The\u00a0efficiency\u00a0of the wave mixing process decreases as $|\\bigtriangleup k|L$ increases( although there are some fluctuations). This is becuase when L gets greater than $\\frac{1}{\\bigtriangleup k}$ the harmonic wave can get out of phase with incident beam and power can flow from the $\\omega_{2}$ back into the 2 $\\omega_{1}$ waves. The coherence length of the interaction \u00a0is $L_{c}=\\frac{2}{\\bigtriangleup k}$ so the phase mismatch factor can be written as $sinc^{2}(\\frac{L}{L_{c}})$<\/p>\n
From the phase mismatch plot we see a big decrease in efficiency when $\\bigtriangleup k \\neq 0$ is not satisfied. This is quite difficult to obtain in labs because the refractive index of materials that are lossless in the range $\\omeg_{1}$ to $\\omega_{2}$ have normal dispersion when $\\frac{dn}{d\\lambda}<0$. The refractive index is an increasing function of frequency. For the case of second harmonic $n\\omega_{1} = n\\omega_{2}$, this is not possible since $n(\\omega)$ increases with $\\omega$. So what is generally used is birefringence of crystals ie.the dependence of the refractive index on the direction of polarization of the optical radiation. This slows down out of phase waves to get a perfect mismatch.<\/p>\n","protected":false},"excerpt":{"rendered":"
The\u00a0efficiency\u00a0of the wave mixing process decreases as $|\\bigtriangleup k|L$ increases( although there are some fluctuations). This is becuase when L gets greater than $\\frac{1}{\\bigtriangleup k}$ the harmonic wave can get out of phase with incident beam and power can flow from the $\\omega_{2}$ back into the 2 $\\omega_{1}$ waves. The coherence length of the interaction […]<\/p>\n","protected":false},"author":1019,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4101,29905,29902],"tags":[],"class_list":["post-2091","post","type-post","status-publish","format-standard","hentry","category-advanced-em","category-spring-2012","category-tariq"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2091","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/users\/1019"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/comments?post=2091"}],"version-history":[{"count":13,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2091\/revisions"}],"predecessor-version":[{"id":2414,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2091\/revisions\/2414"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=2091"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=2091"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=2091"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}