## Abstract

Achromatic phase matching (APM) involves dispersing the light
entering a nonlinear optical crystal so that a wide range of
wavelengths is simultaneously phase matched. We constructed an APM
apparatus consisting of six prisms, the final dispersion angle of which
was optimized to match to second order in wavelength the type I
phase-matching angle of β barium borate (BBO). With this
apparatus, we doubled tunable fundamental light from 620 to 700 nm in
wavelength using a 4-mm-long BBO crystal. An analogous set of six
prisms after the BBO crystal, optimized to second order in
second-harmonic wavelength, realigned the output second-harmonic
beams. Computer simulations predict that adjustment of a single
prism can compensate angular misalignment of any or all the prisms
before the crystal, and similarly for the prisms after the
crystal. We demonstrated such compensation with the experimental
device. The simulations also indicate that the phase-matching
wavelength band can be shifted and optimized for different crystal
lengths.

© 1999 Optical Society of America

Full Article |

PDF Article
### Equations (8)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$2\frac{500\mathrm{\mu}\mathrm{rad}}{2\mathrm{mrad}/\mathrm{nm}}=0.5\mathrm{nm}.$$
(2)
$$2{\left(\frac{500\mathrm{\mu}\mathrm{rad}}{5\mathrm{\mu}\mathrm{rad}/{\mathrm{nm}}^{2}}\right)}^{1/2}=20\mathrm{nm},$$
(3)
$$\frac{\mathrm{d}\mathrm{\theta}}{\mathrm{d}\mathrm{\lambda}},\frac{{\mathrm{d}}^{2}\mathrm{\theta}}{\mathrm{d}{\mathrm{\lambda}}^{2}},$$
(4)
$$\frac{\mathrm{d}{\mathrm{\theta}}_{\mathrm{out}}}{\mathrm{d}\mathrm{\lambda}}=\frac{\partial {\mathrm{\theta}}_{\mathrm{out}}}{\partial {\mathrm{\theta}}_{\mathrm{in}}}\frac{\mathrm{d}{\mathrm{\theta}}_{\mathrm{in}}}{\mathrm{d}\mathrm{\lambda}}+\frac{\partial {\mathrm{\theta}}_{\mathrm{out}}}{\partial \mathrm{\lambda}},$$
(5)
$$\frac{{\mathrm{d}}^{2}{\mathrm{\theta}}_{\mathrm{out}}}{\mathrm{d}{\mathrm{\lambda}}^{2}}=\frac{\partial {\mathrm{\theta}}_{\mathrm{out}}}{\partial {\mathrm{\theta}}_{\mathrm{in}}}\frac{{\mathrm{d}}^{2}{\mathrm{\theta}}_{\mathrm{in}}}{\mathrm{d}{\mathrm{\lambda}}^{2}}+\frac{{\partial}^{2}{\mathrm{\theta}}_{\mathrm{out}}}{\partial {\mathrm{\lambda}}^{2}}+\frac{{\partial}^{2}{\mathrm{\theta}}_{\mathrm{out}}}{\partial \mathrm{\theta}_{\mathrm{in}}{}^{2}}{\left(\frac{\mathrm{d}{\mathrm{\theta}}_{\mathrm{in}}}{\mathrm{d}\mathrm{\lambda}}\right)}^{2}+2\frac{{\partial}^{2}{\mathrm{\theta}}_{\mathrm{out}}}{\partial \mathrm{\lambda}\partial {\mathrm{\theta}}_{\mathrm{in}}}\frac{\mathrm{d}{\mathrm{\theta}}_{\mathrm{in}}}{\mathrm{d}\mathrm{\lambda}},$$
(6)
$$E=\int {\left|\frac{\mathrm{\theta}\left(\mathrm{\lambda}\right)-\mathrm{\theta}\left({\mathrm{\lambda}}_{0}\right)-\mathrm{\varphi}\left(\mathrm{\lambda}\right)}{\mathrm{\varphi}\left(\mathrm{\lambda}\right)}\right|}^{2}\mathrm{d}\mathrm{\lambda},$$
(7)
$$\mathrm{\beta}_{j}{}^{\left(m\right)}=\mathrm{\beta}_{j}{}^{\left(m-1\right)}+\mathrm{rand},$$
(8)
$$P={\left\{1+exp\left[\frac{{E}^{\left(m-1\right)}-{E}^{\left(m\right)}}{T}\right]\right\}}^{-1},$$