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Physical Review A

Optical rotary saturation in a gas

Yehiam Prior, J. A. Kash, Erwin Louis Hahn

Published Dec 1, 1978• 9 citations
Publisher

Abstract

The optical analog of the nuclear magnetic resonance rotary saturation effect is demonstrated and analyzed. A 9.6-\ensuremath{\mu}m C${\mathrm{O}}_{2}$ laser resonance excitation of vibrational transitions in gaseous C${\mathrm{H}}_{3}$F creates an effective splitting in the interaction representation of the optical two-level system. A radio-frequency standing-wave Stark electric field is tuned in rotary saturation resonance with the splitting. The change in transmitted laser beam intensity, because of rotary resonance, is measured in terms of transient optical signals obtained by the Stark switching method of Brewer and Shoemaker. The measured single and multiphoton rotary saturation resonance signals are compared with perturbation and computer solutions of nonlinear Bloch-Maxwell macroscopic equations. Doppler-free rotary saturation spectra are obtained in the presence of inhomogeneous Doppler broadening by a special scheme of Fourier analysis. A discussion is presented of the coupling of energy between two traveling waves that are in double resonance with the optical two-level system. The concept of spin temperature is discussed in relation to a coherently excited optical level system with a long fluorescence lifetime. The possibility of a cross-relaxation double resonance experiment between an optical system and a spin system is outlined.

