The theory of pulsed polarization spectroscopy in the case of a saturating pump pulse and an optically thick sample is presented, both with and without inhomogeneous broadening. It is found that the molecular anisotropy produced by pumping an R- or P-branch transition is maximized by using a pulse whose flip angle is near 2\ensuremath{\pi} for the M component with the largest Rabi frequency. Calculations with no or extreme inhomogeneous broadening differ insignificantly. Such a pump pulse produces an anisotropy (and thus polarization rotation of the probe beam) of the opposite sign of that produced by weak-field excitation. Pulse-propagation calculations obtained by numerically solving the coupled Maxwell-Bloch equations demonstrate that there exist ``stable-area'' pulses, much like for a two-level system. The lowest such stable pulse produces a flip angle of 2.21\ensuremath{\pi} for the M=0 level and produces close to the maximum polarization anisotropy. This pulse still weakly excites the sample, and thus lengthens as it propagates to conserve area. The effective absorption coefficient, however, is much less than that for weak pulses. It is expected that such pulses should provide an order of magnitude or more sensitivity for polarization spectroscopy than that obtained with nonsaturating pulses.
The theory of pulsed polarization spectroscopy in the case of a saturating pump pulse and an optically thick sample is presented, both with and without inhomogeneous broadening. It is found that the molecular anisotropy produced by pumping an R- or P-branch transition is maximized by using a pulse whose flip angle is near 2\ensuremath{\pi} for the M component with the largest Rabi frequency. Calculations with no or extreme inhomogeneous broadening differ insignificantly. Such a pump pulse produces an anisotropy (and thus polarization rotation of the probe beam) of the opposite sign of that produced by weak-field excitation. Pulse-propagation calculations obtained by numerically solving the coupled Maxwell-Bloch equations demonstrate that there exist ``stable-area'' pulses, much like for a two-level system. The lowest such stable pulse produces a flip angle of 2.21\ensuremath{\pi} for the M=0 level and produces close to the maximum polarization anisotropy. This pulse still weakly excites the sample, and thus lengthens as it propagates to conserve area. The effective absorption coefficient, however, is much less than that for weak pulses. It is expected that such pulses should provide an order of magnitude or more sensitivity for polarization spectroscopy than that obtained with nonsaturating pulses.
This paper presents a theory of lineshapes for molecular Optical-Optical Double Resonance (DR) Spectroscopy with arbitrary strength for both pump and probe fields using the steady-state solutions for the 3-level density matrix. When Doppler broadening can be neglected, the results are analytical, and the probe spectrum is a pair of Lorentzian lines that display Autler-Townes splitting, each with an angular frequency half-width half maximum equal to the relaxation rates, which are assumed to be equal. When Doppler broadening is introduced, one must resort to numerical integration except for the limit of weak pump and probe fields. When the Doppler width is assumed to be much larger than the pump and probe Rabi frequencies and the probe frequency is higher than that of the pump, the calculated DR lineshapes are found to be Lorentzian with a strong pump field limit width that is proportional to the pump Rabi frequency, which is commonly known as power broadening. However, the width does not equal that Rabi frequency and is different for co- and counter-propagating pump and probe fields. Furthermore, that broadening is largely inhomogeneous, despite the Lorentzian shape. The saturation power is found to be about 4 times higher than for the bare probe transition with the same relaxation rate, dramatically lower than that expected if the width is interpreted as homogeneous.
We review our previous work on pump-probe spectroscopy in realistic degenerate two-level systems and model systems. In particular, we discuss the role of transfer of coherence (TOC) between the ground and excited hyperfine states in producing electromagnetically-induced transparency (EIA) peaks in the probe spectrum, when an Fg goes to Fe = Fg +1 transition in an alkali-metal atom interacts with a strong pump and weak probe that have perpendicular polarizations. When the pump is rho+ polarized and the probe pi polarized, this system can be modelled by an N system. We also discuss the role of transfer of population (TOP) between the Zeeman levels of the ground hyperfine state in producing EIA peaks when the pump and probe have the same polarization. This system can be modelled using a double two-level system. The role of Doppler broadening and phase-changing collisions in modifying the EIA-TOC and EIA-TOP absorption and refraction spectra is also discussed. All these spectra were calculated using MATLAB programs that both construct and solve the relevant Bloch equations. In our recent work, we consider the effect of a strong probe on the pump absorption and refraction spectra when the pump and probe polarizations are linear and perpendicular. It is difficult to solve this problem numerically due to the large number frequencies involved. In order to simplify the problem, we considered two cases: (i) rho+ polarized pump and pi polarized probe, and (ii) rho+ polarized pump and rho- polarized probe, and investigated a series of transitions in both Rb and Cs, using modified versions of the MATLAB programs devised for the weakprobe case. A number of interesting differences from the weak-probe case were found. For example, when the probe is sufficiently strong, we found the pump and probe spectra to show complementary behavior. In addition, as the number of Zeeman levels increase, the EIA peaks become progressively sharper, and are accompanied by steeper dispersion.
