Propagation Properties Of Polychromatic Partially Coherent Decentred Laser Beams And Gaussian Beams With Spherical Aberration In Atmospheric Turbulence

The study on the propagation of laser beams through atmosphericturbulence is very important for free-space optical communication, remote sensing andtracking. It has been experimentally shown that the higher layers turbulence mightpossess structure different from the conventional Kolmogorov’s one, callednon-Kolmogorov turbulence. Laser beams produced by unstableopticalresonatorsalways have decentred field. And there are some advantages in some applications byusing broadband laser beams than monochromatic ones. Therefore, studying on thepropagation properties and the beams speading of polychromatic partially coherentdecentred laser beamsinatomosphericturbulenceisveryimportant.On theotherhand,high powerlaser beams are always with spherical aberration due to thermal effects ingeneration process or propagating to the non-ideal optical elements. So it is veryvaluable to study the energy focusability and the on-axis scintillation index Gaussianbeams with spherical aberration in atmospheric turbulence. Themainresultsaresummarized asfollows:1. Based on theextendedHuygens-Fresnelprinciple,the analytical expressionsfor the total intensity, the on-axis spectrum and thedegreeofcoherenceofpolychromat icpartiallycoherentdecentred laser beams propagating in nonKolmogorov turbulence are derived. The influence of the beam decentred parameter,the fractal constant of the atmospheric power spectrum, and the bandwidth ofspectrum on the propagation properties are studied. It is shown that, the larger is, thefarther the centre of beam gravity shifts away from the propagation axis, and the morethe degree of coherence is unsymmetrical. However, the on-axis spectrum is nearlyindependent of The influence of on the total intensity, the on-axis spectrum and the degree of coherence is non-monotonic. When=3.1, the propagation properties aremost affected by turbulence. It is mentioned that at certain propagation distances, theshifts of on-axis spectrum are the same for different values of. Furthermore, theon-axis spectral shift disappears at other certain propagation distances which areindependent of, and these propagation distances decrease due to turbulence.2. Taking the mean-squared beam width, the angular spread, the Rayleigh rangeand the turbulence distance as characteristic parameters, the spreading of partiallycoherent polychromatic decentred laser beams propagating through non-Kolmogorovturbulence is studied. The influence of the bandwidth of spectrum, the beamdecentred parameter, and the fractal constant of the atmospheric power spectrum onthe beam spreading is examined in detail. It is found that polychromatic laser beams areless sensitive to turbulence than monochromatic ones, and decentred laser beams areless sensitive to turbulence than centred ones. The larger the and are, the larger thebeam spreading is in free space, but the less the beam spreading is affected byturbulence. In turbulence laser beams with different values of will have the samedirectionality, which is quite different from the behavior in free space. The beamspreading is largest and the influence of turbulence on the beam spreading is also largestwhen is in a region about3.1. In addition, the dependence of the turbulence distanceon and is also investigated, and some interesting results are obtained.3. By using the four-dimensional (4D) computer code of the time-dependentpropagation of laser beams through atmospheric turbulence, the influence ofatmospheric turbulence on the energy focusability of Gaussian beams with sphericalaberration is studied in detail, where the mean-squared beam width, the powerinthebucket (PIB),the parameterandtheenergyStrehlratioaretakenasthecharacteristicparameters. It is shown that turbulence results in a beam spreading, and the effect ofspherical aberration on the beam spreading decreases due to turbulence. Gaussianbeams with negative spherical aberration are more affected by turbulence than thosewith positive spherical aberration. For the negative spherical aberration case, the focusposition moves to the source plane due to turbulence. It is mentioned that the influenceof turbulence on the energy focusability defined by a certain energy (i.e., PIB=63%) isvery heavy when the negative spherical aberration is very heavy. On the other hand, theinfluence of turbulence on the energy focusability defined by the energy within a givenbucket radius (i.e., mean-squared beam width) is heaviest when a certain negativespherical aberration coefficient is adopted. 4. The influence of spherical aberration on the on-axis scintillation index ofGaussian beams in atmospheric turbulence is studied by using numerical simulationmethod. It is shown that the behavior of the on-axis scintillation index σ2ISp for thenegative spherical aberration case is quite different from σ2ISp for the positivespherical aberration case. In weak turbulence, the positive spherical aberration results ina decrease of the on-axis scintillation index on propagation, but the negative sphericalaberration results in an increase of the on-axis scintillation index when thepropagationdistance z is not large. In particular, in weak turbulence there exist peaks of σ2ISp due to the hollow core in the intensity distribution, which should be avoided in practice.However, the peaks of σ2ISp disappear because the hollow core is filled up inmoderate and strong turbulence. In weak and moderate turbulence it is σ2ISp σ2ISp when z is not large, but in moderate turbulence it is σ2ISp σ2ISp when z is largeenough due to auto-compensation effect. The strong turbulence results in the differencebetween σ2ISp, σ2ISp and σ2IGsbeing not significant, where σ2IG sis the on-axisscintillation index of Gaussian beams without spherical aberration.