Scintillation Characteristics And Energy Focusability Of Annular Beams Propagating Through Atmospheric Turbulence Along A Slanted Path

Scintillations of an optical beam in atmospheric turbulence degrade ratio of signal to noise and will increase bit error rate. The scintillation is detrimental to the performance of free-space optical communication systems, remote sensing systems and imaging systems, etc. Atmospheric turbulence will degrade the energy focusability of laser beams, and, as a consequence, the turbulence-induced spatial broadening of the beam is a limiting factor in most applications. An annular beam is created when a Gaussian beam propagates through an annular aperture, which exists in many telescopes. A telescope is used in both the transmitter and the receiver in free-space optical communication systems and the transmitter in laser weapon systems. In addition, high-power lasers use unstable optical resonators as resonant cavities which produce an annular beam. The propagation of laser beams through atmospheric turbulence along a slanted path is often encountered in many applications, such as free-space optical communications and laser weapons. Therefore, it is very interesting to study scintillation characteristics and energy focusability of annular beams propagating through atmospheric turbulence along a slanted path. The main works of this thesis are summarized as follows:1. The energy focusability of annular beams propagating through atmospheric turbulence along a slanted path is studied in detail by using numerical simulation method. The relative mean-squared beam width wR, the β parameter and the energy Strehl ratio（SR_E） are adopted to characterize the influence of turbulence on the energy focusability which defined by a certain energy and the energy within a given bucket radius, respectively. It is shown that, in general, the influence of turbulence on the energy focusability is large for thick annular beams, and is small for thin annular beams. However, it is found out that the laws of wR, β parameter and SR_E versus the obscure ratio ε of annular beams are quite different, i.e., wR decreases monotonically as ε increases, while changes of β parameter and SR_E versus ε are not monotonic. There exists a maximum of β for thick annular beams, and there exists a minimum of β for thin annular beams. But there only exists a maximum of SR_E for thin annular beams. The values of ε at which β reaches its maximum or minimum and SR_E reaches its maximum are nearly independent of the zenith angle of the slanted path. In practice, the minimum of β and the maximum of SR_E may be used, but the maximum of β should be avoided.Furthermore, taking the encircled-power width defined by the power 86.5% in the bucket as the characteristic parameter, the energy focusability of annular beams propagating through atmospheric turbulence along a slanted path is studied by using the numerical simulation method. It is shown that the energy focusability becomes worse as the obscure ratio and the zenith angle increase, and the influence of turbulence on the energy focusability increases when the zenith angle increases. However, when the obscure ratio is large or small, the influence of turbulence on the energy focusability decreases as the obscure ratio increases; when the obscure ratio is middling, the influence of turbulence on the energy focusability is nearly unchanged versus the obscure ratio. In addition, it is found that the law of the influence of turbulence on the spreading of annular beams is different if the percentage of the power in the bucket is different. The results obtained in this thesis are useful for applications.2. Scintillation characteristics of annular beams propagating through atmospheric turbulence along a slanted path are studied by using numerical simulation method. It is found that, when the zenith angle is not large enough, the saturation phenomenon of scintillation index never appears even if the propagation distance is large enough, which is quite different from the behavior for the horizontal propagation case. However, under the same condition（i.e., the zenith angle is not large enough）, the on-axis scintillation index still approaches an asymptotical value, which increases as the zenith angle increases, and depends on the obscure ratio of annular beams. Furthermore, the relation of the on-axis scintillation index between annular beams and flat-topped beams is also examined in this paper. It is shown that their relation will change as the zenith angle changes. The results obtained in this thesis are explained in physical terms, which are very useful for the ground-to-satellite and ground-airborne-to-space optical communications.3. The characteristics of annular beams propagating through atmospheric turbulence along a downlink path and an uplink path are studied. It is found that in downlink the influence of atmospheric turbulence on the characteristics is quite different from that in uplink because of the altitude-dependent index structure constant. It is shown that, when the zenith angle θ is not large enough, it is always σ_Iup²>σ_Idown² on propagation whatever the value of the obscure ratio ε is, where σ_Iup² and σ_Idown² are the on-axis scintillation index in uplink and downlink respectively. However, when θ is large enough, σ_Idown² is close to σ_Iup² as the propagation distance z increases, and σ_Iup² and σ_Idown² overlap each other as ε increases. Furthermore, as z increases, σ_Iup² approaches an asymptotical value when θ is not large enough, and the saturation phenomenon of σ_Iup² appears when θ is large enough. But the asymptotical value and the saturation phenomenon of σ_Idown² never appear. On the other hand, the energy focusability in downlink is better than that in uplink, and the difference of energy focusability between a downlink and an uplink increases with increasing θ or decreasing ε. In addition, indownlink there may exist sidelobes of intensity distributions when θ is not large enough, but the sidelobes never appear in uplink. The results obtained in this thesis are very useful for optical communications and some military applications.