# Nonlinear Laser Spectroscopy

## Introduction

The high intensity and coherence of lasers allows new types of laser spectroscopy to be applied to physical measurements. Nonlinear spectroscopies rely on driving matter with high intensity lasers to generate or enhance certain light frequencies.

## Theory

When light interacts with matter the electric field of the electromagnetic radiation drives the electron cloud of the matter. At low light intensity the oscillation of the electron cloud exactly matches the oscillation of the incident radiation. At higher light intensity, the electron cloud can no longer keep up with the amplitude of the incident light. In this case we say we are in the nonlinear regime. More on the linear interaction of light and matter.

The terms are called the first, second, and third-order nonlinear susceptibilities.

For atoms or molecules with convenient two-photon transitions, the Doppler width can be eliminated by using counterpropagating beams. In the atomic frame of reference, the two laser beams appear at frequencies of *w*_{o}(1- k*v/c) and *w*_{o}(1+ k*v/c), where *w*_{o} is the frequency halfway to the two-photon level. The velocity dependence cancels out and the net result is that all atoms will absorb photons with a total energy of the two-photon transition. Due to absorption of two photons travelling in the same direction, this method will have some residual absorption of the full Doppler width.

## Four-wave mixing spectroscopy

CARS is the acronym for coherent anti-Stokes Raman spectroscopy. CARS uses multiple laser beams and nonlinear wave mixing to achieve enhancement in the Raman scattering from a molecule.

## Second-harmonic generation (SHG)

Second-harmonic generation occurs in non-centrosymmetric crystals or at surfaces. It is the basis for frequency doubling or tripling that is common to convert the 1064 nm output of Nd:YAG lasers to 532 or 355 nm, respectively. Second-harmonic generation is useful as an analytical tool because the SHG signal can only arise from a surface, and hence is a surface-selective technique.

Copyright © 2000 by Brian M. Tissue, all rights reserved.