Nonparaxial description of reflection and transmission at the interface between an isotropic medium and a uniaxial crystal

Propagation of the radially polarized Airy vortex beams in uniaxial crystals orthogonal to the optical axis

We introduce the radially polarized Airy vortex beams (RPAiVBs) and analytically study their propagation in uniaxial crystals orthogonal to the optical axis. We mainly discuss the effects of the vortex and the ratio of the extraordinary index (n_e) to the ordinary index (n_o) on the propagation properties of the RPAiVBs involving the intensity distributions, the maximum intensity, the radiation forces, the trajectory, and the velocity. The RPAiVBs evolve into the beams produced by the x direction electric field (RPAiXVB) and the y direction electric field (RPAiYVB). It is shown that with the increase in the order of the vortex, the maximum intensity and the radiation forces of the RPAiVBs are greatly enhanced; besides, the intensity focusing position of the RPAiVBs is farther. Furthermore, with the ratio of n_e to n_o increasing, the trajectory of the RPAiXVBs is farther from x=0  mm, and the acceleration is bigger in the x-z plane, but they are opposite in the y-z plane.

Paraxial propagation dynamics of the radially polarized Airy beams in uniaxial crystals orthogonal to the optical axis

We study the paraxial propagation of the radially polarized Airy beams (RPAiBs) in uniaxial crystals orthogonal to the optical axis analytically and numerically. The propagation trajectory, the intensity and the radiation forces of the RPAiBs are investigated and the properties are elucidated by numerical examples in this paper. Results show that the RPAiBs evolve into the beams produced by the x-direction electric field (RPAiXBs) and the y-direction electric field (PRAiYBs) which are totally different in uniaxial crystals. During the propagation, the intensity of the RPAiXBs transfers from the side lobe in the x-direction to the main lobe and finally returns to the side lobe in the x-direction again, but that of the RPAiYBs transfers from the side lobe in the y-direction to the main lobe and flows to the side lobe in the x-direction at last. The effect of the intensity focusing for the RPAiXBs can be modulated by the ratio of the extraordinary index (ne) to the ordinary index (no) in anisotropic medium, which contributes to the intensity focusing of the RPAiBs in a short distance a lot. We can adjust the intensity distribution especially the focusing position, the propagation trajectory and the radiation forces distributions of the RPAiXBs through choosing an appropriate value of the ratio of ne to no to meet the actual usage accordingly.

Nonparaxial propagation of the chirped Airy vortex beams in uniaxial crystal orthogonal to the optical axis

We study both analytically and numerically nonparaxial propagation dynamics of the Chirped Airy vortex (CAiV) beams in uniaxial crystal orthogonal to the optical axis. The propagation trajectory, the intensity, the radiation forces, the Poynting vector and the angular momentum (AM) of the CAiV beams are illustrated by numerical examples. The influences of the ratio of the extraordinary refractive index to the ordinary refractive index, the linear chirp factor and the quadratic chirp factor on the nonparaxial evolution of the CAiV beams are examined in detail. Results show that the linear chirp factor provides an intensity concentration, which is totally different with the influence of the quadratic chirp. Besides, the uniaxial crystals with different refractive index ratios can be used to control the intensity of optical lobes. Moreover, the value and the direction of the radiation forces depend on the propagation distance and the chirp factor. The chirp factor acting on the Poynting vector and the AM mainly occurs in the direction of vectors. The nonparaxial propagation characteristics of the CAiV beams provide a convenient method to the intensity modulation and the optical manipulation of micro particles.

Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of nonparaxial propagation of a polarized elliptical Gaussian vortex beam in uniaxial crystal orthogonal to the optical axis are derived. Intensity and phase distributions of the three components of a polarized elliptical Gaussian vortex beam propagating in a uniaxial crystal orthogonal to the optical axis are illustrated by numerical examples. The influences of the initial beam's parameters and the parameters of the uniaxial crystal on the evolution of the beam's intensity and phase distributions in the uniaxial crystal are examined in detail. Results show that the statistical properties of an elliptical Gaussian vortex beam nonparaxially propagating in uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam's parameters and the parameters of the crystal. The beam waist width ω₀ not only affects the size of the beam profile in uniaxial crystal but also determines the nonparaxial effect of an elliptical Gaussian vortex beam. The profile of an elliptical Gaussian vortex beam in the uniaxial crystal becomes twisted and tilted, whether the elliptical factor α is greater or smaller than unity. The beam profile is tilted to the left in positive crystal. In contrast, it is inclined to the right in negative crystal. The results indicate that uniaxial crystal provides a convenient method to modulate the intensity and phase distributions of an elliptical Gaussian vortex beam, which is beneficial to optical manipulation of microscopic particles and nonlinear optics involving a specific beam profile and phase.

Double refraction of a Gaussian beam into a uniaxial crystal

For a linearly polarized three-dimensional Gaussian beam in air that is normally incident upon a plane interface with a uniaxial crystal with optic axis in an arbitrary direction, we present integral representations for the transmitted field suitable for asymptotic analysis and efficient numerical evaluation and derive analytical expressions for transmitted nontruncated Gaussian beams for the cases in which the incident beam is polarized parallel to the plane containing the optic axis and the interface normal and transverse to it. The general solution for an arbitrary polarization state of an incident Gaussian beam follows by superposition of these two solutions.

The spatially varying polarization of a focused Gaussian beam in quasi-phase-matched superlattice under electro-optic effect

We present in this paper a wave coupling theory of linear electro-optic (EO) effect for quasi-phase matched (QPM) of focused Gaussian beam in an optical superlattice (OSL). The numerical results indicate that, due to the EO effect of an appropriate applied electric field, the output beam will form spatially inhomogeneous polarization, changing continuously in transverse section of beam; the confocal parameter has a significant impact on the output polarization of Gaussian beam and determines the half-wave voltage.

Nonspecular transverse effects of polarized and unpolarized symmetric beams in isotropic-uniaxial interfaces

We analyze the first-order nonspecular effects of three-dimensional beams in interfaces formed by two lineal dielectric media. We also analyze the dependence of the transverse effects on polarization and compare the results with those obtained for isotropic interfaces. In particular, we determine analytically the complex transverse lateral displacements of a beam with Gaussian distribution of intensity when it is reflected on an interface formed by an isotropic medium and a uniaxial anisotropic one and the mean direction of propagation of the beam is contained in each of the characteristic planes of the crystal.