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InTech eBooks

Nonlinear Absorption of Light in Materials with Long-lived Excited States

Francesca Serra, M. Eugene

Published Jan 1, 2010• 6 citations
Publisher

Abstract

The most important conclusion of our work is that one has to be cautious with the classical concept of light absorption, represented by the Lambert-Beer law. Even without considering
DOI
10.5772/6942

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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.
A dynamic extended Beer–Lambert law with photodissociation and recombination is proposed, which is built to describe the interactions between light and molecular gases. The model comprises two spatiotemporally coupled first-order nonlinear partial differential equations. Numerical solutions of these equations systematically reveal the nonlinear transmission properties and steady-state dissociation behavior of the medium from the weak- to intense-light regime. In the weak-light limit, the model naturally reduces to the classic Beer–Lambert law, with the system reaching a steady state characterized by high molecular density and exponential light attenuation. Conversely, in the intense-light regime, low molecular concentration and pronounced photoinduced transparency occurs, and light attenuates linearly instead of exponentially. A method for measuring the recombination rate constant under steady-state conditions is presented, which imposes significantly lower demands on both the light intensity and the temporal resolution of the measurement equipment compared to conventional approaches.