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.
The absorption of a single photon that excites a quantum system from a low to a high energy level is an elementary process of light-matter interaction, and a route towards realizing pure single-photon absorption has both fundamental and practical implications in quantum technology. Due to nonlinear optical effects, however, the probability of pure single-photon absorption is usually very low, which is particularly pertinent in the case of strong ultrafast laser pulses with broad bandwidth. Here we demonstrate theoretically a counterintuitive coherent single-photon absorption scheme by eliminating nonlinear interactions of ultrafast laser pulses with quantum systems. That is, a completely linear response of the system with respect to the spectral energy density of the incident light at the transition frequency can be obtained for all transition probabilities between 0 and 100% in multilevel quantum systems. To that end, a multiobjective optimization algorithm is developed to find an optimal spectral phase of an ultrafast laser pulse, which is capable of eliminating all possible nonlinear optical responses while maximizing the probability of single-photon absorption between quantum states. This work not only deepens our understanding of light-matter interactions, but also offers a way to study photophysical and photochemical processes in the ``absence'' of nonlinear optical effects.
A new method of picosecond and femtosecond transient spectroscopy yielding information about ultrafast relaxation processes without requiring ultrashort light pulses is presented. It is based on the present theoretical analysis of the resonant degenerate four-wave-mixing process excited by two temporally incoherent light beams with wave vectors ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}$ which are originated from a single beam at frequency $\ensuremath{\omega}$ but have mutual time delay $\ensuremath{\tau}$. Under the assumption that the incoherent light field has Gaussian random complex amplitude and that the resonant material consists of the usual two-level atoms, the statistically averaged intensity of the output light field with ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{3}=2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ at $\ensuremath{\omega}$ is calculated as a function of $\ensuremath{\tau}$. Even with the light having a much longer duration than both
T1 (the longitudinal relaxation time) and
T2 (the transverse relaxation time), the correlation trace, i.e., output intensity versus $\ensuremath{\tau}$, represents a decay profile determined mainly by
T2 for both homogeneously and inhomogeneously broadened transitions, as long as the light correlation time ${\ensuremath{\tau}}_{c}$ is much shorter than the relaxation times. The correlation trace does not always represent a single-exponential decay but is sometimes slightly deformed by the
T1 effect. However, it does not cause a significant error in the determination of
T2. Moreover, as $\frac{{T}_{2}}{{T}_{1}}\ensuremath{\rightarrow}0$, the trace becomes a single-exponential decay curve determined only by
T2. The feature of the results obtained by the present method is similar to that obtained by the conventional coherent transient spectroscopy with short pulses, such as the photon echo. The time resolution in the present method, however, is limited only by ${\ensuremath{\tau}}_{c}$ much shorter than the light duration. By regarding the incoherent light as a series of random ultrashort pulses, the present four-wave-mixing process is also interpreted as the ensemble of numerous transient four-wave-mixing processes caused by various combinations of these pulses.
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.
Forced light scattering using broad-bandwidth incoherent pump light (${\ensuremath{\lambda}}_{\mathit{B}}$=508 nm, full width at half maximum \ensuremath{\Delta}${\ensuremath{\lambda}}_{\mathit{B}}$=13.8 nm), and narrow-bandwidth probe light is investigated experimentally and compared with self-diffraction. Forced light scattering improves the dynamic range of measurement by an order of magnitude compared to self-diffraction. A theoretical analysis of this scheme is presented. The technique is used to measure the dephasing kinetics of solutions of crystal violet and bis-(dimethylamino)heptamethine. Resulting from the relatively large autocorrelation time of 40 fs, the experimental signals show no influence from inhomogeneous broadening of the absorption bands; the dephasing kinetics can be characterized by a dephasing time
T2\ensuremath{\approxeq}10 fs and an intrinsic correlation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{C}}$\ensuremath{\approxeq}30 fs with a weak modulation (center frequencies ranging from 800 to 1200 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), which is attributed to a coherent motion of the molecule (vibration). The dephasing kinetics of crystal violet shows a close agreement with the dephasing kinetics of malachite green previously reported for two-pulse photon echoes with ultrashort pulses [P. C. Becker et al., Phys. Rev. Lett. 63, 505 (1989)].
Abstract In the framework of the consistent microscopic theory, universal analytic expressions describing absorption of laser pulses of an arbitrary duration in an optically dense medium have been derived, and their limiting cases have been considered. For the Gaussian and Lorentzian spectral profiles, simple expressions have been obtained for the absorption coefficient as a function of dimensionless parameters (optical thickness of the medium, the pulse duration and carrier frequency). Based on the performed calculations, the effect of the optical thickness of the medium on the dependences of the absorption coefficient on the pulse parameters has been revealed.
The effects of coherent propagation of an ultrashort pulse through an extended collection of multilevel systems is examined. It is found that the transmitted field shows significant deviation from both Beer’s law absorption and the conventional area theorem. In addition, when the system is in a nonstationary state it is found that additional frequencies can appear in the transmitted pulse spectrum. Such effects may be important in several areas of current interest, such as ultrafast pump–probe, coherent control, and inversionless amplification experiments in extended, multilevel media as well as in ultrafast-laser development.