Evaluation of NLO susceptibilities for L-threonine amino acid single crystals using anharmonic oscillator model G. Ramesh Kumar, S. Gokul Raj, V. Mathivanan, M. Kovendhan, Thenneti Raghavalu, R. Mohan * Department of Physics, Presidency College, Kamarajar Salai, Chennai, 600 005 Tamilnadu, India Received 26 February 2007; received in revised form 17 May 2007; accepted 15 August 2007 Available online 29 October 2007 Abstract Three dimensional semi-classical anharmonic oscillator model proposed by Akitt has been used to evaluate the second order and elec- tro-optic susceptibilities of L-threonine. As the ionic contribution to the optical non-linearity for the frequency range under study was negligible, the NLO parameters were calculated by taking the contribution of electronic polarization alone. The data presented here are in reasonable agreement with the experimental ones and the results have been discussed in detail. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Non-linear optical materials; L-threonine; Anharmonicity 1. Introduction The advent of laser has led to the observations of number of non-linear optical phenomena. Optical effects in matter result from the polarization of the electrons in the medium in response to the electromagnetic field associated with the light propagating the medium. A simple model for these interactions is the Lorentz oscillator described in a variety of book sources. Here an electron is bonded to a nucleus by a spring with a natural frequency x 0 and equilibrium dis- placement ‘x’. The electric component of the optical field felt by the electron is represented as a sinusoidally varying field. Considering only the linear response of this object, the equation of motion using harmonic oscillator approxi- mation can be written as d 2 x=dt 2 þ C dx=dt þ x 2 0 x ¼ ðe=m e ÞE x ð1Þ where C– damping constant, e – electronic charge, x 0 – electronic resonance frequency. Solving Eq. (1), the linear susceptibility is given by v 1 ðxÞ¼ N 2 e =½m e e 0 ðx 2 0  x 2  jxCÞ Neglecting the damping term for the range of wavelengths considered, we have v 1 ðxÞ¼ N 2 e =½m e e 0 ðx 2 0  x 2 Þ ð2Þ For the present study, we have considered anharmonic oscillator model first introduced by Bloembergen [1]. Using this model, the expressions for the second order non-linear susceptibilities such as linear electro-optic effect and the second harmonic generation are described by adding anharmonic terms in Eq. (1). 2. Three dimensional anharmonic oscillator (AHO) model Anharmonic oscillator model was well established by many authors [2–4]. In particular, Akitt et al., [5] have utilized two coupled anharmonic oscillators to predict the non-linear susceptibilities for a simple cubic material. The non-linearities are assumed to be due to bound electrons and the fundamental ionic lattice resonance and their mutual interaction. The model predicts non-linear 0925-3467/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2007.08.003 * Corresponding author. Tel.: +91 44 2854 4894; fax: +91 44 2851 0732. E-mail addresses: rameshvandhai@yahoo.co.in (G. Ramesh Kumar), professormohan@yahoo.co.in (R. Mohan). www.elsevier.com/locate/optmat Available online at www.sciencedirect.com Optical Materials 30 (2008) 1405–1409