The Combined Effect of Jet and Atmospheric Turbulence on the Propagation of Airborne Partially Coherent Array Beams

Abstract

The exhaust from engines close to the fuselage can cause extreme turbulence and have a significant impact on the performance of airborne laser systems. In this paper, the combined effect of the jet engine and atmospheric turbulence on propagation of a Gaussian Schell-model (GSM) array beam over long distances is studied in detail. Based on the two-step propagation method, the analytical expressions of the cross-spectral density (CSD) function, mean-squared beam width and spectral degree of spatial coherence (DOC) of GSM array beams are derived. It is shown that the jet engine turbulence has a significant effect on the beam broadening even at a very short distance. As the propagation distance in the jet engine turbulence increases, the beam width is less effected by the spatial coherence. Meanwhile, the resistance of lower spatially coherent beam to the turbulence increases as the distance of the jet engine turbulence or the strength of the atmospheric turbulence increases. It is demonstrated that the effect of jet engine turbulence on the beam spreading can be equivalent to moderate or even severe atmospheric turbulence. Moreover, the DOC is a function with oscillatory phenomenon when the propagation distance is short or the strength of turbulence is low.

Propagation Characteristics of a Partially Coherent Gaussian Schell‐model Array Vortex Beam in the Joint Turbulence Effect of a Jet Engine and Atmosphere

“…In case M = 0, Equation (1) reduces to GSMA beam. [50] Figure 2 depicts the spectral density of a GSMA vortex beam in the input plane with varying N and M. We note from this figure that the beamlets of a GSMA vortex beam have a hollow core, and as N increases, the beamlet number climbs to N. Furthermore, we see that when the topological charge increases, the dark hollow core of the beamlets grows.…”

“…In this illustration, z jet is the propagation distance in jet engine region and z atm is the propagation distance in atmosphere. We consider the GSMA vortex beam described by the cross-spectral density function at the source plane (z = 0) as [37,38,50]…”

“…Under the condition of M = 0, Equa-tion (15) can be reduced to Equation ( 9), as shown in ref. [50], but notice that the double summation is used in Equation ( 9), rather than Equation (10).…”

“…The calculation parameters are 𝜆 = 632.8 nm, T n = 1.6 × 10 −9 m −2∕3 , C 2 n = 10 −14 m −2∕3 , L 0 = 0.5 m, l 0 = 0.67, L s = 1 mm, 𝜇 x = 0.7, 𝜇 y = 1.4, B = 6, 𝜎 0 = 1 + (𝜎 0 ∕𝛿 0 ) 2 . [50] In the case of 𝛽 = 0, the beam is fully incoherent and for 𝛽 = 1 the beam is fully coherent. The propagation process of the GSMA vortex beam passing through the combined jet engine exhaust induced turbulence and atmospheric turbulence is given as z = z jet + z atm .…”

“…Meanwhile, the combined effect of jet and atmospheric turbulence on the propagation of airborne partially coherent array beams has been investigated by. [50] Since jam-to-signal ratio (J/S) is the most important parameter when DIRCM jams the missile seeker, scientists search the ways to increase it. [51] Negative effects of atmosphere combining with plume on J/S is studied, [52] Beam shaping is one method to benefit from high received power and low noise features of the untraditional beams.…”