Beam In non-Kolmogorov Turbulence Research Articles

Properties of a Partially Coherent Sine Beam in Non-Kolmogorov Turbulence

Properties of a Partially Coherent Sine Beam in Non-Kolmogorov Turbulence

Twisted splitting and propagation factor of superimposed twisted Hermite-Gaussian Schell-model beams in turbulent atmosphere

We believe this to be a new superposition twisted Hermite-Gaussian Schell-model (STHGSM) beam hat is proposed. Analytic formulas for the intensity distribution and propagation factor of the STHGSM beam in non-Kolmogorov turbulence are derived by utilizing the generalized Huygens-Fresnel principle (HFP) and the Wigner function. The evolution characteristics of STHGSM beams propagating are numerically calculated and analyzed. Our findings indicate that the light intensity of the STHGSM beam gradually undergoes splitting and rotation around the axis during propagation through non-Kolmogorov turbulence, eventually evolving into a diagonal lobe shape at a certain distance of transmission. The anti-turbulence capability of the beam strengthens with higher beam order or twist factor values.

Beam wander analysis for Gaussian beams in non-Kolmogorov turbulence with its structure constant anchored on the outer scale

In this paper, we show the impact of the outer scale on beam wander for laser beam propagation in non-Kolmogorov turbulence. The analysis is based on a new relation between non-Kolmogorov and Kolmogorov structure constants anchored on the outer scale. This approach is based on a measurable physical entity, the outer scale, and it insures the total power of the fluctuations of the refractive index is conserved when the power law changes.

Beam Quality Factor of Partially Coherent Airy Beam in Non-Kolmogorov Turbulence

A universal formula of the beam quality factor for a partially coherent Airy (PCA) beam in non-Kolmogorov turbulence has been investigated. Results of numerical simulation display that expanding the internal scales of non-Kolmogorov turbulence is good for decreasing the beam quality factor of a PCA beam. Another benefit of reducing the beam quality factor is decreasing the generalized structure constant and the outer scales of non-Kolmogorov turbulence. Similarly, the quality factor decreases with increasing transverse scale of a PCA beam. In the meantime, decreasing a laser beam’s coherence length also leads to the quality factor’s degeneration. What is more, the beam quality factor reaches the maximum value as the generalized exponent parameter of the turbulence is 3.1.

Propagation of a Hermite-cos-Gaussian correlated Schell-model beam in non-Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle, the cross-spectral density of a Hermite-cos-Gaussian correlated Schell-model (HcGCSM) beam propagating in non-Kolmogorov turbulence is derived in theory, and the intensity distribution and coherence properties of a HcGCSM beam propagation in atmospheric turbulence and free space are studied and compared by using numerical simulations. It is found that multiple beam spots of a HcGCSM beam propagation in atmospheric turbulence will combine with each other at the long distance, and the combination properties of multiple beam spots are related with initial beam parameters and strength of atmospheric turbulence. It is also found that spectral degree of coherence of a HcGCSM beam propagation in atmospheric turbulence will decrease faster than the beam propagation in free space as |r2−r1| increases

Near and far field propagation properties of hollow Gaussian beam in non-Kolmogorov turbulence

Based on the Hypergeometric function properties, the analytical expression for the average intensity of Hollow Gaussian beam (HGB) propagating through non-Kolmogorov turbulence is derived. In the near field, influences of generalized refractive-index structure parameter C˜n2, generalized exponent α, beam waist w0 and order of beam n on the dark size of HGB are studied. It is found that changes of dark size with C˜n2, w0, n are monotonic, i.e., dark size decreases as C˜n2 increases, as w0 and n decrease. Besides, the dependence of dark size on α is not monotonic and the dark size is the smallest when α=3.11. In addition, effect of the aforementioned parameters on the spreading of laser beam is investigated in the far filed. It is shown that the beam spreads more seriously for a higher generalized refractive-index structure parameter, a smaller beam waist, a lower beam order, and generalized exponent located at α=3.11.

