Nonparaxial propagation of a partially coherent dark hollow beam

Nonparaxial propagation properties of a vector partially coherent dark hollow beam

“…For the convenience of comparison, the normalized intensity distribution I p ∕I p max and the corresponding cross line (y x) calculated by the paraxial propagation formulas [Eqs. (38), (39), and (44)] are also shown in Figs. 1-3.…”

“…Nonparaxial propagation properties of a scalar or vector coherent DHB have been studied in [35][36][37][38][39][40][41][42][43]. Nonparaxial propagation properties of a scalar partially coherent DHB were reported in [44]. To our knowledge, no results have been reported until now on the nonparaxial propagation of a vector partially coherent DHB.…”

Propagation of a Laguerre–Gaussian correlated Schell-model beam beyond the paraxial approximation

“…Many approaches have been developed to treat the propagation of nonparaxial partially coherent beams, such as generalized Rayleigh-Sommerfeld diffraction integrals, Wigner distribution function, angular spectrum representation and the vectorial moment theory [21][22][23][24]. Based on these methods, propagation properties of nonparaxial scalar and vector GSM beams with various beam profiles have been extensively studied in free space [25][26][27][28][29][30][31][32][33][34]. Recently, Zhang et al performed the nonparaxial propagation of a twisted anisotropic Gaussian Schell-model beam based on the generalized RayleighSommerfeld diffraction integral with the help of a tensor method [35], and they also examined the nonparaxial propagation of a partially coherent beam in uniaxial crystals [36].…”

Propagation dynamics of modified hollow Gaussian beams in strongly nonlocal nonlinear media

“…Nowadays various techniques have been used to generate hollow beams, for example hollow-fiber method [10,11], spatial filtering method [12][13][14], spot-defect mirror method [15], binary spatial light modulator method [16] and so on. Naturally these beams in various optical systems and media have attracted considerable interest, for instance in a turbulent atmosphere [17,18], a lens with spherical aberration [19], a fractional Fourier transform optical system [20][21][22][23], uniaxial crystals orthogonal to the optical axis [24], the far field in free space [25][26][27], nonparaxial optical systems [28][29][30], etc.…”