浙大光电子学课件chapter 8.ppt

Fundamentals of Photonics Question: Is it possible to change the color of a monochromatic light? Two-wave mixing is not, in general, possible. Two waves of arbitrary frequencies w1 and w2 cannot be coupled by the medium without the help of a third wave. Two-wave mixing can occur only in the degenerate case, w2=2w1, in which the second-harmonic of wave 1 contributes to wave 2; and the subharmonic w2/2 of wave 2, which is at the frequency difference w2-w1, contributes to wave 1. Parametric devices are used for coherent light amplification, for the generation of coherent light at frequencies where no lasers are available (e.g., in the UV band), and for the detection of weak light at wavelengths for which sensitive detectors do not exist. Wave Mixing as a Photon Interaction Process conservation of energy and momentum require Figure 19.2-8 Mixing of three photons in a second-order nonlinear medium: (a) photon combining; (b) photon splitting. Photon-Number Conservation Manley-Rowe Relation 19.3 Coupled-wave theory of three-wave mixing Coupled- Wave Equations Rewrite in the compact form Frequency-Matching Condition Three-wave Mixing Coupled Equations Mixing of Three Collinear Uniform Plane Waves slowly varying envelope approximation Three-wave Mixing Coupled Equations A. Second-Harmonic Generation a degenerate case of three-wave mixing w1=w2=w and w3=2w Two forms of interaction occur: ☆ Two photons of frequency o combine to form a photon of frequency 2w (second harmonic). ☆ One photon of frequency 2w splits into two photons, each of frequency w. ☆ The interaction of the two waves is described by the Helmholtz with equations sources. Conservation of momentum requires that by the Helmholtz equations with k3=2k1. Coupled- Wave Equations for Second-Harmonic Generation. where perfect phase matching Coupled Equations (Second-Harmonic Generation) the solution Consequently, the photon flux densities Figure 19.4-1 Second-harmonic generation. (a) A wave of frequency w i