Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Letters

Comment on “Resolving the wave vector and the refractive index from the coefficient of reflectance”

Manuel Pérez Molina, L. Carretero

Published Aug 6, 2008• 5 citations
Publisher

Abstract

In a recent Letter, the reflectance coefficient was used to resolve the sign choice of the wave vector and refractive index in active media. We argue that such a coefficient loses its physical meaning for active media (at real frequencies) when the field amplification is limited only by gain saturation. In this case, the amplitude reflectance coefficient leads to fictitious noncausal reflected fields when the backward Fourier transform is used.

DOI
10.1364/ol.33.001828

Related papers

Reply to comment on “Resolving the wave vector and the refractive index from the coefficient of reflectance”

V. U. Nazarov, Yia‐Chung Chang

We reinterpret our earlier letter [Opt. Lett.32, 2939 (2007)] to demonstrate that the resolution it gives to the problem of the sign of the wave vector and the refractive index is valid for active media without instabilities but invalid otherwise.

Optics Letters•Aug 6, 2008•4 citations

Resolving the wave vector and the refractive index from the coefficient of reflectance

V. U. Nazarov, Yia‐Chung Chang

We resolve the existing controversy concerning the selection of the sign of the normal-to-the-interface component of the wave vector k(z) of an electromagnetic wave in an active (gain) medium. Our method exploits the fact that no ambiguity exists in the case of a film of the active medium, since its coefficient of reflectance is invariant under the inversion of the sign of k(z). Then we show that the limit of the infinite film thickness determines a unique and physically consistent choice of the wave vector and the refractive index. Important practical implications of the theory are identified and discussed.

arXiv:0710.4388•Optics Letters•Oct 4, 2007•14 citations

Wave-mixing and Phase Conjugation in Laser Active Media

Kazuo Kuroda

Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].

CRC Press eBooks•Mar 14, 2002•0 citations

Reflection of light from amplifying medium

R. V. Karapetyan

The existing linear theory of the reflection of light waves from an amplifying medium is debated. The exiting data are often contradictory, a reflection coefficient of amplifying medium of greater than unity is discussed, an upper bound of 5.82 is imposed on this quantity, significant corrections of prelaser concepts regarding the reflection and refraction of light in such media are proposed, etc. This stimulates reconsideration of the existing results. Evidently, the corresponding analysis must be based on the data obtained with a commonly accepted and, preferably, simplest approach. In our opinion, such an approach represents an analytical continuation of the known prelaser achievements (the Airy formulas for the reflection and transmission of light in a transparent medium proposed in 1833) to the domain of the amplifying media. The results presented can improve the basis of a linear theory for the interaction of light with amplifying media.

Laser Physics•Aug 1, 2007•5 citations

Possible use of resonantly excited media in wavefront reversal

А. Н. Ораевский

A theoretical analysis is made of the conditions which a resonantly excited medium must have to act as a wavefront-reversing mirror. In the absence of saturation by the incident signal, the absorption cross section at the frequency of this signal should be considerably less than at the reversed-wave frequency. In the case of strong saturation it is preferable to use substances with narrow spectral lines. If a wavefrontreversing mirror is used to compensate distortions of the front of a wave during amplification, the necessary contrast of the reversed wave is a function of the gain and of the width of its profile.

Soviet Journal of Quantum Electronics•Jan 31, 1979•3 citations

Reflection and refraction of light at saturating active boundaries

Mohammad Azadeh, Lee W. Casperson

This study deals with the topic of reflection and refraction of light from the boundary of a high-gain saturating laser amplifier. Expressions for the electric field and intensity reflection and transmission coefficients are obtained for the case of a wave in a uniform dielectric that is incident normally on a nonlinear saturating active medium. Bistability effects are predicted even for the simplest case of zero frequency detuning from the line centre of the saturating transition.

Journal of Modern Optics•Jan 1, 1997•4 citations
In a recent Letter, the reflectance coefficient was used to resolve the sign choice of the wave vector and refractive index in active media. We argue that such a coefficient loses its physical meaning for active media (at real frequencies) when the field amplification is limited only by gain saturation. In this case, the amplitude reflectance coefficient leads to fictitious noncausal reflected fields when the backward Fourier transform is used.
We resolve the existing controversy concerning the selection of the sign of the normal-to-the-interface component of the wave vector k(z) of an electromagnetic wave in an active (gain) medium. Our method exploits the fact that no ambiguity exists in the case of a film of the active medium, since its coefficient of reflectance is invariant under the inversion of the sign of k(z). Then we show that the limit of the infinite film thickness determines a unique and physically consistent choice of the wave vector and the refractive index. Important practical implications of the theory are identified and discussed.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
The existing linear theory of the reflection of light waves from an amplifying medium is debated. The exiting data are often contradictory, a reflection coefficient of amplifying medium of greater than unity is discussed, an upper bound of 5.82 is imposed on this quantity, significant corrections of prelaser concepts regarding the reflection and refraction of light in such media are proposed, etc. This stimulates reconsideration of the existing results. Evidently, the corresponding analysis must be based on the data obtained with a commonly accepted and, preferably, simplest approach. In our opinion, such an approach represents an analytical continuation of the known prelaser achievements (the Airy formulas for the reflection and transmission of light in a transparent medium proposed in 1833) to the domain of the amplifying media. The results presented can improve the basis of a linear theory for the interaction of light with amplifying media.
A theoretical analysis is made of the conditions which a resonantly excited medium must have to act as a wavefront-reversing mirror. In the absence of saturation by the incident signal, the absorption cross section at the frequency of this signal should be considerably less than at the reversed-wave frequency. In the case of strong saturation it is preferable to use substances with narrow spectral lines. If a wavefrontreversing mirror is used to compensate distortions of the front of a wave during amplification, the necessary contrast of the reversed wave is a function of the gain and of the width of its profile.