Intensity-moments characterization of general pulsed paraxial beams with the Wigner distribution function

On the basis of the space-time Wigner distribution function (STWDF), we use the matrix formalism to study the propagation laws for the intensity moments of quasi-monochromatic and polychromatic pulsed paraxial beams. The advantages of this approach are reviewed. Also, a least-squares fitting method for interpreting the physical meaning of the effective curvature matrix is described by means of the STWDF. Then the concept is extended to the higher-order situation, and what me believe is a novel technique for characterizing the beam phase is presented. (C) 1999 Optical Society of America [S0740-3232(99)001009-1].

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.

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.

Fields of apertured polychromatic laser beams with Gaussian and Hermite-Gaussian transverse modes

Starting from the Huygens-Fresnel diffraction integral, the field expressions of apertured polychromatic laser beams with Gaussian and Hermite-Gaussian transverse modes are derived. Influence of the bandwidth on the intensity distributions of the laser beams is analyzed. It is found that when the bandwidth increases, the amplitudes and numbers of the intensity spikes decrease and beam uniformity is improved in the near field and the width of transverse intensity distribution of the apertured beams decreases in the far field. Thus, the smoothing and narrowing effects can be achieved by increasing the bandwidth. Also, these effects are found in the laser beams with Hermite-Gaussian transverse modes as the bandwidth increases.(c) 2006 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.

The tunable negative refractive index in granular composite

The effective refractive index of a kind of granular composite, which consists of granular metallic and magnetic inclusions with different radius embedded in a host medium, is theoretically investigated. Results show that for certain volume fractions of these two inclusions, the negative permittivity peak shifts to low frequency and the peak value increases with increasing radius ratio of the radius of magnetic granulae to that of metallic granulae. Simultaneously, peak value of permeability decreases with the radius ratio, and value peak shifts to high frequency with increasing volume fraction of magnetic inclusion. Therefore, the radius ratio can affect the effective refractive index considerably, and it is found that by adjusting the radius ratio, the refractive index may change between negative and positive values for certain volume fractions of the two inclusions. (c) 2005 Elsevier B.V. All rights reserved.