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Journal of Applied Physics

Stimulated Raman emission of coherent phonons by impurities in a crystal

Benjamin Fain

Published Sep 1, 1983• 6 citations
Publisher

Abstract

The possibility of stimulated emission of coherent phonons by impurities (ions) embedded in a crystal is considered. It is shown that when the ions with homogeneously broadened levels are subjected to an electromagnetic field, the frequency Ω of which is larger than an eigenfrequency of the ion ω21, at the Raman frequency ωq=Ω−ω21, a coherent stimulated emission of phonons may emerge. The absorption rate of the pumping electromagnetic field has a singularity near the threshold of the phonon self-excitation.

DOI
10.1063/1.332791

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The possibility of stimulated emission of coherent phonons by impurities (ions) embedded in a crystal is considered. It is shown that when the ions with homogeneously broadened levels are subjected to an electromagnetic field, the frequency Ω of which is larger than an eigenfrequency of the ion ω21, at the Raman frequency ωq=Ω−ω21, a coherent stimulated emission of phonons may emerge. The absorption rate of the pumping electromagnetic field has a singularity near the threshold of the phonon self-excitation.
A model consisting of a distribution of three-level systems (defects or ionic impurities) in a lattice characterized by a given phonon spectrum is considered in detail. Equations determining the temporal behavior of such a system in an electromagnetic field are analyzed. A steady-state solution describing three-level saturation in the system is achieved. The possibility of the stimulated emission of phonons is considered. It is shown that laserlike self-excitation of phonons cannot be realized, though phonon flux enhancement may be achieved provided certain conditions are fulfilled.
We study the stimulated Raman scattering (SRS) of light from an atomic system embedded in a photonic crystal and coherently pumped by a laser field. In our study, the electromagnetic field is treated classically and the atomic system is described quantum mechanically. Considering a decomposition of the pump and Stokes fields into the Bloch modes of the photonic crystals and using a multiscale analysis, we derive the Maxwell-Bloch equations for SRS in photonic crystals. These equations contain effective parameters that characterize the SRS gain, the nonlinear atomic response to the electromagnetic field, and the group velocity and that can be calculated in terms of the Bloch modes of the unperturbed photonic crystal. We show that if the pump laser frequency is tuned near a photonic band edge and the atomic system is carefully chosen such that the Stokes mode matches another photonic band edge, low-threshold, enhanced Raman amplification is possible. Possible physical realizations of SRS in photonic crystals are also discussed.
An inhomogeneously broadened three-level electronic system related to impurity ions embedded in a crystal with anisotropic phonon modes is considered. It is shown that such a system can sustain laserlike self-excitation under a steady-state condition, depending on the crystal properties. The anisotropy of the phonons is represented by two sets of modes which are distinguished by their lifetimes. Laserlike self-excitation has been shown to be impossible for isotropic systems. This and the influence of crystal properties on the self-excitation in anisotropic systems are discussed.
The possibility of using stimulated emission to improve the optical pumping of Tm3+ ions embedded in Tm3+:YAG to the 3F4 level is explored. The oscillator strengths and the frequencies of the transitions between the ground crystal field level of 3H4 to the different crystal field levels of 3F4 are measured at low temperature. Stimulated emission measurements at 1461 nm are performed to evaluate the optical pumping efficiency. Application to the spectral tailoring of Tm3+:YAG for quantum information applications is discussed.
We have studied the stimulated Raman spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes ω a and ω b are in resonance with the two atomic transition frequencies. The Green's function formalism has been used in the limit of high photon densities to calculate the excitation spectra near the frequencies ω = ± ω ab = ± (ω a - ω b ). Expressions are derived for the relative intensities, which describe, apart from the usual Raman peak at the frequency ω = ω ab , four pairs of lorentzian lines peaked at the frequencies ω - ω ab = ± Ω a /√2, ± Ω b /√2, ± Ω and ± 2Ω, respectively, and having spectra widths of the order of 3γ0/4. The parameter Ω is defined as Ω2 = (Ω a 2 + Ω b 2)/2, where Ω a and Ω b are the Rabi frequencies of the two laser fields and γ0 is the spontaneous emission probability. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. Conditions have been established for which Raman gain processes are anticipated to take place.
A theoretical study is made of the threshold conditions for the observation of optical bistability and stimulated emission of zero-phonon lines of crystals containing impurities. A reduction in the electron–photon interaction constant ensures that nonlinear absorption due to a purely electronic transition is attained in a lower saturating field and the lasing threshold rises exponentially as the reciprocal of the Debye–Waller factor. It is shown that there are critical temperatures for the appearance of these effects. Experimental studies of the threshold conditions for lasing and optical bistability make it possible to determine directly the Debye–Waller factor at different temperatures of a crystal.