## Abstract

A simple treatment of pulse compression in second-harmonic generation based on the use of an aperiodically poled nonlinear medium is presented. Particular emphasis is placed on the conditions that must be satisfied if the process is to work efficiently. The possible extension to the case of optical parametric amplification and oscillation is considered.

© 2007 Optical Society of America

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### Equations (11)

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(1)
$$\Delta {k}_{p}\left(z\right)(\equiv 2\pi \u2215{\Lambda}_{p})=\Delta {k}_{0}+2G(z-d\u22152),$$
(2)
$${\Lambda}_{p}\left(z\right)\simeq {\Lambda}_{0}(1-\frac{G{\Lambda}_{0}}{\pi}(z-\frac{d}{2})),$$
(3)
$$\Delta {\Lambda}_{p}=-G{\Lambda}_{0}^{2}d\u2215\pi .$$
(4)
$$\Delta {t}_{g}=d(\frac{1}{{v}_{g2}}-\frac{1}{{v}_{g1}})\equiv \gamma d,$$
(5)
$$\Delta {\omega}_{c}=C\Delta {t}_{g}=C\gamma d.$$
(6)
$$\delta \Delta k={\phantom{\mid}\frac{\mathrm{d}k}{\mathrm{d}\omega}\mid}_{{\omega}_{2}}\delta {\omega}_{2}-2{\phantom{\mid}\frac{\mathrm{d}k}{\mathrm{d}\omega}\mid}_{{\omega}_{1}}\delta {\omega}_{1}=\frac{\delta {\omega}_{2}}{{v}_{g2}}-\frac{2\delta {\omega}_{1}}{{v}_{g1}}=2\gamma \delta {\omega}_{1},$$
(8)
$$\rho =\frac{C\Delta {t}^{2}}{K}.$$
(9)
$$\rho \equiv \frac{\Delta t}{\sqrt{2}\Delta {t}_{\mathit{ch}}}=\frac{C\Delta {t}^{2}}{K},$$
(10)
$$C\u2aa2\frac{K}{\Delta {t}^{2}}.$$
(11)
$$G=\pm {\gamma}^{2}C,$$