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Bulletin of the Russian Academy of Sciences Physics

Coherent interactions of radiation with matter in media with population inversion

Aleksandr M Leontovich, A. M. Mozharovskiǐ

Published Mar 1, 1984• 0 citations
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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].

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In this book we treat the interaction of radiation with matter with special application to gain (amplifying) media typically existing in lasers. Tradition­ ally the interaction of radiation with matter is treated in terms of the index of refraction and the absorption of light, utilizing the model of electrons on springs. In Chap. 3 we show that this model is reasonable for some linear absorbing systems but is very awkward, if not outright unworkable, for a microscopic description of gain media. The essential failure of the electron-spring model is its difficulty in yielding net stimulated emission (and therefore gain) for an ensemble of systems.t In contrast, a more physically sound, quantum treatment of matter provides for the concept of population inversion and explains stimulated emission in a natural way. Hence from the very start we are compelled to base our understanding of the interaction of radiation with matter on a quantum-mechanical description of atoms. In Chaps. 1-13 a classical field interacts with quantum-mechanical atoms; in the remainder of the book, both field and atoms are treated quantum mechani­ cally.

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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].
In this book we treat the interaction of radiation with matter with special application to gain (amplifying) media typically existing in lasers. Tradition­ ally the interaction of radiation with matter is treated in terms of the index of refraction and the absorption of light, utilizing the model of electrons on springs. In Chap. 3 we show that this model is reasonable for some linear absorbing systems but is very awkward, if not outright unworkable, for a microscopic description of gain media. The essential failure of the electron-spring model is its difficulty in yielding net stimulated emission (and therefore gain) for an ensemble of systems.t In contrast, a more physically sound, quantum treatment of matter provides for the concept of population inversion and explains stimulated emission in a natural way. Hence from the very start we are compelled to base our understanding of the interaction of radiation with matter on a quantum-mechanical description of atoms. In Chaps. 1-13 a classical field interacts with quantum-mechanical atoms; in the remainder of the book, both field and atoms are treated quantum mechani­ cally.
Virtual gain refers to the simulation of real light amplification using radiation with exponentially decaying amplitude so that its complex frequency corresponds to the scattering pole. We study theoretically virtual gain in a two-level resonant medium for different regimes of light-matter interaction depending on the radiation intensity. We show that virtual gain at the pole can be most clearly observed for low intensities, when the medium is absorbing, in contrast to the saturated medium at high intensities. The efficiency of virtual gain can be tuned with the light intensity and controlled dynamically through the population inversion of the medium. Our results show that resonantly absorbing media paradoxically mimic a gainlike response, which admits a number of related phenomena and methods to mold both optical signals and material properties without relying on instability-prone gain media.