The problem of information transmission by modulating the topological charge of the orbital angular momentum (OAM) of beams synthesized by an array of fiber lasers during radiation propagation through a turbulent atmosphere is investigated. The possibility of adaptive compensation for turbulent distortions of a beam in the periodic process of successive phase matching in the receiver plane and phase modulation in the initial radiation plane for information transmission is demonstrated for the first time. A mathematical model of the process of adaptive control for two modifications of the feedback loop and the results of OAM recognition by machine learning methods are presented.
Analytical equations for mutual spatial coherence functions of counter-propagating laser beams in integrated transmit/receive optical systems are derived. These equations being fourfold integrals allow estimating the diffraction parameters of transceivers and turbulent propagation conditions, under which a cryptographic key can be generated based on the principle of reciprocity. For particular cases, the degree of coherence of counter-propagating beams and the degree of coherence averaged over the receiver aperture are calculated as functions of generalized parameters describing the turbulence intensity and diffraction at the apertures.
The results of an experiment on formation of a scalar vortex beam in the system of coherent combining of fiber laser beams are reported. Stabilization of phase relations between optical beams is achieved by placing a helicoid phase forming diffraction optical element (DOE) made as a phase plate with helical phase profile in the active feedback loop. Time-stable vortex beams with the topological charge p = ±1 are obtained. The vortex character of the obtained beams is confirmed by the results of interferometric measurements.
The control over beams with distributed polarization opens new ways for a wide range of applications from optical communications to laser processing of materials. This paper proposes a simple and efficient method of controlling the spatial characteristics of azimuthally polarized beams synthesized as a result of coherent combining of Gaussian beams emitted by a spatially ordered array of fiber lasers. The proposed method is based on maintaining the specified phase relations between the array subbeams by placing a phase forming element - a liquid crystal spatial light modulator - in the active feedback loop. A distinctive feature of the proposed method is the possibility of full control over beams with distributed polarization with phase control of only one component of the electric field. This leads to the significantly simpler design of the experiment. The mathematical model of beam formation and the algorithm of phase control of beams with spatially distributed polarization are discussed. The generation of beams with spatially distributed polarization, including cylindrical vector beams (CVB) and optical vortex beams (OVB), is demonstrated experimentally. The results of the experiment with an array of six fiber lasers are in a good agreement with the results of numerical simulation.
Statistical characteristics of the orbital angular momentum (OAM) of a Laguerre-Gaussian laser beam propagating through a turbulent atmosphere have been studied in the Monte Carlo numerical simulation. We have analyzed variations in the probability density of OAM versus its initial value, turbulent conditions along the propagation path, the diffraction parameter of the beam, and the receiving aperture size. This distribution is shown to be symmetrical near-Gaussian for an infinite receiving aperture and to be well approximated by an Edgeworth series. The probability density function significantly changes for finite-size apertures. The range of sizes of the receiving aperture has been found where fluctuations of the moment of energy flux density and fluctuations of light flux recorded can be considered uncorrelated.
In the paper effectiveness of four algorithms designed to register optical vortices is assessed numerically and potential fields of their application are discussed. The structure of algorithms is described and input parameters required for the model realization are listed.
We study how to control the orbital angular momentum, the intensity distribution, and the coherence length of a laser beam based on fiber array coherent combining. The features of the formation of nonzero orbital angular momentum of the beams when the controls the piston phase shift of the fiber array were theoretically and experimentally studied. A new method for controlling the distribution of the intensity of a light field synthesized on the basis of fiber array coherent combining were proposed. The possibilities of controlling the degree of spatial coherence of the synthesized laser beam were studied theoretically and experimentally.
Properties of vortex radiation are discussed in the article using the data obtained by the authors and information found in references. Possible applications of such radiation are considered. Special attention is devoted to the methods of vortex registration. Precision of two registration algorithms is compared and particularities of their practical realization are analyzed.
