## Abstract

The self-mixing interference effects with a folding feedback cavity in a Zeeman-birefringence dual frequency laser have been investigated theoretically and experimentally. The fringe frequency of the self-mixing interference system can be doubled due to the hollow cube corner prism, with which a folding cavity is formed. The intensities of the two frequencies are changed periodically in the modulation of the external cavity length. When the phase difference between the two frequencies equals π/2, the intensity modulation curves can be divided into four zones with equal width in a period. Each zone corresponds to one polarization state. Based on the experimental results, a novel displacement sensor with a high resolution of λ/16, as well as functions of direction discrimination, is discussed.

© 2006 Optical Society of America

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### Equations (17)

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(1)
$$\mathbf{E}\left(\mathbf{t}\right)={r}_{1}{r}_{2}\mathrm{exp}(j4\mathrm{\pi v}\frac{\mathrm{nL}}{c}+\mathrm{gL}){\mathbf{E}}_{0}\left(\mathbf{t}\right)+{r}_{1}{r}_{2}{r}_{3}\xi \mathrm{exp}\left(j4\mathrm{\pi v}\frac{\mathrm{nL}+l+\Delta l}{c}+\mathrm{gL}\right){\mathbf{E}}_{0}\left(\mathbf{t}\right),$$
(2)
$${r}_{1}{r}_{2}\mathrm{exp}\left(j4\mathit{\pi v}\frac{\mathrm{nL}}{c}+\mathrm{gL}\right)\phantom{\rule{.2em}{0ex}}\left[1+\frac{{t}_{2}{r}_{3}\zeta}{{r}_{2}}\mathrm{exp}\left(j4\mathrm{\pi v}\frac{l}{c}+j4\mathrm{\pi v}\frac{\Delta 1}{c}\right)\right]=1.$$
(3)
$${r}_{1}{r}_{2}\mathrm{exp}\left(\mathrm{gL}\right){\left\{{\left[1+\alpha \mathrm{cos}\left(\phi +{\delta}_{l}\right)\right]}^{2}+[\alpha \mathrm{sin}\left(\phi +{\delta}_{l}\right){]}^{2}\right\}}^{\xbd}\mathrm{exp}\left[j\left(4\mathrm{\pi v}\frac{\mathrm{nL}}{c}+\theta \right)\right]=1,$$
(4)
$$\mathrm{tan}\theta =\frac{\alpha \mathrm{sin}\left(\phi +{\delta}_{l}\right)}{1+\alpha \mathrm{cos}\left(\phi +{\delta}_{l}\right)}.$$
(5)
$${r}_{1}{r}_{2}\mathrm{exp}\left(\mathrm{gL}\right)\left[1+\alpha \mathrm{cos}\left(\phi +{\delta}_{l}\right)\right]\mathrm{exp}\left[j\left(4\mathrm{\pi v}\frac{\mathrm{nL}}{c}+\theta \right)\right]=1.$$
(6)
$$g=-\frac{1}{L}\left[\mathrm{In}\right({r}_{1}{r}_{2}\left)+\alpha \mathrm{cos}\right(\phi +{\delta}_{l}\left)\right].$$
(7)
$$4\mathrm{\pi v}\frac{\mathrm{nL}}{c}+\theta =2\mathrm{K\pi}.$$
(8)
$${g}_{0}=-\frac{1}{L}\mathrm{In}\left({r}_{1}{r}_{2}\right).$$
(9)
$$\Delta g=g-{g}_{0}=-\frac{\alpha}{L}\mathrm{cos}\left(\phi +{\delta}_{l}\right).$$
(10)
$$I={I}_{0}\left(1-K\Delta g\right),$$
(11)
$${I}_{1}={I}_{0}[\frac{1+\alpha K}{L}\bullet \mathrm{cos}\left(2\phi +{\delta}_{l}\right)],$$
(12)
$${\phi}_{H}=4\mathrm{\pi v\bullet}\frac{2\Delta l}{c}=2\phi .$$
(13)
$${I}_{2}={I}_{0}[\frac{1+\alpha K}{L}\bullet \mathrm{cos}\left(2\phi +{\delta}_{l}\right)].$$
(14)
$$\Delta {g}_{0}=-\Delta {g}_{e}.$$
(15)
$${I}_{o}={I}_{0o}[\frac{1+\alpha K}{L}\bullet \mathrm{cos}\left(2\phi +{\delta}_{\mathrm{lo}}\right)],$$
(16)
$${I}_{e}={I}_{0e}[\frac{1-\alpha K}{L}\bullet \mathrm{cos}\left(2\phi +{\delta}_{\mathrm{le}}\right)],$$
(17)
$$\delta =4\pi \Delta v\frac{l}{c},$$