Propagation properties of a partially coherent four-petal Lorentz–Gauss beam in non-Kolmogorov turbulence

The model of a partially coherent four-petal Lorentz–Gauss beam generated by the Gaussian Schell-model source was first introduced. The cross-spectral density function of a partially coherent four-petal Lorentz–Gauss beam propagating in non-Kolmogorov turbulence was derived by using the extended Huygens–Fresnel integral. The spreading and coherence properties of a partially coherent four-petal Lorentz–Gauss beam propagating in non-Kolmogorov turbulence were studied. The results show that such a beam propagating in non-Kolmogorov turbulence with either larger , smaller , larger , or smaller will lose the four-petal profile distribution and evolve into a solid beam with Gaussian-like distribution more rapidly as the propagation distance increases. The results also show that the spectral degree of coherence of a partially coherent four-petal Lorentz–Gauss beam between two points and will decrease as the distance of two points increases in the far field.

Scintillation index of flat-topped beam through non-Kolmogorov turbulence

The mathematical formula of off-axis scintillation for flat-topped beam through non-Kolmogorov atmospheric turbulence is derived using the generalized non-Kolmogorov spectrum model and the equivalent structure constant based on the Born and Rytov perturbation methods. The variations of the off-axis scintillation at the receiver plane is analyzed comprehensively versus the radial distance. The results can correctly reduce to the existing off-axis intensity fluctuations of Gaussian beams in non-Kolmogorov turbulence. It is indicated that flat-topped beams possess much smaller off-axis scintillation indexes than that of Gaussian beams at large radial distance and the scintillation of flat-topped beam will suffer invariability even descend before increasing with the increment of radial distance. These results can be applied to research of flat-topped laser communication.

Propagation factor and beam wander of electromagnetic Gaussian Schell-model array beams in non-Kolmogorov turbulence

The propagation formulae for the propagation factor (known as M2-factor) and beam wander of electromagnetic Gaussian Schell-model (EGSM) array beams in non-Kolmogorov turbulence are derived by using the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function. The results indicate that the M2-factor and beam wander depend on the beam parameters and turbulence parameters, and the relative M2-factor has a maximum when the generalized exponent parameter α is equal to 3.1. Otherwise, the changes of the separation distances (x0, y0) have great influence on the relative M2-factor. The relative beam wander increases rapidly when 3<α<3.2; however, it increases slowly when 3.2<α<4. It is also shown that the beam spreading of EGSM array beams is more affected by turbulence than the root mean square beam wander.

截断光束在非Kolmogorov湍流中的扩展区域

截断光束在非Kolmogorov湍流中的扩展区域

Propagation properties of partially coherent Lommel beams in non-Kolmogorov turbulence

Based on generalized Huygens–Fresnel principle, the analytical expressions of the partially coherent Lommel beams propagating in turbulent atmosphere are derived. The propagation properties of vortex mode intensity (including mode probability density and crosstalk probability density) of partially coherent Lommel beam in non-Kolmogorov turbulence are investigated in this paper. The research results show that coherence width of partially coherent Lommel beam plays a key role to determine the mode intensity in the process of propagation. The poor coherence of source beams leads to serious dispersion of spiral spectrum distribution. It is worth noting that crosstalk probability density increases to its peak and gradually decreases due to the enhancement of other-order crosstalk. Furthermore, long wavelength and small asymmetry parameter are helpful to mitigate the influence of atmospheric turbulence and restrain the mode crosstalk on the orbital angular momentum mode transmission.

