Last updated 03 December 2006
DR. OLGA KOROTKOVA
|
Scientist Department of Physics & Astronomy, University of Rochester, NY
Mail:
University of Rochester, Department of Physics & Astronomy,
Office 305, Wilson Blvd / Baush & Lomb, Rochester NY 14627 Phone: 1(585)275 8544 Fax: 1 (585) 473 0687 E-mail: korotkov@pas.rochester.edu Web-page: www.pas.rochester.edu/~korotkov |
Research statement
List of publications
My research interests are primarily in the field of optics, especially in the theories of coherence and polarization of light. I have been conducting theoretical investigations relating to generation, free space propagation, interaction with various media and detection of electromagnetic light fields of both deterministic and random nature. Of particular interest to me are recently discovered changes in polarization properties of stochastic light beams on propagation and their applications. My work falls into the following categories:
1. Developing the basic theory of random sources and fields
Perhaps, the most important part of my research concerns the description of spectral, coherence and polarization properties of random electromagnetic fields which propagate in free space and which interact with various kinds of media. We have recently developed a generalization of conventional Stokes parameters [12] , for which the exact propagation laws can be formulated. Using the generalized Stokes parameters we showed that two sources with the same Stokes vectors can, generally, produce fields with different Stokes vectors [25]. We also employed an alternative way, by use of the cross-spectral density matrices, to show how the polarization ellipse associated with a random electromagnetic beam can change on propagation [13]. Further, we have developed the theory which makes it possible to describe changes in statistical properties of random electromagnetic beams on passage through commonly used polarization-changing devices [18]. Very recently we have shown [24], [28] that if a source generating a random beam is electromagnetic then its polarization can affect the shifts of spectral profiles of generated fields in the far-zone. Previously this effect was attributed only to coherence properties of sources.
A great part of my work was devoted to development of a so-called electromagnetic Gaussian Shell-model (GSM) beam. It is a vectorial generalization of so-called scalar GSM beam which is used in the majority of investigations concerning partially coherent light beams. An electromagnetic GSM beam is capable to describe a beam with any spectral, coherence and polarization properties. After formulating the theory for this class of model beams we have extensively studied conditions for sources that generate such beams [9], [15] and also properties that these beams exhibit on propagation [16] and on passage through various devices of polarization optics [19]. We have also proposed a procedure for generation of this class of beams [14].
In certain situations in optics a field might not be a beam-like, e.g. in the near-field of a source or a scatterer or in the focal region of a lens. For such general or, so-called, 3-dimensional field (3D) its statistical properties have to be defined and measured differently from a usual 2D beam-like field. In [11] we defined the degree of coherence of such field. Later, in [21] we have derived propagation laws for such fields and have generalized the basic Van Cittert-Zernike theorem for 3D fields.
In the theory of detection of light besides the knowledge of the second-order statistical properties of the field it is also important to know their higher order statistical moments, and, more generally, their probability density functions. In [20] I have studied changes in the fourth-order moment (intensity fluctuations) of an electromagnetic Gaussian Schell-model beam on propagation in free space and its dependence on the degree of polarization of the source. For the electromagnetic field fluctuations not only in intensity but also in all four Stokes parameters must be calculated, in general. In [23] I have investigated how fluctuation contrasts and the probability density functions of the Stokes parameters of beams behave on propagation in free space. I am planning to continue work in this direction, focusing primarily on propagation of aforementioned statistical properties of beams in different kinds of media.
We have also formulated the theory of scattering of random (scalar) beams from deterministic and random media [30] with a help of so-called pair-scattering matrices. Such matrices connect correlation properties of the incident field in a pair of directions and of the scattered field int another pair of directions. Using this approach one can determine intensity distribution and coherence properties of the scattered field both in the near zone and in the far zone of the scatterer.
2. Applications of the theory for beam propagation in the turbulent atmosphere
Since the work on my dissertation I was interested in propagation of partially coherent beams in the turbulent atmosphere (e.g. [1], [2]). Although most of my studies concerned Gaussian Shell-model beams, very recently we have developed a method, based on the angular spectrum representation of fields, for propagation of second order statistics of any (deterministic or random) beams in the atmosphere [27], [31], [32]. The method proved to be computationally efficient and the results relating to several conventionally used beams (e.g. Gaussian beams) obtained by it were found to be in agreement with ones derived earlier by standard techniques. Moreover, with the help of our new method we managed to determine intensity profiles for (coherent) Bessel beam and (partially coherent) Bessel-correlated beam propagating through atmospheric turbulence.
