## Abstract

A simple fiber-optic sensor based on Fabry–Perot interference for refractive index measurement of optical glass is investigated both theoretically and experimentally. A broadband light source is coupled into an extrinsic fiber Fabry–Perot cavity formed by the surfaces of a sensing fiber end and the measured sample. The interference signals from the cavity are reflected back into the same fiber. The refractive index of the sample can be obtained by measuring the contrast of the interference fringes. The experimental data meet with the theoretical values very well. The proposed technique is a new method for glass refractive index measurement with a simple, solid, and compact structure.

© 2010 Optical Society of America

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### Equations (6)

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(1)
$${R}_{1}=({n}_{f}-{n}_{\text{air}}{)}^{2}/({n}_{f}+{n}_{\text{air}}{)}^{2},\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\phantom{\rule{0ex}{0ex}}{R}_{2}=({n}_{\text{air}}-n{)}^{2}/({n}_{\text{air}}+n{)}^{2}.$$
(2)
$${E}_{r}\approx \sqrt{{R}_{1}}{E}_{i}+(1-{A}_{1})(1-{R}_{1})(1-\alpha )\sqrt{{R}_{2}}{E}_{i}{e}^{-j2\beta L+j\pi},$$
(3)
$${I}_{\mathrm{FP}}(\lambda )=|{E}_{r}/{E}_{i}{|}^{2}={R}_{1}+(1-{A}_{1}{)}^{2}(1-{R}_{1}{)}^{2}(1-\alpha {)}^{2}{R}_{2}+2\sqrt{{R}_{1}{R}_{2}}(1-{A}_{1})(1-{R}_{1})(1-\alpha )\mathrm{cos}(4\pi L{n}_{\text{air}}/\lambda -\pi ).$$
(4)
$$(4\pi L{n}_{\text{air}}/{\lambda}_{\mathrm{max}}-\pi )=2m\pi ,\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\phantom{\rule{0ex}{0ex}}(4\pi L{n}_{\text{air}}/{\lambda}_{\mathrm{min}}-\pi )=(2m+1)\pi ,$$
(5)
$${I}_{\mathrm{FP}}({\lambda}_{\mathrm{max}})=[\sqrt{{R}_{1}}+\sqrt{{R}_{2}}K(1-{R}_{1}){]}^{2},\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\phantom{\rule{0ex}{0ex}}{I}_{\mathrm{FP}}({\lambda}_{\mathrm{min}})=[\sqrt{{R}_{1}}-\sqrt{{R}_{2}}K(1-{R}_{1}){]}^{2},$$
(6)
$$C=10{\mathrm{Log}}_{10}\left[\frac{{I}_{\mathrm{FP}}({\lambda}_{\mathrm{max}})}{{I}_{\mathrm{FP}}({\lambda}_{\mathrm{min}})}\right]=20{\mathrm{Log}}_{10}\left[\frac{\sqrt{{R}_{1}}+K(1-{R}_{1})(n-{n}_{\text{air}})/(n+{n}_{\text{air}})}{\sqrt{{R}_{1}}-K(1-{R}_{1})(n-{n}_{\text{air}})/(n+{n}_{\text{air}})}\right].$$