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Journal of the Optical Society of America B

Theory of pump–probe spectroscopy

G. Khitrova, P. R. Berman, Murray Sargent

Published Jan 1, 1988• 67 citations
Publisher

Abstract

We calculate the two-level pump–probe absorption coefficient including both upper-to-lower-level decay and level decays to a still lower-lying reservoir level. The probe-absorption profile can have arbitrary ratios of the natural linewidth and detuning to the Doppler width. We observe and explain new line-shape features that occur when the two main levels decay to the reservoir level at different rates.

DOI
10.1364/josab.5.000160

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We calculate the two-level pump–probe absorption coefficient including both upper-to-lower-level decay and level decays to a still lower-lying reservoir level. The probe-absorption profile can have arbitrary ratios of the natural linewidth and detuning to the Doppler width. We observe and explain new line-shape features that occur when the two main levels decay to the reservoir level at different rates.
We calculate the two-level pump-probe absorption coefficient including both upper-to-lower-level decay and level decays to a still lower lying reservoir level. We carried out calculations of probe absorption profile for arbitrary ratios of natural width and detuning to the Doppler width associated with a given transition. This theory accounts for contributions from all velocity subclasses of atoms, not only those which are Doppler shifted into resonance with the laser field (Doppler limit).1 We observe and explain new line shape features based on dissimilar decays.
This thesis presents theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrarily strong pump field drives a given atomic transition and a weak probe field drives the same transition. We have carried out calculations of probe absorption in vapors for arbitrary ratios of natural width and detuning to the Doppler width associated with a given transition. New line shape features which were absent in previous theories are observed.
In this paper we present theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrary strong pump field drives a given transition and a probe (weak) field drives the same transition. We have studied the influence of level degeneracy and field polarization on pump-probe and four-wave mixing signals. Our results indicate that for some closed systems (no population loss to the reservoir) it is possible to observe resonances that are characterized by the ground state width. Previous calculations indicate that for a nondegenerate system this resonance can appear only for an open system, the so-called "pressure induced resonances.”1 Our result, which contradicts this conclusion, can be understood by noting the fact that there are in general three irreducible tensor2 (in general) contributions to the line shape (K = 0 population, K = 1 orientation, and K = 2 alignment). Thus, even if the system is closed for the population it may still remain open for orientation or alignment; this effect is responsible for the narrow resonance. Specific calculations are presented for J = 1/2 → 1/2 and J = 1→2 transitions.
A theory of line shape for a Doppler broadened probe in the presence of a strong infrared pump is presented. The optical analog of Bloch equations has been developed; the T1, T2 relaxations are introduced phenomenologically in these equations. Doppler broadening of both the pump and signal transitions are taken into account to obtain the absorption coefficient for the signal. This leads to a Doppler broadened Gaussian function weighted by a pump induced Lorentzian function whose position and linewidth are controlled by the detuning and power respectively of the pump radiation. The absorption coefficient is further modulated by a Lorentzian function containing the fourth power of the radiation. The off-resonance pumping leads to two symmetrically located ‘‘Lamb dips’’ or ‘‘peaks’’ around the Gaussian pedestal for co- and counter propagating laser radiations. A calculation of the line shape of the central sub-Doppler feature for the on-resonance pumping is in good agreement with the observed variation of linewidth with pressure. Numerical results are presented graphically to demonstrate the pump and signal power dependence of the central hole or peak for the bent and cascade-type double resonances. The results obtained confirm the expected behavior based on level populations.
A general theory of the saturated-absorption phenomenon in a two-level atomic system is developed, in which the phase relationships between the oscillating atomic dipoles as well as the population differences between energy levels are taken into account. The absorbing gaseous medium considered in this theory is subjected to irradiation by a quasi-running-wave composed of a strong pump field and a weak probe field propagating in opposite directions. Some new interesting results, not predicted by the so-called hole-burning or rate-equation model, are obtained. In particular, the probe-field-transmission peak line shape is found to be markedly different from what is expected according to the rate equations. For finite Doppler widths and a strong saturating pump field, absorption of the probe field can even change sign, and amplification of this field can actually occur. All these features are explained by a close inspection of the evolution of each atomic ensemble of given velocity. Detailed comparison with similar phenomena already observed in rf experiments is presented and permits us to clarify the new predicted effects.