We have also studied how the polarization properties of random electromagnetic beams behave on propagation in the atmosphere. In [8] and [10] we have proved analytically and demonstrated by many examples, that the degree of polarization of light beam can suffer drastic changes on propagation even at short distances from the source, but at large distances it returns to the same value as it has in the source plane. Later the same phenomenon was shown with regards of polarization ellipse [17]. This self-reconstruction property of electromagnetic GSM beams interacting with the atmosphere turns out to be rather special: as it was shown later (e.g. [26]) that a GSM beam interacting with tissues can not reconstruct its polarization properties. We have also started investigation of behavior of polarization properties of beams different from GSM beams [31], [32].
In almost any application involving propagation of beams in atmospheric turbulence, besides the knowledge of their second-order statistics it is crucial to calculate some of their fourth-order statistics, in particular, the contrast of fluctuating intensity (also known as the scintillation index). For example, to establish high quality communication link through the atmospheric path one must reduce the scintillation index as much as possible. We have shown in [3] – [7] that the use of partially coherent beams instead of conventional coherent beams can lead to significant reduction in scintillation. I have also shown in [22] that partial polarization can be used, together with partial coherence, to reduce the scintillation index even further.
3. Applications of the theory for medical imaging and dagnostics
I have recently started to employ the theory of random electromagnetic beams to study their propagation in human tissues, which is a matter of a great interest for medical imaging and medical diagnostics. We have shown in [26] how the state of polarization of a typical random beam can change on propagation through tissue. The other aspect of this research [34] is related to modification of the spectrum of light propagating in tissues, the analysis which may find uses in medical spectroscopy.
Because of its strong theoretical foundation and its versatile applications I believe that it is important to pursue deeper investigation of stochastic electromagnetic fields and to find particular types of such fields, which are optimal for different applications.
List of publications
1. O. Korotkova, L.C. Andrews, “Speckle Propagation through Atmospheric Turbulence: Effects of Partial Coherence of the target”, Proc. SPIE 4723 (2002).
Based on ABCD ray matrix theory and a random phase screen model for the target surface, analytic expressions are developed for the normalized mutual coherence function (MCF) of a reflected Gaussian-beam wave from a finite target in the presence of atmospheric turbulence. This analysis features both pupil plane and image plane expressions and includes partial and fully developed speckle from the target. The target model is a combination of a thin random phase screen and limiting aperture stop such that a weak screen corresponds to a mildly-rough target and a strong (or deep) random phase screen corresponds to fully developed speckle. From the normalized MCF, estimates are given for the speckle size in the pupil plane and image plane as a function of transmitted beam wave characteristics, size and roughness of the target, and size of the receiver collecting lens.
2. O. Korotkova, L.C. Andrews, R.L. Phillips, “Speckle Propagation through Atmosphere: Effects of a Random Phase Screen at the Source”, Proc. SPIE 4821 (2002).
3. O. Korotkova, L.C. Andrews, R.L. Phillips, “Phase Diffuser at the Transmitter for the Lasercom Link: Effect of partial coherence on Bit-Error Rates”, Proc. SPIE 4976 (2003).By using ABCD ray matrix theory and a random phase screen located near the source, analytic expressions are developed for the mutual coherence function and scintillation index of a Gaussian-beam wave propagating through weak atmospheric turbulence in both the pupil plane and image plane of a receiving system. The phase screen model that we use is based on a previous double-pass analysis by the authors for analyzing speckle propagation from a rough target in a lidar system. In the present context, it serves as a model for a partially coherent Gaussian beam wave that is currently used in laser communications. The effect of partial coherence (induced by a diffuser) on the scintillation index of the beam in the presence of weak atmospheric turbulence is investigated as a function of the correlation length of the diffuser and the propagation distance.
