Intensity third-order polarization

The measured CARS signal Scoh is proportional to the time integral over the absolute value squared of the total third-order polarization, P = Piso + Paniso + Pnr> because of the slow intensity response of the detector ... 

In a homodyne detection scheme, such as in the stimulated photon echo experiments described in the next paragraph, the detector measures the t-integrated intensity of the square of the third-order polarization... 

In the presence of strong absorption at co and 3(o, the intensity of the third harmonic can be written in terms of the third order polarization as (19) ... 

If the pump and probe pulses are well separated in time, these derivatives will tell us the rate of stimulated emission, which will be proportional to the intensity of spontaneous fluorescence. A more refined analysis that incorporates the detailed time courses of the pump and probe pulses requires evaluating the interaction of the probe field with the time-dependent third-order polarization as described in Chap. 11. 

As CARS is a four-wave mixing process [3], the intensity of the CARS signal is proportional to the square modulus of the induced third-order polarization... 

NLO effects result when the polarization response of the valence electrons becomes significantly anharmonic, usually in intense light beams where the magnitude of E is very large. The magnitudes of the coefficients of the terms in equation 2 diminish rapidly at higher orders, and thus readily observable NLO effects are either second-order third-order (X ) processes. Most NLO appHcations rely on second-order processes. However,... 

The two important consequences of the third-order optical nonlinearities represented by x are third-harmonic generation and intensity dependence of the refractive index. Third-harmonic generation (THG) describes the process in which an incident photon field of frequency (oj) generates, through nonlinear polarization in the medium, a coherent optical field at 3a>. Through x interaction, the refractive index of the nonlinear medium is given as n = nQ+n I where n describes intensity dependence of the refractive index ana I is the instantaneous intensity of the laser pulse. There is no symmetry restriction on the third-order processes which can occur in all media including air. 

The second and third terms of the right hand side of Eq. (25) constitute the second- and third-order nonlinear contributions to the total polarization. These corrections to the polarization are responsible for numerous nonlinear optical processes such as the generation of light beams with new frequencies or an intensity dependent refractive index. 

It is not surprising therefore that the optical properties of small metal particles have received a considerable interest worldwide. Their large range of applications goes from surface sensitive spectroscopic analysis to catalysis and even photonics with microwave polarizers [9-15]. These developments have sparked a renewed interest in the optical characterization of metallic particle suspensions, often routinely carried out by transmission electron microscopy (TEM) and UV-visible photo-absorption spectroscopy. The recent observation of large SP enhancements of the non linear optical response from these particles, initially for third order processes and more recently for second order processes has also initiated a particular attention for non linear optical phenomena [16-18]. Furthermore, the paradox that second order processes should vanish at first order for perfectly spherical particles whereas experimentally large intensities were collected for supposedly near-spherical particle suspensions had to be resolved. It is the purpose of tire present review to describe the current picture on the problem. 

The interaction of laser radiation with the medium occurs through the third-order, non-linear, electric susceptibility denoted by and gives rise to an induced polarization field, which acts as a source term in Maxwell s wave equation. On solving the wave equation, one arrives at the following expression for the intensity of the CARS signal ... 

Parametric frequency-conversion interactions can occur in any order of the perturation expansion of Eq. (2). The most commonly observed processes have involved interactions of second and third order, although interactions up to order 11 have been reported. Parametric interactions are characterized by a growth rate for the intensity of the generated wave that depends on a power, or a product of powers, of the intensities of the incident waves, and they are strongly dependent on difference in wave vectors between the nonlinear polarization and the optical fields. 

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