Beams In Inhomogeneous Media Research Articles

Cauchy–Riemann beams in GRIN media

We investigate the propagation characteristics of Cauchy–Riemann beams in gradient-index media. Our study reveals two key findings: first, the preservation of their form during propagation; and second, the surprising feasibility of obtaining the two-dimensional fractional Fourier transform for any arbitrary entire function. We elucidate an explicit and straightforward expression for this transform. Additionally, our results contribute to a deeper understanding of the behavior of Cauchy–Riemann beams in inhomogeneous media, offering insights that may have implications for various applications in optics and wave propagation.

Method of Spherical Phase Screens for Modeling the Propagation of Diverging Beams in Inhomogeneous Media

The phase-screen (split-step) method is widely used for modeling wave propagation in inhomogeneous media. The method of plane phase screens is best known. However, for modeling a 2D problem of radio occultation sounding of the Earth’s atmosphere, the method of cylindrical phase screen was developed many years ago. In this paper, we propose a further generalization of this method for the 3D problem on the basis of spherical phase screens. In the paraxial approximation, we derive the formula for the vacuum screen-to-screen propagator. We also infer the expression for the phase thickness of a thin layer of aisotropic random media. We describe a numerical implementation of this method and give numerical examples of its application for modeling a diverging laser beam propagating on a 25-km-long atmospheric path.

Method of spherical phase screens for the modeling of propagation of diverging beams in inhomogeneous media

The phase-screen (split-step) method is widely used for the modeling of wave propagation in inhomogeneous media. Most known is the method of flat phase screens. An optimized approach based on cylindrical phase screen was introduced for the 2-D modeling of radio occultation sounding of the Earth’s atmosphere. In this paper, we propose a further generalization of this method for the 3-D problem of propagation of diverging beams. Our generalization is based on spherical phase screens. In the paraxial approximation, we derive the formula for the vacuum screen- to-screen propagator. We also derive the expression for the phase thickness of a thin layer of an isotropic random media. We describe a numerical implementation of this method and give numerical examples of its application for the modeling of a diverging laser beam propagating on a 25 km long atmospheric path.

Phase transition of cosh-Airy beams in inhomogeneous media

The cosh-Airy beam is a kind of nondiffracting beam that can be considered as a superposition of two Airy beams with different decay factors and the same propagation trajectory. In this study, we investigate the propagation of a cosh-Airy beam in a quadratic-index inhomogeneous medium and show the periodic phase transition of the cosh-Airy beam, which exhibits a beam transition from the Airy profile to a cosine Gaussian profile periodically. After the phase transition, the field distribution of the cosh-Airy beam is inverted, but the self-acceleration direction of the cosh-Airy beam is unchanged. We show that because of the phase difference of two components of the cosh-Airy beam, the interference effect of the two components plays an important role in the phase transition of the cosh-Airy beam in inhomogeneous medium. Our study may lead to some new potential applications in the manipulation of the Airy beam, signal processing, and other fields.

Физико-технические проблемы управляемого термоядерного синтеза

The lines of scientific activity and the results of investigations carried out at the MPEI Department of General Physics and Nuclear Fusion are briefly reviewed. The conducted activities are mainly focused on the problems of controlled thermonuclear fusion and plasma technologies. Efforts are taken to study heat transfer and hydrodynamics in the plasma-facing structural components of thermonuclear reactors, one-sided heating of which results in essentially nonuniform distributions of heat flux density and wall temperature over the pipe inner perimeter. Another line of research activities is concerned with experimental investigations of nucleate boiling and heat transfer in essentially subcooled flow, of enhanced heat transfer in annular channels and models of pebble fuel element beds, and of heat transfer enhancement as applied to the problems concerned with cooling the International thermonuclear experimental reactor (ITER). A large-scale test bench for studying thermal-hydraulic processes in the models of advanced nuclear fuel assemblies operating with the parameters of a VVER-type reactor has been constructed. Activities are underway on studying the resistance of refractory metals to the effect of powerful plasma and heat fluxes expected to take place in a tokamak-type thermonuclear reactor. A plasma installation equipped with a linear multicusp magnetic system featuring uniquely high parameters has been constructed, which is used to perform tests of materials exposed to megawatt-scale hot plasma. The unique plasma installation has been constructed for studying plasma-to-surface interaction and high-temperature plasma testing of refractory materials like tungsten, molybdenum, steel, etc. The experiments to be performed on the installation are aimed at developing a new technology for producing a highly porous surface nanostructure of refractory metal, including tungsten “fuzz”. Such investigations are topical for inventing new materials that are of considerable interest for nuclear, chemical, power, and biomedical technologies. The main lines of activities on nanotechnologies include obtaining, studying and using carbon nanostructures such as fullerenes, carbon nanotubes, graphene, and their derivatives. Within the framework of studying the strengthening phenomenon, the extent of steel surface strengthening as a function of the type and intensity of incident radiation, and the type of nanocarbon material is considered. The interaction of charged particles and radiation with structural materials is investigated. Experimental and theoretical investigations of the interaction of electrons and light ions with inhomogeneous solid bodies are continued to solve the problems concerned with scattering ion beams in inhomogeneous media. Innovative methods for destructive and non-destructive analysis of thin films are developed, including layer-wise analysis techniques. Unique plasma installations have been constructed at the department, such as a high-frequency induction plasmatron for carrying out chemical spectral analysis, an arc plasmatron for studying the free plasma burning processes, a high-voltage installation for studying streamer and arc discharges with electrolysis, and a cold plasma installation for studying the effect of discharge on biological tissues. All these installations are successfully used for carrying out both research activities and student training laboratory works.

