Reflection and transmission of Gaussian beam from a uniaxial crystal slab

We investigate the characteristics of Gaussian beams reflected and transmitted from a uniaxial crystal slab with an arbitrary orientation of its optical axis. The formulas of the total electric and magnetic fields inside and outside the slab are derived by use of Maxwell's equations and by matching the boundary conditions at the interfaces. Numerical simulations are presented and the field values as well as the power densities are computed. Negative refractions are demonstrated when the beam is transmitted through a uniaxial crystal slab. Beam splitting of the reflected beam is observed and is explained by the resonant transmission for plane waves. Dependences of the lateral shift on the incident angle and beam width are discussed. Negative and positive lateral shifts are observed due to the spatial anisotropic properties.

Approximate analytical description for fundamental-mode fields of graded-index fibers: Beyond the Gaussian approximation

An approximate analytical description for fundamental-mode fields of graded-index fibers is explicitly presented by use of the power-series expansion method, the maximum-value condition at the fiber axis, the decay properties of fundamental-mode fields at large distance from the fiber axis, and the approximate modal parameters U obtained from the Gaussian approximation. This analytical description is much more accurate than the Gaussian approximation and at the same time keep the simplicity of the latter. As two special examples, we present the approximate analytical formulas for the fundamental-mode fields of a step profile fiber and a Gaussian profile fiber, and we find that they are both highly accurate in the single-mode range by comparing them with the corresponding exact solutions.

Pure-phase plates for super-Gaussian focal-plane irradiance profile generations of extremely high order

A set of recursive formulas for diffractive optical plates design is described. The pure-phase plates simulated by this method homogeneously concentrate more than 96% of the incident laser energy in the desired focal-plane region. The intensity focal-plane profile fits a lath-order super-Gaussian function and has a nearly perfect flat top. Its fit to the required profile measured in the mean square error is 3.576 x 10(-3). (C) 1996 Optical Society of America

Applicability Range of Stoneys Formula and Modified Formulas for a Film/Substrate Bilayer

In addition to the layer thickness and effective Young’s modulus, the impact of the kinematic assumptions, interfacial condition, in-plane force, boundary conditions, and structure dimensions on the curvature of a film/substrate bilayer is examined. Different models for the analysis of the bilayer curvature are compared. It is demonstrated in our model that the assumption of a uniform curvature is valid only if there is no in-plane force. The effects of boundary conditions and structure dimensions, which are not-fully-included in previous models are shown to be significant. Three different approaches for deriving the curvature of a film/substrate bilayer are presented, compared, and analyzed. A more comprehensive study of the conditions regarding the applicability of Stoney’s formula and modified formulas is presented.

Diffraction integral formulas of the pulsed wave field in the temporal domain

To resolve the diffraction problems of the pulsed wave field directly in the temporal domain, we extend the Rayleigh diffraction integrals to the temporal domain and then discuss the approximation condition of this diffraction formula. (C) 1997 Optical Society of America.

ABCD matrix for reflection and refraction of Gaussian beams at the surface of a parabola of revolution

We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surface of a parabola of revolution that separate media of different refractive indices based on optical phase matching. The equations for the spot sizes and wave-front radii of the beams are also obtained by using the ABCD matrix. With these matrices, we can more conveniently design and evaluate some special optical systems, including these kinds of elements. (c) 2005 Optical Society of America

Changes in the coherence of quasi-monochromatic electromagnetic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the mutual coherence function of quasi-monochromatic electromagnetic Gaussian Schell-model (EGSM) beams propagating through turbulent atmosphere is derived analytically. By employing the lateral and the longitudinal coherence length of EGSM beams to characterize the spatial and the temporal coherence of the beams, the behavior of changes in the spatial and the temporal coherence of those beams is studied. The results show that with a fixed set of beam parameters and under particular atmospheric turbulence model, the lateral coherence of an EGSM beam reaches its maximum value as the beam propagates a certain distance in the turbulent atmosphere, then it begins degrading and keeps decreasing along with the further distance. However, the longitudinal coherence length of an EGSM beam keeps unchanging in this propagation. Lastly, a qualitative explanation is given to these results. (c) 2007 Elsevier B.V. All rights reserved.

Effects of coherence on anisotropic electromagnetic Gaussian-Schell model beams on propagation

An analytical formula for the cross-spectral density matrix of the electric field of anisotropic electromagnetic Gaussian-Schell model beams propagating in free space is derived by using a tensor method. The effects of coherence on those beams are studied. It is shown that two anisotropic stochastic electromagnetic beams that propagate from the source plane z = 0 into the half-space z > 0 may have different beam shapes (i.e., spectral density) and states of polarization in the half-space, even though they have the same beam shape and states of polarization in the source plane. This fact is due to a difference in the coherence properties of the field in the source plane. (C) 2007 Optical Society of America.

Series representation of the Gaussian beam far-field diffracted by annular aperture

Accurate, analytical series expressions for the far-field diffraction of it Gaussian beam normally incident on a circular and central obscured aperture are derived with the help of the integration of parts method. With this expression, the far-field intensity distribution pattern can be obtained and the divergence angle is deduced too. Using the first five items of the series, the accuracy can satisfy most laser application fields. Compared with the conventional numerical integral method, the series representation is very convenient for understanding the physical meanings. (C) 2007 Elsevier GmbH. All rights reserved.

The far-field spatial coherence of Gaussian Schell-model beam in turbulence in terms of position vectors

Spatial coherence properties of beam produced by Gaussian Schell-model source when the beam is propagating through atmosphere have been analyzed in terms of position vectors. New expressions for cross-spectral density of optical field and spectral degree of coherence as well as radiant intensity have been developed. Numerical results illustrated in this paper indicate the coherence degradation suffered from atmospheric turbulence and their directional dependence. (C) 2007 Elsevier GmbH. All rights reserved.

Effects of the frequency chirp on the fields of a chirped Gaussian pulse passing through a hard-edged aperture

Based on the Huygens-Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulse passing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-field and far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by the modulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity. A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect is achieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite-Gaussian transverse profile when the frequency chirp increases. (C) 2005 Elsevier B.V. All rights reserved.

Comparison between complex amplitude envelope representation and complex analytic signal representation in studying pulsed Gaussian beam

Analytic propagation expressions of pulsed Gaussian beam are deduced by using complex amplitude envelope representation and complex analytic signal representation. Numerical calculations are given to illustrate the differences between them. The results show that the major difference between them is that there exists singularity in the beam obtained by using complex amplitude envelope representation. It is also found that singularity presents near propagation axis in the case of broadband and locates far from propagation axis in the case of narrowband. The critical condition to determine what representation should be adopted in studying pulsed Gaussian beam is also given. (C) 2004 Elsevier B.V. All rights reserved.

Focal switch in unapertured converging Hermite-cosh-Gaussian beams

Based on the Huygens-Fresnel diffraction integral, analytical representation of unapertured converging Hermite-cosh-Gaussian beams is derived. Focal switch of Hermite-cosh-Gaussian beams is studied detailedly with numerical calculation examples and a physical interpretation of focal switch is presented. It is found that decentered parameter is the dominant factor for the emergence of focal switch, and Fresnel number affects the amplitude of focal switch and the value of critical decentered parameter to determine emergence of focal switch. Physically, the emergence of focal switch of Hermite-cosh-Gaussian beams is resulted from competition between two major maximum intensities and switch of the absolute maximum intensity from a point to another when decentered parameter increases. (C) 2005 Elsevier Ltd. All rights reserved.