Bessel–Gauss photon beams with fractional order vortex propagation in weak non-Kolmogorov turbulence

WemodeltheeffectsofweakfluctuationsontheprobabilitydensitiesandnormalizedpowersofvortexmodelsfortheBessel–Gaussphotonbeamwithfractionaltopologicalchargeintheparaxialnon-Kolmogorovturbulencechannel.Wefindthatprobabilitydensityofsignalvortexmodelsisafunctionofdeviationfromthecenterofthephotonbeam,andthefartherawayfromthebeamcenteritis,thesmallertheprobabilitydensityis.Forfractionaltopologicalcharge,theaverageprobabilitydensitiesofsignal/crosstalkvortexmodesoscillatealongthebeamradiusexceptthehalf-integerorder.Asthebeamwaistofthephotonsourcegrows,theaverageprobabilitydensityofsignalandcrosstalkvortexmodesgrowtogether.Moreover,thepeakoftheaverageprobabilitydensityofcrosstalkvortexmodesshiftsoutwardfromthebeamcenterasthebeamwaistgetslarger.Theresultsalsoshowthatthesmallerindexofnon-Kolmogorovturbulenceandthesmallergeneralizedrefractive-indexstructureparametermayleadtothehigheraverageprobabilitydensitiesofsignalvortexmodesandloweraverageprobabilitydensitiesofcrosstalkvortexmodes.Lower-coherenceradiusorbeamwaistcangiverisetolessreductionofthenormalizedpowersofthesignalvortexmodes,whichisoppositetothenormalizedpowersofcrosstalkvortexmodes.