Propagation of radially polarized multi-cosine Gaussian Schell-model beams in non-Kolmogorov turbulence

Recently, we introduced a new class of radially polarized beams with multi-cosine Gaussian Schell-model(MCGSM) correlation function based on the partially coherent theory (Tang et al., 2017). In this manuscript, we extend the work to study the statistical properties such as the spectral density, the degree of coherence, the degree of polarization, and the state of polarization of the beam propagating in isotropic turbulence with a non-Kolmogorov power spectrum. Analytical formulas for the cross-spectral density matrix elements of a radially polarized MCGSM beam in non-Kolmogorov turbulence are derived. Numerical results show that lattice-like intensity pattern of the beam, which keeps propagation-invariant in free space, is destroyed by the turbulence when it passes at sufficiently large distances from the source. It is also shown that the polarization properties are mainly affected by the source correlation functions, and change in the turbulent statistics plays a relatively small effect. In addition, the polarization state exhibits self-splitting property and each beamlet evolves into radially polarized structure upon propagation.

Kurtosis parameter K of arbitrary electromagnetic beams propagating through non-Kolmogorov turbulence

General analytical formulae for the kurtosis parameters K (K parameters) of the arbitrary electromagnetic (AE) beams propagating through non-Kolmogorov turbulence are derived, and according to the unified theory of polarization and coherence, the effect of degree of polarization (DOP) of an electromagnetic beam on the K parameter is studied. The analytical formulae can be given by the second-order moments and fourth-order moments of the Wigner distribution function for AE beams at source plane, the two turbulence quantities relating to the spatial power spectrum, and the propagation distance. Our results can also be extended to the arbitrary beams and the arbitrary spatial power spectra of Kolmogorov turbulence or non-Kolmogorov turbulence. Taking the stochastic electromagnetic Gaussian Schell-model (SEGSM) beam as an example, the numerical examples indicate that the K parameters of a SEGSM beam in non-Kolmogorov turbulence depend on propagation distance, the beam parameters and turbulence parameters. The K parameter of a SEGM beam is more sensitive to effect of turbulence with smaller inner scale and generalized exponent parameter. A non-polarized light has the strongest ability of resisting turbulence (ART), however, a fully polarized SEGSM beam has the poorest ART.

Propagation factor of electromagnetic concentric rings Schell-model beams in non-Kolmogorov turbulence**Project supported by the National Basic Research Program of China (Grant No. 2013CBA01702), the National Natural Science Foundation of China (Grant Nos. 61377016, 11104049, 10974039, 61575055, and 61575053), the Fundamental Research Funds for the Central Universities, China (Grant No. HIT.BRETIII.201406), and the Program for New Century Excellent Talents in University,

We derive an analytical expression for the propagation factor (known as M2-factor) of electromagnetic concentric rings Schell-model (EM CRSM) beams in non-Kolmogorov turbulence by utilizing the extended Huygens–Fresnel diffraction integral formula and the second-order moments of the Wigner distribution function (WDF). Our results show that the EM CRSM beam has advantage over the scalar CRSM beam for reducing the turbulence-induced degradation under suitable conditions. The EM CRSM beam with multi-rings far-fields in free space is less affected by the turbulence than the one with dark-hollow far-fields or the electromagnetic Gaussian Schell-model (EGSM) beam. The dependence of the M2-factor on the beam parameters and the turbulence are investigated in detail.

Correlation singularities of a partially coherent radially polarized beam in non-Kolmogorov turbulence

We have investigated the correlation singularities of a partially coherent radially polarized beam propagating through non-Kolmogorov turbulence. An analytical expression for the radius of a ring dislocation is derived. It is shown that the dependence of the radius of a ring dislocation on spatial coherence width in non-Kolmogorov turbulence is quite different from that in free space. The relation between spatial coherence width and beam width affects the change trends of the radius of a ring dislocation versus spatial coherence width. For different value ranges of the power law, the change of the radius of a ring dislocation with power law has an opposite trend. It is also found that the propagation distance plays an important role in determining the change of the radius of a ring dislocation. Our results will be useful in measuring the statistical properties of a random medium or a random field.