4. O. Korotkova, L.C. Andrews, R.L. Phillips, “Laser radar in turbulent atmosphere: Effect of Target with Arbitrary Roughness on II and IV Order Statistics of Gaussian Beam”, Proc. SPIE 5086 (2003) .By using a complex phase screen model for a diffuser located at the transmitter, analytic expressions are developed for the scintillation index of a lowest order Gaussian-beam wave in the pupil plane of the receiver in weak and strong atmospheric conditions. The effect of partial coherence on the scintillation index is analyzed as a function of the propagation distance and the correlation length of the diffuser. The reduction in the scintillation level (due to the transmitter aperture averaging effect) is shown under all atmospheric conditions. The signal to noise ratio and the bit error rates (for OOK signal modulation) are discussed.
5. O. Korotkova, L.C. Andrews, R.L. Phillips, “The Effect of Partially Coherent Quasi-Monochromatic Gaussian-Beam on the Probability of Fade”, Proc. SPIE 5160 (2003).Analytic expressions for the mutual coherence function and the scintillation index of the lowest order Gaussian beam as a function of target roughness are developed for a bistatic configuration in weak and strong atmospheric turbulence. Results are based on Rytov theory and Kolmogorov spectrum model. The surface roughness is modeled by a thin complex phase screen with a Gaussian spectrum. The limiting cases of perfectly smooth and Lambertian targets are deduced. The particular cases of incident spherical and plane waves are also considered.
6. O. Korotkova, L.C. Andrews, R.L. Phillips, “LIDAR Model for a Rough-Surface Target: Method of Partial Coherence”, Proc. SPIE 5237 (2003).The effect of a (spatially) partially coherent quasi-monochromatic lowest order Gaussian-beam on the direct detection system is studied in weak and strong atmospheric turbulence. The analytic expression for the scintillation index has been developed and analyzed as a function of the spatial correlation distance and the correlation time, associated with the source, as well as the strength of turbulence and the integration time of the detector. The probability of fade is also discussed as a function of relative detector speed,. including limiting cases of slow and fast detector.
7. O. Korotkova, L.C. Andrews, R.L. Phillips, “A Model for a Partially Coherent Gaussian Beam in Atmospheric Turbulence with Application in Lasercom”,Renewed interest in the propagation characteristics of a partially coherent beam has led to several recent studies that have extended theoretical developments started in the 1970s and 1980s. In this paper we use a model developed by the authors for single-pass propagation of a partially coherent beam and extend it to the case of a Gaussian-beam wave reflected from a finite rough-surface reflecting target. This model can be modeled as a random phase screen (or diffuser) in front of a smooth finite reflector. The target acts like a deep random phase screen for the case of a fully diffuse surface and becomes a continually weakening phase screen as the target surface become smoother. We present mathematical models for the mutual coherence function (MCF) and the scintillation index of the reflected Gaussian beam wave in the presence of atmospheric turbulence. This analysis includes partial and fully developed speckle from the target. From the normalized MCF, estimates are given for the speckle size in the pupil plane and image plane as a function of transmitted beam wave characteristics, size and roughness of the target, and size of the receiver-collecting lens. Expressions for the scint illation index are valid under weak-to-strong fluctuation conditions and are shown to agree with well-known results in limiting cases of a fully diffuse target and a smooth reflector.
Opt. Eng. 43(2), 330-341 (2004).8. O. Korotkova, M. Salem and E. Wolf, “The far-zone behavior of the degree of polarization of partially coherent beams propagating through atmospheric turbulence”, Opt. Comm. 233, 225-230 (2004).Analytic expressions for the mutual coherence function (MCF) and the scintillation index of a partially coherent lowest-order Gaussian-beam wave propagating through the atmosphere (based on Kolmogorov spectrum model) are developed for the pupil plane of a receiving system. Partial coherence of the beam is modeled as a thin (complex) phase screen with Gaussian spectrum (Rytov theory and ABCD ray-matrices are applied). The relation between the second and fourth order statistics for a beam with any degree of coherence in the atmosphere is introduced with the help of “effective” beam parameters, deduced from the free space MCF. In particular, the scintillation (in weak and strong atmospheric conditions), based on these parameters, is studied as a function of the diffuser’s strength and that of the atmosphere. The model is applied for the calculation of the signal to noise ratio and Bit-Error Rates (OOK modulation) of the communication link with diffuser at the transmitter and slow detection system. The improvement of Bit-Error rates is observed in weak and strong atmospheric turbulence. In weak regime the optimal diffuser can be found.
