Influence Of Oceanic Turbulence On Propagation Of Laser Beams

The refraction index in seawater is not only caused by temperature fluctuations, but also by fluctuations of salinity. The fluctuation of power spectrum of oceanic turbulence is determined by refraction index fluctuation. With the development of underwater optical communications, imaging, sensor and laser radar, the further study of propagation characteristics of laser beams through water medium is especially important. On the other hand, due to the absorption and scattering of seawater, the propagation distance of laser beam in oceanic turbulence is shorter than that in atmospheric turbulence, it is much important how to obtain higher beam quality and so on. In this paper, combining the analytical expressions and numerical calculations, the three main works in this thesis are summarized as follows:1. Light propagation in the turbulent ocean(1) The spatial coherence length in oceanic turbulenceThe analytical formulae for the WSF and the spatial coherence radius of a plane wave and a spherical wave propagating through oceanic turbulence have been derived in this paper, which are valid both in weak and strong fluctuations. It has been shown that under Rytov approximation, the Kolmogorov five-thirds power law of WSF is also valid for the oceanic turbulence in the inertial range if the power spectrum of oceanic turbulence proposed by Nikishov, and the salinity-induced turbulence is stronger than temperature-induced turbulence. Curves of the WSF versus three oceanic parameters are shown. It can be seen that both for plane waves and spherical waves, WSF increases as w and χT increase and as ε decreases. In addition, WSF of a plane wave is larger than that of a spherical wave. In this part, to the coherence degradation of laser beams aspect, the spatial coherence radius can be represented the strength of oceanic turbulence. Changes of the spatial coherence radius versus three oceanic parameters are shown. It can be seen that both for plane waves and spherical waves, ρ0 decreases as w and χT increase and as ε decreases. In addition, the difference of ρ0 between a spherical wave and a plane wave is that the spatial coherence radius of a spherical wave is larger than that of a plane wave. Particularly, the case of w=0 is studied in detail as follows:on the one hand, if the water is not isothermal, the power spectrum is invalidation. On the other hand, if the water is isothermal, the gradient of mean temperature is null and the power spectrum is equal to zero. It is essential to obtain a new expression which is valid in isothermal case. In this paper, using the rate of dissipation of mean-squared salinity, we obtained this expression and edited the range of w, i.e., w∈[-5,0).(2) Phase fluctuations(i) Angle of arrival (AOA) fluctuations in oceanic turbulenceIn this paper, we get the analytic expressions of phase structure function and AOA fluctuations for plane and spherical wave models of oceanic turbulence. We give a comparison of results of AOA fluctuations calculated by the analytical expressions obtained in this paper and the numerical calculations of definitions. It is shown that these analytical expressions are accurate. The turbulent flow contains eddies of various sizes, and the energy is transferred from larger eddies to smaller eddies until it is drained out by viscous dissipation. Kolmogorov’s hypothesis asserts that for large Reynolds numbers (i.e., inertial subrange) the small scale structure of turbulence is statistically steady, isotropic and locally homogeneous, and independent of the detailed structure of the large scale components of turbulence. In our previous work, we defined the active region and strongly stratified region. The active region has small scales inducing weak turbulence while the strongly stratified water can be regarded as stable and deeper boundary layer, including abyssal region, where has large scales leading to strong turbulence. In this paper, to the coherence degradation of laser beams aspect, the spatial coherence radius can be represented the strength of oceanic turbulence.(ii) Beam wander on laser beam propagating through oceanic turbulenceIn this paper, based on the oceanic power spectrum, we study the beam wander effect with analytical and numerical methods in weak fluctuation theory. The results indicate that the beam wander increases as ε decreases, χT increases, and salinity-induced dominates both in collimated-beam and focused-beam cases. The difference of beam wander between focused and collimated beam is that a collimated beam has a smaller value. Besides, the smaller beam radius W0 at transmitter leads to the stronger beam wander effect. In addition, based on the dimensionless quantity Bw, the relation between beam wander and the turbulence-induced beam spot size is investigated. It is shown that the beam wander of collimated beam has the less influence on turbulence-induced beam spot size compared to that of focused beam. Particularly, according to the definition of the relative beam wander, it is shown that the relative beam wander is small when the value of beam curvature parameter at transmitter (?)0 is close to 1 (i.e., (?)�'1).(3) Intensity fluctuations(i) Rytov varianceThe Rytov variance in oceanic turbulence is an indispensable quantity that can distinguish the weak, moderate and strong fluctuation oceanic turbulent conditions, and the quantity is widely used as a measure of the strength of turbulence. Until now, there has been no paper concerning how to distinguish the oceanic turbulent strength quantitatively. Thus, similar to the Rytov variance in atmospheric turbulence, the expression of Rytov variance in oceanic turbulent case is obtained.