Bond models in linear and nonlinear optics

Abstract

Atomic-scale descriptions of linear-optical properties such as reflection are nearly a century old, but surprisingly, analogous models describing nonlinear-optical (NLO) properties as the natural dynamic response of bond charges driven by an external field are a recent development. These bond-charge models have proven to be particularly useful in describing the relevant physics of second-, third-, and fourth-harmonic generation, identifying previously unrecognized contributions to NLO responses, and uncovering well-disguised correlations in tensor parameters determined phenomenologically from symmetry conditions. Current capabilities are discussed, and opportunities for improved understanding noted. 1 Introduction The availability of continuum sources of radiation covering wide spectral ranges has not only made linear-optical spectroscopy possible, but also linear-optical techniques indispensable for determining information nondestructively about materials, interfaces, and structures. Owing to the higher-order tensors involved, in principle nonlinear-optical (NLO) probes are much more powerful, but spectroscopic data [1-5] have been difficult to acquire. However, commercial femtosecond systems that can tune over wide wavelength ranges are becoming available, and we are rapidly reaching the point where NLO spectroscopy will be routine.The potentially greater diagnostic power of NLO comes at a price, specifically the need to use more complex models and methods to interpret these more complex data. For most linear-optical applications, measurements can be analyzed using macroscopic parameters such as the dielectric function e, which for isotropic materials is a scalar and anisotropic materials a second-rank tensor. Here a return to fundamentals is generally unnecessary, and the last contact most linear-optical spectroscopists have had with atomic scale properties is the textbook derivation of the ClausiusMossotti relation [6], which relates the dielectric constant to local polarizabilities in the static limit.For NLO, quantities equivalent to e are the susceptibility tensors x ijk , x ijkl , etc. [7]. Symmetry-allowed NLO tensor components have been determined for all crystal classes, and

Bond orbital description of the strain-induced second-order optical susceptibility in silicon

“…The deformation potentials theory relies on the de-localisation of the Bloch wavefunction over the entire crystal and proves to be a good description for the study of transport properties of electrons. However, it is known now that the nonlinear optical properties in covalent crystals are mainly due to the properties of the localized electrons in the covalent bonds between the different atoms of the crystal [13][14][15][16][17]. Thus, theories based on the deformation potentials not only prove to be very limiting for extracting the different χ (2) components in terms ofε , but also do not show a very good numerical agreement with the experimental data for χ (2) in strained silicon [11,18].…”

Bond Model and Group Theory of Second Harmonic Generation in GaAs(001)

“…As noted by Aspnes in Ref. [27] this method is inspired by the Ewald-Oseen extinction theory where it has been shown in Ref. [28] that the formulas for reflection and transmission in linear optics can be derived microscopically within a classical framework in agreement with the macroscopic derivation using Maxwell boundary conditions.…”

“…Their effort was motivated by the complexity arising from phenomenological theory and notion that SHG experimental intensities from centrosymmetric system particularly vicinal Si(111) should be reproducable by another model using fewer parameters. Inspired by Ewald-Oseen's method [11,12] to calculate far field intensities in linear optics via superposition of dipoles, they extend this principle to nonlinear optics and obtain surprisingly a simplier analysis than the linear case [13]. The core idea of SBHM is that the driving field oscillates the charge in the material surface/interface harmonically and anharmonically along the bond direction between the atoms and because in classical electrodynamics an accelerated charge radiates, it produces linear and nonlinear harmonics in the reflection spectra.…”

Classical Model of Surface Enhanced Infrared Absorption (SEIRA) Spectroscopy

“…It is also necessary for a cohesive theory that explains all surface-enhanced spectroscopies. We have embarked on a systematic approach toward such a theory based on atomic-bond-model (ABM) methods that have antecedents in the calculation of Lorentz polarizability. − We have called this approach the Classical Correlation Method (CCM) to represent the fact that we are applying classical electrodynamics to spectroscopic problems that have heretofore been solved using quantum mechanics.…”