Elsevier

Optics Communications

Volume 278, Issue 1, 1 October 2007, Pages 17-22
Optics Communications

Transmittance of partially coherent cosh-Gaussian, cos-Gaussian and annular beams in turbulence

https://doi.org/10.1016/j.optcom.2007.05.039Get rights and content

Abstract

Average relative power transmittance is evaluated, by incorporating atmospheric turbulence, for partially coherent cosh-Gaussian, cos-Gaussian, Gaussian and annular beams. For all the collimated versions of these beams, against the increasing propagation length, there is a typical trend of the decrease in the relative average power transmittance with incremental drop being much less for partially coherent cos-Gaussian beams. The change in the transmittance versus the propagation length will be similar to the corresponding collimated cases, when these beams are focused at a certain focal length. Also partially coherent beams are less sensitive to propagation length changes, except for cos-Gaussian case. Partially coherent cosh-Gaussian beams exhibit a drop in the transmittance as the displacement parameter of the beam is made larger, whereas this trend is just the opposite for partially coherent cos-Gaussian beams. When examined versus the source size, for all the four types of beams, the transmittance has a similar behavior, i.e., it becomes high at small source sizes, falling with increasing source size, and following a dip, it starts to rise, eventually approaching the plane wave limit of unity. The occurrence of the dip coincides with the smallest source size for cosh-Gaussian, with the largest for cos-Gaussian, and about the same source size for Gaussian and annular beams. In general, the average relative power transmittance of coherent beam is affected much more than the partially coherent beams against the variations in source properties.

Introduction

Transmittance is a measure indicating how much optical power will be received under the given medium conditions in atmospheric optical links. The atmosphere assesses the transmission at optical frequencies mainly due to molecular, aerosol and turbulence effects. There exists a wide range of work in molecular spectroscopic aspects and the aerosol refractive indices which lead to refining the optical transmittance calculations. Comprehensive updates of these studies are provided in Refs. [1], [2]. In certain applications, atmospheric turbulence effects also shape the transmittance, so it is of interest to know the behavior of the optical windows when turbulence is taken into account. In our earlier work [3], we investigated the average intensity and power transmittance in turbulence for a partially coherent Gaussian beam.

In atmospheric turbulence, propagation characteristics of different types of incidences exhibit differences, which will influence the performance of atmospheric optical links. Cai and He examined various dark hollow [4] and elliptical Gaussian beams [5] in turbulence. We have investigated in detail the received intensity profiles in turbulence for incidences of cosh-Gaussian [6], cos-Gaussian [7], higher-order annular beams [8]. Propagation of laser beams in turbulent atmosphere is studied in detail by many researchers [9], [10], [11], [12], [13], [14], [15], [16], [17], majority of these works also involve partial coherence. In the current paper, we incorporate partial coherence into cosh-Gaussian, cos-Gaussian and annular beams and examine the relative average power transmittance in a turbulent atmospheric horizontal link. Average power transmittance for partially coherent Gaussian beam is the limiting case of our solution. We envisage that the presented results can bring more insight into the overall transmittance evaluations involving the molecular and aerosol effects, thus helping to better understand the power reception in atmospheric optical links when different types of incidences are employed.

Section snippets

Formulation

The source field expression of the lowest order generalized beam is [18]us(s)=us(sx,sy)==1NAexp(-jθ)exp-(0.5kαxsx2+jVxsx)exp-(0.5kαysy2+jVysy),where (sx, sy) designates the decomposition of the vector s into x and y components. A and θ are respectively the amplitude and the phase of the ℓth component of the source field,αx=1/(kαsx2)+j/Fx,αy=1/(kαsy2)+j/Fy.Here αsx and αsy are Gaussian source sizes, Fx and Fy are the source focusing parameters along sx and sy directions, k = 2π/λ

Results and discussion

This section provides graphical illustrations based on the numerical evaluation of Eq. (10). Note that, the intensity expressions in Eq. (10) are in Cartesian coordinates, whereas the integration is in polar coordinates. The necessary conversion is implemented during numerical integration phase. Additionally, the average vacuum intensity, 〈Iν(p, L)〉 is developed from Eq. (5) in the following manner:Iν(p,L)=Γr(p1=p2,L)|ρ0.

Although the nature of formulation in Eq. (5) allows us to evaluate the

Conclusion

In atmospheric optical links, the relative average power transmittance is examined in the presence of turbulence, when partially coherent cosh-Gaussian, cos-Gaussian and annular beam excitations are employed. It is found that all of the collimated forms of these excitations have relative average power transmittances which drop with increasing propagation lengths, the drop being much less for cos-Gaussian beam as compared with the other beams mentioned. At a fixed propagation length, all the

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