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Conference on Precision Electromagnetic Measurements

Optical heterodyne four-wave mixing spectroscopy with subnatural linewidth

Tai Hyun Yoon

Published Nov 7, 2002• 0 citations
Publisher

Abstract

We introduce an optical heterodyne four-wave mixing (HFWM) spectroscopy with subnatural linewidth. In the HFWM spectroscopy strong bichromatic pump and an arbitrarily intense monochromatic probe field are employed. We show that a coherent two-photon emission by the HFWM process could result in subnatural linewidth.
DOI
10.1109/cpem.2000.851160

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Abstract This tutorial provides a joint theoretical and experimental overview of heterodyne wave mixing spectroscopy, focusing mainly on four-wave mixing (FWM). This powerful and versatile time-resolved nonlinear optical spectroscopy technique enables the investigation of individual localized single photon emitters, as well as microscopy of extended samples, e.g. two-dimensional transition metal dichalcogenides. Starting with the fundamental theory of optically driven two-level systems, we motivate the utility of wave mixing spectroscopy via a discussion on homogeneous and inhomogeneous linewidths which can be independently measured using FWM. We then provide a detailed overview of the heterodyne wave mixing setup operated by one of the authors (JK) at Institut Néel in Grenoble, supported by theoretical modeling of the signal detection process. Throughout the paper we elaborate on important benefits of heterodyne wave mixing spectroscopy, e.g. background-free detection, measurement of the full signal field including amplitude and phase, and investigation of coupling mechanisms in few-level systems. Within the context of the latter point we discuss the significance of two-dimensional FWM spectra. This tutorial is dedicated to students, young researchers, as well as experts in the field of nonlinear spectroscopy in general and FWM in particular. It explains the fundamental concepts and building blocks required to operate a heterodyne wave mixing experiment both from the experimental and theoretical side. This joint approach is helpful for theoreticians who want to accurately and quantitatively model wave mixing signals, as well as for experimentalists who aim to interpret their recorded data.
The two-photon resonant four-wave mixing processes are investigated when they are excited by non-monochromatic pump waves. Expressions for the intensity and linewidth of the generated wave are obtained. It is shown that the intensity of the generated wave is a Lorentzian about the two-photon resonance. The width of the Lorentzian varies linearly with the pump linewidth. The maximum and minimum in the coherent anti-Stokes Raman scattering (CARS) lineshape are shifted farther when excited by non-monochromatic beams. The shift varies linearly with the pump linewidth. In the incoherent regime, the intensity of the wave generated is directly proportional to the interaction length (L) and its linewidth Delta omega approximately 1/L.
A variant of the double-optical-resonance method is proposed in which the pumping step is a two-photon transition, either stimulated Raman scattering or two-photon absorption. It is shown that the probe linewidth can be minimized by proper choice of pump frequencies and assignment of pump beam propagation directions relative to the probe beam. The minimum linewidth is smaller than the value obtained by the usual one-photon pumping technique, and the method does not require any relations among level spacings.
In this article, we analyse a new sensitive spectroscopic technique in which a sample cell is irradiated by a two-frequency pump beam (ω + Δ ± δ/2) and a counter-propagating probe beam (ω). The phase-conjugate fields re-emitted at frequencies ω ± δ, via four-wave mixing processes, are detected through their heterodyne beating with the probe field. The properties of the heterodyne beat signal are studied by means of a perturbation calculation of the nonlinear response of the medium, carried out to the third order in the incident fields. In resonant gas media, the emission lineshape exhibits a Doppler-free doublet structure [frequency splitting 3 δ/2 for single-photon resonances, and δ/2 for two-photon transitions]. By using a phase-sensitive detection of the beat signal, one can separately analyse real (dispersion) or imaginary parts (absorption) of the nonlinear susceptibility. For single-photon transitions, the signal phase shift is related to the atomic levels lifetime and allows one to study the relaxation dynamics in gas phase (like quenching collisions, velocity diffusion, etc...). This is particularly interesting for cross-over resonances, in which only the common level contributes. In three-level systems, one also predicts a selective resonant enhancement of the phase-conjugate emission through Raman-type two-photon processes. Most of these predictions have been experimentally verified.
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.