Physical conditions for sources radiating a cosh-Gaussian model beam

Abstract

Tianjin University of Technology and Springer-Verlag Berlin Heidelberg 2011 C Based on the coherence theory of diffracted optical field and the model for partially coherent beams, analytical expressions for the cross-spectral density and the irradiance spectral density in the far zone are derived, respectively. Utilizing the theoretical model of radiation from secondary planar sources, the physical conditions for sources generating a cosh-Gaussian (CHG) beam are investigated. Analytical results demonstrate that the parametric conditions strongly depend on the coherence property of sources. When almost coherence property is satisfied in the source plane, the conditions are the same as those for fundamental Gaussian beams; when partial coherence or almost incoherence property is satisfied in the spatial source plane, the conditions are the same as those for Gaussian-Schell model beams. The results also indicate that the variance of cosine parameters has no influence on the conditions. Our results may provide potential applications for some investigations such as the modulations of cosh-Gaussian beams and the designs of source beam parameters.In recent years, the quantitative description and quality control of laser beams have attracted much attention, because of the invaluable applications to many fields such as remote sensing, objective tracking and laser ladar. On the other hand, experimental methods for generating some special distributed beams have been reported and have been applied in some works, for example, optical measurements, free space optical communications, etc. Based on the Helmholtz equations, Casperson et al [1,2] derived one particular solution of Hermitesine-Gaussian model beams, by disposing and solving the wave equations. In the same report, they further pointed out that this class of beam could be produced in the experimental aspect, by performing the optical systems involving a sineGaussian aperture and a laser cavity [3] . Among the existing solutions of such laser beams, the cosh-Gaussian (CHG) beam has shown many advantages, and the flat-topped Gaussian and hollow Gaussian beams with certain spatial intensity distributions at the output plane have been obtained by modulating parameters of CHG beams [4,5] , in order to trap small particles. Based on the second-order statistical moments of apertured laser beams, B. Lu et al [6,7] studied the beam factor of CHG beams. In free-space optical communications, the issue that how to control the quality of laser beams in atmosphere has become a hot-spot of recent researches [8,9] . In * E-mail: lijiafeifei@sina.com addition, the sources radiating highly directional lasers have found wide applications, such as laser guidance, projective aiming, remote sensing and free-space optical communications. Wolf et al [10] have taken detailed researches on the topic. Subsequently, Korotkova et al [11] further extended the analytical condition for generating scalar Gaussian Schell-model beams into the one for radiating the stochastic electromagnetic beams with ...