The intermediate results of the experiment on vortex laser beam synthesis based on coherent combining laser subbeams formed by a fiber collimators array are presented. The wave field results from interference of individual subbeams in this case and is determined by the phase relationships between them. A functional diagram of the experimental setup is given. The experimental results of synthesis of a laser beam with an orbital angular momentum are described. It is suggested to use a spiral phase plate to determine the sign of the topological charge of an optical vortex; the efficiency of this approach is estimated.
The efficiency of using an Airy axisymmetric beam for energy transfer and concentration to a given point in a randomly inhomogeneous medium is studied. Capabilities of this beam are assessed in comparison with beams of other types. The variance of beam wandering is calculated. For the given parameters of the transmitting system, path length, and degree of turbulent distortions, the intensity at the axis of the considered Airy beam is shown to be much lower than that of other beams, the Airy beam is compared with. In addition, the Airy beam is characterized by smaller wandering.
The algorithm of an optical vortex coordinates and topological charge detection is considered. In the algorithm a vortex is localized as a point of an interference fringe branching. With application of the algorithm interference patterns obtained in laboratory and numerical experiments are analyzed and characteristics of vortices revealed in corresponding examples are presented.
The distribution laws of fluctuations of the field amplitude and intensity of laser beams propagating through the atmosphere are studied based on numerical simulation. The calculations are performed for the beams having the orbital angular momentum (vortex beams) at different points of their cross section. The transformation of probability densities of fluctuations of the field amplitude and intensity of the beams is studied for the relative variance of intensity fluctuations (scintillation index) varying from unity to three. It is shown that if the scintillation index has the same values at different points of the beam, the probability density of intensity has the same form, whereas the probability density of the real and imaginary parts of the field amplitude can differ.
The generation of optical beams with a possibility of quick variations in the orbital angular momentum (OAM) and the degree of spatial coherence is shown in laboratory experiments. The methods for OAM and coherence control are based on the phase control in the fiber array optical channels. The approach suggested allows one to change the OAM (the topological charge of a vortex beam) with a high speed determined by the phase shifter operation speed. The generation of a vortex beam is shown for six coherent Gauss-like beams arranged in a circle and having a constant phase shift between neighboring beams, providing the total phase shift equal to 2π around the circle. It is shown that the far field is characterized by an annular intensity distribution and a spiral-like distribution of the Poynting vector. In addition, the features of the OAM and the topological charge of a fiber-array-based vortex beam in a homogeneous medium are investigated in numerical experiments. The method for controlling the length of spatial coherence of the beam synthesized is based on introducing pseudo-random phase fluctuations in a fiber array. The value of the coherence length which exceeds the subbeam size is set by the correlation function of pseudo-random phase fluctuations in neighboring subbeams. The value of the coherence length smaller than beamlet size is set by the divergence of the subbeams with delta correlated phase fluctuations. The effect of the number of pseudo-random realizations of the fiber array phase on the average intensity distribution is studied in the laboratory experiments. The influence of the spatial coherence of the laser beam on the bit error rate of FSO communication systems in a turbulent atmosphere is studied theoretically.
For a vortex axisymmetric Airy beam, the second-order mutual coherence function for the complex amplitude of the wave field was calculated by two methods. The first method assumed previous calculation of the complex amplitude of wave field of the beam in a turbulent medium based on the Monte Carlo technique, while the second method used the well-known representation of the solution of equation for the second-order spatial coherence function. Coherent properties of the beam at different values of parameters are studied.
In this study, we predict qualitatively the random wander of the Airy vortex beam propagating in a statistically homogeneous turbulent atmosphere based on the earlier revealed regularity [5] that the variances of random wander of vortex laser beams propagating in the turbulent atmosphere and having identical orbital angular momenta and identical transverse size in the source plane are different, if the effective volumes occupied by the beams in the homogeneous medium are different. The larger is the volume occupied by the beam in space, the smaller is the variance of the beam wander.
