Intensive vectors linear dependence

There is a separation of charges in a nonlinear optical (NLO) medium under the application of an electric field. For weak electric fields, the applied electric vector, E, induces a polarization, P, in the material which is linearly dependent on the electric field, linear = E, where is the susceptibility tensor. The net polarization in the medium under the influence of several fields is a linear superposition of the effects of the same fields acting independently. At high intensities the optical fields can interact with each other through the higher order terms in the polarization vector. P can now be expanded as j (l) E + j (2) E E + j (3) E E E +. .. The nonlinear susceptibilities, etc., of... 

Steady-State Fluorescence Depolarization Spectroscopy. For steady state depolarization measurements, the sample is excited with linearly polarized lig t of constant intensity. Observed values of P depend on the angle between the absorption and emission dipole moment vectors. In equation 2 (9), Po is the limiting value of polarization for a dilute solution of fluorophores randomly oriented in a rigid medium that permits no rotation and no energy transfer to other fluorophores ... 

Figure 1.17 An experimental set-up for electron spectrometry with synchrotron radiation which is well suited to angle-resolved measurements. A double-sector analyser and a monitor analyser are placed in a plane perpendicular to the direction of the photon beam and view the source volume Q. The double-sector analyser can be rotated around the direction of the photon beam thus changing the angle between the setting of the analyser and the electric field vector of linearly polarized incident photons. In this way an angle-dependent intensity as described by equ. (1.55a) can be recorded. The monitor analyser is at a fixed position in space and is used to provide a reference signal against which the signals from the rotatable analyser can be normalized. For all three analysers the trajectories of accepted electrons are indicated by the black areas which go from the source volume Q to the respective channeltron detectors. Reprinted from Nucl. Instr. Meth., A260, Derenbach et al, 258 (1987) with kind permission of Elsevier Science—NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.

Equation (6) shows that the sum-frequency intensity is dependent on the second-order polarization However, that polarization is a vector quantity P f. Within the electric dipole approximation the local fields E and re coupled by the second-order non-linear susceptibility, [16], inducing the following non-linear polarization at... 

Consider a time-resolved, electronically nonresonant CARS spectrum from a molecular liquid. In the CARS process, the laser pump pulses create a linear combination (that is the inteimolecular rovibrational coherence) of Raman active rovibrational transitions between molecules at position rr and r in the mixture. This stimulated Raman scattering process is carried out by two-coincident laser pulsesfl, II) with central frequenciesfwave vectors) C0i(k ) and (Oiiikii). By applying the third pulse with C0 (kni) to the liquid after time delay t, the time dependence of the inteimolecular rovibrational coherence is detected through the measurement of the intensity of the scattered photon with kj... 

Infrared dichroism is based on the interaction between linearly polarized infrared radiation and the oriented material. The atoms of a polymer molecule vibrate in characteristic normal modes, each of which produces a change in dipole moment (the transition moment) that has a specific direction. Each mode absorbs infrared energy at a characteristic frequency, giving rise to peaks in the infrared spectrum. The peak intensity (i.e. the absorbance) depends on the angle between the transition moment and the electric field vector of the radiation, and it is this that provides information on the molecular orientation. The orientation is defined in terms of the second moment of the orientation function Pjlcos 0), where ... 

If a polarizer which rotates the polarisation plane of the incident wave is placed between two crossed linear polarizers (Fig. 2.13) the electric vector of the input beam will be turned and the crossed polarizer transmits only a fraction of the input intensity which depends on the turning angle 9 of the rotating polarizer. The Jones formahsm yields the output electric vector as... 

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