Polarization vector, molecular photonics

Here, Ho is the molecular Hamiltonian in the BO approximation, and V is the nonadiabatic coupling operator. U(t) = —/x e(r)cos(a)/t) is the pulse excitation operator. Here, e t) is the amplitude of the laser pulse with photon polarization vector e, and coi is laser central frequency. In Eq. 6.18, i] denotes the parameter depending on photon polarization direction of the linearly polarized laser pulse = 1 for the polarization vector e+, while r] = -l for e. ... 

Amplitudes of molecular optical events are proportional to off-diagonal matrix elements of interaction operators between the wavefunctions of the initial, final, and possibly also intermediate states of the molecule, 0), f), and /) respectively. These operators are projections of molecular transition vector and tensor operators onto the polarization directions of photons created or annihilated in the event (Table 1). The amplitudes depend on the wavenumber of the light used and can be real or complex. The probability of an optical event W is proportional to the square of the absolute value of its amplitude (Table 2). The proportionality constant is of no... 

The polarization vector of the photons does not affect the molecular wave fimctions. A quantity called electric transition dipole may, therefore, be defined... 

Figure 2. The three time-ordered diagrams representing second harmonic generation. Pump photons of wave vector k and polarization X impinge on the molecule from the left and the subsequent harmonic (k, leaves the molecular world line from the right. We assume the initial and final state of the molecule is the ground state 0 the intermediate states are labelled r and s.

In these equations the position of the molecule is described by the vector R the wavevectors of the two beams of modes r2 and are k2 and k3 respectively, with ( 2) and (q3) the corresponding mean photon numbers (mode occupancies) and is a unit vector describing the polarization state of mode rn. In deriving Eqs. (120) and (121), the state vectors describing the radiation fields have been assumed to be coherent laser states, and so, for example, (<72) = (oc n a(2 ), where a ) is the coherent state representing mode 2 and h is the number operator a similar expression may be written for (<73). Also, the molecular parameters apparent in Eqs. (120) and (121) are the components of the transition dipole, p °, and the index-symmetric second-order molecular transition tensor,... 

To quantitatively analyze the molecular distribution within the rubbed polymer surfaces we have recorded absorption spectra for a series of electric field vector orientations within the two principal planes perpendicular to the film surface. These are the previously introduced planes parallel x-z) and perpendicular (y-z) to the rubbing direction. The polarization dependence is summarized by the intensity of the tt resonance in the normalized AEY spectra, which are plotted versus the photon incidence angle a as soUd and open symbols in Fig. 6.7. The solid lines are the result of a fit to the data using (6.3). 

In the case of coherent laser light, the pulses are characterized by well-defined phase relationships and slowly varying amplitudes (Haken, 1970). Such quasi-classical light pulses have spectral and temporal distributions that are also strictly related by a Fourier transformation, and are hence usually refered to as Fourier-transform-limited. They are required in the typical experiments of coherent optical spectroscopy, such as optical nutation, free induction decay, or photon echoes (Brewer, 1977). Here, the theoretical treatments generally adopt a semiclassical procedure, using a density matrix or Bloch formalism to describe the molecular system subject to a pulsed or continuous classical optical field, which generates a macroscopic sample polarization. In principle, a fully quantal description is possible if one represents the state of the field by the coherent or quasi-classical state vectors (Glauber, 1965 Freed and Villaeys, 1978). For our purpose, however. 

An incident laser light beam of wave vector k,, frequency and polarization e, falls perpendicularly on the surface of a sample. Part of this incident radiation is Rayleigh scattered and part is Raman scattered (see Sec. V) with a wave vector k, a frequency and a polarization e. The interaction of the incident photon with the substance can be thought of as a shock between the photon and an elementary (quantum) vibration of the substance, either phonon (if crystalline) or molecular in the sense of Secs. IV and V. 

In electronic and vibrational spectroscopy we can neglect both molecular dimensions relative to the wavelength and the effects of the magnetic field of light relative to those of its electric field (electric dipole approximation). Then, the interaction of a single l7-polarized photon with a molecule is described by the projection of the electric dipole moment vector operator M (Table 3) into eP (photon creation) or eP (photon annihilation). Creation... 

Saupe matrix elements T = two-photon absorption tensor U V = photon electric field vector direction (polarization) x, y, = molecular orientation axes x y, z - arbitrary molecular axes X, Y, Z = laboratory axes a, P, / = Euler angles ... 

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