## Abstract

Dispersive mirrors can be designed to create cavities that resonate at set multiple frequencies while simultaneously meeting the conditions for efficient nonlinear wave mixing. We analyze the conditions that such a cavity design must meet and the free parameters that can be used for optimization. Using numerical methods, we show the benefit in conversion efficiency attained with multiple resonances, and draw conclusions concerning the design parameters. As a specific example, we consider parametric downconversion in a triply-resonant cavity.

© 2005 Optical Society of America

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### Equations (11)

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(1)
$$\frac{d{A}_{q}\left(z\right)}{\mathit{dz}}=-i\frac{{\omega}_{q}{\chi}_{\mathit{eff}}}{{c}_{0}{n}_{q}}\prod _{p\ne q}^{P}{A}_{p}\left(z\right)\mathrm{exp}\left(i\Delta \mathit{k}\phantom{\rule{.2em}{0ex}}z\right)\mathrm{exp}\left(i\Delta \mathit{\omega t}\right),$$
(2)
$$\Delta k=\sum _{r}^{R}{k}_{r}-\sum _{s}^{S}{k}_{s},$$
(3)
$$\Delta \mathit{\omega}=\sum _{r}^{R}{\omega}_{r}-\sum _{s}^{S}{\omega}_{s},$$
(4)
$$2\Delta \mathit{kL}+\sum _{p}^{P}\left({\phi}_{p}^{\left(\mathit{left}\right)}+{\phi}_{p}^{\left(\mathit{right}\right)}\right)=2\pi {a}^{\left(1\right)},$$
(5)
$$r\left(\omega \right)=\mid r\left(\omega \right)\mid \mathrm{exp}\left(\mathit{i\phi}\left(\omega \right)\right).$$
(6)
$$2{k}_{p}L={\phi}_{p}^{\mathit{left}}-{\phi}_{p}^{\mathit{right}}=2\pi {a}^{\left(2\right)},$$
(7)
$${A}_{\mathit{Internal}}=\frac{\sqrt{1-R}}{1-\sqrt{R}}{A}_{\mathit{Incident}},$$
(8)
$$\U0001d4d5=\frac{\pi \sqrt{R}}{1-R}.$$
(9)
$${t}_{c}=\frac{\mathit{nL}}{\pi {c}_{0}}\U0001d4d5\phantom{\rule{.2em}{0ex}},$$
(10)
$${P}_{\mathit{out}}=C\U0001d4d5{\mathrm{sin}}^{2}\left(\frac{\pi}{{L}_{c}}L\right),$$
(11)
$${P}_{\mathit{NL}}={\chi}^{\left(2\right)}{E}_{p}{E}_{i}^{*},$$