Partially coherent beam propagation in atmospheric turbulence [Invited]

Abstract

Partially coherent beams hold much promise in free-space optical communications for their resistance to the deleterious effects of atmospheric turbulence. We describe the basic theoretical and computational tools used to investigate these effects, and review the research to date.

Wave optics simulation of anisotropic turbulence

“…where the symbol r( ... ) is the gamma function. A random numerical realization of a turbulence screen can be generated as follows [12,13]: 1) Define the physical side length of the screen L and sample number N (along one dimension). The 2-D coordinates of the samples K and K 'x y , can be described as: Kx = K y = 2nlL-(-NI2 : NI2-1); 2) form the products fJxKx and fJ y K y ; 3) fill the samples with normally distributed random numbers with unitary standard deviation; 4) calculate the square root of the power spectral density function, (2n � Z<l>n) ll2 , where k is the wavenumber and Z is the propagation distance, then multiply the random samples in step 3); 5) take the 2-D inverse fast Fourier transform.…”

“…Instead of repeating these details here, we simply point out that the anisotropic atmospheric turbulence is also simulated with a split-step approach and the number of evenly-spaced screens (Nd used to model a given homogeneous path is determined by [12,16] N TS > ( 1Oa� ji ll . (4) For example, if a i = 9, then NTS > 11.6 and at least 12 turbulence screens are required.…”

Spatial coherence measurement and partially coherent diffractive imaging using self-referencing holography

“…It describes the statistical correlation between fields at a pair of locations. However, the measurement of spatial coherence is remarkably challenging, which limits the control and the optimization of spatial coherence in a broad range of key applications such as beam shaping [1,2], optical communication through a turbulent atmosphere [3], illumination for advanced imaging systems (e.g. optical lithography) [4] and superresolution imaging [5].…”

Experimentally generating any desired partially coherent Schell-model source using phase-only control

“…For example, numerous published articles exist predicting the polarization, coherence, and beam shape of partially coherent light after propagating through free space and random media [1][2][3][4][5][6][7][8][9][10] or scattering from deterministic and random objects/media. [11][12][13][14][15][16][17][18][19][20][21] Much work has also been performed exploiting coherence to control beam shape [22][23][24][25][26][27][28][29][30] and even as an encoding scheme for holography.…”