Second harmonic generation in partially ordered media and at interfaces: analysis of dynamical and orientational factors

Abstract

A new method of modelling molecular orientational dynamics is presented and illustrated by application to optical second harmonic generation (SHG). The method highlights the intricate dependence of the harmonic signal on the form and evolution of the molecular orientational distribution, and reference is made to some examples taken from the recent literature. Specifically, the cases considered relate to SHG in (a) poled polymers, (b) molecules oriented within molecular sieves and (c) molecules in films or adsorbed on surfaces. The technique invokes rotational averages weighted by static or time-dependent distribution functions expressed in terms of Legendre polynomials. Rotational diffusion is used to model the decay of second harmonic intensity associated with a growth or recovery of bulk isotropy, the results allowing several discrete contributions associated with different time constants to be characterised. For polarisation studies using surfaces and films, it is shown that caution is required in how the results are interpreted to reflect molecular orientation, approximations in commonly employed theory readily producing spurious results.

Temperature Effects on Molecular Alignments at the Surface of Ultrathin Films Studied by SHG and Fluorescence Techniques.

“…We propose that a secondary transition undergoing at the PMMA layer is responsible for this loss; during this transition, the so-called rotation diffusion occurs at the sub-chain sites of PMMA molecules. 8 Our argument is supported by the studies on mechanical relaxing and vibrational and rotational spectroscopy of PMMA molecules, which indicated the secondary transition taking place between 20 °C and 80 °C, 9 although our DSC resulted in a single glass transition at 115 °C without any signal at lower temperatures.…”

Sum frequency generation from partially ordered media and interfaces: a polarization analysis

“…It should be noted that these components are solely associated with the orientational averaging of the hyperpolarizability tensor and not the underlying molecular mechanisms responsible for orientational relaxation. For SHG from molecules reorienting via stochastic rotational diffusion this leads to a signal in the form of a multiexponential decay as detailed previously [8]. In the general case of SFG, the explicit forms for the coefficients B n in (20) are…”

“…As described in detail in [8], averaging is now accomplished by expanding the distribution function in terms of Legendre polynomials: f (θ, t) = ∞ n=0 a n (t)P n (cos θ) where P n is the Legendre polynomial of order n and a n (t) is a set of time-dependent coefficients. Thus we require…”

Optical vortices in six-wave mixing

“…Interpreting the Feynman diagrams delivers the form of the material states, thus providing the structure for the associated optical susceptibility tensor -in this case a fifth rank tensor (5) χ . The full result for the quantum amplitude for six-wave conversion at a position r now emerges in a form that is readily cast in terms of the Cartesian components of polarization vectors for the input and output, e and e respectively.…”