Propagation of a random electromagnetic beam through a misaligned optical system in turbulent atmosphere

On the basis of the generalized diffraction integral formula for misaligned optical systems in the spatial domain, an analytical propagation expression for the elements of the cross-spectral density matrix of a random electromagnetic beam passing through a misaligned optical system in turbulent atmosphere is derived. Some analyses are illustrated by numerical examples relating to changes in the state of polarization of an electromagnetic Gaussian Schell-model beam propagating through such an optical system. It is shown that the misalignment has a significant influence on the intensity profile and the state of polarization of the beam, but the influence becomes smaller for the beam propagating in strong turbulent atmosphere. The method in this paper can be applied for sources that are either isotropic or anisotropic. It is shown that the isotropic sources and the anisotropic sources have different polarization properties on beam propagation.     

Spiral spectrum of anomalous vortex beams propagating in a weakly turbulent atmosphere

ABSTRACT

We study the spiral spectrum of anomalous vortex beams propagating through a turbulent atmosphere. Based on the Huygens–Fresnel integral and the Rytov approximation, the integral expression and then the analytical expression for the spiral spectrum of anomalous vortex beams in the weakly turbulent atmosphere are derived. The capacity of wireless optical links using the anomalous vortex beam is obtained. It is found that the spiral spectrum of the anomalous vortex beam is less affected by turbulence than that of the Laguerre-Gaussian beam. And thus, the information capacity of wireless optical links using the anomalous vortex beam is larger than that using the Laguerre-Gaussian beam. The influence of beam order, wavelength, topological charge, propagation distance, refractive index structure constant and the radius of receiver aperture on spiral spectrum is investigated. These results contribute to reduce the disturbing effects of atmospheric turbulence on the orbital angular momentum of the vortex beam.     

Spectral shift of a partially coherent standard or elegant Laguerre–Gaussian beam in turbulent atmosphere

Spectral changes of a partially coherent standard or elegant Laguerre–Gaussian (LG) beam propagating in turbulent atmosphere were studied numerically. Our results show that the spectral changes of a partially coherent standard or elegant LG beam in turbulent atmosphere are determined by both the structure constant of the turbulent atmosphere and the initial beam parameters. Furthermore, it is found that a partially coherent elegant LG beam is less affected by the turbulent atmosphere than a partially coherent standard LG beam from the aspect of the on-axis spectral shift, and this advantage is enhanced for small structure constant, small beam waist size, large mode orders, and large transverse coherence length. Our results will be useful in long-distance free-space optical communications.     

Dipole influence on Shack-Hartmann vortex detection in scintillated beams

Optical vortices can appear in an optical beam that propagates over a long distance through a turbulent atmosphere. A Shack-Hartmann wavefront sensor can be used to detect such vortices. However, the morphology of these vortices, which changes with beam propagation, and nearby oppositely charged vortices will affect this vortex detection. The influence of the morphology and the separation distance from oppositely charged vortices on the Shack-Hartmann vortex detection is studied. Numerical simulations for vortex detection under these turbulent atmospheric circumstances are also provided.     

Stochastic electromagnetic beams focused by a bifocal lens

In this paper, we study the focusing of a stochastic electromagnetic beam by a bifocal lens. By taking the electromagnetic Gaussian Schell-model (EGSM) beam as an example, the changes in the spectral density, in the spectral degree of coherence, and in the spectral degree of polarization of the EGSM beam as the beam is focused by an unapertured bifocal lens are investigated. It is shown that the spectral density, the spectral degree of coherence, and the spectral degree of polarization of the focused electromagnetic EGSM beams depend upon the coherence lengths and focal lengths of the bifocal lens. The influence of the coherence lengths and the focal lengths on the focused spectral density, the spectral degree of coherence, and the spectral degree of polarization are investigated in great detail.     

Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere

We study the changes in the degree of polarization of an electromagnetic Gaussian Schell-model beam, as the beam propagates through the turbulent atmosphere. We demonstrate that, within the framework of the Tatarskii model of the turbulent atmosphere, the degree of polarization of the beam changes appreciably at relatively short propagation distances in the atmosphere. In the long-propagation distance limit, however, we find that the degree of polarization of the beam tends to the value that it has in the source plane.     

Determination of the coherency matrix of a broadband stochastic electromagnetic light beam

The statistical ensemble of a fluctuating, statistically-stationary electromagnetic light beam is presented in terms of a 2 × 2 matrix, so-called coherency matrix. The method to determine such matrix for a quasi-monochromatic light beam has been proposed for many years. In this paper, we demonstrate that the method needs to be only slightly modified to determine the matrix elements of a broadband stochastic electromagnetic light beam, if one uses the representation of statistical wave fields in the space–frequency domain. The implementation of the method is demonstrated, and the coherency matrix measurement is validated using a well-defined elliptically polarized beam.     

