Twisted speckle entities inside wave-front reversal mirrors

The previously unknown property of the optical speckle pattern reported. The interference of a speckle with the counterpropagating phase-conjugated (PC) speckle wave produces a randomly distributed ensemble of a twisted entities (ropes) surrounding optical vortex lines. These entities appear in a wide range of a randomly chosen speckle parameters inside the phase-conjugating mirrors regardless to an internal physical mechanism of the wave-front reversal. These numerically generated interference patterns are relevant to the Brillouin PC mirrors and to a four-wave mixing PC mirrors based upon laser trapped ultracold atomic cloud.

Figure 1

Grayscale intensity plot for a small volume of a speckle pattern inside PC mirror in $\left(X,Z\right)$ plane $\left(Y=23\mu \text{m}\right)$. The mean transverse size of a speckle is $D\sim 8\mu \text{m}$. The mean longitudinal length of a speckle entity is of the order of the Rayleigh range $L_R\approx D^2/\lambda$ for $\lambda \sim 1\mu \text{m}$. The size of the volume is $32\mu \text{m}$ in transverse $\left(X,Y\right)$ directions and $128\mu \text{m}$ in longitudinal $\left(Z\right)$ direction. The step of longitudinal modulation $\text{cos}\left[\left(k_p+k_s\right)z\pm 2\varphi \right]$ induced by the interference of counterpropagating pump and Stokes waves is enlarged here eight times for visualization purposes. The characteristic $\pi$ phase jump is clearly visible in between adjacent Bragg’s cosine-modulated roll patterns.

Figure 2

The plot of the light intensity maxima at a given moment $t$ in a small volume inside the PC mirror. The four pairs of spiral interference patterns with opposite handedness are located randomly in space. Their diameters and directions are changed smoothly due to diffraction. The step of longitudinal modulation $\text{cos}\left[\left(k_p+k_s\right)z\pm 2\varphi \right]$ is enlarged here 16 times.

Figure 3

Grayscale intensity plot for the variational ansatz [Eq. (7)] substituted into Eq. (5). The $128\times 2048$ point arrays are used for the intensity distributions [Eq. (5)] in $\left(X,Z\right)$ planes at fixed $Y=64$. The single sinusoidally modulated ${\text{LG}}_0^1$ vortex line [see Eq. (7)] is shown for (a) $M=0.1D$ and (b) $M=D$. Two ${\text{LG}}_0^1$ distant vortex lines (c) with parallel, (d) and opposite (e) topological charges $\pm \ell$ constitute the rope when the distance between them is reduced to zero (d,e). The step of longitudinal modulation is enlarged here 32 times.