Light-sheet generation in inhomogeneous media using self-reconstructing beams and the STED-principle.

Self-reconstruction of Bessel beams in inhomogeneous media is beneficial in light-sheet based microscopy. Although the beam's ring system enables propagation stability, the resulting image contrast is reduced. Here, we show that by a combination of two self-reconstructing beams with different orbital angular momenta it is possible to inhibit fluorescence from the ring system by using stimulated emission depletion (STED) even in strongly scattering media. Our theoretical study shows that the remaining fluorescence γ depends non-linearly on the beams' relative radial and orbital angular momenta. For various scattering media we demonstrate that γ remains remarkably stable over long beam propagation distances.

Analytical and numerical modeling of light scattering in composite transmission laser welding process

Analytical and numerical models for laser beam scattering in the thermoplastics composites are presented. The numerical model is based on Ray Tracing, an optical method to compute the optical propagation of laser beams in inhomogeneous media with spatially varying dispersion of the refractive index. In this study, only the case of unidirectional thermoplastic composites (UD) is presented. During transmission laser welding process, a divergence of the laser beam is observed in the first part (transparent in the laser wavelength) due to the internal refraction at the microscopic scale of the beam at each matrix-fiber interface. At the macroscopic scale, this phenomenon leads to the light scattering of the laser beam in this heterogeneous media. Under these conditions, a modeling of the propagation of a laser beam appears essential. An analytical model compared to numerical model is proposed, that enables to simulate and to optimize the laser source at the welding interface. This model provides a good estimation of the laser beam intensity profile at the welding interface (radiative heat well defined) and the beam widening. Those steps are necessary to describe the heat source in the laser welding process thermal simulations. The distribution of the heat source at the interface is one of the most important parameter in the description of the laser welding process.

Spiral laser beams in inhomogeneous media

Explicit solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation are applied to wave fields with invariant features, such as oscillating laser beams in a parabolic waveguide and spiral light beams in varying media. A similar effect of superfocusing of particle beams in a thin monocrystal film, harmonic oscillations of cold trapped atoms, and motion in magnetic field are also mentioned.

