Atmospheric propagation of space-fractional Gaussian-beam waves in a FSO communication system

Abstract

We present a novel, self-consistent analytical model of Gaussian-beam propagation through the atmospheric turbulence by solving the paraxial wave equation in a fractional-dimension space of dimension D , in the range 2 &lt; D ≤ 3, corresponding to the effective spatial dimension experienced by the beam under given turbulent conditions in a free space optical (FSO) communication system. The well-known refractive index structure parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> ) has been mapped from D = 2.668 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>≈</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>13</mml:mn> </mml:mrow> </mml:msup> </mml:math> , strong fluctuations) to D = 2.999 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>≈</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:math> , weak fluctuations) in our simple analytical model, whereas D = 3 corresponds to the ideal case of free-space propagation under zero turbulence. Finally, an optimization problem is developed to mitigate the effects of atmospheric turbulence, leading to efficient transceiver design for the FSO communication system to ensure the reliability of links under varying atmospheric turbulence.