The methods of calculating the deviations from Beer-Lambert's law and other related phenomena in solutions illuminated by a ruby laser are analyzed and criticized carefully. These methods include the steady-state and optically thin approximation as compared with the exact solution of a set of coupled differential equations which describe the temporal and spatial changes of the photons and populations of the various energy levels. Critical evaluation of the validity of the approximation is given. The computations are compared with the experimental data of Beer's law deviations, pulse shaping, recovery of the ground state after excitation, and blue and red fluorescence of solutions of cryptocyanine. A set of absorption cross sections and decay rates which fits best all these experiments is deduced.
The methods of calculating the deviations from Beer-Lambert's law and other related phenomena in solutions illuminated by a ruby laser are analyzed and criticized carefully. These methods include the steady-state and optically thin approximation as compared with the exact solution of a set of coupled differential equations which describe the temporal and spatial changes of the photons and populations of the various energy levels. Critical evaluation of the validity of the approximation is given. The computations are compared with the experimental data of Beer's law deviations, pulse shaping, recovery of the ground state after excitation, and blue and red fluorescence of solutions of cryptocyanine. A set of absorption cross sections and decay rates which fits best all these experiments is deduced.
The broad white-light continuum generated on the passage of ultrashort pulses of laser light through suitable media has found numerous applications in the physical, chemical, and biological sciences. Many of these are based on use of the continuum to probe the absorption characteristics of transient species, in order to obtain information on their decay kinetics. The processing of data from such experiments is generally based on the implicit assumption that the absorption of white light is subject to the normal Beer-Lambert law, in that the absorption at any particular frequency is linearly proportional to the intensity of the probe light at that frequency. In this paper it is shown that the validity of this underlying assumption should be seriously questioned. At high intensities, the uncertainty principle allows for photon pairs with differing frequencies to provide the energy for the cooperative excitation of molecules in close proximity. This nonlinear absorption, which depends on the frequency autocorrelation function and intensity of the continuum light, results in a rate of absorption which may depart significantly from the normal Beer-Lambert behavior. Hence the interpretation of continuum-probe experiments may need to be reexamined.
We develop an analytical approach to the dynamics of band populations of reverse saturable absorbers modeled by the three-level approximation of the five-level rate equations. We find high-accuracy approximate solutions to these rate equations, taking into account the temporal shape of the incident laser pulse for different regimes of excitation. The results obtained are confirmed by direct numerical integration of the rate equations and are verified by solution of the full system of the rate and the propagation equations. The validity ranges of the approximations are determined. We also prove that for input pulses that are much longer than the lifetime of the first excited state the ground-state depletion obeys the same functional dependence on the input fluence as in the case of rectangular input pulses. The dynamics of the excited states, however, explicitly depends on the pulse shape. We quantitatively estimate the effect of various parameters on the nonlinear absorption coefficient and discuss implementation of the approach by a beam propagation method to reduce the computational time.
Optical absorption cross sections and the fluorescent quantum efficiency in ruby have been determined. This data has been used to correlate calculations with the analysis of the preceding paper. Stimulated emission from ruby under pulsed excitation has been studied in some detail; the observations are found to depend strongly on the perfection of the particular crystal under study. A peak power output of approximately 5 kw, total output energy of near 1 joule, beam collimation of less than ${10}^{\ensuremath{-}2}$ rad, and a spectral width of individual components in the output radiation of about 6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$A at 6943 A have been measured. It is suggested that mode instabilities due to temperature shifts and a time-varying magnetic field are contributing to an oscillatory behavior of the output pulse.
