Detector of Optical Vortices as the Main Element of the System of Data Transfer: Principles of Operation, Numerical Model, and Influence of Noise and Atmospheric Turbulence

<table>Two-dimensional probability density <svg height="16.625" id="M396" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 65.324997 16.625" width="65.324997" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><use xlink:href="#x1D70C"></use></g><g transform="matrix(.017,-0,0,-.017,9.225,12.138)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,15.106,12.138)"><use xlink:href="#x1D43C"></use></g>
<g transform="matrix(.012,-0,0,-.012,22.538,16.213)"><use xlink:href="#x1D45F"></use></g><g transform="matrix(.012,-0,0,-.012,27.559,16.213)"><use xlink:href="#x30"></use></g>
<g transform="matrix(.017,-0,0,-.017,33.888,12.138)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,40.585,12.138)"><use xlink:href="#x1D43C"></use></g>
<g transform="matrix(.012,-0,0,-.012,48.025,16.213)"><use xlink:href="#x1D45F"></use></g><g transform="matrix(.012,-0,0,-.012,53.046,16.213)"><use xlink:href="#x31"></use></g>
<g transform="matrix(.017,-0,0,-.017,59.388,12.138)"><use xlink:href="#x29"></use></g>
</svg> obtained with <svg height="15.6875" id="M397" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 98.487503 15.6875" width="98.487503" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><use xlink:href="#x1D446"></use></g>
<g transform="matrix(.012,-0,0,-.012,8.225,15.475)"><use xlink:href="#x210E"></use></g><g transform="matrix(.012,-0,0,-.012,14.365,15.475)"><use xlink:href="#x1D465"></use></g>
<g transform="matrix(.017,-0,0,-.017,26.363,11.4)"><path d="M537 353q-54 -70 -120 -70q-47 0 -137 43q-78 38 -108 38q-55 0 -91 -57l-31 33q51 74 122 74q45 0 137 -44q76 -37 108 -37q55 0 91 57zM537 168q-54 -70 -120 -70q-47 0 -137 43q-78 38 -108 38q-55 0 -91 -57l-31 33q51 74 122 74q45 0 137 -44q76 -37 108 -37
q55 0 91 57z" id="x2248"></path></g><g transform="matrix(.017,-0,0,-.017,41.049,11.4)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,49.209,11.4)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,53.085,11.4)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g><g transform="matrix(.017,-0,0,-.017,61.244,11.4)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,69.403,11.4)"><use xlink:href="#x34"></use></g><g transform="matrix(.017,-0,0,-.017,77.563,11.4)"><use xlink:href="#x1D45F"></use></g>
<g transform="matrix(.012,-0,0,-.012,84.75,15.475)"><use xlink:href="#x30"></use></g><g transform="matrix(.012,-0,0,-.012,90.461,15.475)"><use xlink:href="#x1D435"></use></g>
</svg>, <svg height="15.4" id="M398" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 91.675003 15.4" width="91.675003" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D440"></use></g>
<g transform="matrix(.012,-0,0,-.012,17.412,15.187)"><use xlink:href="#x6F"></use></g><g transform="matrix(.012,-0,0,-.012,23.362,15.187)"><use xlink:href="#x75"></use></g><g transform="matrix(.012,-0,0,-.012,29.537,15.187)"><use xlink:href="#x74"></use></g><g transform="matrix(.012,-0,0,-.012,33.095,15.187)"><use xlink:href="#x65"></use></g><g transform="matrix(.012,-0,0,-.012,38.152,15.187)"><use xlink:href="#x72"></use></g>
<g transform="matrix(.017,-0,0,-.017,47.9,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,62.604,11.112)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,70.763,11.112)"><use xlink:href="#x1D45F"></use></g>
<g transform="matrix(.012,-0,0,-.012,77.938,15.187)"><use xlink:href="#x30"></use></g><g transform="matrix(.012,-0,0,-.012,83.649,15.187)"><use xlink:href="#x1D435"></use></g>
</svg>, and different values of <svg height="15.4" id="M399" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 25.674999 15.4" width="25.674999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D449"></use></g>
<g transform="matrix(.012,-0,0,-.012,12.675,15.187)"><use xlink:href="#x1D451"></use></g><g transform="matrix(.012,-0,0,-.012,19.279,15.187)"><use xlink:href="#x30"></use></g>
</svg>, <svg height="15.4" id="M400" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 25.674999 15.4" width="25.674999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D449"></use></g>
<g transform="matrix(.012,-0,0,-.012,12.675,15.187)"><use xlink:href="#x1D451"></use></g><g transform="matrix(.012,-0,0,-.012,19.279,15.187)"><use xlink:href="#x31"></use></g>
</svg>, <svg height="15.25" id="M401" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 17.85 15.25" width="17.85" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D43F"></use></g>
<g transform="matrix(.012,-0,0,-.012,9.763,15.187)"><use xlink:href="#x1D439"></use></g>
</svg>, and <svg height="11.425" id="M402" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.025 11.425" width="11.025" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><use xlink:href="#x394"></use></g>
</svg>.</table>

International Journal of Optics

fig10

Figure 10

Figure 10: Detector of Optical Vortices as the Main Element of the System of Data Transfer: Principles of Operation, Numerical Model, and Influence of Noise and Atmospheric Turbulence 

Figure 10 | Detector of Optical Vortices as the Main Element of the System of Data Transfer: Principles of Operation, Numerical Model, and Influence of Noise and Atmospheric Turbulence 