Second harmonic polarization

The value of 3 and its dispersion for a molecule, or polymer chain, can be experimentally determined by DC induced second harmonic generation (DCSHG) measurements of liquid solutions -1 2). The experimental arrangement requiring an applied DC field E° to remove the natural center of inversion symmetry of the solution is described in Figure 4. The second harmonic polarization of the solution is expressed as... 

Figure 9.11 (a) and (b) Comparison between the second-harmonic -polarized signals... 

Readout of the with a third beam (o(M) at fundamental frequency produces a nondisappearing second harmonic polarization, with the complex... 

In the SHG technique attention is focussed on the frequency 2co. The induced second-harmonic polarization per unit volume, P (2 o), can formally be written as )... 

When the liquid is submitted to a static electric held an incident laser electric held E at angular frequency (o produces a second-harmonic polarization... 

The introduction of the local field factor in nonlinear optics is more complex due to the interplay of linear and nonlinear polarization. The reader is referred to two textbooks [16,17] for a rigorous derivation. The correct second-harmonic polarization... 

In the mm2 symmetry of stretch-oriented and poled PVDF films, there arc three independent second-aider nonlinear ooefifidenia. and the components of tbe second-harmonic polarization arc given in lenns of the electric field components of the inddcnl light by [4]... 

Zhao X L, Ong S W and Eisenthal K B 1993 Polarization of water-molecules at a charged interface. Second harmonic studies of charged monolayers at the air/water interface Chem. Phys. Lett. 202 513-20... 

The second term on the right-hand side, a component oscillating at frequency 2co, represents the second harmonic of the incident beam. This component of the polarization vector can radiate light at the frequency 2co. Observation of the second harmonic generation was demonstrated in the early 1960s using mby lasers (59). 

In a second kind of infrared ellipsometer a dynamic retarder, consisting of a photoelastic modulator (PEM), replaces the static one. The PEM produces a sinusoidal phase shift of approximately 40 kHz and supplies the detector exit with signals of the ground frequency and the second harmonic. From these two frequencies and two settings of the polarizer and PEM the ellipsometric spectra are determined [4.316]. This ellipsometer system is mainly used for rapid and relative measurements. 

A very simple equation exists that relates spontaneous polarization to the intensity of the second harmonic signal. Spontaneous polarization is conceived as the sum of the products of each of the charges in a dielectric material by each of their displacements from the centrosymmetric positions. Hence, the relationship between spontaneous polarization and the second harmonic signal value can be presented as follows ... 

Because the second harmonic response is sensitive to the polarizability of the interface, it is sensitive to the adsorption and desorption of surface species and is capable of quantifying surface species concentrations. Furthermore, SHG can be used to quantify surface order and determine surface symmetry by measuring the anisotropic polarization dependence of the second harmonic response. SHG can also be used to determine important molecular-level and electrochemical quantities such as molecular orientation and surface charge density. 

Recently, Eisenthal and coworkers have developed time-resolved surface second harmonic techniques to probe dynamics of polar solvation and isomerization reactions occurring at liquid liquid, liquid air, and liquid solid interfaces [22]. As these experiments afford subpicosecond time resolution, they are analogous to ultrafast pump probe measurements. Specifically, they excite a dye molecule residing at the interface and follow its dynamics via the resonance enhance second harmonic signal. 

FIG. 3 Solvation dynamics dependence of coumarin 314 probe molecule orientation at the air-water interface. Signals are generated with a 420 nm pump photon and probed by surface second harmonic signal with 840 nm (SH at 420), x Sx element. The normalized change in SH field is plotted vs. pump delay, r is derived from a single exponential fit to the data, (a) Pump polarization S (inplane), (b) Pump polarization P (out-of-plane). (Reprinted from Ref 24 with permission from the American Chemical Society.)... 

Nonlinear second order optical properties such as second harmonic generation and the linear electrooptic effect arise from the first non-linear term in the constitutive relation for the polarization P(t) of a medium in an applied electric field E(t) = E cos ot. 

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. 

For crystalline solids, comparative quantities for second harmonic generation and the linear electrooptic coefficient are given by Miller s delta and the polarization optic coefficient f. The quantity 6 is defined by the relation... 

The dominance of the tt -electron excitations in MNA is demonstrated by the experimental finding that along the polar, axis the second harmonic susceptibility X 2 ) (-2< > < >, m/V is the same as the... 

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