We consider the possibilities of information transmission in free space optical communication systems based on encoding with the help of the polarization structure of the synthesized laser beam. To control the polarization structure of beams, an approach based on the fiber array coherent combining with the possibility of changing the direction of subbeam polarization is used. On the basis of numerical simulation, the influence of atmospheric turbulent distortions, as well as the possibility of their adaptive compensation, is analyzed. Situations with different directions of subbeam polarization are considered. It is shown that, for the problems of information transmission, the most stable are the synthesized beams formed at the azimuthal or radial polarization of the subbeams.
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.
In laboratory conditions, experimental testing of a passive method for real-time retrieval of the instantaneous value of the crosswind speed and computer correction of images was carried out. The possibility is shown of processing a video data stream with a shooting frequency of more than 100 Hz in order to determine the wind speed.
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 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.
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.
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.
The influence of the receiving aperture size and photo detector array resolution on the accuracy of crosswind speed estimation from the correlation analysis of turbulent distortions in optical images is studied in numerical simulation. Receiving optical system (video camera) parameters optimal for the technique for passive estimation of crosswind speed are determined.
The effectiveness of reconstruction of images formed by single- and multi-aperture systems and disturbed by atmospheric turbulence is analyzed. Based on the numerical simulation, we show that the use of multi-aperture observation systems for the computer correction of atmospheric disturbances under anisoplanatism allows a significant reduction of the exposure time. Main distortions are well corrected in this case during imaging for the short exposure time, which corresponds to the “frozen” turbulence of the medium. The time required for the correction of residual small-scale disturbances is an-order-of-magnitude shorter than in the case where long-exposure images are synthesized with traditional single-aperture observation systems.
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.
Possibilities a passive method developed for estimation of the crosswind velocity from a video sequence of incoherent images along 1 km observation paths are analyzed. The method results are compared with anemometer measurements.
Modern research devices allow obtaining a large amount of information in remote laser sensing of atmospheric aerosols. However, the increase in the data volume processed by the Fredholm integral equation of the first kind increases the processing time non-linearly. The paper describes a method using known algorithms for integral equation processing with the data of aerosols laser sensing. The use of several samples from the transmission spectrum at more than 1000 wavelengths makes it possible to determine the dispersed particles sizes in a short time with an acceptable error. The developed algorithm is approved for determining the granulometric composition of laboratory heterogeneous systems. The results of laser diagnostics and the particle sizes determined from the electron microscope images were compared.
Statistical parameters of laser beams counter propagating in the atmosphere are analyzed on the basis of numerical simulation, as well as a possibility of implementing the reciprocity principle of the counter propagation of optical waves from point sources with the aim of cryptographic keying with the help of finite-size receiving-transmitting apertures. The dependences of the degree of correlation of signals from coupled wireless optical communication laser systems on the distance and aperture sizes are studied. The quantitative dependence of the aperture size on the space between the laser systems is derived with the aim of maintaining the correlation degree at a level above 0.9999.
Possibilities of enhancing the operational efficiency of optical multiaperture systems in a turbulent atmosphere were studied through numerical simulation. Features of synthesizing an object image as a sum (superposition) of images from every individual aperture were analyzed in the presence of turbulent distortions. The quality of images synthesized by an array of N×N subapertures (N=5–15) was examined. It is shown that turbulent distortions in an image synthesized by many subapertures with allowance made for shifts of subimages at every subaperture are isoplanatic in a wide range of atmospheric conditions. This allows significant improvement of the image quality by means of computer correction. In this case, there is an optimal subaperture size mainly determined by the Fried parameter, which characterizes the degree of turbulent distortions.
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.
