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Soviet Journal of Quantum Electronics

Line profile of coherent radiation in separated fields due to the F2(2)transition in methane

Семибаламут Владимир Михайлович

Published Jul 31, 1979• 0 citations
Publisher

Abstract

The theory of coherent radiation in separated fields (CRSF) is generalized to allow for the magnetic hyperfine line structure. An investigation is made of the frequency dependence of the CRSF intensity due to the F2(2) transition in methane. The field shift of the central CRSF maximum is determined and the pressure dependence of the amplitude and half-width of the central CRSF maximum is obtained.

DOI
10.1070/qe1979v009n07abeh009216

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The theory of coherent radiation in separated fields (CRSF) is generalized to allow for the magnetic hyperfine line structure. An investigation is made of the frequency dependence of the CRSF intensity due to the F2(2) transition in methane. The field shift of the central CRSF maximum is determined and the pressure dependence of the amplitude and half-width of the central CRSF maximum is obtained.
An investigation was made of signals of coherent radiation generated by time-separated fields in an SF6 gas at moments t =T+nT (n =1,2,3,4) under the action of two pulses of standing-wave CO2 laser radiation. The amplitudes of such signals were investigated as a function of the detuning of the laser frequency relative to the center of the transition line of SF6, as a function of the amplitude of the exciting radiation, and also as as a function of T. The rates of relaxation of the polarization, ?12= (46?5)?106 sec?1?Torr ?1, and of the populations, ? = (42?4)?106 sec?1?Torr ?1, were found at pressures of 1?5 (mTorr). A comparison of ?12 and ? gave information on the nature of collisions in the SF6 gas.
The amplitude and polarization are found for the first coherent radiation pulse generated in time-separated fields with the aid of resonant levels exhibiting a hyperfine structure. It is shown that such hyperfine splitting of the resonant levels does not alter qualitatively the conclusion that it should be possible to observe narrow structures in the intensity of such a pulse under conditions of scanning of the frequency of the exciting pulses. This feature is important because of possible technical applications of such narrow structures. The polarization properties of the first coherent radiation pulse generated in time-separated fields depend strongly on whether one or all hyperfine components of each of the resonant levels participate in the formation of a pulse.
An equation has been developed for the polarization, and the angle of maximum polarization of resonance radiation as observed along a magnetic field perpendicular to the electric vector and the direction of propagation of the incident beam. Explicit application has been made to the polarization and the angle for the line $^{1}S_{0}\ensuremath{-}^{1}P_{1}$ for various values of the ratio of the hyperfine separation constant to the natural breadth of the levels, for a nuclear moment of \textonehalf{}. It was noted here that the form of the curves might differ widely from that to be expected from classical considerations. The polarization, and the angle of maximum polarization for the sodium D lines, for several values of the same ratio, were computed and compared with experimental observations. Thus a range of possible values of AAA was determined, which is not in disagreement with previous figures, and a value for $\ensuremath{\tau}$ established which agrees well with that calculated from optical dispersion data.
The results are given of an experimental investigation of the structure of the λ= 3.39 μ methane line by recording saturated dispersion resonances. A method is described for reducing the intensity of the laser field in the absorbing medium to a value of < 10-6 W/cm2 and thus ensuring that the resolving power of the method is determined mainly by the collisional and field broadening of the lines, and exceeds considerably the transit limit. A 2.2 kHz doublet line splitting, resulting from the recoil effect, was recorded using a laser having a 3-cm diameter beam.
The line shape of a pair of Doppler-broadened closely spaced transitions sharing a common lower level and under the effect of a standing-wave monochromatic radiation field is studied. The eight steady-state optical Bloch equations are solved analytically to obtain the polarization by retaining terms up to the third power in the electric-field amplitude. The absorption coefficient derived for the standing-wave case consists of two Lamb dips for the two allowed transitions at ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$ and a crossover resonance dip at the intermediate frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$=(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$)/2. The Lamp-dip peak frequencies show intensity-dependent shifts. Numerical computations are presented for different values of Rabi frequencies and relaxation linewidth parameters, which are small compared to the frequency difference \ensuremath{\Delta}=${\mathrm{\ensuremath{\omega}}}_{2}$-${\mathrm{\ensuremath{\omega}}}_{1}$. The computed line shape and frequency shift are compared with the observed results in the Balmer ${\mathrm{H}}_{\mathrm{\ensuremath{\alpha}}}$ line of hydrogen and the infrared Zeeman spectra of methane.
From resonance equations using density matrix formalism, we obtain several features of rf or mw optical double resonance experiments at zero field. Resonance signal intensity formulas are derived. The question of the spatial and polarization dependence is then reduced to a minimum number of parameters through the use of multipole tensors; the effect of a resonance within the excited state is formulated as a redistribution of excited state multipole moments. In the case of transitions between hyperfine sublevels which are separated on the order of the natural linewidth, coherence is produced by interference between different rf-optical transition pathways. Depending on the method of detection, such interference may lead to a dispersion-shaped contribution to the ODR line shape, as observed in the experiments on the NO A state (Bergeman and Zare, accompanying paper). Second order radiation field corrections for multiplet transitions (generalizations of the Bloch-Siegert shift) are also derived.