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Quantum Electronics

Transformation of the spectrum of an intracavity field by a resonantly absorbing medium

А. В. Алексеев, N. V. Sushilov, E. D. Kholodkevich

Published May 31, 1994• 0 citations
Publisher

Abstract

Analytic expressions are obtained for the spectral composition of laser radiation inside a resonator cavity filled with a gas of two-level atoms. The intracavity radiation field is approximated by a trichromatic field with an intermode frequency interval governed by the laser resonator frequency Ω = c /2 L ( L is the resonator cavity length). The radiation spectrum consists of a large number of harmonics which are multiples of Ω. The amplitudes of these harmonics exhibit a periodic dependence on the concentration of the absorbing atoms and on the resonator length. The maxima of the harmonics correspond to specific relationships between the parameters, which are the conditions for what is known as an intracavity parametric resonance.

DOI
10.1070/qe1994v024n05abeh000104

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Optics and Spectroscopy•Dec 1, 2019•0 citations
Analytic expressions are obtained for the spectral composition of laser radiation inside a resonator cavity filled with a gas of two-level atoms. The intracavity radiation field is approximated by a trichromatic field with an intermode frequency interval governed by the laser resonator frequency Ω = c /2 L ( L is the resonator cavity length). The radiation spectrum consists of a large number of harmonics which are multiples of Ω. The amplitudes of these harmonics exhibit a periodic dependence on the concentration of the absorbing atoms and on the resonator length. The maxima of the harmonics correspond to specific relationships between the parameters, which are the conditions for what is known as an intracavity parametric resonance.
An experimental investigation was made of the dependence of the signal in intracavity laser magnetic resonance (LMR) spectroscopy on the modulation frequency (frequency characteristic). It was found that a simple theory developed in the approximation of kinetic equations, small gain per pass, and exponential relaxation of the active medium described qualitatively the experimental data. A quantitative agreement was obtained only to within a factor of 2. Experimental and theoretical studies were made of the frequency characteristics of a laser containing a saturable absorbing gas inside the resonator. It was found that for certain values of the parameters of this gas the resonance peak of the frequency characteristic could have an unlimited amplitude. The behavior of the frequency characteristic was analyzed bearing in mind the behavior of its poles. An estimate was obtained of the influence of small amounts of a saturable gas on the sensitivity of an LMR spectrometer in the case of resonance and adiabatic modulations.
Let us consider preliminary two situations. In the first of them the monochromatic radiation is absorbing. The increase of its intensity leads to the diminution of an absorption down to zero in a limiting case, i.e. to the effect of saturated absorption. In the second case an absorption of test radiation with a small intensity is observing, while two—level atom is strongly interacting with a perturbing field. This case is characterized by asymmetric dependence of absorption on the frequency difference w- w = A, where w and w are the frequencies of two light waves. As it was shown by Rautian and Sobelman in 19611, the amplification of test radiation arises in a certain range of frequency offsets A instead of the absorption, and the energy transfers from a strong wave to a weak one. In this paper we study the problem which appears from the above situation, when the intensity of test radiation increases. Such an increase leads to new maxima in absorption spectra of test radiation at frequencies A = i n = 2, 3 4 . . . which are additional to the main maxima at n R A = where R the Rabi frequency. These new resonances were observed by Bonch-Bruevich, Vartanyan, and Chigir in 19792 and cal led the subradiat ive structure. We have the following simple approximate expression for R obtained in the case of interaction with two fields: Q =d(?+E2)1"2/h. (1) R 0 1 There are two essential effects in the described situation: the saturation of absorption and the nonlinear interference effect. The last causes the redistribution of an absorbed energy between radiation components, the negative absorption (amplification) without population inversion, and the multiphoton parametric resonances at difference frequencies. The laser generation on the base7of the negative absorption without population inversion was obtained in 1989. The following problems arise from the facts reviewed above: 1. The calculation of absorption coefficients for individual components of a strong polychromatic radiation with an equidistant spectrum. 2. Determining of a generalized Rabi frequency and verification of the simple formula A = In for maxima of resonances. n R The aim of this paper is to solve these problems.
The resonance fluorescence spectrum of one and two two-level atoms in an ideal cavity with one resonant mode is investigated as a function of the initial excitation of the system. The analysis is carried out in the Stark representation with respect to the cavity's field and in first-order perturbation theory with respect to the fluorescence field. In the absence of the field of the cavity (n c = 0) and under an initial excitation of one atom only, the spectrum consists of two lines which are symmetrical with respect to ωa. In all other cases the spectrum has a central line at ωa and other lines at ωa ± 2 Ω. The intensity of the higher (ωa ± 4 Ω) harmonics is small and decreases as 1/ 2 c c with increasing n>c. The nonlinearity of the interaction hamiltonian results in the parametric (with respect to the field of the cavity) amplification of the ωa + 2 Ω harmonic and the attenuation of the ωa − 2 Ω harmonic. The stimulated emission of the ωa ± 2 Ω harmonics, vanishing in a strong (n c » 1) field, is shown to exist for two atoms.
The standard theory of resonance fluorescence is a weak-coupling theory.1 If n ¯ is the mean photon number for the driving field, g is the atom field coupling constant, and γ is the Einstein A coefficient, formally the standard theory of resonance fluorescence assumes the limit n ¯ → ∞ , g/ γ → 0, with the ratio of Rabi frequency to atomic linewidth 2 n ¯ n g / γ finite. The limit g/γ → 0 allows the variation of the Rabi frequency 2 n g across the photon number distribution of the driving field to be neglected. By placing the atom inside an optical cavity the ratio g/γ can be changed. In this paper we calculate spectra for intracavity resonance fluorescence in the strong-coupling limit g/γ ≫ 1, g/κ ≫ 1, where κ is the cavity linewidth. We consider a single two-level atom interacting on resonance with a single cavity mode driven by a resonant coherent field. The cavity subtends a small solid angle at the atom, so that the spontaneous emission into free-space modes is not negligible. We calculate the spectrum of the light transmitted by the cavity (the transmitted spectrum) and the spectrum of the light radiated by the atom into free space (the fluorescent spectrum). The transmitted and fluorescent spectra show fundamental differences from the (weak-coupling) spectrum of free-space resonance fluorescence.
A study was made of the modulation of the coherent emission spectrum by spatial gratings of the refractive index, produced by the dye laser field in an absorbing medium inside the resonator. It was found that the frequencies of the reflection maxima of a nonlinear mirror resulting from the inhomogeneity of the refractive index along the direction of propagation of the light wave were in agreement with the frequencies satisfying the conditions for the maxima of interference reflection in the presence of an additional plane in the resonator.
Abstract The radiation of a two-level resonant medium that is placed into a cavity and is excited by a periodically phase modulated laser pulse is studied theoretically. The radiation is analyzed based on the analytical and numerical solutions of the system of Maxwell–Bloch equations under conditions of a strong coupling between the field and the matter. Under these conditions, this system is similar to a polariton laser. The excitation efficiency of a polariton laser by a phase-modulated radiation pulse is shown to be high compared to a pulse without phase modulation of the carrier frequency. It is shown that the main reason for the efficient excitation of polariton modes in the medium is the appearance of difference combination parametric resonance. The obtained results open up new possibilities for the excitation of radiation of polariton lasers by low-power frequency-modulated pump laser radiation.