It has been shown recently that molecular gas samples excited with coherent light can display a variety of transient phenomena, similar to those found in nuclear magnetic resonance. This article elucidates how these coherence effects can be used to isolate or unfold molecular collision mechanisms that normally remain hidden within the optical line shape. Elastic collisions, for example, are easily detected here in two-pulse photon echo experiments for a
13CH3F vibration-rotation transition. The echo-decay function which provides a signature for the velocity-changing collision diffusion mechanism, is not just a simple exponential in time but exhibits an $\mathrm{exp}(\ensuremath{-}K{t}^{3})$ contribution for short times and an $\mathrm{exp}(\ensuremath{-}\ensuremath{\Gamma}t)$ decay for long times. This behavior, which is unknown heretofore, contrasts with spin echoes in molecular liquids where Brownian motion leads only to the cubic decay law. An $\mathrm{exp}(\ensuremath{-}K{t}^{3})$ behavior can be understood in terms of a solution of the Fokker-Planck equation which describes the effect of Brownian motion on echo decay. Such a treatment is valid for small phase excursions; in the case of a gas, this implies the Doppler phase factor $k\ensuremath{\Delta}u\ensuremath{\tau}\ensuremath{\ll}1$, where $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ is the propagation vector of light, $\ensuremath{\Delta}u$ is a characteristic velocity jump for a binary collision, and $\ensuremath{\tau}$ is the echo-pulse delay time. When $k\ensuremath{\Delta}u\ensuremath{\tau}\ensuremath{\gg}1$ as in the long-time regime, the Fokker-Planck solution fails. We, therefore, present a new solution to the Boltzmann transport equation using a weak collision model and find agreement with the entire echo time dependence observed. The echo measurements indicate very small changes in longitudinal velocity per
13CH3F-
13CH3F collision, i.e., $\ensuremath{\Delta}u=85$ cm/sec, thereby justifying the weak-collision model. The total elastic collision cross section is 430
A˚2. It follows that elastic collisions lead to velocity thermalization in a time of \ensuremath{\sim}5 sec when the
13CH3F pressure is 1 mTorr. A comparison is also made of the
13CH3F dephasing time ${\ensuremath{\tau}}_{2}$ in a coherent Raman beat decay, which is independent of velocity-changing collisions, with the longitudinal decay time
T1. Here,
T1 represents the molecule-optical interaction time, due largely to jumps in molecular rotation (
J) and orientation (
M) state, and is obtained from a delayed nutation measurement. The fact that the pressure dependent part of ${\ensuremath{\tau}}_{2}={T}_{1}$ shows that
T1 is also independent of velocity diffusion. Futhermore, when a hole is burned in the Doppler distribution, population recovery must be due to inelastic rather than elastic collisions. Optical Carr-Purcell echoes, multiple pulse echoes, provide a direct measure of the
13CH3F transverse dephasing time
T2 without the effect of elastic collisions while being sensitive to "phase interrupting collisions." Again, we find that
T2=T1 so that phase interruptions are negligible. Had such a process dominated the two-pulse echo, an $\mathrm{exp}(\ensuremath{-}\frac{t}{{T}_{2}})$ damping would have been noticed with no $\mathrm{exp}(\ensuremath{-}K{t}^{3})$ contribution. Thus, the present study covers several new aspects of molecular collisions. It represents the first detailed examination of velocity-changing collisions by coherence methods and without the complication of Doppler broadening.
I. A new technique utilizing the electro-optic frequency switching of a single mode ( 6 Mhz) dye laser was used to observe free induction decay and optical nutation in iodine gas and optical nutation in an organic mixed crystal (pentacene in p-terphenyl) at low temperature. A new technique, incoherent resonance decay (IRO) was also developed. These experiments allow one to determine T_1 and T_2, the longitudinal and transverse relaxation times of the excited ensemble, in analogy with magnetic resonance. For I_2(g) at O∙C; T_l = 2.3 x 10^(-7) sec, T_2 ≃ 1 x 10^(-7) sec. These techniques are limited to a time scale > 10 nsec.
II. The construction and characterization of cw, mode-locked dye laser capable of putting out a continuous train of reproducible sub-picosecond pulses is described. Experiments utilizing this laser for the measurement of picosecond coherent transients and time resolved absorption spectroscopy are proposed.