We suggest a method for filtration of incoherent optical images of objects in the atmosphere, which allows one to observe cross shifts of turbulent air inhomogeneities at the observation path. It is shown that the characteristic size of anisoplanatic distortions in images observed through the atmosphere is mainly determined by the distance to the layer of turbulent inhomogeneities that cause these distortions. An algorithm is suggested for the filtration of turbulent distortions by their characteristic size in order to mark out the effect of turbulent medium layers specified. The capabilities of the algorithm for cross wind retrieval from the analysis of a video sequence of short-exposure images at surface horizontal paths are shown. The main advantage of the suggested method for cross wind retrieval from the analysis of two neighbor frames of video sequence is its high speed since there is no need to accumulate statistics of the analyzed parameters. The retrieved wind speed is compared with data of acoustic anemometers located along an observation path 500 m long. The good accuracy of retrieval of the cross wind at path segments close to an observer, as well as of the average wind speed over the entire observation path, is demonstrated.
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.
Possibilities of the wind speed profiling along an observation path of a distant object from the analysis of a video sequence of images of the object are studied in this work by numerical simulation. The method is based on the analysis of two neighbor frames of a video sequence of incoherent images. It is more rapid than analogous methods, due to the absence of need in accumulation of the statistics of parameters analyzed. It is shown that the drift speed of several (no less than 3) turbulent layers, located at different distances between the object observed and the receiving optical system, can be determined for some turbulent conditions and object parameters. The method accuracy is estimated for wide ranges of atmospheric conditions and parameters of the object observed.
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.
Possibilities of determining optimal conditions for laser beam focusing in a turbulent atmosphere on the basis of the analysis of target image distortions are analyzed. A series of metrics is considered, which characterize the efficiency of laser beam focusing and the target image quality. A correlation is found between metric fluctuations in the target and observation planes in a dynamically varying turbulent atmosphere in the case of aligned optical axes of the beam focusing and observing systems. As applied to wireless communications, it is shown from the analysis of object images (radiation detector) that the adaptive control of tilts of optical axis of only the transmitting laser system significantly increases the efficiency of data communications.
We present a physics-based model for analysis of atmospheric turbulence and aerosol scattering effects on imaging of remote extended objects under daylight and laser illumination. The technique is based on joint solution of the parabolic wave equation and equation for the brightness function. Turbulent distortions are simulated with the use of the conventional phase-screen approach. Scattering effects are accounted for by representing the aerosol medium by a set of aerosol screens. The coherent and incoherent components of the scattered field are obtained in the single scattering approximation at each aerosol screen. In addition, a simplified model considering the natural background radiation effect on the contrast of an image formed is discussed. Numerical simulation results are presented.
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.
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.
Possibilities of retrieval of the drift velocity of atmospheric turbulence inhomogeneities from a video sequence of incoherent images of an object are studied numerically in the work. A method for filtration of turbulent distortions of an image by their characteristic sizes is suggested with the aim to determine the wind speed at different segments of an observation path. The method testing for the cases of two layers of turbulent inhomogeneities that drift in different (mutually normal) directions has shown high accuracy of retrieval of their drift velocities.
An effect of turbulent inhomogeneities, differently distant from an observer, on distortions of atmospheric object images is analyzed on the basis of numerical simulation. A technique for determining the atmospheric inhomogeneity wind drift from sequence of images of an object specified is suggested. A capability of the technique of determining the atmospheric inhomogeneity wind drift from two images is shown.
A new approach is suggested to the numerical simulation of laser beam propagation through large-scale atmospheric inhomogeneities. Within this approach, the propagation medium is represented as a continuous 3D distribution of largescale inhomogeneities and a set of common 2D phase screens. A new highly effective simulation method with accounting for the effect of large-scale inhomogeneities is suggested within the aberration-free approximation. It is shown that experimentally observed large-scale inhomogeneities can strongly affect long-distance radiation propagation.
Compensation of turbulence in atmospheric imaging is usually hampered by the lack of a reference point source. We
consider the possibility of phase compensation based on the reference wave scattered by the rough surface of an object
under review. Analysis has been made on the basis of numerical simulation. The recently developed method for
incoherent imaging through the atmosphere in anisoplanatic turbulent conditions allows simulating both long-exposure
and short-exposure images. We analyze the influence of the size of object reflecting reference wave on the efficiency of
phase compensation. Image quality enhancement is observed for the object size significantly exceeding the diffractivelimited
size with respect to the receiving aperture. Also we consider the features of phase compensation with the
reference wavelength different from visible light ones.