DOI
10.1103/physreva.18.2603

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The optical analog of the nuclear magnetic resonance rotary saturation effect is demonstrated and analyzed. A 9.6-\ensuremath{\mu}m CO2{\mathrm{O}}_{2}O2​ laser resonance excitation of vibrational transitions in gaseous CH3{\mathrm{H}}_{3}H3​F creates an effective splitting in the interaction representation of the optical two-level system. A radio-frequency standing-wave Stark electric field is tuned in rotary saturation resonance with the splitting. The change in transmitted laser beam intensity, because of rotary resonance, is measured in terms of transient optical signals obtained by the Stark switching method of Brewer and Shoemaker. The measured single and multiphoton rotary saturation resonance signals are compared with perturbation and computer solutions of nonlinear Bloch-Maxwell macroscopic equations. Doppler-free rotary saturation spectra are obtained in the presence of inhomogeneous Doppler broadening by a special scheme of Fourier analysis. A discussion is presented of the coupling of energy between two traveling waves that are in double resonance with the optical two-level system. The concept of spin temperature is discussed in relation to a coherently excited optical level system with a long fluorescence lifetime. The possibility of a cross-relaxation double resonance experiment between an optical system and a spin system is outlined.
The first observation of optical rotary echoes, the optical analog of rotary spin echoes, is reported. Rotary echoes are produced in a quantum-mechanical two-level system which is driven resonantly (nutation effect) by a coherent field that suffers a sudden phase retardation. The initial nutation transient dephases, because of an inhomogeneity in either the driving field or the transition frequency of the sample, and then rephases to form an echo following the phase-shifting pulse. Hence, optical rotary and photon echoes are similar processes---the former being an interference in nutation and the latter an interference in free precession. Perturbative solutions of the Bloch equations are derived for the case where inhomogeneous dephasing arises from Doppler broadening and the Rabi frequency exceeds the homogeneous damping rate. Observations of the optical rotary echo in I2{\mathrm{I}}_{2}I2​ vapor are facilitated by the technique of laser frequency switching, which generates precise phase shifts in the optical field. The measurements corroborate detailed theoretical predictions.
The first observation of optical rotary saturation is reported. Bloch-like equations of motion for rotary saturation are solved by a perturbation calculation and also numerically on a computer. In addition to the rotary-saturation resonance, multiphoton transitions are predicted and observed. A "Debye resonance in the rotating frame" naturally emerges from the equations. The case of two traveling waves interacting with a two-level system is shown to be mathematically equivalent to the rotary-saturation equations.
A simple application of the Stark-pulse technique, developed by Brewer and Shoemaker, demonstrates optical free induction decay-the optical analog of free induction decay in NMR. A molecular sample which is coherently prepared by a cw laser beam exhibits such a decay when it is suddenly switched out of resonance by a Stark field. Observations are presented for a nondegenerate Doppler-broadened infrared transition of NH2{\mathrm{H}}_{2}H2​D, where the sample is optically thin, and the decay behavior can be compared quantitatively with a solution of the Bloch equations. When the molecular sample is prepared under steady-state conditions, the solutions are analytic; for pulse excitation, a numerical solution is required. The treatment invokes a hard-collision relaxation model. Such characteristics as the abrupt termination of the decay and the related edge echo, which result from Doppler dephasing, can be examined for Stark pulses of finite extent.
The nonlinear absorption or gain characteristics of an optical-frequency, Doppler-broadened atomic resonance involving levels with closely spaced structure are analyzed. The level structures are assumed to be resolved with respect to their natural widths, but not necessarily with respect to the Doppler width at the optical transition. The radiation field consists of two closely spaced monochromatic frequencies lying within the Doppler width of the resonance. This type of radiation field may be obtained, for example, from a laser operating in two of its Fabry-Perot resonator modes. It is shown that, because of saturation of level populations and double-quantum Raman transitions between levels, appreciable nonlinear coupling takes place between the two fields. This coupling shows a resonance behavior when the frequency separation of the two applied fields becomes equal to the frequency splitting between two of the components which form either level structure. The width of this resonance is determined entirely by the natural widths of these two level components and not by the Doppler width of the optical transition or the natural width of other level components. When such a resonance occurs, the over-all gain or attenuation characteristics of the atomic resonance change drastically. In practice the frequency spacing of the fields may be kept constant while the level structures are tuned, e.g., magnetically. The effects are analyzed for cases of running-wave and standing-wave radiation fields. The use of this effect in precise determination of level structures as well as mode or transition coupling of a gas laser is discussed. Portions of the analysis are applicable to resonances with more general forms of inhomogeneous broadening.
The authors study the phenomenon of coherent Raman beats in 15N^{15}\mathrm{N}15NH3{\mathrm{H}}_{3}H3​ using a CO2{\mathrm{O}}_{2}O2​ laser and Stark switching. In particular, a three-level system in which the two upper levels always remain split by a few MHz is prepared by switching the transitions into resonance with a short Stark pulse whose bandwidth is large enough to coherently excite both transitions. When one of the coherently excited levels remains in resonance with the laser after the Stark pulse, this system exhibits a qualitatively new effect which has not been seen heretofore. For Stark shifts on the order of the upper-state splitting or smaller, the Raman beat is amplitude modulated at a frequency related to the optical nutation frequency. This is interpreted as being due to an interaction between the two-photon coherent Raman beat process and a single-photon optical nutation process which occurs simultaneously. Numerical calculations as well as a simple analytic model are presented to support this interpretation. By reducing the laser power, one can make the modulation of the Raman beat disappear. From the Raman signal in this regime the permanent electric dipole moment of 15N^{15}\mathrm{N}15NH3{\mathrm{H}}_{3}H3​ in an excited vibrational state is determined and the Raman beat decay rate measured. By comparing the latter result with a delayed optical nutation measurement we show that phase-changing collisions are negligible for the transition studied.
This paper describes a new class of techniques, called time-delayed laser saturation spectroscopy, which combine frequency- and time-domain methods of laser spectroscopy to provide a way of studying a molecular system as it evolves from an initially prepared stationary state to a second, final state. The specific example analyzed here is three-level free induction decay, in which the time-dependent gain of a Doppler-broadened molecular transition is probed after the sudden termination of an intense field resonating with a coupled transition. The theoretical calculation is based on the coupled density-matrix equations of motion in the slowly-varying envelope approximation. The time-delayed line shapes, which may be studied in either transmission or side fluorescence, exhibit linewidth asymmetries, line-shape deformations, Ramsey-type fringes, power broadening and dephasing, and dynamic Stark splittings and oscillatory decays. The technique provides a unique way of distinguishing the influence of Raman-type processes from that of population saturation and a means to separately measure the associated decay rates. The relationship of the present work to other studies is also discussed.