Random sources generating ring-shaped beams

Abstract

Two classes of scalar, stochastic sources are introduced, each capable of producing far fields with intensities forming rings. Although the Bessel-Gaussian and the Laguerre-Gaussian Schell-model sources are described by two different math models, the behavior of their degrees of coherence and, hence, the shapes of their far fields are qualitatively similar. The new beams are of importance for optical methods of particle manipulation.

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

“…22,36 It is clear from the above expression that the source-plane spectral density S ¼ Wðq; qÞ is Gaussian. With the BGSM cross-spectral density W provided above, a closed-form expression for the far-zone W can easily be derived.…”

“…With the BGSM cross-spectral density W provided above, a closed-form expression for the far-zone W can easily be derived. 22,36 In the experiments, the far-zone BGSM W is produced by using a lens, where the lens and source plane are collocated. This scenario is equivalent to the classic Fourier optics problem of an input placed against a lens.…”

“…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. 31 Excellent reviews and more in-depth discussions of these topics can be found in Refs.…”

“…The first is a GSM source variant that has been theoretically analyzed in past literature. 22,36 The experimental results are compared to the theoretical predictions to validate the proposed approach. The second and third partially coherent sources are sources which cannot be synthesized using existing techniques.…”

Correlation-induced self-focusing and self-shaping effect of a partially coherent beam

“…Various partially coherent beams with prescribed correlation functions have been investigated in both theory and experiment since Gori and collaborators derived the sufficient condition for constructing the genuine correlation functions [2,3] . Recent studies have shown that specially correlated partially coherent beams display many unique but interesting properties, e.g., self-splitting effect appears in a Hermite-Gaussian correlated Schellmodel beam on propagation [9][10][11] , partially coherent beams with multi-Gaussian, Bessel-Gaussian and cosine-Gaussian correlated Schell-model functions exhibit prescribed farfield intensity distributions [12][13][14][15] , Laguerre-Gaussian correlated Schell-model beam produces an optical cage near the focal plane [16,17] . Due to those extraordinary properties, specially correlated partially coherent beams are useful in some applications, such as optical imaging, particle trapping, atom guiding and free-space optical communications.…”