Statistical characteristics of vortex beams propagating in the atmosphere are analyzed on the basis of numerical simulation. The probability density function of the intensity fluctuations are compared for common vortex beams and vortex beams synthesized by combining a fiber laser array. It is shown that the intensity fluctuations are lognormally distributed on the axis of a Gaussian beam when radiation is propagating through a turbulent atmosphere under weak fluctuations (the Rytov parameter is much lower than unity), while the probability density function of the intensity fluctuations at the axes of vortex beams is well approximated to the exponential distribution typical for strong fluctuations (the Rytov parameter is much higher than unity). This function is well approximated to a gamma distribution in the cases where the scintillation index is lower than unity independently of the beam type and observation point position relative to the propagation axis.
The dependences of the orbital angular momentum of a Laguerre–Gaussian beam propagating through a turbulent atmosphere on its azimuthal index and atmospheric turbulence strength are analyzed in the numerical simulation. The effect of errors in alignment of the beam and receiver axes on the average value and variance of orbital angular momentum fluctuations is studied. The statistics of the orbital angular momentum distribution at the end of the atmospheric propagation path is analyzed.
We suggest a technique for generation of optical vortex beams with a variable orbital angular momentum based on a fiber laser array. The technique uses the phase control of each single subbeam. Requirements for the number of subbeams and the spatial arrangement for the vortex beam generation are determined. The propagation dynamics of a vortex beam synthesized is compared with that of a continuous Laguerre–Gaussian beam in free space and in a turbulent atmosphere. Spectral properties of a beam synthesized, which is represented as a superposition of different azimuth modes, are determined during its free-space propagation. It is shown that energy and statistical parameters coincide for synthesized and continuous vortex beams when propagating through a turbulent medium. Probability density functions of the beam intensity fluctuations are well approximated to a gamma distribution in the cases where the scintillation index is lower than unity independently of the beam type and observation point position relative to the propagation axis.
In this paper, the role of the vortex phase in the initial structure of wave field of the modified Bessel-Gaussian laser beam propagating in the atmosphere with weak turbulence, as well as in statistical regularities of beam wandering is studied by the semi-analytical method. The variance of the beam wandering depending on the diffraction conditions and the degree of turbulent distortions is determined. It is shown that the higher is the topological charge of the beam and its radial frequency, the smaller is the random wandering of the beam.
Numerical simulation and analytical calculations of the variance of fluctuations of the total orbital angular momentum (OAM) of Laguerre—Gaussian and Gaussian laser beams propagating in the randomly inhomogeneous atmosphere have been carried out. It is shown that as such beams propagate in the weakly turbulent atmosphere, the relative variance of OAM fluctuations remains much smaller than the relative variance of intensity fluctuations.
A technique for generation of optical vortex beams with a variable orbital angular momentum on the basis of a fiber laser array is suggested. The technique is based on controlling the radiation phase of individual subapertures of the array. Requirements for parameters of a device for vortex beam generation are determined (the number and size of subapertures and their arrangement). The propagation dynamics of a vortex beam synthesized is compared with that of a continuous vortex beam in free space and in a turbulent atmosphere. Spectral properties of a beam synthesized, which is represented as a superposition of different azimuth modes, are determined during its free-space propagation. It is shown that energy and statistical parameters coincide for synthesized and continuous vortex beams when propagating through a turbulent medium.
The main objective of the current investigation is to reveal the influence of atmospheric distortions on the parameters of vortex laser beams, to find the characteristic not influenced by such distortions, and to compare the obtained results with data corresponding to Gaussian beams.
Statistical characteristics of the vortex laser beams propagating in the turbulent atmosphere are analyzed. The vortex beams are appeared to be less affected by turbulence as compared with the conventional beams: for the vortex beam the variance of random displacements and the variance for fluctuations of the orbital angular momentum, which are induced by atmospheric turbulence less than these characteristics for the vortexless beam, beams having a larger topological charge are founded to be more stable.