9. O. Korotkova, M. Salem and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source”, Opt. Lett. 29(11), 1173-1175 (2004).It is shown analytically that the degree of polarization of a beam generated by a partially polarized Gaussian-Schell model source which propagates through atmospheric turbulence tends to its value at the source plane with increasing distance of propagation. This result is independent of the spectral degree of coherence of the source and of the strength of atmospheric turbulence. These conclusions are illustrated by a numerical example.
10. M. Salem, O. Korotkova, A. Dogariu and E. Wolf, “Polarization changes in partially coherent EM beams propagating through turbulent atmosphere”,It has been shown not long ago, that the basic properties of a fluctuating electromagnetic beam may be derived from the knowledge of a cross-spectral density matrix of the electric field in the source plane. However, not every such matrix represents a source which will generate a beam-like field. In this Letter we derive conditions which the matrix has to satisfy in order that the source generates an electromagnetic Gaussian Schell-model beam.
Waves in Random Media 14(4), 513-523 (2004).11. O. Korotkova and E. Wolf, “The Spectral Degree of Coherence for random electromagnetic fields”, J. Opt. Soc. Am. A 21(12), 2382-2385 (2004).In this paper we study the effects of turbulent atmosphere on the degree of polarization of a partially coherent electromagnetic beam, which propagates through it. The beam is described by a 22 cross-spectral density matrix and is assumed to be generated by a planar, secondary, electromagnetic Gaussian Schell-model source. The analysis is based on a recently formulated unified theory of coherence and polarization and on the extended Huygens-Fresnel principle. We study the behavior of the degree of polarization in the intermediate zone, i.e. in the region of space where coherence properties of the beam and the atmospheric turbulence are competing. We illustrate the analysis by numerical examples.
12. O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams", Opt. Lett. 30(2) 198-200 (2005).The complex spectral degree of coherence of a general random, statistically stationary, electromagnetic field is introduced in a manner similar to the way it is defined for a beam-like field, namely by means of Young’s interference experiment. Both its modulus and its phase are measurable. We illustrate the definition by considering a blackbody radiation field. The results are of particular interest for near-field optics.
13. O. Korotkova and E. Wolf, "Changes in the state of polarization of a random electromagnetic beam on propagation”, Opt. Comm., 246(3) 35-43 (2005).In this paper a generalization of the Stokes parameters of a random electromagnetic beam is introduced. Unlike the usual Stokes parameters which depend on one spatial variable, the generalized Stokes parameters depend on two spatial variables. They are shown to obey precise laws of propagation, both in free space and in any linear medium, whether deterministic or random. With the help of the generalized Stokes parameters, the changes of the ordinary Stokes parameters on propagation can be determined. Numerical examples of such changes are presented. The generalized Stokes parameters contain information not only about the polarization properties of the beam but also about its coherence properties. We illustrate this fact by deriving an expression for the degree of coherence of the electromagnetic beam in terms of one of the generalized Stokes parameters.
14. T. Shirai, O. Korotkova and E. Wolf, "A method of generating electromagnetic Gaussian Schell-model beams", J. Opt. A: Pure Appl. Opt. 7 232-237 (2005).We show that the state of polarization of the polarized portion of a random, statistically stationary, electromagnetic beam may change on propagation, even in free space. We derive analytic formulas for the orientation angle and for the magnitudes of the major and of the minor axes of the polarization ellipse in terms of the elements of the 2x2 cross-spectral density matrix of the electric field. We also obtain conditions for the invariance of the state of polarization on propagation. We illustrate the results by a numerical example relating to an electromagnetic Gaussian Schell-model beam.
15. H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources", Opt. Comm. 249(4), 379-385 (2005).A method of generating electromagnetic Gaussian Schell-model (GSM) source from two coherent linearly polarized plane waves is described. This method involves two mutually correlated phase-only liquid-crystal spatial light modulators (SLMs) placed in the arms of a Mach–Zehnder interferometer. The sources, produced by this method can be used to generate a wide class of electromagnetic beams with prescribed coherence and polarization properties.