Modern laser tracking systems use digital video cameras for imaging the tracked objects in atmosphere. Using images
from camera for measurement lead to a measurement error of object coordinates and all other related parameters due to
atmospheric turbulence and thermal blooming of laser beam which track the object.
In our investigation the turbulent and thermal blooming features of object coordinates measurement error are considered.
The estimations in the conditions of mutual action of distorting atmospheric effects mentioned above are generated.
The calculation of error using our estimations in most cases became two orders faster. Modeling is performed for the
case of strong turbulent fluctuations as well as for the case of weak turbulence.
We present the development of a novel technique for numerical simulation and analysis of wide field-of-view (FOV)
incoherent and anisoplanatic imaging of an object through volume turbulence. This technique is based on the recently
developed brightness function method [J. Opt. Soc. Am. A, v. 22, p. 126 (2005)]. We present computer simulation
results demonstrating the anisoplanatic turbulence effects on an object image quality.
The paper considers the error caused by atmospheric turbulence, in determining the motion speed of an object by using
its successive images recorded on a matrix of a digital camera. Numerical modeling of the image of a moving object in
successive time moments is performed. Fluctuation variance of the image mass centre affecting the measurement error
is calculated. Error dependences on the distance to the object and path slope angle are obtained for different turbulence
models. Considered are the situations, when the angular displacement of the object between two immediate shots of the digital camera is greater than the isoplanatism angle as well as the situations when the angular displacement is smaller
than this angle.
The error caused by atmospheric turbulence, in determining the orientation angle of an object (a series of reflectors) has
been studied. The orientation angle was determined by studying the image of the object. Numerical modeling was
performed involving construction of the image of a series of reflectors as if they were observed through a turbulent
medium, calculation of the coordinates of reflector mass centers, finding of the line closest to the reflector mass centers,
and determination of its slope angle. Variance of the slope angle fluctuations is calculated.
The problem of propagation in a turbulent atmosphere of the speckle field reflected from rough surface (the scattered
field) is considered. Two methods of numerical analysis of the averaged field characteristics are compared: the Monte-
Carlo method based on solution of a parabolic equation and the method of solving a transfer equation Fourier-conjugate
to the second order field momentum equation. It is demonstrated that the use of the transfer equation allows us to
considerably (up to several orders) shorten the time taken by numerical modeling, which is important for this type of
problems. It was found that in the case of frozen (stationary) turbulence, the extent of turbulence manifestation but
insignificantly affects the mean correlation field characteristics.
A new approach to formation of random turbulent screens is proposed. Simulation of temporal fluctuations of refractive index inhomogeneities helps in removing the spatial periodicity arising at the transversal displacement of the screen. This improvement allows the formation of random turbulent screens having an infinite extension. Some examples of the problems of atmospheric turbulent optics are presented along with their numerical solution obtained using the algorithm proposed. The problems under consideration involve simulating long (in time) observation series of characteristics of laser beams propagating through the atmosphere.
The propagation of a partially coherent wave field in inhomogeneous media is investigated. The influence of linear and nonlinear refraction and refraction parameter fluctuations on target characteristics of radiation are taken into consideration. The exact solution expressed in quadrature is obtained for the partially coherent radiation propagating through a turbulent medium with the Kolmogorov spectrum of fluctuations and a parabolic distribution of the mean refractive index. On the basis of comparison with this solution the accuracy of the solution of the equation for a coherence function of the second order obtained by the effective ray-tracing technique and taking into account the influence of turbulence and a nonlinearity of a medium to the propagation of a radiation with an arbitrary initial coherence is investigated.
Investigations of the dynamics of turbulent characteristics were carried out for different tracking paths based on theoretical equations. A multi-screen model and single-screen one for turbulent atmosphere have been constructed for numerical simulation of laser beam propagation along atmospheric paths within the framework of the paraxial approximation. These models are suitable for simulation of the propagation along both homogeneous and inhomogeneous paths. Within this model, the Fried radius, the scintillation index, the effective beam radius, and the coherence length of radiation were calculated. The values obtained in the numerical experiment were compared with those calculated analytically.
