Relationship between elegant Laguerre-Gauss and Bessel-Gauss beams

We show that the elegant Laguerre-Gauss light beams of high radial order n are asymptotically equal to Bessel-Gauss light beams. The Bessel-Gauss beam equivalent to each elegant Laguerre-Gauss beam is found and shown to have almost identical propagation factors M2. In the limit n-->infinity, elegant Laguerre-Gauss beams can be identified with Durnin's Bessel beam. Our results suggest a new experimental procedure for generating light beams with nondiffractinglike properties directly from the output of a stable resonator.     

Propagation-invariant beams in uniaxial crystals

Propagation-invariant electromagnetic beams, propagating along the optical axis of a uniaxially anisotropic crystal, are investigated. The beams are a superposition of propagation-invariant ordinary and extraordinary fields, with different polarizations states and Bessel profiles. The analytical expression of the Poynting vector reveals an azimuthal transverse energy flow that becomes pure longitudinal, if the complex amplitudes of the ordinary and extraordinary fields are either in phase or in phase opposition.     

Nonparaxial Bessel-Gauss beams.

We study the nonparaxial propagation of Bessel-Gauss beams of any order. Closed-form expressions of all corrections to be added to the solution that is pertinent to the corresponding paraxial problem are found. Such corrections are expressed in terms of two families of polynomials, defined through recurrence rules, that encompass the Laguerre-Gauss polynomials for the particular case of a fundamental Gaussian beam. Numerical examples are shown.     

Scalar modified Bessel-Gauss beams and waves

For modified Bessel-Gauss beams, the modulating function for the Gaussian, instead of a Bessel function of real argument, is a Bessel function of imaginary argument. The modified Bessel-Gauss beams and their full wave generalizations are treated with particular attention to the spreading properties on propagation for the azimuthal mode numbers m=0 and m=1. The spreading on propagation of the peak and the null in the radiation pattern obtained in the propagation direction for m=0 and m=1, respectively, is substantially less for the modified Bessel-Gauss waves than that for the corresponding Bessel-Gauss waves. The total power transported by the waves is determined and compared with that of the corresponding paraxial beam to assess the quality of the paraxial beam approximation for the wave. The powers in the Bessel-Gauss wave and the modified Bessel-Gauss wave are finite in contrast to that in the Bessel wave. With respect to both the spreading properties and the quality of the paraxial beam approximation, the modified Bessel-Gauss beam is an improvement over the Bessel-Gauss beam.     

Imaging of generalized Bessel-Gauss beams

Abstract

Different kinds of Bessel-Gauss beam have been recently introduced. By considering the effect of a lens on the field, we analyse how these different sets of fields transform into one another and illustrate how a superposition model of Gaussian beams allows this transformation to be clearly interpreted.     

Electromagnetic modified Bessel-Gauss beams and waves

The transverse magnetic (TM) modified Bessel-Gauss beams and their full-wave generalizations are treated. Attention is paid to the spreading properties on propagation of the null in the radiation intensity pattern for the azimuthal mode numbers m=0 and 1. The rate of spreading of the null in the propagation direction is significantly less for the TM modified Bessel-Gauss waves than those for the corresponding TM Bessel-Gauss waves. The total power transported by the waves is determined and compared with that of the corresponding paraxial beam to estimate the quality of the paraxial beam approximation of the wave. The dependence of the quality of the paraxial beam approximation on the azimuthal mode number, the beam shape parameter, and the ratio of the beam waist to the wavelength has a regular pattern for the TM Bessel-Gauss wave and not for the TM modified Bessel-Gauss wave.     

Decentered Gaussian beams, ray bundles, and Bessel-Gauss beams

The concept of ray parameters for decentered Gaussian beams is developed on a formal basis. When the beam propagates through first-order optical systems, these parameters are transformed as the ray parameters of geometrical optics. It is shown how this feature helps one to understand the behavior of more sophisticated beams that can be considered as bundles of decentered Gaussian beams. In particular, the case of Bessel-Gauss beams and their recently introduced generalizations is analyzed, and simple transformation formulas are obtained.     

Application of the Jones calculus for Gaussian beams in uniaxial crystals

Following our recent approach in which the Jones matrix calculus was applied to a modulated double-refracted and partially interfering light beam propagating in a homogeneous electro-optic crystal [J. Opt. Soc. Am. A21, 132 (2004)], we generalize the method for any distribution of the light intensity. Special attention is paid to Gaussian, flat-topped Gaussian, and quasi-Gaussian beams for which the intensity of the light emerging from the optical system is found analytically. Application of the method to an optical system with an electro-optic crystal is described.     

Propagation properties of partially coherent anomalous hollow beams in uniaxial crystals

Analytical propagation formulae for partially coherent anomalous hollow beams in uniaxial crystals are derived. Paraxial propagation of partially coherent anomalous hollow beams in uniaxial crystals orthogonal to the optical axis is investigated based on the beam propagation equations. The propagation properties of partially coherent anomalous hollow beams in uniaxial crystals and in free space are studied numerically and comparatively. It is found that the propagation properties of partially coherent anomalous hollow beams in uniaxial crystals behave very differently from those in free space and are closely determined by the parameters of the uniaxial crystals and the initial coherence width. The uniaxial crystals provide an effective way for generating astigmatic beams.     

