Temporal propagation characteristics of ultrashort space-time Gaussian pulses in a laser satellite communication system

Tractable analytic expressions are obtained for the temporal broadening and scintillations of a narrowband, space-time Gaussian pulse propagating through clear-air weak atmospheric turbulence in a laser satellite communication system. The temporal broadening is deduced from the {dollar}1/esp2{dollar} point of the temporal mean intensity and calculation of the temporal scintillations involves the second moment of intensity. Integral representations for the first and second moment of intensity are obtained by means of the two-frequency mutual coherence function and four-frequency cross-coherence function, respectively. Analytic approximations to these integrals are then made based on the modified von Karman spectrum model for the refractive-index fluctuations and the Hufnagel-Valley turbulence profile model.; We present the general results for a collimated Gaussian pulse and for nominal parameter values characteristic of laser satellite communication. Specific numerical examples are calculated for both upper atmosphere UAV-UAV cross-links (near field) and uplink/downlink communication propagation paths (far field).; It is shown that both the temporal broadening and temporal scintillations increase with the strength of turbulence and the outer scale. The inner scale has an insignificant effect on the temporal broadening but inner scale effects on the temporal scintillations were not included in this analysis. The temporal broadening is independent of the optical wavelength, whereas the temporal scintillations decrease with optical wavelength. Both the temporal broadening and temporal scintillations decrease with increasing pulsewidth, with the percent broadening and scintillations being substantially greater for narrow pulses than for wide pulses. In particular, pulses of the order 10-20 fsec can broaden by more than 100% and the temporal scintillation index can exceed 1, whereas wide pulses have negligible broadening and less scintillations. Furthermore, the scintillations at spatial off-axis points and at the leading/trailing edge of the pulse are greater than the on-axis scintillations. Lastly, we show that the temporal broadening and temporal scintillations for a downlink communication channel are the same as those for an uplink communication channel.