The sensing of phase front of the vortex laser beams has been carried out with the help of a Hartmann-Shack sensor. The
vortex beam is generated in the form of a Laguerre-Gaussian beam (LG0
1 mode) with the help of the special helicoidal
phase plates manufactured by the kinoform technology. The measured shifts of focal spots on the hartmannogram are
compared with the calculated shifts. From the measured wave front tilts the reconstruction of singular phase surface has
been performed with using the novel reconstruction technique. The phase surface reconstruction is demonstrated in the
case of distorted vortices as well. The correction of an optical vortex is undertaken in the close-loop adaptive system including
the bimorph deformable piezoceramics-based mirror.
The spatial dynamics of vortex dipole nested in a Gaussian optical beam is analyzed with scalar diffraction theory. It is
shown that the generation and annihilation of vortices are accompanied by extreme wave front distortions. Process of
nucleation and annihilation of vortex dipole is considered to confirm the vortex aftereffect in the process of
transformation of an aberration wave front into a singular one. After the vortex dipole annihilation the absolute values of
the average and Gaussian curvatures increase greatly in the local areas of wave front. The phase reconstruction error
increases in these areas in the process of wave front sensing. To investigate the features of the vortex aftereffect for
simple field the light rays which take part in the combined translational and rotary motion of energy around the field
zero-lines are constructed. The phase is computed as a potential of the optical field using the light rays. Integration of the
phase gradient along the ray or energy-stream line allows a unique value of the phase to be connected with a point of the
ray. Wave front of the beam is constructed from the computed phase. As in the vicinity of the vortex core the energy-stream
line takes a spiral shape the phase incursion along the line increases. After the vortex annihilation and vanishing
of the spiral shape the incursion remains and creates the vortex aftereffect in the form of the extreme wave front
distortions. The revealed effect should be taken into account when constructing the systems of adaptive optics aimed at
functioning in strong turbulence conditions.
The sensing of phase front of the vortex laser beam has been carried out with the help of a Hartmann-Shack sensor. The vortex beam is generated in the form of a Laguerre-Gaussian beam (LG01 mode) with the help of the special helicoidal phase plates manufactured by the kinoform technology. The measured shifts of focal spots on the hartmannogram are compared with the calculated shifts. From the measured wave front tilts the reconstruction of singular phase surface has been performed.
In the present report the possibility of singular points detections using a Shack-Hartmann sensor is described and the precision of the developed detection algorithm is estimated. Also the algorithms of a singular wave front reconstruction are analyzed. Two algorithms are considered and their properties compared. One of them was developed by D. Fried, its description was found in literature. The second algorithm was developed by authors of the report. The both algorithms were introduced into the software of the sensor and insured satisfactory quality of singular phase reconstruction. The precision of algorithms compared in numerical investigations as well in real laboratory experiments.
In the present report the possibility of singular points detections using a Shack-Hartmann sensor is described and the precision of the developed detection algorithm is estimated. Also the algorithms of a singular wave front reconstruction are analyzed. Two algorithms are considered and their properties compared. One of them was developed by D. Fried, its description was found in literature. The second algorithm was developed by authors of the report. The both algorithms were introduced into the software of the sensor and insured satisfactory quality of singular phase reconstruction. The precision of algorithms compared in numerical investigations as well in real laboratory experiments.
The algorithms for screening singular points of the phase gradient vector field are developed, where vector field components can be measured with a Shack-Hartmann wavefront sensor or shearing interferometer. Special attention is focused on the singular points that allow localization of optical vortices (wavefront dislocations). Determination of the coordinates and the topological vortex charges is of special importance in optical vortex interferometry, in operation of optjcal communication devices that encode information by means of optical vortices, and for reconstruction of phase distribution of optical beams that propagate in a medium with dislocations. On basis of numerical modeling, accuracy of the algorithm is verified, comparison with other algorithms executed, and its advantages and drawbacks are analyzed. Performance results are presented of the singular wavefront recovery algorithm, whose operating requirement is preliminary detection of optical vortex dislocations.
