Geometrical optics of inhomogeneous media

2019 ◽  
pp. 10-43
Author(s):  
A.A. Fuki ◽  
Yu. A. Kravtsov ◽  
O.N. Naida ◽  
S.D. Danilov
Keyword(s):  
Geometrical Optics ◽  
Inhomogeneous Media

Normal moveout revisited: Inhomogeneous media and curved interfaces

Geophysics ◽  
1988 ◽  
Vol 53 (2) ◽  
pp. 143-157 ◽  
Author(s):  
Eric de Bazelaire
Keyword(s):  
Real World ◽  
Text Analysis ◽  
Geometrical Optics ◽  
Inhomogeneous Media ◽  
Order Equation ◽  
Time Axis ◽  
Vector Computer ◽  
Dynamic Correction ◽  
The Real ◽  
Static Correction

The equation of normal moveout, [Formula: see text], is valid for a reflection from the base of a single homogeneous and isotropic bed, but is only an approximation in the real world of multilayered, inhomogeneous media and curved interfaces. Using the theory of geometrical optics, we can find another second‐order equation which represents hyperbolas that are also symmetrical about the time axis. However, the centers of these hyperbolas do not coincide with the center of coordinates, but are shifted along the time axis. The equation describing this second type of hyperbola is [Formula: see text], where [Formula: see text] is the time of focusing depth and [Formula: see text], the velocity of the input medium. This equation is not only more accurate than the usual normal moveout, but its use is more economical on a vector computer because the traditional dynamic correction is a static correction in the [Formula: see text] analysis. This procedure makes it possible to compute velocities for all the samples of all the stacked traces and produces a velocity section. [Formula: see text] analysis can also be used to build a stacked section without any manual picking of velocities. The same concepts can be extended to the section after stack, allowing recognition of the geometrical patterns of the reflectors.

Evolution of the polarization of electromagnetic waves in weakly anisotropic inhomogeneous media — a comparison of quasi-isotropic approximations of the geometrical optics method and the Stokes vector formalism

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Yury Kravtsov ◽  
Bohdan Bieg
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Waves ◽  
Normal Modes ◽  
Geometrical Optics ◽  
Inhomogeneous Media ◽  
Stokes Vector ◽  
Coupled Equations ◽  
Isotropic Approximation ◽  
Total Phase ◽  
Electromagnetic Beams

AbstractThe main methods describing polarization of electromagnetic waves in weakly anisotropic inhomogeneous media are reviewed: the quasi-isotropic approximation (QIA) of geometrical optics method that deals with coupled equations for electromagnetic field components, and the Stokes vector formalism (SVF), dealing with Stokes vector components, which are quadratic in electromagnetic field intensity. The equation for the Stokes vector evolution is shown to be derived directly from QIA, whereas the inverse cannot be true. Derivation of SVF from QIA establishes a deep unity of these two approaches, which happen to be equivalent up to total phase. It is pointed out that in contrast to QIA, the Stokes vector cannot be applied for a polarization analysis of the superposition of coherent electromagnetic beams. Additionally, the ability of QIA to describe a normal modes conversion in inhomogeneous media is emphasized.

scholarly journals Electromagnetic wave polarization state evolution in weakly anisotropic and nonuniform media with dissipation

2017 ◽  
Vol 9 (3) ◽  
pp. 94
Author(s):  
Bohdan Bieg ◽  
Janusz Chrzanowski
Keyword(s):  
Polarization State ◽  
Geometrical Optics ◽  
Inhomogeneous Media ◽  
Plasma Phys ◽  
Magnetized Plasma ◽  
Tokamak Plasma ◽  
Dielectric Tensor ◽  
Stokes Vector ◽  
Poloidal Magnetic Field ◽  
Isotropic Approximation

The change of the polarization state of electromagnetic beam propagating in weakly anisotropic and smoothly inhomogeneous media with dissipation is analysed. On the basis of a quasi-isotropic approximation, which provides the consequent asymptotic solution of Maxwell's equation, the differential equation for the evolution of four component Stokes vector is derived. Obtained equation generalizes previous results for the nonadsorbing media and is written in terms of the dielectric tensor of birefringent media with dissipation. The formalism is illustrated by an example of magnetised plasma with dissipation due to the electron collisions. Full Text: PDF ReferencesK.G.Budden, Radio Waves in the Ionosphere (Cambridge U. Press 1961).V.I.Ginzburg, Propagation of Electromagnetic Waves in Plasma (Gordon & Breach 1970).Yu.A.Kravtsov, ""Quasiisotropic" Approximation to Geometrical Optics", Sov. Phys. Dokl. 13, 1125 (1969).A.A. Fuki, Yu.A. Kravtsov, and O.N. Naida, Geometrical Optics of Weakly Anisotropic Media (Gordon & Breach, Lond., N.Y. 1997).Yu.A. Kravtsov and Yu.I. Orlov, Geometrical optics of inhomogeneous media (Springer Verlag, Berlin, Heidelberg 1990). CrossRef Yu.A. Kravtsov et al., "Waves in weakly anisotropic 3D inhomogeneous media: quasi-isotropic approximation of geometrical optics", Physics-Uspekhi 39, 129(1996). CrossRef F.De Marco, S.E.Segre, "The polarization of an e.m. wave propagating in a plasma with magnetic shear. The measurement of poloidal magnetic field in a Tokamak", Plasma Phys. 14, 245 (1972). DirectLink S.E.Segre, "A review of plasma polarimetry - theory and methods", Plasma Phys. Control. Fusion 41, R57 (1999). CrossRef M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford 1980). CrossRef B.Bieg et al., "Quasi-Isotropic Approximation of Geometrical Optics Method as Adequate Electrodynamical Basis for Tokamak Plasma Polarimetry", Physics Procedia 62, 102 (2015). CrossRef B.Bieg et al., "Two approaches to plasma polarimetry: Angular variables technique and Stokes vector formalism", Nucl. Instr. Meth. Phys. Res. Sect. A 720, 157 (2013). CrossRef S.E.Segre, "New formalism for the analysis of polarization evolution for radiation in a weakly nonuniform, fully anisotropic medium: a magnetized plasma", J. Opt. Soc. Am. A 18, 2601 (2001). CrossRef

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