(ii) Scintillation indexThe analytical expressions of radial and longitudinal components of scintillation index are deduced under weak turbulence regime for the first time. The influences of radial component of scintillation index with the off-axis distance, propagation distance and three main oceanic parameters (i.e., the ratio of temperature to salinity contribution to the refractive index spectrum w, and the rate of dissipation of the mean squared temperature χT and the rate of dissipation of the turbulent kinetic energy ε) for Gaussian wave are investigated. The radial component of scintillation index for Gaussian wave is evaluated in oceanic turbulence. It is shown that the radial component of scintillation index increases as the off-axis distancer, propagation distance L, the ratio of temperature to salinity contribution to the refractive index spectrum w, and the rate of dissipation of the mean squared temperature χT increase while the radial component of scintillation index increases as the rate of dissipation of the turbulent kinetic energy ε decreases. Similar to radial component of scintillation index, the longitudinal component of scintillation index increases as propagation distance L, the relative strength of temperature and salinity w and the rate of dissipation of the mean squared temperature χT increase, and the rate of dissipation of the turbulent kinetic energy ε decreases. Besides, the longitudinal component of scintillations increases more drastically for plane wave than others, which indicates the plane wave is affected significantly at the fixed turbulent strength. The longest weak turbulence distance for a plane wave is shorter than that for a Gaussian or spherical wave.2. Gaussian array beams propagation in oceanic turbulence(1) Average intensity of M×N Gaussian array beams in oceanic turbulenceLaser array beams have already been attracted much attention for which played an important role in obtaining higher quality and high power laser system. Although the wide applications with laser array beam, it is less explored how to focus the intensity at one position at the receiver plane. Introducing the phase front radius of curvature F0 in this paper, and deducing the analytical expression of average intensity of M x N Gaussian array beams in oceanic turbulence, it is shown that the intensity can be focused at the same point. It is found that both for coherent and incoherent combinations, the average intensity is affected significantly by oceanic turbulence. Based on the definition of relative average intensity, the intensity influenced by oceanic turbulence for incoherent combination is less sensitive than the coherent combination.(2) Beam spreading of oceanic turbulence on propagation of Gaussian array beamsBased on the RMS beam width and the effective radius of curvature, the beam spreading of Gaussian array beams propagating through oceanic turbulence is investigated. The analytical expression of oceanic parameter F is deduced for the first time. Comparing the results of analytical expression and the numerical calculations of integration, it is found that the analytical expression is valid in oceanic turbulence. Then, based on the oceanic parameter, the analytical expression of Rms beam width is obtained. Besides, according to the general formulae of the second moments of partially coherent beams propagating through turbulence, the analytical expression of effective radius of curvature is given. The strength of turbulence determines the value of effective radius of curvature and in reverse. The stronger oceanic turbulence induced smaller effective radius of curvature and wider beam spreading. Furthermore, the effective radius of curvature can be described the strength of turbulence.3. Influences of ultra-short pulses propagating through oceanic turbulenceIn this paper, the results of three approaches of the correlation function of the complex phase perturbed by oceanic turbulence is shown:(1) The quadratic approximation in Rytov’s phase structure function (i.e., (exp[Ψ(r1,r,L;ω1)+Ψ*(r2,r,L;ω2)]>m(?)exp[-(r1-r2)2/ρ02]) (2) the second order approximation (i.e., Jo (κζ|r2-r1|)≈1-κ2ζ2|r2-r1|2/4) and (3) expanding the zero-order Bessel function directly. It is clear that a significant difference among three approaches occurs:the new approach is much smaller than the second order approximation and much close to quadratic approximation. Based on the quantity of Rytov variance in oceanic turbulence, we investigate the changes of on-axis relative pulse broadening of ultra-short pulses with propagation length, wavelength, initial pulse half-width and initial Gaussian beam radius from free space to strong turbulent regions. It is shown that the on-axis relative pulse broadening decreases as initial pulse half-width increases, and increases as propagation length, wavelength and initial Gaussian beam radius increases. In this paper, the on-axis turbulent effective coefficient is described as the single factor of pulse broadening by oceanic turbulence. The on-axis turbulent effective coefficient decreases as the initial pulse half-width increases and increases as Gaussian beam radius increases. Besides, Gaussian beam radius increases large enough, the on-axis turbulent effective coefficient doesn’t change any more.By these three aspects, we studied light propagation in the turbulent ocean, the effects of laser beam propagating through oceanic turbulence and influences of ultra-short pulses propagating through oceanic turbulence. These results can be understood laser beam propagation through oceanic turbulence, and the findings benefit to offer theoretic in applications for underwater communicating, imaging and sensing systems.