Gaussian beam evolution in logarithmically saturable nonlinear media

The method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. The power of PCGO method is presented on the example of GB evolution in logarithmically saturable medium with defocusing refractive profile. The solutions obtained by PCGO method are compared with numerical results of Nonlinear Schrodinger Equation by beam propagation method (BPM). Full Text: PDF References Yu.A. Kravtsov, "Complex rays and complex caustics", Radiophys. Quantum Electronics 10, 719 (1967). CrossRef .B. Keller, W. Streifer, "Complex Rays with an Application to Gaussian Beams", J. Opt. Soc. Am. 61, 40 (1971). CrossRef G. A. Deschamps, "Gaussian beam as a bundle of complex rays", Electron. Lett. 7(23), 684 (1971). CrossRef Yu.A. Kravtsov, G.W. Forbes, A.A. Asatryan, Theory and applications of complex rays, in Progress in Optics, edited by E. Wolf, 39, 3 (Elsevier, Amsterdam, 1999). S.J. Chapman, J.M. Lawry, J.R. Ockendon, R.H. Tew, "On the Theory of Complex Rays", SIAM Review 41, 417 (1999). CrossRef Yu.A. Kravtsov, P. Berczynski, "Gaussian beams in inhomogeneous media: A review", Stud. Geophys. Geod. 51(1), 1 (2007). CrossRef Yu.A. Kravtsov N.Y. Zhu. Theory of diffraction: Heuristic Approaches (Alpha Science International, ISBN 1842653725, 2009). P. Berczynski, Yu.A. Kravtsov, "Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eikonal form of complex geometrical optics", Phys. Lett. A 331(3-4), 265 (2004). CrossRef P. Berczynski, K.Yu. Bliokh, Yu.A. Kravtsov, A. Stateczny, "Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach", J. Opt. Soc. Am. A, 23(6), 1442 (2006). CrossRef P. Berczyński, Yu. Kravtsov, "Gaussian beam evolution in nonlinear inhomogeneous fibres", Phot. Lett. Poland 4(1), 26 (2012). CrossRef P. Berczynski, Yu. A. Kravtsov, G. Zeglinski, "Gaussian beam diffraction in inhomogeneous media of cylindrical symmetry", Optica Applicata 40(3), 705 (2010). DirectLink A.W. Snyder, J.D. Mitchell, "Mighty morphing spatial solitons and bullets", Optics Letters 22(1), 16 (1997). CrossRef Y.L. Tang, J.G Chen, D.Y Li, J. Kang, Y. Li, "Specific gaussian beams propagating inside logarithmically saturable nonlinear media", J. Modern Optics 46(8), 1177 (1999). CrossRef T. Hansson, D. Anderson, M. Lisak, "Soliton interaction in logarithmically saturable media", Opt. Comm. 283(2), 318 (2010). CrossRef

Gaussian beam evolution in nonlinear media of Kerr type

The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. PCGO deals with ordinary differential equations for the beam amplitude and for complex curvature of the wave front which describe evolution of axially symmetric GB in Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in medium of Kerr type. Full Text: PDF References Yu. A. Kravtsov, "Complex rays and complex caustics", Radiophys. Quantum Electronics 10, 719−730 (1967). CrossRef J. B. Keller and W. Streifer, "Complex rays with application to Gaussian beams", J. Opt. Soc. Am. 61, 40−43 (1971) CrossRef G. A. Deschamps, "Gaussian beam as a bundle of complex rays", Electron. Lett. 7(23), 684−685 (1971). CrossRef Yu. A. Kravtsov, G.W. Forbes, and A.A. Asatryan, "Theory and applications of complex rays", in Progress in Optics, edited by E.Wolf, 39, 1−62 (Elsevier, Amsterdam, 1999). CrossRef S. J. Chapman, J.M. Lawry, J.R. Ockendon, and R.H. Tew, "On the theory of complex rays", SIAM Review 41, 417−509 (1999). CrossRef Yu. A. Kravtsov, P. Berczynski, "Gaussian beams in inhomogeneous media: a review", Stud. Geophys. Geod. 51(1), 1-36 (2007). CrossRef Yu. A. Kravtsov, "Geometrical Optics in Engineering Physics", Alpha Science International, UK (2005) S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov, "Self-focusing and light diffraction in nonlinear medium", Soviet Phys. Uspekhi 10, 609-636 (1968). CrossRef S. A. Akhmanov, R.V. Khokhlov, and A. P. Sukhorukov, "Self-focusing, Self-defocusing and Self-modulation of Laser Beams", in Laser Handbook, F.T.Arecchi and E.O. Shulz-Dubois, Eds. (Elsevier, New York, 1972), Vol. 2, 1151-1228.6 S303 (2004). P. Berczyński, Yu. Kravtsov, "Gaussian beam evolution in nonlinear inhomogeneous fibres", Photonics Letters of Poland, Vol 4, No 1, 26-28 (2012). CrossRef

Diffraction-free beams in inhomogeneous media

Diffraction-free beams in inhomogeneous media

Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media

A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.