Fine structure of “white” optical vortices in crystals

Representation of a perturbed optical vortex past a uniaxial crystal and a polarization filter on the complex plane and the orbital Poincaré sphere was experimentally and theoretically studied. It is shown that the main properties of a polychromatic optical vortex are adequately described using eight experimentally measured quantities, including four orbital and four spin Stokes parameters of a singular beam.     

Spectral shift of an electromagnetic Gaussian Schell-model beam propagating through tissue

Based on the unified theory of coherence and polarization for stochastic electromagnetic beams, spectral changes of an electromagnetic Gaussian Schell-model (EGSM) beam propagating through tissue are investigated in detail. Numerical results show that the spectral shift of an electromagnetic GSM beam is closely determined by the parameters of the tissue (e.g. the fractal dimension of tissue and the ensemble-averaged variance of the refractive index fluctuations). The spectral shift changes from blue-shift to red-shift with the increase of the transverse coordinate.     

A New Method for Spectral Performance Evaluation of a Chromatic and Achromatic Quarter-Wave Retarder

When a polarized polychromatic beam passes through a quarter-wave retarder, the constituent spectral components suffer different changes in the state of polarization. As a result, when the beam passes through an analyzer, the intensity of the resultant beam changes, depending on the orientation of the analyzer, state of polarization of the input beam, spectral and spatial intensity distribution of the source and the wavelength-dependent retardance of the quarter-wave retarder. The intensity variation of the resulting beam is theoretically and experimentally observed, with the variation of the azimuthal angle of the analyzer for film-type chromatic and prism-type achromatic quarter-wave retarders. The spectral performances of achromatic retarders are generally evaluated by measuring retardances at discrete wavelengths by using a monochromatic beam of light over the wavelength range of interest. In this study, a simple method is used for computing the fractional nonlinear polarization (FNLP) from theoretically and experimentally obtained intensity variations for evaluating the spectral performance of both achromatic and chromatic quarter-wave retarders operating over a broad spectral range in the visible region using a polychromatic beam of light. FNLP variation is also shown for a film-type chromatic quarter-wave retarder using a monochromatic source of light. The experimentally obtained values are compared with theoretical values and a good agreement is observed. The applications of the method for the performance evaluation of quarter-wave retarders are discussed.     

Effects of atmosphere on spectrum of modified partially coherent flat-topped beams

The analytical formulas for the spectrum of modified partially coherent flat-topped (MPCFT) beams propagating in a turbulent atmosphere have been derived under strong fluctuation condition of turbulence. The spectral properties of MPCFT beams propagating in a strong turbulence have been investigated, and the changes of on-axis and off-axis spectral distributions have been analyzed quantitatively. The results show that the on-axis relative spectral shift of the modified partially coherent flat-topped beam exhibits spectral switch for the beam order M > 1, and with the increasing propagation distance the blue-shift gradually decreases in atmospheric turbulence. A rapid transition for the off-axis spectrum appears at one critical position in turbulence, and the position decreases with the increasing beam order for the lower beam order and the nearer propagation distance. The spectral properties and the spectral shifts of MPCFT beams also depend on the inner scale, the spatial coherence parameter.     

Coupling characteristics and kurtosis parameter of partially coherent beams in turbulent atmosphere

Coupling properties and kurtosis parameter (K parameter) of arbitrary beams propagating through atmospheric turbulence are investigated. A correlation factor (C⁴-factor) is introduced to describe the influence of turbulence on coupling characteristics. The general analytical expression for C⁴-factor of arbitrary beams in atmospheric turbulence is derived. It is shown that C⁴-factor of arbitrary beams in the turbulent atmosphere depends on the initial second-order moments and fourth-order moments and turbulence quantities. Taking the partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam as an example, we can obtain that C⁴-factor decreases as structure constant of the refractive index fluctuations and inner scale increase, and waist width and transverse coherence length decrease when z?>?5?km. Moreover, K parameter of PCAEHG beam in turbulent atmosphere converges to 2 when propagation distance is large enough. It indicates that the profile of PCAEHG beams in turbulent atmosphere finally evolves into fundamental Gaussian distribution.     

Transition to Quantum Turbulence Generated by Thin Vibrating Wires in Superfluid 4He

We report the turbulent transition in superfluid ⁴He generated by a vibrating wire as a function of its thickness. The response of a vibrating wire with a 3 μm diameter in superfluid ⁴He at 1.2 K reveals a hysteresis at the turbulent transition between an up sweep and a down sweep of driving force, while no hysteresis appears for wires with a thickness larger than 4.7 μm diameter. These results indicate that the 3 μm wire is efficient for reducing the number of vortex lines attached to it. A cover box and slow cooling also prevent vortex lines from attaching to a wire, resulting in a vortex-free vibrating wire. The effective mass of the vortex-free vibrating wire is almost constant in a wide range of velocities up to 400 mm/s; however, the wire density estimated from the resonance frequency is a half of the expected value of wire material, suggesting that a wire mass becomes lighter or a wire diameter becomes larger in the superfluid effectively.     

