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A macroscopic formalism to describe the second-order nonlinear optical response of nanostructures

Brian K Canfield1,3, Sami Kujala1, Konstantins Jefimovs2, Yuri Svirko2, Jari Turunen2 and Martti Kauranen1

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We present a macroscopic formalism to describe the second-order nonlinear optical response of nanostructures. Rapid variations in local nonlinearity and electric field distributions on scales smaller than a wavelength preclude a simple, direct relationship between the macroscopic and nanoscopic nonlinear response functions in arrays of metal nanoparticles. We develop an approach that bypasses these difficulties by focusing on the macroscopic nonlinear optical response of the sample in terms of the input and output fields. The main advantage of this macroscopic formalism is that it naturally includes contributions from higher multipoles, although symmetry properties can be addressed using electric-dipole-type selection rules. It is limited by being specific to the experimental geometry, although experimental variations are expected to provide additional insight into the underlying physical processes. The formalism is applied to the second-harmonic response of an array of L-shaped gold nanoparticles.


PACS

42.65.-k Nonlinear optics

78.67.Bf Nanocrystals and nanoparticles

78.20.Ek Optical activity

42.70.Nq Other nonlinear optical materials; photorefractive and semiconductor materials

Subjects

Condensed matter: electrical, magnetic and optical

Optics, quantum optics and lasers

Nanoscale science and low-D systems

Dates

Issue 4 (April 2006)

Received 5 October 2005, accepted for publication 20 February 2006

Published 27 March 2006



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