Vectorial theory of propagation in uniaxially anisotropic media

Abstract

We describe propagation in a uniaxially anisotropic medium by relying on a suitable plane-wave angularspectrum representation of the electromagnetic field. We obtain paraxial expressions for both ordinary and extraordinary components that satisfy two decoupled parabolic equations. As an application, we obtain, for a particular input beam (a quasi-Gaussian beam), analytical results that allow us to identify some relevant features of propagation in uniaxial crystals.

Modeling of the propagation of Bessel beams in a uniaxial crystal at different positions of the crystal axis

“…However, it is difficult to define wave characteristics of generated fields in this case. Therefore, we have considered the focusing of radiation in an anisotropic medium on the basis of the wave theory of diffraction [21][22][23][24][25][26]. The input Gaussian beam is submitted with a converging wave front corresponding to the thin lens in the path of the beam.…”

“…One tool for such transformations are anisotropic crystals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. One method of modelling the propagation of electromagnetic waves in anisotropic media is the method of plane waves expansion [21][22][23][24][25][26]. As a rule, the use of this method causes large computational problems due to the need to calculate the direct and inverse Fourier transforms for all electromagnetic field components.…”

Evolution Properties of a Partially Coherent Flat-topped Vortex Hollow Beam Propagating in Uniaxial Crystals Orthogonal to the Optical Axis

“…In this case, we mainly consider a laser beam propagating in uniaxial crystals orthogonal to the optical axis. Within the framework of paraxial approximation, the components of the laser beam propagating in uniaxial crystals orthogonal to the optical axis can be treated by the following formulas [2][3][4]: …”

“…The propagation properties of laser beams in uniaxial crystals have been treated by solving the boundary value problems of Maxwell's equations in uniaxial crystals [2][3][4]. Since the vectorial theory of laser beam propagation in uniaxial crystals was constructed, propagation of various laser beams [5][6][7][8][9][10][11][12][13][14][15][16][17][18], such as Laguerre-Gauss and Bessel-Gauss beams, Hermite-Gauss beams, dark hollow beams, flat-topped beams, elliptical Gaussian beams, elliptical Gaussian vortex beams and beams generated by a Gaussian mirror resonator in uniaxial crystals, partially coherent flat-topped beams, partially polarized and partially coherent beams, LaguerreGaussian correlated Schell model beams, coherent and partially coherent four-petal Gaussian vortex beams, has been widely investigated.…”

Diffraction of Lorentz-Gauss beam in uniaxial crystals: orthogonal to optical axis

“…[14]. Because of its importance in practical applications, in past years, researchers have studied the propagation of various laser beams in uniaxial crystals by solving Maxwell's equations, in cases of beams propagating orthogonal to the optical axis [15][16][17][18][19][20][21] and along the optical axis [22][23][24][25][26][27]. The works referred above are invaluable and significant; however, to the best of our knowledge, there has been no report on diffraction properties of the Lorentz-Gauss beam in anisotropic media, so it is essential to know its exact diffraction field in uniaxial crystals.…”