Beam wander and M2-factor of partially coherent electromagnetic hollow Gaussian beam propagating through non-Kolmogorov turbulence

Propagation formulae for M2-factor and beam wander of partially coherent electromagnetic hollow Gaussian (PCEHG) beam in non-Kolmogorov turbulence are derived based on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function. Our results indicate that the normalized M2-factors of PCEHG beam with larger beam order, waist width, inner scale of turbulence, the generalized exponent parameter, and smaller transverse coherent widths, outer scale of turbulence, the generalized structure parameter are less affected by the turbulence. The root mean square beam wander and relative beam wander are more obvious for PCEHG beam with smaller beam order, larger inner and outer scales of turbulence, exponent parameter, transverse coherent widths, and the generalized structure parameter. What is more, the beam wander properties of PCEHG beam in non-Kolmogorov turbulence are very different from M2-factor and spreading properties of beam in turbulence.

Propagation factors of standard and elegant Laguerre Gaussian beams in non-Kolmogorov turbulence

Analytical formulae are derived for the propagation factors (M2-factors) of standard Laguerre Gaussian (SLG) beam and elegant Laguerre Gaussian (ELG) beam in non-Kolmogorov turbulence based on the extended Huygens-Fresnel principle and second order moments of the Wigner distribution function. The M2-factors of SLG beam and ELG beam in non-Kolmogorov turbulence have been discussed numerically and comparatively. It is shown that the relative M2-factors of ELG beam are more affected by the turbulence and keep the better beam quality in comparison with that of SLG beam. Furthermore, the normalized M2-factors of SLG beam and ELG beam with higher orders, longer wavelength, larger waist width, larger inner scale of turbulence and the generalized exponent parameter, smaller outer scale of turbulence and smaller the generalized structure parameter are less affected by the non-Kolmogorov turbulence.

Spreading and evolution behavior of coherent vortices of multi-Gaussian Schell-model vortex beams propagating through non-Kolmogorov turbulence

The explicit closed-form expressions for the beam width and angular spread of multi-Gaussian Schell-model vortex (MGSMV) beams propagating through atmospheric turbulence are derived in this paper. The spreading and evolution behavior of coherent vortices of MGSMV beams in non-Kolmogorov turbulence are investigated quantitatively by some typical numerical examples, where the evolution behavior of coherent vortices is stressed in particular. It is illustrated that MGSMV beams are more resistant to atmospheric turbulence than multi-Gaussian Schell-model (MGSM) non-vortex beams. By increasing the beam index of MGSMV beams, the deleterious turbulence effects can be reduced gradually. As MGSMV beams propagate in non-Kolmogorov turbulence, the position and number of coherent vortices are changeable. The impact of the beam index and fluctuations of atmospheric turbulence on the conservation distance of the topological charge is also explored in depth.

Propagation properties of Laguerre-Gaussian correlated Schell-model beam in non-Kolmogorov turbulence.

Analytical formulas are derived for the average intensity, the root-mean-square (rms) angular width, and the M2-factor of Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in non-Kolmogorov turbulence. The influence of the beam and turbulence parameters on the LGCSM beam is numerically calculated. It is shown that the quality of the LGCSM beam can be improved by choosing appropriate beam or turbulence parameter values. It is also found that the LGCSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation. Our results will have some theoretical reference value for optical communications.

Propagation factors of multi-sinc Schell-model beams in non-Kolmogorov turbulence

We derive several analytical expressions for the root-mean-square (rms) angular width and the M(2)-factor of the multi-sinc Schell-model (MSSM) beams propagating in non-Kolmogorov turbulence with the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function. Numerical results show that a MSSM beam with dark-hollow far fields in free space has advantage over the one with flat-topped or multi-rings far fields for reducing the turbulence-induced degradation, which will become more obvious with larger dark-hollow size. Beam quality of MSSM beams can be further improved with longer wavelength and larger beam width, or under the condition of weaker turbulence. We also demonstrate that the non-Kolmogorov turbulence has significantly less effect on the MSSM beams than the Gaussian Schell-model beam.