Reliability analysis of the flat-topped array beam FSO communication link

Free-space optical communication systems are affected by turbulent atmosphere. The atmospheric transmission is affected by absorption, scattering and turbulence. In this paper, the effects of absorption and scattering are taken into account using Beer’s law and the effects of turbulence are considered in calculating the average intensity distribution. An analytical expression for the average intensity distribution of a partially coherent flat-topped array (PCFTA) beam in turbulent atmosphere is derived based on the extended Huygens–Fresnel principle. The average intensity, power in bucket, signal to noise ratio, and bit error rate of this kind of beam are investigated in details. It is shown by numerical results and analytical methods that the average intensity and link parameters of PCFTA beams change during propagation and these changes are dependent upon both source parameters and weather conditions.     

Wind profiling based on the optical beam intensity statistics in a turbulent atmosphere

Reconstruction of the wind profile from the statistics of intensity fluctuations of an optical beam propagating in a turbulent atmosphere is considered. The equations for the spatiotemporal correlation function and the spectrum of weak intensity fluctuations of a Gaussian beam are obtained. The algorithms of wind profile retrieval from the spatiotemporal intensity spectrum are described and the results of end-to-end computer experiments on wind profiling based on the developed algorithms are presented. It is shown that the developed algorithms allow retrieval of the wind profile from the turbulent optical beam intensity fluctuations with acceptable accuracy in many practically feasible laser measurements set up in the atmosphere.     

Phenomenon of spectral switches as a new effect in singular optics with polychromatic light

It is shown that the recently discovered phenomenon of so-called spectral switches has a natural interpretation in the framework of singular optics with polychromatic light and that it should be regarded as being primarily a manifestation of diffraction-induced spectral changes rather than correlation-induced spectral changes as was suggested in the original papers [the first one appearing in Opt. Commun. 162, 57 (1999)] reporting this effect.     

Propagation of multi-Gaussian beams in incoherent combination through turbulent atmosphere and their beam quality

Based on the extended Huygens–Fresnel principle, the propagation of M?×?N multi-Gaussian beams in incoherent combination through turbulent atmosphere, and their beam quality are studied. The power in the bucket (PIB), β parameter and strehl ratio (S_R ) are taken as the characteristic parameters of beam quality, and analytical expressions for PIB and S_R are derived. It is shown that multi-Gaussian beams in turbulent atmosphere undergo three stages of evolution with increasing propagation distance z, and turbulence accelerates the evolution of the three stages which multi-Gaussian beams undergo. The turbulence results in a degradation of the beam quality, and multi-Gaussian beams with higher numbers M and N are less sensitive to the effects of turbulence than those with lower M and N.     

Analysing the behaviour of partially coherent divergent Gaussian beams propagating through oceanic turbulence

Theoretical study of propagation behaviour of partially coherent divergent Gaussian beams through oceanic turbulence has been performed. Based on the previously developed knowledge of propagation of a partially coherent beam in atmosphere, the spatial power spectrum of the refractive index of ocean water, extended Huygens–Fresnel principle and the unified theory of coherence and polarization, analytical formulas for cross-spectral density matrix elements are derived. The analytical formulas for intensity distribution, beam width and spectral degree of coherence are determined by using cross-spectral density matrix elements. Then, the effects of some source factors and turbulent ocean parameters on statistical properties of divergent Gaussian beam propagating through turbulent water are analysed. It is found that beam’s statistical propagation behaviour is affected by both environmental and source parameters variations.     

A comparative study of standard and elegant Hermite–Gaussian beams propagating through turbulent atmosphere

Based on the extended Huygens–Fresnel principle and the definition of the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the root-mean-square (rms) beam width and far-field divergence angle, curvature radius and M ²-factor of standard Hermite–Gaussian (SHG) and elegant Hermite–Gaussian (EHG) beams passing through turbulent atmosphere are derived and compared. It is shown that in turbulent atmosphere the far-field divergence angle of SHG and EHG beams is equal under the same conditions, but the rms beam width, curvature radius and the M ²-factor of SHG and EHG beams are different except for beam orders m?=?0 and m?=?1. The relative rms beam width, relative curvature radius and relative M ²-factor of SHG beams are less than those of EHG beams. Therefore, the conclusion that SHG beams are less influenced by turbulence than EHG beams can be drawn if we examine one of the above three relative beam parameters.