The diffraction of narrow sharply focused beam propagating through the free space and nonlinear medium was studied. The validity of two approximated approaches for analysis of narrow beam diffraction was studied on the base of comparison with the solution of Kirchgof-Helmholtz diffraction. Both of these approaches is based on the particular solution of Helmholtz equation, which is corresponded with propagation of unidirectional wave. In the first of them attenuating waves are taken into account for the case where the spatial spectrum width is greater than the wave number. The second one is based on the neglect of contribution from attenuating waves. Also, validity of a parabolic wave equation for these situations was researched.
Numerical results of a propagation of the CW laser radiation for extensive slightly elevated atmospheric paths are presented in the paper. The calculations are carried out in the limits of the small-angle equation for the coherence function of the second order describing the partially coherent beam self-action. To solve the equation a new ray-tracing technique creating an effective numerical algorithm was used. The gas absorption was taken into account in frameworks of the average seasonal summer model of an atmosphere. The average cyclic and the volcanic models of an atmosphere were used for aerosol attenuation. High-altitude vertical profiles of turbulent fluctuations of a refractive index were determined for the best, average and worst turbulent conditions. Calculations were obtained for the radiation sources located at altitudes from 10 Km up to 25 Km. Paths up to 500 Km were considered. Let's note, that it is necessary to take into account the influence of the Earth surface curvature for these paths.
To studying the problem of a minimization of an atmosphere influence on an energy transfer as a numerical criterion was selected the effective power density:
Ieff = P/Seff,
where P is a power of radiation at the reception plane, Seff is an effective square of a beam at the reception plane. The initial power, the initial beam focusing and the wavelength of radiation were optimized.
The propagation problem for partially coherent wave fields in inhomogeneous media is considered in this work. The influence of refraction, inhomogeneity of gain medium properties and refraction parameter fluctuations on target characteristics of radiation are taken into consideration. Such problems arise in the study of laser propagation on atmosphere paths, under investigation of directional radiation pattern forming for lasers which gain media is characterized by strong fluctuation of dielectric constant and for lasers which resonator have an atmosphere area. The ray-tracing technique allows us to make effective algorithms for modeling of a partially coherent wave field propagation through inhomogeneous random media is presented for case when the influecne of an optical wave refraction, the influence of the inhomogeiety of radiaitn amplification or absorption, and also the influence of fluctuations of a refraction parameter on target radiation parameters are basic. Novelty of the technique consists in the account of the additional refraction caused by inhomogeneity of gain, and also in the method of an account of turbulent distortions of a beam with any initial coherence allowing to execute construction of effective numerical algorithms. The technique based on the solution of the equation for coherence function of the second order.
Test data of a propagation of the CW laser radiation for extensive weak sloping atmospheric paths are studied in this paper. The calculations are carried out in the limits of the small-angle equation for a coherence function of the second order describing the partially coherent beam self-action. The gas absorption was taken into account in frameworks of the average seasonal summer model of an atmosphere. The average cyclic and the colvanic models of an atmosphere were used for aerosol attenuation. High-altitude vertical profiles of turbulent fluctuations of a refractive index were determined for best, average and worst turbulent conditions. Calculations were obtained for radiation sources located at altitudes from 10 Km up to 25 Km. Paths up to 500 Km were considered. Let's note, that it is necessary to take into account an influence of the Earth surface curvature for these paths. The initial power, the initial beam focusing and the wavelength of radiation were optimized.
The beam dynamics for equal power ray tubes and equal coherence ray tubes is investigated for the partially coherent radiation propagating in non-linear media. The Gaussian beam propagation through media with Kerr non- linearity and thermal blooming is considered on the basis of the solution of the equation for coherence function of the second order. Calculations are adduced for the two- dimensional beam. The dimension of a coherence function decreases from five down to three for this case. Consequently, the numerical solution of this equation is possible by means of the method of a separation on physical factors, widely using for a solution of the parabolic wave equation, with using the algorithm of fast Fourier transformation. The comparable analysis of the equal power and equal coherence ray tubes behavior is carried out. The same analysis is carried out for solutions of the equation for coherence function obtaining by the ray-tracing technique allowing to create effective numerical algorithms for the three dimensional problem. The technique is asymptotically exact since it gives exact solutions at limiting cases when the coherence length tends to zero or when the distribution of complex dielectric constant of medium has the parabolic form.
