Generation of Non-Rayleigh Nondiffracting Speckles

Optical speckle fields with both non-Rayleigh statistics and nondiffracting characteristics in propagation are an important light source for many applications. However, tailoring either non-Rayleigh statistical speckles or nondiffracting speckles are only investigated independently in previous studies. Here, we report the first observation of optical speckles that remain diffraction-free over a long axial distance while keeping non-Rayleigh statistics simultaneously. We further show the enhancement of Anderson localization of light with the non-Rayleigh nondiffracting speckles. The work presented here provides a versatile framework for customizing optical fields with desired speckle patterns for applications in the fields of solid-state physics, cold atoms, and optical imaging.

Figure 1

Phase masks for tailoring the statistical and diffractive characteristics of speckles. (a) Random phases on a plane. (b) Random phases on a ring-shaped slit. (c) Random phases on a ring-shaped slit with central antisymmetry.

Figure 2

Experimentally recorded speckles. (a) Non-Rayleigh speckle pattern with contrast $C=1.36$. (b) Nondiffracting speckle pattern with $C=0.98$. (c) NRND-speckle pattern with $C=1.35$.

Figure 3

Diffracting and statistical properties of NRND speckles. (a)–(e) The recorded NRND speckles at 5 axis positions: $d=0$, 4.34, 8.68, 13.02, 17.36 Rayleigh ranges. (f) The PDFs of nondiffracting speckles and NRND speckles. Solid purple and green lines denote the computational simulated PDFs of NRND speckles and nondiffracting (ND) speckles. Dashed red and blue lines denote the experimental PDFs of NRND speckles and ND speckles. (g) The axial propagation property of contrast of non-Rayleigh speckles and NRND speckles. The triangles and squares are experimental data and solid lines are simulation results.

Figure 4

The inverse Fourier transform (IFT) intensity $|{\mathcal{F}}^{-1}[g_0^n(x,y)]{|}^2$ of powered NRND-speckle pattern with complex field $g_0(x,y)$ and whose intensity contrast is $C=\sqrt{2}$. (a)–(i) are the IFT intensity patterns of complex fields $g_0(x,y)$, $g_0^2(x,y)$, $\cdots$, and $g_0^9(x,y)$. The solid yellow line in each figure represents the detailed data of one extracted line of the IFT intensity pattern. All the extracted lines locate the same position as the white dashed line shown in (c).

Figure 5

Experimental generation of NRND speckles with higher intensity contrast. (a),(b),(c) and (d) Camera recorded NRND speckles with odd power $n=3$, 5, 7, 9. (e) The axial propagation property of contrast for different odd powered NRND speckles. The dot data and solid line data represent the experimental and simulated results, respectively.

Figure 6

The effective width ${\omega }_{\mathrm{eff}}$ of the intensity profile while probe light propagating in the disordered lattice generated by speckles with various intensity contrasts. Average of over 100 realizations of NRND speckles for each kind of intensity contrast.