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Optics Letters

Modulation transfer processes in optical heterodyne saturation spectroscopy

J.H. Shirley

Published Nov 1, 1982• 307 citations
Publisher

Abstract

Transfer of modulation from a phase-modulated laser beam to an unmodulated, oppositely running beam occurs in a sufficiently nonlinear resonant gaseous medium. Two mechanisms account for this transfer: modulated hole burning and reflection from an induced population grating. Heterodyne detection of the transferred modulation reveals multiplet patterns that are distinct for the two mechanisms. In particular, a central dispersion feature in the dispersive phase pattern is a diagnostic indication of the reflection process.

DOI
10.1364/ol.7.000537

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Physical Review A•Feb 1, 1982•20 citations
Transfer of modulation from a phase-modulated laser beam to an unmodulated, oppositely running beam occurs in a sufficiently nonlinear resonant gaseous medium. Two mechanisms account for this transfer: modulated hole burning and reflection from an induced population grating. Heterodyne detection of the transferred modulation reveals multiplet patterns that are distinct for the two mechanisms. In particular, a central dispersion feature in the dispersive phase pattern is a diagnostic indication of the reflection process.
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Optical heterodyne spectroscopy is one of the ultrasensitive and high resolution laser spectroscopies. During past years, it has extended from saturation absorption to two-photon transitions in a three level quantum system of atoms and ions. The particularly interesting case is the modulation transfer spectroscopy, where the optical heterodyne detection is performed via nearly degenerate four-wave mixing (NDFWM) in the nonlinear medium. In this report, the modulation transfer spectroscopy is used to observe the optical heterodyne saturation absorption and two-photon transition spectra simultaneously in Na2 without Doppler background. The line shapes of optical heterodyne signal are discussed in detail.
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].
We present a theoretical analysis of high-frequency optical heterodyne saturation spectroscopy in Doppler-broadened coupled three-level systems. The saturating beam, which is assumed to be amplitude modulated at frequency δ (double-sideband suppressed carrier amplitude modulation) is resonant for one of the transitions. Through non-degenerate four-wave mixing processes, this modulation is transferred to a probe beam, resonant for the coupled transition. Saturating and probe fields may be either co-propagating or counter-propagating. The lineshape of the probe modulation is analysed via a third-order perturbation expansion of the atomic density matrix with respect to the incident field amplitudes. The resulting signal is integrated over velocities, in the Doppler limit approximation. Both population saturation effects and coherent (Raman-type, or two-photon) processes contribute to the signal. The various contributions appear as Lorentzian-type resonance doublets. We show that, in the absence of relaxation processes (collisional dephasing, or radiative cascades), destructive interferences between population saturation and coherent two-photon processes are responsible for the disappearance of one resonance doublet. Phase-interrupting collisions are thus predicted to lead to the existence of a « pressure-induced extra-resonance » (PIER) doublet, which could yield information on collisional processes in the impact regime. The properties of the predicted PIER doublets are analysed in relation with other types of PIER signals studied in four-wave mixing, and in time-resolved saturation spectroscopy.
A theory of modulation of optical bistability of a main (signal) beam by an additional (control) beam is presented. It is supposed that the mirrors composing a Fabry-Perot cavity are highly reflective to the signal beam but transparent to the control beam. We show that the property of a medium in the cavity, and hence the transmission of the signal beam through the cavity, is modulated by the control beam which changes the dielectric susceptibility of the intracavity medium. Amplification of the signal beam occurs in the limit of a strong control beam. The process can be viewed as a parametric transfer of energy between the signal beam and the control beam with the nonlinear medium providing the nonlinear susceptibility that couples the beams. In addition, multibistability in the transmission characteristics of the signal beam is predicted and attributed to the saturation effect of the multiphoton processes.