The original algorithm of phase reconstruction is proposed and its characteristics are estimated. This algorithm requires detection of dislocation coordinates so it should be used together with the algorithm of dislocation localization. In the paper the comparison is performed of the proposed algorithm with the well known Fried's algorithm. After that the phase reconstruction technique is included into the model of a typical adaptive optics system.
This paper studies the effect of turbulence on the orbital angular momentum (OAM) of the Laguerre-Gaussian beam propagating through the atmosphere. An integral representation of laser beam OAM through the beam intensity distribution and the gradient of the medium permittivity is derived. The equations are obtained for the first OAM statistical moments: the mean and the mean square. It is shown that the OAM value, averaged over medium realizations, coincides with the OAM value in a homogeneous medium. Asymptotic equations are derived, which allow OAM fluctuations to be estimated under the extreme conditions of weak and strong turbulence, depending on the diffraction parameters of the beam. It is found that the rate of growth of OAM fluctuations increases, as the propagating beam passes from the conditions of weak turbulence to the conditions of strong turbulence.
A new algorithm of the dislocation localization is suggested. It is based on the analysis of projections field of phase gradients. Accuracy of the algorithm is verified by numerical simulation. Special attention is focused on the precision of singular points (wavefront dislocations) screening. The algorithm is evaluated with respect to others and its advantages and drawbacks are cleared up. The method described can be included in the software of the Hartmann's sensor and be used in the full-scale experiments. Also the original algorithm of phase reconstruction is proposed and its characteristics are estimated. This algorithm requires detection of dislocation coordinates so it should be used together with the algorithm of dislocation localization. In the paper the comparison is performed of the proposed algorithm with the well known Fried's algorithm. After that the phase reconstruction technique is included into the model of a typical adaptive optics system.
Laser ablation of porous silicon as a function of laser wavelength and width of silicon nanowires was studied in our experiments. The time-resolved evolution of the cloud of the porous silicon particles produced by laser ablation is studied by the analysis of the kinetics of photoluminescence (PL) signal. The laser ablation of porous silicon produced by pulses of 532 nm or 337 nm radiation with addition of synchronized power pulses of 1064 nm radiation. The cloud of the nanometer-sized silicon crystallites had the high enhancement of luminescence quantum efficiency in the red region of spectra. The slow PL kinetics component, which is due to the localized carriers, decays on a millisecond time scale. The mechanism of destruction of the strongly correlated nanostructures was considered. Experimental results were analyzed from the point of view of theoretical models of laser interaction with nanostructures and the theory "Lattinger liquid" proposed by P.W. Anderson (1) for low dimensional nanosystems.
It is commonly believed that the main obstacles in functioning of adaptive optical systems in the atmosphere under the conditions of strong turbulence are wave front dislocations (optical vortices). It is assumed in this case that wave front singularities connected with vortices disappear at disappearance (annihilation) of vortices, so it makes no problem to correct for the distorting effect of the atmosphere on the propagating laser beam using, for example, flexible mirrors. This paper is devoted to the study of properties of the wave front phase distribution at the stage following annihilation of optical vortices. It is established that the absolute values of the mean curvature and the Gaussian curvature of wave front parts increase greatly in the areas of vortex aftereffect. It is shown that the efficiency of an adaptive optical system reduces due to the increase of the error at the stage of retrieval of such phase distribution in the process of wave front sensing. This effect should be also taken into consideration when developing principles of construction of single-mirror and multiple-mirror adaptive optical systems operating by the phase conjugation method and intended for work under the conditions of strong atmospheric turbulence.
