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Title: Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity

Abstract

We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurementsmore » include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.« less

Authors:
;
Publication Date:
OSTI Identifier:
22043634
Resource Type:
Journal Article
Resource Relation:
Journal Name: Quantum Electronics (Woodbury, N.Y.); Journal Volume: 41; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; COORDINATES; DISPERSIONS; INCIDENCE ANGLE; INTERACTIONS; MONOCHROMATIC RADIATION; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PERMITTIVITY; PLATES; SPECTROSCOPY; SURFACES

Citation Formats

Golubkov, A A, and Makarov, Vladimir A. Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. United States: N. p., 2011. Web. doi:10.1070/QE2011V041N11ABEH014710.
Golubkov, A A, & Makarov, Vladimir A. Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. United States. doi:10.1070/QE2011V041N11ABEH014710.
Golubkov, A A, and Makarov, Vladimir A. 2011. "Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity". United States. doi:10.1070/QE2011V041N11ABEH014710.
@article{osti_22043634,
title = {Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity},
author = {Golubkov, A A and Makarov, Vladimir A},
abstractNote = {We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.},
doi = {10.1070/QE2011V041N11ABEH014710},
journal = {Quantum Electronics (Woodbury, N.Y.)},
number = 11,
volume = 41,
place = {United States},
year = 2011,
month =
}
  • For a one-dimensionally inhomogeneous plate whose linear dielectric properties are also inhomogeneous and are characterized by a diagonal permittivity tensor, it is proved that the spatial profiles of all components of the complex quadratic susceptibility tensor {Chi}{sup 2} (z, 2{omega}; {omega}, {omega}) responsible for the second harmonic generation can be uniquely determined, and an appropriate method is proposed. To implement this method, one should measure the complex coefficient of transformation of a fundamental plane wave incident on the plate into a reflected second-harmonic wave in a certain range of angles of incidence. By varying the plane of incidence of themore » wave and (or) its polarization and measuring the coefficients of transformation into s- and p-polarized waves of double frequency, one can uniquely determine the spatial profiles of all components of the quadratic susceptibility tensor. The method involves the measurement of the intensities of the second-harmonic waves generated under special conditions with the use of two auxiliary reference plates and thus allows one to avoid complicated phase measurements.« less
  • Eikonal approximation is used to derive equations describing propagation of monochromatic electromagnetic waves in a three-dimensionally inhomogeneous medium, including volume Fresnel reflection from inhomogeneities. The analysis is based on a locality principle. Separation into reflection and transmission effects is performed. The former effects are found to be isotropic, whereas the latter are anisotropic and depend on interference phenomena. Interference effects lead to violation of the Rytov law of polarization rotation. Brewster phenomena in layered and three-dimensionally inhomogeneous media are shown to occur under different conditions.
  • Mandelstam-Brillouin (MB) steady-state scattering in an elastic medium with a dense local zone inhomogeneity is considered in the 1D approximation. It is shown that for a certain size of inhomogeneity, the scattered radiation spectrum contains individual resonances whose frequencies depend on the elastic properties of microscopic inclusions. Experiments were performed using coherent four-photon scattering spectroscopy in the range 0-1 cm{sup -1} with a resolution of 0.06 cm{sup -1} in specially processed distilled water and in an aqueous solution of {alpha}-chymotrypsin albumin. In both media, the presence of MB resonances displaced is detected relative to the water resonance ( Almost-Equal-To 0.25more » cm{sup -1}) in different directions and corresponding to different types of microinclusions.« less
  • The influence of the quadratic polarization of a nonlinear medium on the necessary conditions for self-locking of longitudinal and transverse modes in an active medium is studied experimentally and theoretically. It is shown that doubling of the fundamental radiation and simultaneous generation of the difference frequency between one of the second harmonics and one of the fundamental frequencies induces a cascade cubic polarization. This polarization is comparable with the cubic polarization due to the interaction of modes in an active medium of an YAG:Nd/sup 3 +/ laser under the same conditions. The mode-locking range is governed by the relative positionsmore » of the active medium and nonlinear crystal, and can both be increased or completely compensated.« less