We model the response of a molecular medium to an intense pulse of light. We begin by reducing the Maxwell-Bloch equations for a multilevel molecular model system to a set of simplified propagation equations. We thereby obtain expressions for the frequency, temperature, and field intensity dependence of the ground and excited electronic state absorption cross sections, and the emission cross section, as well as the temperature dependence of the decay rate of the excited state. The phenomena of saturation, excited-state absorption, optically induced dichroism and birefringence, vibronic energy transfer, induced molecular alignment, decay of the matter-field interaction energy, and rotational diffusion are considered within the general formalism for describing the propagation of an intense pulse of light in the molecular medium. We find that the cross section for absorption (emission) of a photon is not identical to the cross section for molecular excitation (deexcitation) via the matter-field interaction. This is explained in terms of an energy balance between the matter, radiation, the matter-radiation interaction, and the bath responsible for the broadening of the molecular transitions. The inequality of these cross sections determines whether the system supplies or draws energy from the thermal bath. The rise in the vibrational temperature of molecules subjected to an intense short pulse is shown to significantly affect propagation of the pulse. The alignment of the molecular system resulting from saturation of the ground-state transition by a polarized laser pulse and the effects of the orientational dependence of the matter-field interaction including effects of rotational diffusion are determined. As an example of the formalism we consider pulse propagation in a Rhodamine 6G solution. We fit the parameters of the model to determine the frequency dependence of the ground- and excited-state absorption cross sections and the emission cross section and compare with experimentally determined cross sections. We describe the propagation of a pulse whose temporal width is comparable to the rotational diffusion time of the molecules in the dye solution and calculate polarization pulse probe signals.
A theory of saturation spectroscopy is developed which accounts for effects of level degeneracy. The theory can be applied to those situations in which a pump laser field of arbitrary strength and polarization acts between two manifolds of degenerate or nearly degenerate atomic levels, while a probe laser field of arbitrary strength and polarization acts between a coupled manifold of levels. As such, this theory of "three-level" systems could, in principle, include effects arising from level degeneracy, optical pumping, atomic motion, transient laser fields, different polarizations and strengths for pump and probe fields, and atomic transit across the laser fields. The present calculation, however, is limited to a study of optical pumping and field polarization effects for pump fields of arbitrary strength and weak probe fields interacting with a single velocity subclass of atoms. Probe absorption line shapes clearly display the effects of pump-field strength (Rabi splittings), pump-field polarization (positions and number of Rabi-split resonance peaks), pump-field detuning (positions of resonance peaks), and optical pumping (relative strengths of the resonance peaks). The calculation is carried out with the use of an irreducible tensor basis for the atomic density matrix although a standard (m-basis) calculation is included in an appendix.
Abilities of the method of accumulation of coherent unstable response of a medium for amplification of the rotated component of the probe wave’s polarization in the atomic medium of three-level atoms are studied. Probe wave is examined in frames of the perturbation theory and its frequency is considered near to one photon resonance from the ground to the first excited level. The intense monochromatic pump field connects two excited energy levels and propagates through the medium without a change. The broadening of spectral lines caused by the relaxation processes and the Doppler broadening are included into the calculations. It is shown that by multiple consistent instantaneous change of input probe field’s phase from 0 to π and back, it is possible to obtain, in the tail part of the rotated component of the probe field, a separate narrowed light pulse along with the increase in intensity by more than an order of magnitude with respect to the input field.
A theoretical analysis of the relative intensities of the Doppler-free signals in saturation spectroscopy, velocity selective optical pumping (VSOP) spectroscopy, polarization spectroscopy and a mixing of saturation and polarization spectroscopies is presented using the approximation of a single cycle of optical pumping in a four-level system. An optical pumping process in the Zeeman sublevels is taken into account owing to the important role of spontaneous emission even if the sublevels are degenerate. Arbitrary polarization combinations are considered for pump and probe beams. The similarities and differences between three kinds of spectroscopy are made clear. Both circular and linear optical anisotropies induced by the pump beam are considered in this theoretical calculation. The magnitude and sign of Doppler-free resonances in each spectroscopy are quite different owing to the polarizations of the pump and probe beams. The four-level system is important as a three-level approximation. The results obtained from the four-level optical pumping theory are in good agreement with experimental reports.