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Physical Review Letters

Generation of Coherent Light by a Moving Medium

Anatoly A. Svidzinsky, Fu Li, Xiwen Zhang

Published Mar 23, 2017• 8 citations
Publisher

Abstract

We show that steady nonuniform motion of a medium through an optical resonator can yield light amplification at the resonator frequency. High gain can be achieved if at the generated frequency the medium refractive index is close to zero or the medium has a very strong frequency dispersion. We also discuss an analogy between light amplification by a moving medium and the generation of sound waves when gas flows along a tube with acoustically closed-open boundaries.

DOI
10.1103/physrevlett.118.123902

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We show that steady nonuniform motion of a medium through an optical resonator can yield light amplification at the resonator frequency. High gain can be achieved if at the generated frequency the medium refractive index is close to zero or the medium has a very strong frequency dispersion. We also discuss an analogy between light amplification by a moving medium and the generation of sound waves when gas flows along a tube with acoustically closed-open boundaries.
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.
The propagation of a strong coherent "pump" wave traveling through a resonant medium is discussed. The medium is assumed to consist of identical stationary atoms, and the pump-wave frequency is assumed to coincide exactly with the resonance frequency for transitions between a particular pair of atomic states. A previously developed theory of the response of a strongly driven atom to a weak nearly resonant "signal" field is used to deduce the existence of a coupling between any two waves travelling parallel to the pump wave whose (nearly equal) frequencies sum to twice the pump-wave frequency. In the limit of very intense (highly saturating) pump fields, the coupling between the two waves of nearby frequencies leads to amplification of both waves if their frequencies lie within an interval about the pump-wave frequency equal to the Rabi frequency of population inversion. The basic process, which is roughly described by travelling-wave parametric-amplifier equations of motion, consists of the absorption of two pump-field photons followed by their emission at different nearby frequencies, and thus implies a frequency instability of the initially coherent pump wave.
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 control of the optical properties of a medium by atomic coherence and quantum interference effects is an important area of research, not only for its fundamental aspects in the understanding of radiation and matter interaction, but also for its potential applications in the design of optical devices. Atomic coherence can emerge in a medium through the coupling of a strong coherent field to an atomic transition. This coupling affects the optical properties of the medium in a very interesting ways. For example, it may yield light amplification without population inversion. Also, it can modify the traditional dispersion of an optical medium in such a way that maximum variations of the refractive index occur around a spectral region of vanishing absorption. In the first part of this work we investigate some fundamental aspects of this coherent dynamics. We investigate how this non-inversion gain is affected by the presence of atomic motion. The coherent interaction between atom and radiation can lead to the interference between optical paths of decay. We report on an atomic setting where the interference structures depend upon the phase of the coherent field, an new effect which is absent in other resonance fluorescent phenomena. As a potential application, we investigate a novel approach for the modulation of optical signal. This approach consists of injecting atomic coherence in the medium in order to tailor its optical properties so it is a more suitable medium for modulation.