The electromagnetic Gaussian Schell-model (EGSM) beam is the simplest analytical model of a random electromagnetic beam. The model has been successfully used in studies of spectral, polarization and coherence properties of random electromagnetic beams on propagation in free space or in any linear medium, deterministic or random. The most general type of source which produces electromagnetic Gaussian Schell-model beam is characterized by ten parameters. Using properties of the cross-spectral density matrix of such a beam we derive necessary and sufficient conditions which the parameters of the source must satisfy in order to generate a physically realizable beam of this type. The conditions provide certain constraints for synthesis, simulations and any application of such beams.16. O. Korotkova, B. Hoover, V. Gamiz and E. Wolf, "Coherence and polarization properties of far-fields generated by electromagnetic quasi-homogeneous sources", J. Opt. Soc. Am. A 22(11), 2547-2556 (2005).
17. O. Korotkova, M. Salem, A. Dogariu and E. Wolf, “Changes in the polarization ellipse of random electromagnetic beams propagating through turbulent atmosphere”, Waves in Random and Complex Media 15, 353-364 (2005).In studies of radiation from partially coherent sources the so-called quasi-homogeneous (QH) model sources have been very useful, for instance in elucidating the behavior of fields produced by thermal sources. The analysis of the fields generated by such sources has, however, been largely carried out in the framework of scalar wave theory. In this paper we generalize the concept of the QH source to the domain of the electromagnetic theory and we derive expressions for the elements of the cross-spectral density matrix, for the spectral density, for the spectral degree of coherence, for the degree of polarization and the Stokes parameters of the far-field generated by planar QH sources of a uniform state of polarization. We then derive reciprocity relations analogous to those familiar in connection with the generalized van Cittert-Zernike theorem for radiation from scalar sources. We illustrate the results by determining the properties of the far field produced by transmission of an electromagnetic beam through a system of spatial light modulators.
In the last few years changes in the state of polarization of a class of random electromagnetic beams (so-called electromagnetic Gaussian Schell-model beams), propagating in free space have been investigated. In the present paper we extend the analysis to propagation of such beams in homogeneous, isotropic, non-absorbing atmospheric turbulence. We find that the effects of turbulence on the state of polarization are most significant when the atmospheric fluctuations are weak or moderate, while in strong regime of atmospheric fluctuations the state of polarization of the beam returns to its original state. Our results might find useful applications for sensing, imaging and communication through the atmosphere.18. O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part I. General theory”, J. Mod. Opt. 52, 2659-2671 (2005).
19. O. Korotkova and E. Wolf, “Effects of linear non-image forming devices on coherence and polarization properties of random electromagnetic beams. Part II. Examples”, J. Mod. Opt. 52, 2673-2685 (2005).The classic theoretical techniques of polarization optics are the Jones calculus and the Stokes-Mueller calculus. Both deal with transmission of certain “one-point” quantities, which are associated with a light beam. Recently “two-point” quantities were introduced, which are the elements of a cross-spectral density matrix that characterizes the correlations at two points in a beam or which are expressible in terms of them. Unlike the quantities with which the Jones and the Stokes calculus deal, these generalized quantities contain information not only about the polarization properties of the beam but also about its coherence properties. In this paper we present a generalization of the Jones calculus and of the Stokes-Mueller calculus which deal with transformations of the new two-point quantities by linear non-image forming devices. These devices may act on the beam in a deterministic or in a random manner.
20. O. Korotkova, “Changes in the statistics of random electromagnetic beams on propagation”, J. Opt. A: Pure Appl. Opt. 8, 30-37 (2006).The theory developed in Part I of this investigation [19] is applied to determine the changes in the spectrum, in the degree of polarization and in the degree of coherence of a random electromagnetic beam which passes through each of the common devices of polarization optics namely the polarizers, the compensators, the rotators and the absorbers. The general formulas are illustrated by examples.
21. M. A. Alonso, O. Korotkova and E. Wolf, “Propagation of the electric correlation matrix and the van Cittert-Zernike theorem for random electromagnetic fields”, J. Mod. Opt. 53, 969-978 (2006).We discuss fourth-order correlation properties of a wide-sense statistically stationary, quasi-monochromatic, electromagnetic beams, assuming that the fluctuations in the electric field at any point are governed by Gaussian statistics. In particular, we derive expressions for the covariance function and for the contrast (scintillation index) of the fluctuating intensity of an electromagnetic Gaussian Schell-model beam, propagating in free space. For such beams we also derive expressions relating to fluctuations in the power and discuss the effects of transmitter and receiver aperture averaging. We show that the fluctuations of the intensity and of the power of the beam can be controlled by suitable choice of the states of coherence and of polarization of the source.
