and the number of points is 256.