Polarization nonlinear induced

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

The extensive jt-delocalized system of metal-dithiolene complexes is also responsible for the nonlinear optical properties (NLO) which have been recently reviewed . The interaction of radiation with the matter induces an instantaneous displacement (polarization Pq = /X = aE, where a is the linear polarizability) of the electronic density away from the nucleus at small field (linear optics). At high fields (laser light) the polarizability of the molecule can be driven beyond the linear regime and a nonlinear polarization is induced (NLO) = aE + fiE" + y E + and for the bulk material... 

For a nonresonant process, light is not absorbed by the sample. The optical nonlinearity basically originates from the anharmonicity of the electronic system. Traditionally, the nonresonant optical nonlinearity of a material is described via the perturbational approach. In this approach, the polarization, Pd, induced in a medium by an external electromagnetic field, E, can be written as... 

Nonlinear optical (NLO) properties of organic polymers can be viewed as dielectric phenomena, and their origins can conveniently be explained by considering a planar wave propagation through a nonlinear dielectric medium [1-4]. In a dielectric medium the polarization P induced by the incident field E can be written as a power series of the field strength as follows ... 

To keep track of the origin and interconnection of the nonlinear optical processes we recall that these are related to the different polarization terms in the power series expansion of the polarization P induced in the medium by an incident electric field E which in the dipolar approximation takes the form... 

A RIKES experunent is essentially identical to that of CW CARS, except the probe laser need not be tunable. The probe beam is linearly polarized at 0° (—>), while the polarization of the tunable pump beam is controlled by a linear polarizer and a quarter waveplate. The pump and probe beams, whose frequency difference must match the Raman frequency, are overlapped in the sample (just as in CARS). The strong pump beam propagating tlirough a nonlinear medium induces an anisotropic change in the refractive mdices seen by tlie weaker probe wave, which alters the polarization of a probe beam [96]. The signal field is polarized orthogonally to the probe laser and any altered polarization may be detected as an increase in intensity transmitted tlirough a crossed polarizer. When the pump beam is Imearly polarized at 45° y), contributions... 

The higher-order bulk contribution to the nonlmear response arises, as just mentioned, from a spatially nonlocal response in which the induced nonlinear polarization does not depend solely on the value of the fiindamental electric field at the same point. To leading order, we may represent these non-local tenns as bemg proportional to a nonlinear response incorporating a first spatial derivative of the fiindamental electric field. Such tenns conespond in the microscopic theory to the inclusion of electric-quadnipole and magnetic-dipole contributions. The fonn of these bulk contributions may be derived on the basis of synnnetry considerations. As an example of a frequently encountered situation, we indicate here the non-local polarization for SFIG in a cubic material excited by a plane wave (co) ... 

Takmg advantage of the synunetry changes induced by the presence of a surface. Many nonlinear teclmiques rely on the fact that the surface breaks the centrosynuuetrical nature of the bulk. The use of polarized light can also discriminate among dipole moments in different orientations. 

Polarization which can be induced in nonconducting materials by means of an externally appHed electric field is one of the most important parameters in the theory of insulators, which are called dielectrics when their polarizabiUty is under consideration (1). Experimental investigations have shown that these materials can be divided into linear and nonlinear dielectrics in accordance with their behavior in a realizable range of the electric field. The electric polarization PI of linear dielectrics depends linearly on the electric field E, whereas that of nonlinear dielectrics is a nonlinear function of the electric field (2). The polarization values which can be measured in linear (normal) dielectrics upon appHcation of experimentally attainable electric fields are usually small. However, a certain group of nonlinear dielectrics exhibit polarization values which are several orders of magnitude larger than those observed in normal dielectrics (3). Consequentiy, a number of useful physical properties related to the polarization of the materials, such as elastic, thermal, optical, electromechanical, etc, are observed in these groups of nonlinear dielectrics (4). 

CARS spectroscopy utilizes three incident fields including a pump field (coi), a Stokes field (CO2 C02nonlinear polarization at cOcars = 2c0i — CO2. When coi — CO2 coincides with one of the molecular-vibration frequencies of a given sample, the anti-Stokes Raman signal is resonantly generated [22, 23]. We induce the CARS polarization by the tip-enhanced field at the metallic tip end of the nanometric scale. 

In the theoretical section above, the nonlinear polarization induced by the fundamental wave incident on a planar interface for a system made of two centrosymmetrical materials in contact was described. However, if one considers small spheres of a centrosymmetrical material embedded in another centrosymmetrical material, like bubbles of a liquid in another liquid, the nonlinear polarization at the interface of a single sphere is a spherical sheet instead of the planar one obtained at planar surfaces. When the radius of curvature is much smaller than the wavelength of light, the electric field amplitude of the fundamental electromagnetic wave can be taken as constant over the whole sphere (see Fig. 7). Hence, one can always find for any infinitely small surface element of the surface... 

We have shown in this paper the relationships between the fundamental electrical parameters, such as the dipole moment, polarizability and hyperpolarizability, and the conformations of flexible polymers which are manifested in a number of their electrooptic and dielectric properties. These include the Kerr effect, dielectric polarization and saturation, electric field induced light scattering and second harmonic generation. Our experimental and theoretical studies of the Kerr effect show that it is very useful for the characterization of polymer microstructure. Our theoretical studies of the NLDE, EFLS and EFSHG also show that these effects are potentially useful, but there are very few experimental results reported in the literature with which to test the calculations. More experimental studies are needed to further our understanding of the nonlinear electrooptic and dielectric properties of flexible polymers. 

To introduce the subject matter of this volume, the fundamental concepts of nonlinear optics and their relationship to chemical structures are briefly summarized. In the dipolar approximation, the polarization induced in an atom or molecule by an external field E can be written as... 

For weak electric fields the magnitude of the induced polarization is linearly proportional with the amplitude of the electric field. Yet, when the field strength increases, the linear relationship no longer holds, and nonlinear terms have to be taken into account. In this case, the induced dipole moment and polarization can be expressed up to second order in the electric field as11... 

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