Coherent transient phenomena can be generated by the abrupt changes of parameters either of the electromagnetic field or of the matter. Comparative analysis of these two approaches, made on the base of experimental research in molecular gases SF6, 15NH3, HFCO and 13CH3F, excited by the radiation of CW CO2 and 13CO2 lasers, is presented. The first approach of photon echo (and its modifications) generation, based on electro-optic pulses formation from the resonant CW exciting radiation, has proven to be successful for intense infrared molecular transitions. The coherent responses are sufficiently powerful to be applied in high resolution spectroscopy, the spectral markers creation ,and molecular collisions investigations. However, this technique is not very effective for the free polarization decay investigations. Another approach based on the Stark switching molecular levels of polar gas, irradiated by CW laser, was demonstrated for free polarization decay and photon echo generation in 13CH3F. Free polarization decay has shown the pronounced frequency shift because of dynamic Stark effect in the CW radiation field. This specific feature of coherent transients, created by Stark switching, limits the high resolution spectroscopy by the low intensity range of exciting radiation. From other viewpoint, it gives unique possibility to investigate coherent transients generated at the dressed molecular levels.
Elastic velocity-changing collisions have been observed for the first time to our knowledge in a nonpolar molecule by photon-echo studies of SF(6) using a frequency-switched CO(2) laser that we have developed. The photon-echo decay is nonexponential and reveals the velocity-changing collision cross section to be sigma(vc) = 180 A(2), with an average velocity change per collision of Deltau = 155 cm/sec. Using delayed optical nutation, we also determine the cross section for the population decay rate (1/T(1)) to be sigma(pop)=335 A(2). To within experimental accuracy, we find that phaseinterrupting collisions are not important (T(1) approximately T(2)). A comparison of these cross sections with those for the polar molecule (13)CH(3)F is made.
A simple method for observing coherent optical-transient phenomena is described. Effects such as photon echoes and free induction decay (FID) should allow studies of the dynamic properties of atoms, molecules, and solids on a time scale ranging from milliseconds to \ensuremath{\sim} 50 ps. The frequency of a cw dye laser is switched with an intracavity electro-optic modulator, producing in an external sample coherent transients which are detected in the forward beam. Measurements of long dephasing times are possible, as in FID, because the laser can oscillate indefinitely at the new frequency following a step-function switching pulse. Measurements of short decay times are also practical because the switching time is not restricted by the laser gain or cavity ringing time. In addition, the dye's dephasing time of a few picoseconds or less is too rapid to interfere with these observations. Since the pulse sequence can be preselected, the entire class of coherent optical transients is accessible. The method thus incorporates all of the advantages inherent in Stark switching, including heterodyne detection and high sensitivity, without being restricted to Stark-tunable systems. Laser frequency switching is discussed also in terms of a theoretical model which exposes the time-dependent properties of a phase-modulated cavity mode. Dephasing studies have been carried out thus far in atomic and molecular gases and low-temperature solids containing inorganic impurity ions or large organic molecules. The utility of the FID effect is emphasized where precise dephasing times are obtained from time-frequency Fourier transformation of FID signals using a digital computer. The first quantitative and detailed test of FID theory is provided by these experimental techniques.
Recently we have reported[1] on the measurements of electronic dephasing (T_2) and radiationless decay (T_1) in molecules using emission spectroscopy as a probe for the detection of the photon echo. This right-angle photon echo utilizes a single mode of a narrow-band (~MHz) cw dye laser and an intracavity electro-optical (EO) element that modulates the frequency of the laser.[2] Applying voltage pulses into the EO crystal switches the laser frequency from ω_0 (the peak frequency of the transition resonance) into another frequency ω. This switching procedure introduced by Brewer et al. for the observation of transients in the forward direction of the laser allows one to observe coherent transients in gases,[1,2] solids[3-5] and molecular beams.[6] Typically, the dispersion of the nonlinear EO crystal (e.g., AD*P) gives a 60 MHz frequency shift within the inhomogeneous resonance of the optical transition (width ~GHz or larger). Therefore, to switch the laser frequency further, one must use high-voltage signals that are usually hard to obtain especially for multiple-pulse experiments. Secondly, there is a limit on the frequency shift which is conditioned by the mode spacing of the cavity. Thirdly, because the laser is switched into a new group of molecules some complications may arise in interpreting the transient spectra especially in large molecules. This is because in large molecules the density of excited states is high and thus the buildup of transients of w molecules (which could be complex) will be superimposed on the decay of ω_0 molecules. Finally, off-resonance effects (e.g., beats) between the molecules at frequency ω and ω_0 cannot be avoided.