Laser ablation of porous silicon as a function of laser wavelength and width of silicon nanowires was studied in our experiments. The time-resolved evolution of the cloud of the porous silicon particles produced by laser ablation is studied in situ by the analysis of the kinetics of photoluminescence signal. The laser ablation of porous silicon produced by pulses of 532 nm or 337 nm radiation with addition of synchronized power pulses of 1064 nm radiation. The cloud
of the nanometer-sized silicon crystallites had the high enhancement of luminescence quantum efficiency in the red region of spectra. The slow PL kinetics component, which is due to the localized carriers, decays on a millisecond time scale. The squeezed electron-hole plasma heating by IR-laser radiation may produce a damage of silicon nanowires. The fragments of nanowires in cloud must be smaller, than the critical length. The energy of excitation of e-h pair in
fragment with contribution of longitude quantum modes must be lower than energy of the excited photons. Particles with lesser length don't absorb excited laser radiation and don't damage. For this case we may speak about the quantum mechanism of laser ablation of nanowires.
Regularities of appearance and evolution of optical vortices (wave-front dislocations) in the light field of laser beam in the inhomogeneous refractive medium are studied with the use of simple field models. We associate a dynamic system for the intensity and phase transformation with the parabolic equation describing the light propagation. Redistribution of energy fluxes when appearance and annihilation of the dislocations is considered in the phase space of this system. The hydrodynamics approach to the dislocation problem based on an analogy of the phase gradient vector field to the liquid flow vector field is developed in the paper. Novel method to calculate the dislocation statistical characteristics in the turbulent atmosphere is proposed on the base of the before-derived equation connecting the phase vortex density and intensity spatial distribution.
An equation connecting the phase vortex density (wave front dislocation density) and intensity distribution of a light beam is derived. On this base a new method for calculation of the statistical characteristics of dislocations in the turbulent atmosphere is proposed. In the case of the lognormal law distribution of intensity fluctuations an integral representation of average dislocation density in terms of the correlation functions of intensity logarithm in a beam cross section is obtained.
New method to calculate the statistical characteristics of dislocations in the turbulent atmosphere is proposed based on the relation obtained before which connects the density of phase vortices with the intensity distribution. For the lognormal distribution of intensity fluctuations the integral representation of the average density of dislocations in a cross-section of light beam through the correlation functions of logarithm of intensity is obtained.
We report the studies of process of laser annealing of island Ge films on the SI substrates. Based on the time- resolved reflectivity measurements, we obtained the data concerning melting, the dissolution and the resolidification of Ge thin films on the SI after laser annealing with nanosecond laser pulse We observed periodic melting of the interface Ge-Si under an illumination by series of laser pulses that connected with the peculiarity of the solution Ge in Si.
We study the periodic damage structures that can be produced don the rough-surface of semiconductor when they are irradiated with a single beam of intense laser radiation. We observed a formation of periodic surface structures for porous Si with microscopic surface roughens. In the case of more strong rough Ge we observed an opposite effect to ripple formation: i.e. an effective destruction of resonance Fourier components of the random disturbed surface.
We have investigated the correlation of photoluminescence (PL) properties with certain etching conditions and laser annealing of porous silicon (PS). We used the optical second-harmonic generation and photoluminescence methods for studies of IR laser annealing of porous silicon. We observed that IR illumination by series of laser pulses causes decreasing of SH signal and increasing of luminescence efficiency for PS samples.
The time-resolved evolution of the cloud of the porous silicon (PS) particles produced by laser ablation is studied in situ by the analysis of the kinetics of photoluminescence (PL) signal. The cloud of the nanometer-sized silicon crystallites had the high enchantment of luminescence quantum efficiency (QE) in the red region of spectra. The slow PL kinetics component, which is due to the localized carriers, decays on a millisecond time scale. We observed high intensity of laser ablation process for light excited PS. We also study the emission of photons from remnants of porous silicon after laser ablation of PS sample. The red light generation was observed in this case of excitation of PS. Time-resolved experiments on the luminescence show that likely there are large lifetime phonons in quantum silicon wires.