Gaussian beams in inhomogeneous media: A review

The paper outlines the most important results of the paraxial complex geometrical optics (CGO) in respect to Gaussian beams diffraction in the smooth inhomogeneous media and discusses interrelations between CGO and other asymptotic methods, which reduce the problem of Gaussian beam diffraction to the solution of ordinary differential equations, namely: (i) Babich’s method, which deals with the abridged parabolic equation and describes diffraction of the Gaussian beams; (ii) complex form of the dynamic ray tracing method, which generalizes paraxial ray approximation on Gaussian beams and (iii) paraxial WKB approximation by Pereverzev, which gives the results, quite close to those of Babich’s method. For Gaussian beams all the methods under consideration lead to the similar ordinary differential equations, which are complex-valued nonlinear Riccati equation and related system of complex-valued linear equations of paraxial ray approximation. It is pointed out that Babich’s method provides diffraction substantiation both for the paraxial CGO and for complex-valued dynamic ray tracing method. It is emphasized also that the latter two methods are conceptually equivalent to each other, operate with the equivalent equations and in fact are twins, though they differ by names. The paper illustrates abilities of the paraxial CGO method by two available analytical solutions: Gaussian beam diffraction in the homogeneous and in the lens-like media, and by the numerical example: Gaussian beam reflection from a plane-layered medium.

EPR dosimetry of radiotherapy photon beams in inhomogeneous media using alanine films

In the current work, EPR (electron paramagnetic resonance) dosimetry using alanine films (134 µm thick) was utilized for dose measurements in inhomogeneous phantoms irradiated with radiotherapy photon beams. The main phantom material was PMMA, while either Styrofoam or aluminium was introduced as an inhomogeneity. The phantoms were irradiated to a maximum dose of about 30 Gy with 6 or 15 MV photons. The performance of the alanine film dosimeters was investigated and compared to results from ion chamber dosimetry, Monte Carlo simulations and radiotherapy treatment planning calculations. It was found that the alanine film dosimeters had a linear dose response above approximately 5 Gy, while a background signal obscured the response at lower dose levels. For doses between 5 and 60 Gy, the standard deviation of single alanine film dose estimates was about 2%. The alanine film dose estimates yielded results comparable to those from the Monte Carlo simulations and the ion chamber measurements, with absolute differences between estimates in the order of 1–15%. The treatment planning calculations exhibited limited applicability. The current work shows that alanine film dosimetry is a method suitable for estimating radiotherapeutical doses and for dose measurements in inhomogeneous media.

Coherent properties of focused wide partially coherent beams in inhomogeneous media

The quasioptics approximation is used to analyze the propagation of a partially coherent radiation beam in a statistically inhomogeneous medium with a regular refractive index profile. This involves solving the parabolic equation for the complex field amplitude which in particular makes it possible to generalize the van Cittert–Zernike theorem (propagation of radiation in inhomogeneous media). The coherence radius is calculated and its ratio to the transverse size of the beam is analyzed.

An introduction to Maslov's asymptotic method

Summary. Familiar concepts such as asymptotic ray theory and geometrical spreading are now recognized as an asymptotic form of a more general asymptotic solution to the non-separable wave equation. In seismology, the name Maslov asymptotic theory has been attached to this solution. In its simplest form, it may be thought of as a justification of disc-ray theory and it can be reduced to the WKBJ seismogram. It is a uniformly valid asymptotic solution, though. The method involves properties of the wavefronts and ray paths of the wave equation which have been established for over a century. The integral operators which build on these properties have been investigated only comparatively recently. These operators are introduced very simply by appealing to the asymptotic Fourier transform of Ziolkowski & Deschamps. This leads quite naturally to the result that phase functions in different domains of the spatial Fourier transform are related by a Legendre transformation. The amplitude transformation can also be inferred by this method. Liouville's theorem (the incompressibility of a phase space of position and slowness) ensures that it is always possible to obtain a uniformly asymptotic solution. This theorem can be derived by methods familiar to seismologists and which do not rely on the traditional formalism of classical mechanics. It can also be derived from the sympletic property of the equations of geometrical spreading and canonical transformations in general. The symplectic property plays a central role in the theory of high-frequency beams in inhomogeneous media.

Second harmonic generation by focused beams in layer media

A theoretical study is made of second harmonic generation by focused beams in inhomogeneous media where the nonlinear susceptibility changes sign from one layer to another. It is found that the second harmonic power l and the coherence length lc. A detailed analysis is made of the case l = 2lc and it is established that under optimal focusing conditions, the maximum second harmonic power in a layer medium is almost the same as that in a homogeneous medium.

Gaussian Light Beams in Inhomogeneous Media

Vector wave solutions are obtained for the propagation of beams of light in media having slow spatial variations of the gain, loss, or index of refraction. The formalism developed here is applicable to a wide range of problems, and an exa mple considered in detail is the propagation of off-axis beams in lenslike laser materials and optical waveguides. A procedure is also described for the diagnosis of localized dielectric inhomogeneities such as plasmas by means of Gaussian laser beams.