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Type of Document	Dissertation
Author	Adles, Eric J.,
URN	etd-03212007-090709
Title	Anisotropic Bond Model of Nonlinear Optics and Applications to Silicon and Silicon-Dielectric Interfaces.
Degree	PhD
Graduate Program	Physics
Advisory Committee	Advisor Name Title D. E. Aspnes Committee Chair C. R. Roland Committee Member G. J. Iafrate Committee Member J. E. Rowe Committee Member
Keywords	anistropic bond model nanocrystalline hyperpolarizability amorphous second-harmonic generation silicon polarizability
Date of Defense	2007-03-22
Availability	unrestricted
Abstract Nonlinear optical (NLO) techniques are important for the characterization and studying of materials, thin films and interfaces, particularly in this era of nanotechnology and photonics. However, interpretation of nonlinear optical data has been difficult and phenomenological. Here we present the Anisotropic Bond Model (ABM), which is an extension of the previous simplified bond-hyperpolarizability model (SBHM) to include gradient effects. Both the ABM and SBHM describe NLO data with physically meaningful parameters and much simpler mathematics than alternative approaches. We use the ABM to describe second-harmonic generation (SHG) from planar crystalline silicon (c-Si), amorphous materials and nanocrystalline silicon (nc-Si) spheres embedded in glass. Data for nc-Si spheres in glass were recently reported by Figliozzi et al. [1] and provide a critical new test of the theory in that they can only be described when gradient effects are included. We begin by reviewing previous theoretical treatments, including the Ewald-Oseen Extinction Theorem and the SBHM. The SBHM is effectively the Extinction Theorem for NLO, but as we point out, is one of the rare instances where the nonlinear problem is much simpler than the linear problem because NLO signals are generally weak and at a different frequency from the driving field. Therefore, a self-consistent solution is not required. This leads to the completely counter-intuitive result that the NLO treatment is actually easier than that for linear optics. We next develop necessary theoretical tools for our model, starting from the Liénard-Wiechart potentials and calculating the far-field radiation from point charges in terms of their displacements from equilibrium positions. From this we are able to identify the various physical mechanisms contributing to SHG: intrinsic bond anharmonicity, spatial dispersion (field gradient) effects, and higher multipole contributions. Specifically, we show the latter are equivalent to frequency or phase modulation. We then calculate the SHG from amorphous materials and nc-Si. By carefully considering gradient effects we show that the transverse field gradient can be neglected in planar geometries but must be included to describe SHG from amorphous materials and embedded nc-Si spheres. In particular, the amorphous-material results open the way to apply the approach to a wide range of new materials including biological materials. We next use the ABM to revisit SHG anisotropy at several wavelengths from a set of vicinal (111) Si-dielectric samples involving planar interfaces with SiO2 and Si3N4. While p-p and p-s data were previously reported, the s-p and s-s data are new. Also, the analysis has been upgraded to include the dipole-forbidden bulk contribution, which was not available previously. Our objective is to investigate the possibility of using the bulk contribution as a standard reference for all samples, and thereby enable a quantitative comparison across the different samples independent of misorientation and interface processing. This would be an improvement over the standard method of using one of the 4 Si bonds, usually a back bond, as a phase and amplitude reference. Our results show that this may be possible under certain conditions, but may not be a valid procedure in all situations.
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