The problems to ensure an effective functioning of the controlled optical systems at the long paths in the turbulent atmosphere are presented. It is shown that the conventional techniques of adaptive optics do not allow us to suppress the optical field distortions under the conditions of the strong turbulence, when the intensity distribution acquire the pronounced speckle-structure and the wave front gains the topological defects (dislocations). Dynamical and statistical dislocation characteristics typical for the turbulent atmosphere are considered. Novel theoretical and experimental approaches to the dislocation problem are proposed and prospect of its practical solution are estimated.
Process of speckle-field forming when a light beam is distorted by optical inhomogeneities is considered, spatial ray dynamics is studied, and also regularities of birth of the wave-front dislocations are revealed. The energy-stream lines are constructed for the Gaussian beam passed through an optical inhomogeneity on the basis of the solution of the parabolic equation for the complex amplitude of the monochromatic wave field. Simulating of the ray trajectories is accompanied by the study of the complete set of the critical points. The angular divergence of radiation is calculated as an integral characteristic of the wave front. The ray spatial dynamics shows the basic features of transformation of the first smooth wave front into the singular one. It is established that this process is accompanied by the energy redistribution in the space manifested as a local beam focusing. The intensity distribution in the plane transversal to the beam propagation direction transforms according the rays' behavior. The discovered ray local focusing is the forerunner of subsequent beginnings of the pair screw wave front dislocations in the points of zero intensity. When the beam propagates through the medium having the refractive index inhomogeneities the dislocations can annihilate and then born again and the intensity acquires the speckle-structure.
Phase reconstruction under the conditions of strong scintillation is limited by the presence of phase discontinuities (singularities) that accompany the intensity nulls in speckle field. The singularities are hidden for the wave front sensors of conventional adaptive optics systems. Rigorous theory has been developed in the paper to reconstruct the singular phase with allowance for the vortex nature of the phase gradient vector field. Singular functions of the wavefront slope (phase gradient) are exposed to an appropriate regularization; the divergence and rotor of the regularized phase gradient are determined. It has been established that the divergence of the phase gradients contains singularities of the same type as gradient and, therefore, proper phase reconstruction can be executed using the regularized slopes only. Topological transformation of the wave front in the process of appearance and annihilation of the discontinuities is manifested as changing in relief of the regularized rotor, the relief characteristics correspond to the discontinuity parameters. With the use of Pompeiu integral the phase gradient is presented as a sum of divergent and rotor parts added by the term depending on the receiving aperture boundary conditions. The obtained wavefront slopes are unwrapped into the singular phase ignoring the noise and singularities of the phase gradient divergence and rotor. Derived analytical expression connecting the phase reconstruction from the measurements of wavefront slopes. Examples of such a reconstruction are given. The developed approach can be base for creating the discrete phase reconstruction algorithms.
Spatial dynamics of distortions of the of the laser beam wavefront under the conditions of forming and evolution of the optical vortices have been study, energy streamlines have been constructed, and regularities of appearing the wave-front dislocations have been revealed. The system of differential equations for the energy streamlines (rays) in the three- dimensional space derived based on the parabolic equation for the complex amplitude of the monochromatic wave field was solved by the Euler technique with an automatic step choice. An analysis of the structure of the Umov-Poynting vector field for the different longitudinal coordinates in combination with the solution of the equation system allowed the rays spatial dynamics to be investigated. It was established that the rays were focused in the vicinities of the points corresponding to the nodes of the Umov-Poynting vector field for the beam having first the smooth wavefront. Such an energy distribution in the space stimulated appearing the points with zero intensity in the plane transversal to the propagation direction, the pairs of optical vortices were born in these points (bifurcation 'nodes - focuses'). Rays trajectories gained the spiral form in the vicinities of arising dislocations. In the process of the beam propagation the vortices first diverged and then drew together and annihilated, the wave-front was transformed from the singular to the smooth one, the rays stopped to twist and then focused as far as the next branch point. The initial point configuration determined the further ray trajectories and vortex evolution.
