Free Space Optical System Performance for a Gaussian Beam Propagating Through Non-Kolmogorov Weak Turbulence

Abstract

Atmospheric turbulence has been described for many years by Kolmogorov's power spectral density model because of its simplicity. Unfortunately several experiments have been reported recently that show Kolmogorov theory is sometimes incomplete to describe atmospheric statistics properly, in particular in portions of the troposphere and stratosphere. It is known that free space laser system performance is limited by atmospheric turbulence. In this paper we use a non-Kolmogorov power spectrum which uses a generalized exponent instead of constant standard exponent value 11/3 and a generalized amplitude factor instead of constant value 0.033. Using this spectrum in weak turbulence, we carry out, for a Gaussian beam propagating along a horizontal path, analysis of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">term</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">beam</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spread,</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scintillation,</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">probability</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">of</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fade,</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mean</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">signal</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">to</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">noise</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ratio</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mean</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bit</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">error</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rate</i> as variation of the spectrum exponent. Our theoretical results show that for alpha values lower than alpha = 11/3, but not for alpha close to alpha = 3, there is a remarkable increase of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scintillation</i> and consequently a major penalty on the system performance. However when alpha assumes values close to alpha = 3 or for alpha values higher than alpha = 11/3 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scintillation</i> decreases leading to an improvement on the system performance.