Nonparaxial propagation of vectorial hollow Gaussian beams

Based on the vectorial Raleigh-Sommerfeld diffraction integral, the nonparaxial. propagation of vectorial hollow Gaussian beams (HGBs) in free space is studied. The far-field and paraxial cases can be treated as special cases of our general results. The typical numerical examples are given to illustrate our analytical results and comparisons between the different approximations present that the f parameter still plays an important role in determining the nonparaxiality of vectorial diffracted HGBs. (c) 2007 Optical Society of America.

Analytical vectorial structure of hollow Gaussian beams in the far field

The analytical vectorial structure of HGB is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HGB in the far-field, which is composed of TE term and TM term, are demonstrated. The physics pictures of HGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HGB propagation. (c) 2008 Optical Society of America.

Propagation and polarization properties of hollow Gaussian beams in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of hollow Gaussian beams (HGBs) in uniaxial crystals, and given the typical numerical example to illustrate our analytical results. Due to the anisotropy crystals, the ordinary and extraordinary beams originated by incident HGBs propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of incident HGBs do not remain during propagating in crystals. (c) 2007 Published by Elsevier B.V.

Spectral anomalies of focused hollow Gaussian beams at the geometrical focal plane

On the basis of diffraction integral and the expansion of the hard-aperture function into a finite series of complex Gaussian functions, an approximate expression for spatially fully coherent polychromatic hollow Gaussian beams passing through aperture lens is obtained. Detailed numerical results indicate that remarkable spectral changes always occurs near the points where the field amplitude has zero value. The effects of truncation parameter, Fresnel number and the beam order on spectral shifts and spectral switches are investigated numerically. (C) 2008 Elsevier B.V. All rights reserved.

Far-field intensity distribution and M-2 factor of hollow Gaussian beams

The far-field intensity distribution of hollow Gaussian beams was investigated based on scalar diffraction theory. An analytical expression of the M-2 factor of the beams was derived on the basis of the second-order moments. Moreover, numerical examples to illustrate our analytical results are given. (c) 2005 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

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.

Spatiotemporal behaviors and singularity of ultrashort pulsed Elegant Hermite-Gaussian beams

Analytical propagation expressions of ultrashort pulsed Elegant Hermite-Gaussian beams are derived and spatiotemporal properties of the pulses with different transverse modes are studied. Singularity of the complex amplitude envelope solution of the pulses obtained under slowly varying envelope approximation is analyzed in detail. The rigorous analytical solution of the pulse is deduced and no singularity emerges in the solution. The obtained results indicate that the transverse mode affects not only the spatiotemporal properties but also the singularity of the pulses. Time delay of the off-axis maximum intensity is more obvious and the singularity is located nearer to the z-axis for the pulse with higher transverse modes. (C) 2007 Elsevier GmbH. All rights reserved.

Propagation properties of beams generated by Gaussian mirror resonator in uniaxial crystals

Based on the paraxial vectorial theory of beams propagating in uniaxially anisotropic media, we have derived the analytical propagation equations of beams generated by Gaussian mirror resonator (GMR) in uniaxial crystals, and given the typical numerical example to illustrate our analytical results. Due to the anisotropy crystals, the ordinary and extraordinary beams originated by incident beams generated by GMR propagate with different diffraction lengths, thus the linear polarization state and axial symmetry of the incident beams generated by GMR do not remain during propagating in crystals. (c) 2006 Elsevier GmbH. All rights reserved.

Focal shifts in focused Hermite-cosh-Gaussian laser beams

A closed-form propagation equation of Hermite-cosh-Gaussian beams passing through an unapertured thin lens is derived. Focal shifts are analyzed by means of two different methods according to the facts that the axial intensity of some focused Hermite-cosh-Gaussian beams are null and that of some others are not null but the principal maximum intensity may be located on the axis or off the axis. Optimal focusing for the beams is studied, and the condition of optimal focusing ensuring the smallest beam width is also given. (c) 2005 Elsevier GmbH. All rights reserved.

Investigation of the influence of the aberration induced by a plane interface on STED microscopy

The structure of the inhibition patterns is important to the stimulated emission depletion (STED) microscopy. Usually, Laguerre-Gaussian (LG) beam and the central zero-intensity patterns created by inserting phase masks in Gaussian beams are used as the erase beam in STED microscopy. Aberration is generated when focusing beams through an interface between the media of the mismatched refractive indices. By use of the vectorial integral, the effects of such aberration on the shape of depletion patterns and the size of fluorescence emission spot in the STED microscopy are studied. Results are presented as a comparison between the aberration-free case and the aberrated cases. (C) 2009 Optical Society of America

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.