The algorithms of reconstruction of singular phase from the measurements of wave front slopes by Hartmann sensor, shear interferometer, and from the interference measurements of Knox-Thompson are proposed. Based on the hydrodynamic approach to description of the wave front spatial dynamics we have developed the algorithms which make it possible the singular phase of an optical speckle field to be reconstructed with the use of analytic representation of the phase in terms of its partial derivatives with the allowance for the vortex nature of the phase gradient vector field.
The hydrodynamic description of light propagation through the randomly inhomogeneous medium is developed based on the analogy of the vortex phase dislocations with the potential circular flow of liquid caused by the isolated point vortexes. It is shown that the determining factor in forming of the wave fronts structure of optical speckle-fields is a spatial dynamics of the phase gradient rotor. The singular equations for description of the rotor are derived and methods to regularize these equations are proposed.
Feasibility of noninterferometric methods to measure the phase distribution in laser beam cross-section for visualization of the vortex dislocations of optical speckle-field wavefront is analyzed. Peculiarities of the phase retrieval from the measured intensity distribution (the phase problem in optics) and from the wave front slopes measured by the Hartman sensor are discussed. A concept of the vortex and potential parts of the phase is introduced. An analytic formula to retrieve the potential phase from the measured intensity distribution of optical speckle-field has been obtained. We show that the considered ways of measurements allow the positions of the dislocations centers to be sensed and spatial configuration of the intensity zero-lines to be reconstructed.
Wave front dislocations generated by the vortex flow of the light energy in vicinity of the points where the field intensity equals zero are studied on the basis of obtained relation between the phase and intensity in optical beam (the phase problem solution). Reasons of an ambiguity of the phase problem solution are discussed. An analytic formula for retrieving the potential phase from the known intensity distribution has been obtained. A possibility to use an information on the potential phase for correction of singular phase distortions by the optical adaptive systems is discussed.
The algorithms are produced from the analytical solutions of the three-dimensional spatial- temporal problem of conversion of the boundary conditions, which were derived earlier. Numerical and laboratory experiments to reconstruct the laser beam intensity distribution with the arbitrary spatial distribution from the temperature field of the heated surface were carried out.
A new method for the studies of the spontaneous magnetic field in quasi-2D systems such as high-temperature oxide superconductors is presented. For measuring of magnetic field was used deconfinement anyons at interplanar hopping induced by laser irradiation. Magnetometer with optical access was used for measurement of the light induced changes of magnetization at different temperature and intensity of light and external magnetic field. Observed behavior is probably the evidence of the existing of a phase with fractional statistics and spontaneous magnetic field.
Use of airborne DIAL return signals from the Earth's surface in combination with a tomographic data processing technique enables one to essentially lower the sounding radiation power sufficient for effective sensing of the atmosphere. An optical arrangement of sounding and an algorithm of lidar data inversion aimed at reconstruction of two-dimensional fields of atmospheric parameters are proposed. Some results of numerical simulations of the technique are presented.
The problem with reconstructing the laser beam intensity distribution from temperature distribution over the front surface of the target heated by the beam has been solved analytically. Formulas allow one to retrieve the thermal flux for arbitrary values of thermal and physical parameters. The efficiency of algorithmic implementation is studied in numerical experiments.
A formula, which denotes the phase profile of two-dimensional light field by means of measurements of its intensity has been derived on the basis of the Radon transformation of measurements of distributions.
Ferroelectrical phase transition, induced by laser nonthermal action, has been observed and studied in Ge-doped quartz. Optical second harmonic generation (SHG) is used to study the tensor of the nonlinear susceptibility that reflects the symmetry of the ferroelectrical phase. The maximum value of the tensor component calculated from the experimental data is equal to 2 10-12 m V-1. The increased dielectric constant of new phase has been also observed. The direction of the laser induced anisotropy has been determined by the laser pulse polarization. The effect of the laser-induced diffusion of impurities in transparent dielectrics has been described in cases of Ge and W.
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