22. O. Korotkova, “Control of the intensity fluctuations of random electromagnetic beams on propagation in weak atmospheric turbulence”, Proc. SPIE 61050V, 1-9 (2006).The basic mathematical tool of the theory of random, statistically stationary, electromagnetic optical fields is a correlation matrix of its electric field. In this paper we derive formulas for propagation of this matrix from a plane into the half-space , and find an analog for electromagnetic fields to the propagation law derived by Zernike for scalar fields.
23. O. Korotkova, “Changes in statistics of the instantaneous Stokes parameters of a quasi-monochromatic electromagnetic beam on propagation”, Opt. Comm. 261, 218-224 (2006).The dependence of the fluctuating intensity of a class of stochastic electromagnetic beams on its polarization properties is studied as the beam propagates in a non-absorbing, homogeneous atmospheric turbulence described by the Kolmogorov’s model. We show that partially polarized and unpolarized beams can be employed instead of fully polarized beams in order to reduce the normalized variance of intensity fluctuations (the scintillation index) anywhere in the cross-section of the beam which propagates through weak and strong turbulence.
24. J. Pu, O. Korotkova and E. Wolf, “Invariance and non-invariance of the spectrum and of the degree of polarization of stochastic electromagnetic beams onThe changes in the probability density functions (PDFs) are discussed, of the instantaneous Stokes parameters of a quasi-monochromatic electromagnetic beam propagating in free space. Such changes may be caused by correlations between the components of the electric field at a pair of points in the source plane. When the fluctuations of the electric field are governed by Gaussian statistics the PDFs of the instantaneous Stokes parameters at any distance from the source are completely determined by the two-point correlation properties of the field in the source plane. These results can be used for synthesis of sources generating random beams with prescribed statistical properties. They also may find applications in remote sensing, tomography and communications with partially coherent and partially polarized light.
propagation”, Opt. Lett. 31, 2097-2099 (2006).25. M. Salem, O. Korotkova, and E. Wolf, “Can two planar sources with the same sets of Stokes parameters generate beams with different sets of StokesIt has been known for some time that the spectrum of light may change on propagation, even in free space. The theory of this phenomena was developed within the framework of scalar theory. In this paper we generalize it to electromagnetic beams, generated by planar, secondary, stochastic sources. We also derive an electromagnetic analog of the so-called scaling law. When this law is satisfied the normalized spectrum of the beam is the same throughout the far zone and is the same as the normalized source spectrum. We illustrate our analysis by an example.
parameters?” Opt. Lett. 31, 3025-3027 (2006).26. W. Gao and O. Korotkova, “Changes in the state of polarization of a random electromagnetic beam propagating through tissue”, Opt. Comm. (2007, in press).It is shown that two stochastic electromagnetic beams which propagate from the source plane into the half-space may have different degrees of polarization throughout the half-space, even though they have the same sets of Stokes parameters in the source plane . This fact is due to a possible difference in the coherence properties of the field in that plane but other reasons are also possible. The result is illustrated by an example.
27. G. Gbur and O. Korotkova, “Angular spectrum representation for propagation of arbitrary coherent and partially coherent beams through atmospheric turbulence”, J. Opt. Soc. Am. A (2007, in press).Based on the recently proposed unified theory of coherence and polarization of random electromagnetic beams, we have derived formulae describing changes in the state of polarization of a random electromagnetic beam propagating through tissue. A so-called electromagnetic Gaussian Schell-model beam is used to illustrate the theory. The results may find possible applications in tissue imaging.
28. O. Korotkova, J. Pu and E. Wolf, “Effects of source polarization and source coherence on far-zone spectra of stochastic beams" (submitted toAn angular spectrum representation is applied for a description of statistical properties of arbitrary beamlike fields propagating through atmospheric turbulence. The Rytov theory is used for the characterization of the perturbation of the field by the atmosphere. In particular, we derive expressions for the cross-spectral density of a coherent and a partially coherent beam of arbitrary type in the case when the power spectrum of atmospheric fluctuations is described by the von Karman model. We illustrate the new method by applying it to propagation of several model beams through the atmosphere.