According to the Beer-Lambert law, the spectral density of weak electromagnetic radiation is attenuated exponentially, with the characteristic length depending on atomic density and the frequency-dependent photoabsorption cross section of the target. We discuss an analog of the Beer-Lambert law in the time domain, showing that the temporal profile of the initial light pulse enters explicitly into each term of expansion of the exponential function as a multiconvolution with the corresponding temporal response of an atom. The form invokes a description of pulse propagation in terms of the temporal base functions, which may be precalculated for a chosen initial pulse shape, allowing us to obtain the attenuated profile at a given target depth simply by summing up a sufficient number of weighted base functions. The variant with a 100-fs initial Gaussian pulse is worked out in detail, with the atomic response exhibiting either pure exponential or mixed prompt-exponential decay, characteristic of a photoexcited bound state or a Fano resonance. The method is shown to be valid for an arbitrary temporal profile of the initial electric field and is illustrated for pulses resonantly tuned to the low-lying doubly excited states of the He atom.
We present a theoretical framework for studying spatially dependent absorption in a thermal vapor of multilevel atoms, of arbitrary optical thickness. The atomic state dynamics, governed by a standard atom-optical master equation, are self-consistently coupled to the axial evolution of the probe beam intensity and the effusive gas dynamics. We derive steady-state equations for the spatially varying distributions of atomic populations and the probe beam intensity. From the latter, absorption coefficients in both the saturated and unsaturated regimes can be calculated. We present solutions to the resulting equations at various levels of approximation, including an example of the full numerical solution of a saturated, optically thick vapor of three-level atoms, demonstrating a breakdown of Beer's law, among other measurable effects.
This thesis describes three experiments performed in gases. Chapter 2 describes the first observation of four wave degenerate mixing in cesium vapor. Its basis in nonlinear optics is explained and a simple set of equations are derived which predict the resonant behavior, density dependence, and the power dependence of the signal. Experimental results are then compared to those predicted and reasonable agreement is obtained. A value of (chi)(,zxxz) is measured as (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) compared to the value calculated of 2.8(.)10('-30) esu/atom. The agreement is satisfactory considering the competing processes involved such as photoionization, two-photon absorption, etc. which would tend to reduce the signal observed. The experimental difficulties encountered, i.e., large background and absorption of the laser, limit the usefulness of the process as a probe of the nonlinear optics of cesium. In the third chapter, results are given for measurements of inelastic scattering cross-sections for the 9D and 10D states of cesium. The cross-sections measured (in units of 10('-13)cm('2)) for the fine structure-changing collisions (sigma)(,21) Cs(n('2)D(,5/2)) + Cs(6('2)S(,1/2)) Cs(n('2)D(,3/2)) + Cs(6('2)S(,1/2)) (sigma)(,12) for n = 9 and n = 10 are 1.50 (+OR-) 0.3 and 2.01 (+OR-) 0.4, for (sigma)(,t1) respectively. The cross sections for nonradiative relaxation (sigma)(,t2) Cs(n('2)D(,5/2)) + Cs(6('2)S(,1/2)) out of D states (sigma)(,t1) Cs(n('2)D(,3/2) )+(, )Cs(6('2)S(,1/2)) out of D states for n = 9 and n = 10 are 0.66 (+OR-) 0.3 and 1.4 (+OR-) 0.4 for (sigma)(,t1) and 1.1 (+OR-) 0.4 and 1.7 (+OR-) 0.4 for (sigma)(,t2), respectively. The cross-sections agree well with previously measured values, where available, and represented the first experimental verification that the cross-sections (sigma)(,t1) and (sigma)(,t2) are the same within our experimental uncertainties. In chapter 4 we report the observation of cancellation of rotational e-fects in the intensity of ultraviolet b and s of OH. The b and oscillator strength for transition in the (1,0) b and of OH has been measured and found to be independent of rotational excitation. This independence is explained in terms of the cancellation of a rotationally induced increase in the Franck-Condon factor by an equivalent decrease in the electronic transition moment. We have also remeasured the (0,0) b and oscillator strength as a function of rotational energy and obtained a value for (rho) = 0.75 (+OR-) 0.02A('-1). This value is used along with spectroscopic data to fit a simple model for explaining rotationally induced effects. Very good agreement is found with our data and previous calculations.