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CRC Press eBooks

Electromagnetic Waves in Amplifying Media

Vladimir Mitin, Dmitry I. Sementsov

Published Nov 18, 2016• 0 citations
Publisher

Abstract

The analysis of the phenomenon of refraction of electromagnetic waves at the interface between two media suggests that their velocity when passing from one medium to another changes. This chapter describes the basic principles of amplification and discusses the main features of wave propagation in amplifying media. Amplification occurs due to the induced coherent emission by excited atoms under the influence of the field of the electromagnetic wave. The chapter illustrates the attenuation of waves in an absorbing medium by using the Bouguer’s law. Bouguer’s law holds for a wide range of electromagnetic radiation—from radio waves to X-rays and gamma rays. The chapter discusses the main features of the different types of lasers such as solid-state lasers, gas lasers, dye lasers, and semiconductor lasers. It also includes some exercise problems related to the propagation of electromagnetic waves in amplifying media.

DOI
10.1201/9781315366944-16

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The analysis of the phenomenon of refraction of electromagnetic waves at the interface between two media suggests that their velocity when passing from one medium to another changes. This chapter describes the basic principles of amplification and discusses the main features of wave propagation in amplifying media. Amplification occurs due to the induced coherent emission by excited atoms under the influence of the field of the electromagnetic wave. The chapter illustrates the attenuation of waves in an absorbing medium by using the Bouguer’s law. Bouguer’s law holds for a wide range of electromagnetic radiation—from radio waves to X-rays and gamma rays. The chapter discusses the main features of the different types of lasers such as solid-state lasers, gas lasers, dye lasers, and semiconductor lasers. It also includes some exercise problems related to the propagation of electromagnetic waves in amplifying media.
Introduction Previous discussions (see Section 10.4) suggested that stimulated emission can be used to generate optical gain, that is, to amplify radiation. The reader certainly has experience in the amplification of electronic signal. For example, radio receivers capture faint radio waves and turn them into a signal that is powerful enough to drive large speakers. This electronic amplification increases the amplitude of the signal while faithfully preserving its acoustic frequencies and modulation characteristics. Similarly, optical amplification is expected to increase the amplitude of an optical signal while preserving its frequency, its modulation characteristics, and its coherence. The latter requirement is of particular significance for optical radiation, where the coherence of naturally occurring radiation rarely exceeds one micrometer. Lasers are the primary source for coherent radiation. They depend on stimulated emission for amplification and for the generation of coherent radiation (the word laser is the acronym of Light Amplification by Stimulated Emission of Radiation). For amplification, an atomic system that is part of the laser medium must be prepared with a sufficiently large number of particles in the excited state. (The term atomic system is used here to describe all microscopic systems including molecules and free electrons.) Radiation passing through that excited medium encounters multiple events of stimulated emission, each event contributing one photon that is added coherently to the propagating beam. When the number of events of stimulated emission exceed all losses by absorption or scattering, the incident radiation is amplified.
Abstract : A method of amplifying electromagnetic radiation is proposed, based on the use of induced emission phenomena, theoretically developed by A. Einstein in 1917. At the given method of amplification there is no conversion of energy of amplified radiation into other forms of energy. The method is suitable for amplification of ultraviolet, visible, infrared radio range waves. To bring the described amplification method into realization, a medium is produced having a negative absorption factor for radiations. The intensity of the radiation stream, passed through such a medium, rises, which produces the amplification effect. The amplification factor equals e to the (K)L, where K is the absorption coefficient and L is the thickness of the layer.
A review of basic analytical results on coherent propagation of optical pulses through nondegenerate amplifying media is presented. Original numerical results concerning pulse coherent amplification by degenerate media and, in particular, by the amplifying medium of an iodine laser are described also. Furthermore, some analytical results on coherent effects in the pulsed mode of laser generation are given. We have pointed out that the stochastic mode of laser radiation is related also to the coherency of interaction of a laser field with matter.
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].
All optical oscillators and amplifiers can be analyzed as an electromagnetic structure, such as a cavity or a transmission line, which contains an amplifying medium. The operating characteristics of lasers are governed by both the electromagnetic properties of the structures and the properties of the amplifying medium. Stimulated emission and absorption of radiation from energy states are the physical basis of amplification in all laser materials. In order to study lasers, it is necessary to understand the energy levels of the amplifying medium and the stimulated transitions involving them. Quantum mechanical analysis of the energy states and the stimulated emission and absorption is presented in most books on lasers. However, quantum mechanical analyses cover only the analysis of individual atoms. We need to relate the effects of the quantum mechanical interactions to the macroscopic properties of the materials so that properties of the lasers may be analyzed. Therefore, the macroscopic susceptibility of materials related to stimulated emission and absorption is the focus of discussion in this chapter. It is not the purpose of this book to teach quantum mechanics. There are already many excellent books on this topic. The readers are assumed to have a fundamental knowledge of quantum mechanics. However, it is necessary first to review some of the major steps in order to understand precisely the notation used and the meaning of the results. This is presented in Section 5.1.
Based on the equation for the second-order coherence function, the propagation of partially coherent radiation is studied under the combined action of diffraction and refraction caused by the inhomogeneous distribution of the real and imaginary parts of the perturbation of the permittivity of a medium in the case of inhomogeneous absorption (amplification). The limits of application of the method of geometrical optics for inhomogeneously absorbing (amplifying) media are studied, as well as of the methods that neglect refraction caused by the inhomogeneous distribution of the imaginary part of the permittivity of the medium.