## Phase matching >[!Notice] >In this page, phase matching using [[Birefringence|birefringence]] is the main focus. For [[Quasi-phase-matching]] and other techniques like [[Advanced phase matching]], check these corresponding pages. ### Why phase matching? Generally speaking, from a microscopic point of view, phase matching is to ensure energy and momentum conservation. For continues medium, phase matching is to ensure sufficiently high conversion efficiency of nonlinear process can be obtained. The latter one may be illustrated by the following picture. (This is shown in [[Nonlinear Optics]] page 65) - Consider the individual response of atoms/molecule inside a nonlinear material. - With some input fields from outside hits the material, the atom would response to these input field and generate some polarization, then radiate some new frequencies in the form of a dipole radiation pattern. - Now consider the bulk material. With $N$ atomic dipoles in total, each one has its phase. - Only in constructive "interference", the new frequencies may become a well-defined beam. - And this condition, when individual dipoles added constructive, is called phase matching condition. ### Phase matching under wave equation description Recall in [[Sum frequency generation under wave equation description#Phase-matching considerations, amplitude and intensity]], we developed the relation between the intensity of output wave and the wavevector mismatch