Four-wave mixing

Glazer, A. M.; Cox, K. G.

doi:10.1107/97809553602060000633

International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. D. ch. 1.6, pp. 151-152

Section 1.6.2.9. Four-wave mixing $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}E_k^{\omega_2}E_\ell^{\omega_3}]$

A. M. Glazer^a ^* and K. G. Cox^b ^‡

^a Department of Physics, University of Oxford, Parks Roads, Oxford OX1 3PU, England, and ^bDepartment of Earth Sciences, University of Oxford, Parks Roads, Oxford OX1 3PR, England
Correspondence e-mail: glazer@physics.ox.ac.uk

1.6.2.9. Four-wave mixing $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}E_k^{\omega_2}E_\ell^{\omega_3}]$

| top | pdf |

One use of a third-order nonlinear optical susceptibility is in the important area of four-wave mixing. In this case, the complex amplitude of the induced polarization at the frequency $[\omega_1 = \omega_2 + \omega_3 - \omega_4]$ is given by $[P_i^{\omega_1} = \varepsilon_o\chi_{ijk\ell}(-\omega_1;\omega_2,\omega_3,-\omega_4) E_j^{\omega_2}E_k^{\omega_3}E_\ell^{*\omega_4}.]$ Thus if a nonlinear crystal is pumped by two counter-propagating beams of frequency $[\omega_1 = \omega_2 = \omega]$ , and another beam $[\omega_4 = \omega]$ is input at some angle, a fourth beam $[\omega_3 = \omega]$ results whose complex amplitude will be the complex conjugate of the $[\omega_4]$ beam. Thus four-wave mixing is an important arrangement for producing phase conjugation.

References

International Tables for Crystallography (2006). Vol. D. ch. 1.6, pp. 151-152