The propagation problem of the partially coherent radiation in inhomogeneous media is investigated in this paper. The error of the ray-tracing technique for solving the equation for coherence function of the second order is estimated. The ray- tracing technique is asymptotically exact since it gives the exact solution in following limiting cases: within the limit of the geometrical optics ((lambda) yields 0), when the coherence length tends to zero, or when the distribution of the medium complex dielectric permeability has a parabolic form. To estimate an error of the ray-tracing technique for both coherence length and wave length not equal to zero and for an arbitrary distribution of the dielectric permeability the comparison of solutions obtained by the ray-tracing technique with exact ones is performed. The exact solutions are obtained for a model propagation problem of a two-dimensional slit beam for which the dimensionality of the equation decreases from five up to three. To solve the coherence function equation the exact splitting method is used in a combination with the fast Fourier transform. It was obtained that the relative error of the power and statistical characteristics calculating by the ray-tracing technique is no more than 15% at worst. For the majority of problems having practical meaning the relative error of the ray-tracing technique does not exceed 3 - 5%.
The propagation problem for a partially coherent wave field in inhomogeneous random media is considered in this work. The influence of the refraction, the inhomogeneity of gain (absorbing) medium properties and refraction parameter fluctuations on target radiation characteristics are taken into consideration. On the basis of the solution of the equation for the second order coherence function the ray- tracing technique makes an algorithm of the account of turbulence and medium inhomogeneity for arbitrary initial coherence.
Propagation of optical radiation through media with complex dielectric constant is studied in this paper. The rigorous solution of this problems taking into account for curvature of ray trajectories caused by the inhomogeneous absorption is obtained on the basis of the ray-tracing technique. For a parabolic distribution of dielectric constant the analytical solution for a field is obtained. For this and other distributions of the complex dielectric constant such as Gaussian and power-low distribution the comparison is made for exact solutions and solutions neglecting the refraction caused by inhomogeneities of the imaginary component of the complex dielectric constant. It has been found that in the media where the imaginary component of the dielectric constant is comparable to or larger than the real component the effect of the curvature of the ray trajectories due to the inhomogeneity of the imaginary component is essential or dominate, respectively. The validity of solutions neglecting the refraction caused by inhomogeneous absorption is investigated.
Radiation propagating through inhomogeneously absorbing media is investigated within of the geometric optics approach. On the basis of the equation obtained for a real ray trajectory, numerical analysis of propagation features is carried out for various symmetrical distributions of complex dielectric constant such as parabolic, Gaussian and power low distribution. On the basis of the numerical simulations the validity of the solutions constructed on real geometric rays is determined for a propagation problem of coherent and partially coherent radiation. It is shown that the solutions of the propagation problem within the geometric optics limit approach the exact solutions for partially coherent radiation faster than for the coherent one. Recognizing that the equation for the real ray trajectory is not the equation of the second order, we show that two initial conditions do not suffice the problem, namely index point and initial slope angle for the unique definition of the real ray trajectory. On the basis of the analytical solution obtained for the case of parabolic distribution of dielectric constant it was proved analytically that the ray trajectory in highly absorbing inhomogeneous media depends not only on the complex dielectric constant distribution, but also on the wave phase front distribution.
Propagation of partially coherent radiation through strongly absorbing media is studied in this paper. The equation for coherency function was used in the investigation. It was shown that the equation could be reduced to a system of ray equations, assuming a construction of an efficient numerical procedure for its solution. For parabolic distribution of the dielectric constant and an initial Gaussian distribution of the average radiation intensity the analytical solution for a field was obtained. Based on this, the influence of the refraction on inhomogeneous profiles of the refraction index, the absorptance on the statistical, and energy characteristics of radiation were investigated. The peculiarities of coherent and partially coherent radiation propagation through inhomogeneous media were found.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.