## Abstract

Phase locking of two beams of a $Q$-switched single-longitudinal-mode Nd:YAG laser is investigated. Phase locking and phase conjugation of these beams are achieved by mutual reflection in a Brillouin cell containing nitrogen at 75 bars. Phase locking is measured interferometrically as a function of the energy, the energy ratio, the separation in the far field, the separation in the near field, and the separation of the beam waists along the propagation path. The change of the relative phase from pulse to pulse of the two output beams is reduced to less than $\u220a=\mathrm{\lambda}/27$ under optimized conditions (50% criterion). A strong influence of phase locking on the reflectivity of the Brillouin cell is observed.

© 1998 Optical Society of America

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### Equations (9)

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(1)
$${\int}_{0}^{\u220a}p(\delta )\mathrm{d}\delta ={\int}_{\u220a}^{\pi}p(\delta )\mathrm{d}\delta ,$$
(2)
$$\mathcal{K}=1-2\u220a/\pi ,$$
(3)
$${\mathbf{E}}_{1}(\mathbf{r},t)={\widehat{\mathbf{e}}}_{P}{E}_{1}exp\left\{i\left[\omega t-\frac{\omega}{c}\stackrel{\u02c6}{\mathbf{P}}\mathbf{r}-{\varphi}_{P}(\mathbf{r})\right]\right\},$$
(4)
$${\mathbf{E}}_{2}(\mathbf{r},t)={\widehat{\mathbf{e}}}_{P}{E}_{2}exp\left\{i\left[(\omega -{\omega}_{B})t+\frac{\omega -{\omega}_{B}}{c}\stackrel{\u02c6}{\mathbf{P}}\mathbf{r}+{\varphi}_{P}(\mathbf{r})+{\varphi}_{1}\right]\right\},$$
(5)
$${\mathbf{E}}_{3}(\mathbf{r},t)={\widehat{\mathbf{e}}}_{S}{E}_{1}exp\left\{i\left[\omega t-\frac{\omega}{c}\stackrel{\u02c6}{\mathbf{S}}\mathbf{r}-{\varphi}_{S}(\mathbf{r})\right]\right\},$$
(6)
$${\mathbf{E}}_{4}(\mathbf{r},t)={\widehat{\mathbf{e}}}_{S}{E}_{2}exp\left\{i\left[(\omega -{\omega}_{B})t+\frac{\omega -{\omega}_{B}}{c}\stackrel{\u02c6}{\mathbf{S}}\mathbf{r}+{\varphi}_{S}(\mathbf{r})+{\varphi}_{2}\right]\right\},$$
(7)
$${I}_{2,3}(\mathbf{r},t)=\xbd{\u220a}_{0}\mathit{cn}(\omega )|{\mathbf{E}}_{2}+{\mathbf{E}}_{3}{|}^{2}\propto {{E}_{2}}^{2}+{{E}_{3}}^{2}+2({\mathbf{e}}_{P}\cdot {\mathbf{e}}_{S}){E}_{2}{E}_{3}\times cos\left[{\omega}_{B}t-\frac{\omega}{c}(\stackrel{\u02c6}{\mathbf{P}}\mathbf{r}+\stackrel{\u02c6}{\mathbf{S}}\mathbf{r})+\frac{{\omega}_{B}}{c}\stackrel{\u02c6}{\mathbf{P}}\mathbf{r}-{\varphi}_{P}(\mathbf{r})-{\varphi}_{S}(\mathbf{r})-{\varphi}_{1}\right],$$
(8)
$${\mathrm{\lambda}}_{\mathrm{grating},2,3}\approx \mathrm{\lambda}(\omega )/2cos\alpha ,$$
(9)
$${v}_{\mathrm{grating},2,3}\approx c{\omega}_{B}/2\omega cos\alpha $$