Vector singularities of Gaussian beams in uniaxial crystals: Optical vortex generation

The propagation of a circularly polarized singular beam through a uniaxial crystal is accompanied by the appearance of additional singularities in the polarization structure of the beam field. These vector singularities combine to form concentric ombilic lines—degenerate ombilic points of the star type, thus significantly changing the entire fine structure of the field. When the beam passes through a birefringent quarter-wave plate and a polarizer, the vector singularities transform into the usual optical vortices. Rotation of the polarizer and/or of the quarter-wave plate drives the vortices to move by preset trajectories, merge with one another, or break into elementary singularities. These processes are studied using theoretical and experimental methods.     

Eigenfields and output beams of an unstable Bessel-Gauss resonator

We evaluate the eigenfields of an unstable Bessel-Gauss resonator (UBGR) by use of the transfer-matrix method in which the transverse profiles and their corresponding losses of the UBGR are considered as the eigenvectors and eigenvalues of a transfer matrix so that the dominant mode fields and their losses of the UBGR can be readily extracted in terms of the matrix eigenvalue algorithm. Moreover, based on the eigenfields across two mirrors that resulted from the transfer-matrix method, we simulate the field distributions in the cavity and the propagation of output beams by means of the angular spectrum method. The computation results show that the UBGR easily produces a fundamental Bessel-Gauss mode of good quality, and the output beams retain the original Bessel-Gauss distribution during propagation.     

受光阑限制贝塞耳-高斯光束的衍射特性

对贝塞耳-高斯光束经不同几何构形光阑的衍射作了比较研究。结果表明,在选取合适的光阑参数情况下,锯齿光阑能减弱所关心区域(F=20)轴上光强的衍射调制,而超高斯光阑能抑制大部分菲涅耳区(F>3.7)的衍射调制。锯齿光阑和超高斯光阑都有较大的填充因子,使用合适的超高斯光阑可得到有较大填充因子(如fSuper-Gaussian=0.25)又更平滑的横向光强分布。数值计算说明,为有效抑制光强的衍射调制,适当选取超高斯光阑的阶数n和半宽ws(如n=4,ws=0.4mm)是必要的。     

Complex-argument Laguerre-Gauss beams: transport of mean-squared beam width

For the azimuthally varying complex-argument Laguerre-Gauss beams, the Fourier integral representation is used to obtain the time-averaged power and the transport equation for the mean-squared beam width. From the coefficients in the transport equation, two propagation parameters are derived and compared with the previous treatments.     

Elegant Laguerre-Gauss beams as a new tool for describing axisymmetric flattened Gaussian beams.

A new superposition scheme for representing flattened Gaussian (FG) beams is proposed. Such a representation, unlike the original proposed by Gori [Opt. Commun. 107, 335 (1994)], is based on an expansion in terms of the so-called elegant Laguerre-Gaussian beams. This new representation allows us to obtain the closed-form expression of a FG beam of any order propagating through a paraxial ABCD optical system by means of a simple recurrence rule, which turns out to be particularly stable even when it is applied to FG beams of very high orders (> 10(4)).     

Bessel-Gauss beams as rigorous solutions of the Helmholtz equation

The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.     

Reflectivity of uniaxial absorbing crystals

Equations for the reflectances of ordinary and extraordinary waves from the basal plane of strongly absorbing uniaxial crystals are extended to reflectances from planes parallel to the optic axis for configurations likely to be useful and convenient for experimentalists.     

Self-healing of tightly focused scalar and vector Bessel-Gauss beams at the focal plane

The property of self-healing at the focal plane for both scalar and vector Bessel-Gauss (BG) beams is investigated in the tight focusing condition. For the BG beam, which is partially obstructed at the pupil plane, the spatial intensity distribution at the focal plane is well recovered. Furthermore, recovery of not only intensity but also polarization distribution is observed for an obstructed vector BG beam. This self-healing effect for both the intensity and polarization components is recognized even when the half of the beam is obstructed by a semicircular obstacle. The effect of the size of the obstacle on recovery of polarization and intensity distribution is studied. The role of the beam size at the pupil plane is also discussed.     

Circularly polarized beams and vortex generation in uniaxial media

We deduce the expressions for the two circularly polarized components of a paraxial beam propagating along the optical axis of a uniaxial crystal. We find that each of them is the sum of two contributions, the first being a free field and the second describing the interaction with the opposite component. Moreover, we expand both components as a superposition of vortices of any order, thus obtaining a complete physical picture of the interaction dynamics. Consequently, we argue that a left-hand circularly polarized incoming beam, endowed with a circular symmetric profile, gives rise, inside the crystal, to a right-hand circularly polarized vortex of order 2. The efficiency of this vortex generation is investigated by means of a power exchange analysis. The Gaussian case is fully discussed, showing the relevant features of the vortex generation.     

Comment on "Eigenfields and output beams of an unstable Bessel-Gauss resonator"

We comment on a recent paper by D. Ling et al. [Appl. Opt. 45, 4102 (2006)]. In that paper, the authors adopted the entire matrix formalism that we established in a previous work [J. Opt. Soc. Am. A 22, 1909 (2005)] for finding the eigenmodes of an unstable Bessel resonator. Nevertheless, the results are inaccurate mainly because (a) it was overlooked that light crosses through the axicon twice in a complete round trip and (b) the numerical method used to evaluate the diffraction integral equations cannot resolve the eigenvalues and eigenfields for the given resonator configuration.