The propagation of a Lorentz-Gauss beam in turbulent atmosphere is investigated. Based on the extended Huygens-Fresnel integral and the Hermite-Gaussian expansion of a Lorentz function, analytical formulae for the average intensity and the effective beam size of a Lorentz-Gauss beam are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of a Lorentz-Gauss beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of a Lorentz-Gauss beam in turbulent atmosphere are also discussed in detail.

Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere.

Based on the generalized Huygens-Fresnel integral and the Hermite-Gaussian expansion of a Lorentz distribution, analytical expressions for the mutual coherence function, the effective beam size, and the spatial complex degree of coherence of a partially coherent Lorentz-Gauss beam through a paraxial and real ABCD optical system are derived, respectively. As a numerical example, the focusing of a partially coherent Lorentz-Gauss beam is considered. The normalized intensity distribution, the effective beam size, and the spatial complex degree of coherence for the focused partially coherent Lorentz-Gauss beam are numerically demonstrated in the focal plane. The influence of the spatial coherence length on the normalized intensity distribution, the effective beam size, and the spatial complex degree of coherence is mainly discussed.

Propagation of a partially coherent Lorentz-Gauss beam through a paraxial ABCD optical system.

A radial phased-locked (PL) Lorentz beam array provides an appropriate theoretical model to describe a coherent diode laser array, which is an efficient radiation source for high-power beaming use. The propagation of a radial PL Lorentz beam array in turbulent atmosphere is investigated. Based on the extended Huygens-Fresnel integral and some mathematical techniques, analytical formulae for the average intensity and the effective beam size of a radial PL Lorentz beam array are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of a radial PL Lorentz beam array in turbulent atmosphere are numerically calculated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of a radial PL Lorentz beam array in turbulent atmosphere are discussed in detail.

Propagation of a radial phased-locked Lorentz beam array in turbulent atmosphere

Based on the generalized Huygens–Fresnel integral, propagation of partially coherent Lorentz and Lorentz–Gauss beams through a paraxial ABCD optical system in a turbulent atmosphere was investigated. Analytical propagation formulae were derived for the cross-spectral densities of partially coherent Lorentz and Lorentz–Gauss beams. As an application example, the focusing properties of partially coherent Gaussian, Lorentz and Lorentz–Gauss beams in a turbulent atmosphere and in free space were studied numerically and comparatively. It is found that the focusing properties of such beams are closely related to the initial coherence length and the structure constant of turbulence. By choosing a suitable initial coherence length, a partially coherent Lorentz beam can be focused more tightly than a Gaussian or Lorentz–Gauss beam in free space or in a turbulent atmosphere with small structure constant at the geometrical focal plane.

Propagation of partially coherent Lorentz and Lorentz–Gauss beams through a paraxial ABCD optical system in a turbulent atmosphere

Based on the Huygens-Fresnel integral and the relationship of Lorentz distribution and Hermite-Gauss function, the average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence have been investigated by using numerical examples. The influences of beam parameters and oceanic turbulence on the propagation properties are also discussed in details. It is shown that the partially coherent Lorentz-Gauss beam with smaller coherence length will spread faster in oceanic turbulence, and the stronger oceanic turbulence will accelerate the spreading of partially coherent Lorentz-Gauss beam in oceanic turbulence.

Average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence

Diode lasers develop very fast and are widely used in various optical equipment. Diode laser sources produce fields that
show fundamental variations with respect to the canonical Gaussian beam. A partially coherent Lorentz model is
employed to describe the far field of a single mode diode laser beam. This paper is concerned with laser junctions
significantly narrower than the wavelength. Two lenses system are placed in front of the laser diode, so that the
diverging beam is transformed into a converging beam. The across spectral density function in the plane perpendicular to
the diode junction is considered in detail, and subsequently employed to predict the light intensity at various beam cross
sections near the focus by using the generalized Huygens diffraction integral. The intensity profile at a focused spot
produced by a partially coherent Lorentz beam is investigated and compared with that of Gaussian Schell-model beam. It
is shown that it has a simple form but fairly describes the optical field in the focal region. The theoretical results are well
fit to the practical results in this model and the variations between theory and the experiments are quite less than that of
in Gaussian beams. Since Gaussian beams have a minimum uncertainty field, i.e. it possesses the minimum achievable
angular spreading once the spatial extension is fixed. Since diode lasers produce highly diverging fields, a Gaussian
description for the transverse fields fails. In this case, our results show that partially coherent Lorentz model is a better
approximation, and the numerical simulation and discussions are given in detail.

Jiong Yang

Papers

Focusing of diode laser beams : a partially coherent Lorentz model