Phys. Rev. E).29. A. Al-Qasiami, D.F.V. James, O. Korotkova and E. Wolf, “Definitions of the degree of polarization of a light beam” (submitted to Opt. Lett.).It was shown some years ago that the spectrum of a stochastic scalar field depends not only on the source spectrum but also on the degree of coherence of the source. In this paper we show that there are electromagnetic sources, whose degree of polarization also affects the spectrum of the radiated field. We illustrate the analysis by diagrams which show the far-zone spectra of some stochastic electromagnetic beams generated by sources of different states of coherence and different degrees of polarization. The spectra of the radiated field depend both on coherence properties of the source and its degree of polarization and are found to be different in different directions of observation.
30. O. Korotkova and E. Wolf, “Scattering Matrix Theory for stochastic scalar fields” (submitted to Phys. Rev. E).A necessary and sufficient condition is derived for certain ad hoc expressions that are frequently used in the literature to represent correctly the degree of polarization of a light beam.
31. O. Korotkova and G. Gbur, ”Propagation of beams of any spectral, coherence and polarization properties in turbulent atmosphere”, Proc. SPIE. 6457 (2007).We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a new scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation the new scattering matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the scattered field, the new scattering matrix makes it possible to determine the changes in the spectrum and in the state of coherence of field produced on scattering.32. O. Korotkova and G. Gbur, “Angular spectrum approach for propagation of electromagnetic beam-like fields in random medium” (in preparation).The combination of an angular spectrum representation (in space-frequency domain) and of the Rytov perturbation theory is applied for description of the second-order statistical properties of arbitrary (coherent and partially coherent) stochastic fields (whether scalar or electromagnetic) which propagate in turbulent atmosphere. The analysis is restricted to weak regime of atmospheric fluctuations. We first introduce the new method for scalar fields and derive expressions for the cross-spectral density function, from which the spectral and the coherence properties of the propagating fields can be determined. Next we extend the new technique to electromagnetic domain, i.e. we derive expressions for the elements of the 2x2 cross-spectral density matrix of the electric field from which its spectral, coherence and polarization properties can then be found. We illustrate the new method by applying it to propagation of several model beams through the atmosphere. In particular, we consider Gaussian beam, Bessel beam, Gaussian Schell-model beam in their scalar or electromagnetic versions. We find that the results obtained on the basis of the new theory are in good agreement with those obtained earlier by standard techniques.
33. V. L. Gamiz, O. Korotkova and E. Wolf, “The spectral degree of coherence of Gaussian Schell-model beams propagating in the turbulent atmosphere”The combination of an angular spectrum representation (in space-frequency domain) and the second-order Rytov's perturbation theory is applied for description of the second-order statistical properties of arbitrary (coherent and partially coherent) stochastic electromagnetic beam-like fields which propagate in turbulent atmosphere. In particular, we derive the expressions for the elements of the cross-spectral density matrix of the beam from which its spectral, coherence and polarization properties can be found. We illustrate the new method by applying it to propagation of several electromagnetic model beams through the atmosphere.
(in preparation).34. O. Korotkova, “Scintillation index of a random electromagnetic beam propagating through turbulent atmosphere” (in preparation).Expressions are derived for determining the changes in the spectral degree of coherence of a stochastic Gaussian Schell–model electromagnetic beam which propagates in free space or in the turbulent atmosphere. The results are illustrated by numerical examples.
35. O. Korotkova and W. Gao, “Spectral changes of beams propagating in human tissue” (in preparation).We study the behavior of the scintillation index (the contrast of fluctuating intensity) of a wide-sense statistically stationary, quasi-monochromatic, electromagnetic beam on propagation through atmospheric turbulence. In particular, we show that in the case when the beam is electromagnetic not only its degree of coherence but also its degree of polarization in the source plane can affect the values of the scintillation index along the propagation path. We find that, generally, unpolarized beams lead to reduced level of scintillation compared with polarized beams which have the same intensity in the source plane. These results may find applications in free space optical communications.
It is well known that the spectrum of light can change on propagation, even in free space. Such change is due to the correlation properties of the source. We determine how the spectrum of a beam of light of any state of coherence changes on propagation in human tissue. We illustrate results by examining spectral shifts of typical Gaussian Schell-model beam with Gaussian spectral line, which propagate through the epidermis, the upper level of human skin. The results may be of importance to spectroscopy.