Nonlinear optical interaction

Nonlinear Optical Interactions in Organic Crystal Cored Fibers... 

We believe that our model can be extended even further to accurately describe other nonlinear optical interactions such as sum and difference frequency mixing, as well as higher-order harmonics generation. 

I. Biaggio, P. Kerkoc, L.S. Wu, P. Gunter, and B. Zysset, Refractive-indexes of orthorhomhic KNbOs Phase-matching configurations for nonlinear-optical interactions, Journal of the Optical Society of America B 9(4), 507-517 (1992). 

Interest in the field of nonlinear optics has grown tremendously in recent years. This is due, at least partially, to the technological potential of certain nonlinear optical effects for photonic based technologies. In addition, the responses generated through nonlinear optical interactions in molecules and materials are intimately related to molecular electronic structure as well as atomic and molecular arrangement in condensed states of matter. 

In the above equation a is the linear polarizability. The terms 3 and Y, called first and second hyperpolarizabilities, describe the2 nonlinear optical interactions and are microscopic analogues of x and x... 

THIRD ORDER NONLINEAR OPTICAL INTERACTIONS IN SOME BIOENGINEERED POLYMERS... 

Nonlinear optical interactions in micrometer-size liquid droplets are readily observable. New data on the stimulated Raman scattering of benzene droplets (up to the 6th-order Stokes), and water droplets containing KNO ... 

In contrast to meter-long optical fibers, nonlinear optical interactions from a single micrometer-size liquid droplet are usually considered to be weak because of the short length for possible nonlinear interactions and because of the inability to maintain a high intensity in the form of a guided wave along the propagation direction. We will review several experimentally observed nonlinear optical processes associated with the the liquid,... 

Output resonance is reached (for a droplet with a fixed radius) when specific wavelengths within the inelastic emission profile correspond to MDR s with different n,t values. For those wavelengths, the droplet can be envisioned as an optical cavity with a large Fresnel number and Q-factors which are dependent on the specific n and I values. The portion of the inelastic radiation detected is that allowed to "leak" out of the droplet cavity. However, it is the internal field distributions of the electromagnetic waves at X, and X, which are best described by spherical harmonic functions and not by plane waves as in the case of an extended medium, that affect the nonlinear optical interactions. Such interactions in droplets can be illustrated by several well known examples in nonlinear spectroscopy of liquids in an optical cell. 

FIGURE 2 Schematic illustration of an anharmonic potential well (solid line) that can be responsible for nonlinear optical interactions. A harmonic potential well that does not result in nonlinear interactions is shown for comparison (dashed line). 

The coefficients in the various terms in Eqs. (2a) and (2b) are termed the nth-order susceptibilities. The first-order susceptibilities describe the linear optical effects, while the remaining terms describe the nth order nonlinear optical effects. The coefficients are the nth-order electric dipole susceptibilities, the coefficients G " are the nth-order quadrupole susceptibilities, and so on. Similar terminology is used for the various magnetic susceptibilities. For most nonlinear optical interactions, the electric dipole susceptibilities are the dominant terms because the wavelength of the radiation is usually much longer than the scattering centers. These will be the ones considered primarily from now on. 

Here Pi is the amplitude of the nonlinear polarization with frequency tw,. It is determined by an appropriate combination of optical fields and nonlinear susceptibilities according to the expansion in Eq. (2a). It serves as a source term for the optical field with frequency < ,. The wave-vector of the nonlinear polarization fcf is in general different from the wave-vector of the optical field at the same frequency. This difference plays a very important role in determining the effectiveness of many nonlinear optical interactions. 

Coherent nonlinear effects involve interactions that occur before the wave functions that describe the excitations of the medium have time to relax or dephase. They occur primarily when the nonlinear interaction involves one- or two-photon resonances, and the duration of the laser pulse is shorter than the dephasing time of the excited state wave functions, a time that is equivalent to the inverse of the linewidth of the appropriate transition. Coherent nonlinear optical interactions generally involve significant population transfer between the states of the medium involved in the resonance. As a result, the nonlinear polarization cannot be described by the simple perturbation expansion given in Eq. (2), which assumed that the population was in the ground state. Rather, it must be solved for as a dynamic variable along with the optical fields. 

In the previous sections the basic nonlinear optical interactions have been described, along with some of their properties. In the following sections we shall describe applications of the various nonlinear interactions. Some applications have already been noted in the description given for certain effects. Here we shall describe applications that can be made with a wide variety of interactions. 

Nonlinear spectroscopy involves the use of a nonlinear optical interaction for spectroscopic studies. It makes use of the frequency variation of the nonlinear susceptibility to obtain information about a material in much the same way that variation of the linear susceptibility with frequency provides information in linear spectroscopy. In nonlinear spectroscopy the spectroscopic information is obtained directly from the nonlinear interaction as the frequency of the pump radiation is varied. This can be contrasted with linear spectroscopy that is done with radiation that is generated in a nonlinear interaction and used separately for spectroscopic studies. 

Somekh, S., and Yariv, A., Phase-matchable nonlinear optical interactions in periodic thin films, Appl. Phys. Lett., 21, 140-141 (1972). 

RAO N.D., SWIATKIEWICZ J., CHOPRA P., GHOSHAL S.K. and PRASAD P.N., (1986), Third-Order Nonlinear Optical Interactions in Thin Films of Poly-p-phenylenebenzobisthiazale Polymer Investigated by Picosecond and Subpicosecond Degenerate Four Nave Nixing, Appl. Phys. Lett., 48,... 

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