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Soviet Journal of Quantum Electronics

Characteristic features of field broadening in intracavity frequency-modulation spectroscopy

M. V. Danileǐko, V. N. Nechiporenko, Леонід Петрович Яценко

Published Nov 30, 1990• 1 citation
Publisher

Abstract

An analysis is made of the characteristic features of the field-induced broadening in intracavity frequency-modulation spectroscopy. Simple but effective methods for eliminating field broadening of nonlinear resonances are proposed. It is shown that in the case of frequency-modulation resonances of the dispersion and absorption, which set the detuning from the center of the absorption line to a value equal to the modulation frequency, and also in the case of dispersion resonances, which set the detuning at zero, it is possible to avoid the field-induced broadening by a suitable selection of a specific frequency modulation index.

DOI
10.1070/qe1990v020n11abeh007515

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An analysis is made of the characteristic features of the field-induced broadening in intracavity frequency-modulation spectroscopy. Simple but effective methods for eliminating field broadening of nonlinear resonances are proposed. It is shown that in the case of frequency-modulation resonances of the dispersion and absorption, which set the detuning from the center of the absorption line to a value equal to the modulation frequency, and also in the case of dispersion resonances, which set the detuning at zero, it is possible to avoid the field-induced broadening by a suitable selection of a specific frequency modulation index.
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We calculate the third-order nonlinear absorption and dispersion (self-phase-modulation and cross-phase modulation) of a homogeneously broadened two-level molecular system with permanent dipole moments interacting with (1) an optical field of frequency \ensuremath{\omega}, and (2) two optical fields of frequency ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, i.e., the susceptibilities ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-\ensuremath{\omega};\ensuremath{\omega},-\ensuremath{\omega},\ensuremath{\omega}) and ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-${\mathrm{\ensuremath{\omega}}}_{1}$;${\mathrm{\ensuremath{\omega}}}_{1}$,-${\mathrm{\ensuremath{\omega}}}_{2}$,${\mathrm{\ensuremath{\omega}}}_{2}$). Sharp features in the nonlinear absorption and dispersion appear whenever one- or two-photon resonance conditions are met. Only features corresponding to one-photon resonance arise if the difference between the permanent dipole moments of the levels, \ensuremath{\Delta}\ensuremath{\mu}, vanishes. The ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-\ensuremath{\omega};\ensuremath{\omega},-\ensuremath{\omega},\ensuremath{\omega}) spectrum has two features, one at frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$ dominated by contributions proportional to ${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{b}}^{4}$, where ${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{b}}$ is the transition dipole moment of the two levels with transition frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$, and the other at frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$/2 dominated by contributions proportional to (\ensuremath{\Delta}\ensuremath{\mu})2{)}^{2})2${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{b}}^{2}$. Sharp features in ${\mathrm{\ensuremath{\chi}}}^{(3)}$(-${\mathrm{\ensuremath{\omega}}}_{1}$;${\mathrm{\ensuremath{\omega}}}_{2}$,-${\mathrm{\ensuremath{\omega}}}_{2}$,${\mathrm{\ensuremath{\omega}}}_{1}$) appear when ${\mathrm{\ensuremath{\omega}}}_{2}$ is near ${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$,${\mathrm{\ensuremath{\omega}}}_{1}$,${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$, and \ensuremath{\Vert}${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{\mathit{b}\mathit{a}}$\ensuremath{\Vert}.
Within the framework of the classical model, which describes electrons as damped harmonic oscillators in an external electromagnetic field, expressions for the absorption and dispersion coefficients in the second order of smallness in the saturation parameter are found for a uniformly broadened line at a low concentration of oscillators, when the amplitude of the field produced by neighboring electrons is significantly less amplitude of the external field. It is shown that with increasing saturation parameter, the shape of the dispersion resonance becomes asymmetric, that at small saturation parameter leads to its linear shift to the "red" region. At the same time, as the saturation parameter increases, the dispersion resonance broadens (increases the interval between the maximum and minimum of the dispersion curve) and, in addition, there is a relative increase in the low-frequency amplitude compared to the high-frequency one. As for the shape of the absorption line, just as for the dispersion resonance, as saturation parameter increases, an asymmetry of the line shape appears which is accompanied by a shift to the "red" region. Because the low-frequency wing of the absorption line shifts toward the resonance center faster than the high-frequency wing moves away from the center, a narrowing of the resonance from the saturation parameter is observed. The dependence of this narrowing is nonlinear. In this case, the maximum of the absorption resonance linearly shifts to the "blue" region at the same speed as the dispersion line shifts to the "red" one.
The advent of lasers has revolutionized the methods and possibilities of spectroscopy. Their monochromaticity permits the study of extremely narrow spectral features which would not have been resolved using classical techniques. Moreover, their extreme spectral power density, in giving rise to the field of nonlinear optics, which will be studied in Chapter 7, has resulted in the development of new and powerful spectroscopic techniques. These techniques, of which we describe briefly some examples in this complement, have as their basis the fact that an atom does not respond linearly when subjected to a very intense light field. First of all we shall describe the broadening mechanisms that explain the fact that the experimentally measured widths of atomic or molecular resonances are larger than those that would be observed if the atoms were isolated and at rest. We shall introduce in Section 3G.1 the concept of homogeneous width, which can be considered as the intrinsic width of a transition, and inhomogeneous width which concerns the variation of the frequency of a given transition that occurs because of the state of motion of the atom, or because of factors in its environment. We shall explain why it is possible, using nonlinear optical techniques to eliminate the effects of inhomogeneous broadening on recorded spectra, resulting in an improvement over the resolution of conventional techniques. We shall then concentrate more specifically on Doppler broadening , which is the most commonly encountered source of inhomogeneous broadening, describing two nonlinear optical techniques, saturated absorption spectroscopy (in Section 3G.2) and two-photon spectroscopy (in Section 3G.3), which enable it to be overcome.
We have compared the impact of loss, pump, and frequency modulations on a single-mode homogeneously broadened laser under varying detunings and modulation frequencies. In the case of loss and gain modulations the impact on intensity shows a minimal behavior at the line center for gain values more than twice the lasing threshold. The system relaxation time with respect to any transient perturbation depends on the magnitude of detuning and is minimal at the line center. In the case of frequency modulation, the impact on intensity vanishes at the line center irrespective of the gain values. These results are based on linear analysis.
The spectral features of FM two-photon resonant interaction processes have been calculated for five different frequency modulation versions of counter-propagating incident fields. It is found that the proposed new modulation version (case b in the text) provides novel spectral features for a completely canceled absorption and a sharp dispersion shape at the fundamental beat note. Moreover, its absorption feature appears at the second harmonic of the RF modulation frequency generated by the joint modes via six interaction pathways without mutual phase shift. Such features persist even when the effects of the second-order sidebands of the incident fields are taken into account. Application potentials are emphasized.