Improving the measurement accuracy of refractive index of GaAs and Sapphire Crystal by laser feedback interferometry

Chunyu Yuan; Yang Cao; Yong Deng; Shulian Zhang

doi:10.3788/IRLA20210400

Journals >Infrared and Laser Engineering >Volume 51 >Issue 3 >Page 20210400 > Article

Infrared and Laser Engineering
Vol. 51, Issue 3, 20210400 (2022)

Improving the measurement accuracy of refractive index of GaAs and Sapphire Crystal by laser feedback interferometry

Chunyu Yuan¹, Yang Cao¹, Yong Deng¹, and Shulian Zhang^2、*

Author Affiliations

¹School of Mechanical Engineering, Nantong University, Nantong 226019, China

²The State Key Lab of Precision Measurement Technology and Instrument, Department of Precision Instruments, Tsinghua University, Beijing 100084, China

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DOI: 10.3788/IRLA20210400 Cite this Article

Chunyu Yuan, Yang Cao, Yong Deng, Shulian Zhang. Improving the measurement accuracy of refractive index of GaAs and Sapphire Crystal by laser feedback interferometry[J]. Infrared and Laser Engineering, 2022, 51(3): 20210400 Copy Citation Text

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Abstract

GaAs and Sapphire Crystal has been widely used in infrared region, optoelectronics field and military equipment, so the measurement of refractive index of two materials is of great significance to optical design, metrological inspection and industrial application. To improve the measurement accuracy of refractive index of two materials, microchip laser feedback interferometer technology was used to simultaneously measure refractive index and thickness. The system combined heterodyne modulation and quasi-common path to compensate for airflow and vibration, so it has the characteristics of high sensitivity, high precision and high stability, especially the simultaneous measurement and only the material needs to be processed into flake rather than prism shape. The experimental results demonstrate that the measurement accuracy of refractive index of GaAs and Sapphire Crystal (under ordinary light) has been enhanced to 10^-3 and 10^-4 respectively and thickness is 10^-4 mm.

Keywords

accuracy feedback interferometry GaAs refractive index Sapphire Crystal

$ \Delta I(2\varOmega )=\kappa G(2\varOmega )\mathrm{cos}\left[2\pi (2\varOmega )t-\varphi +{\varphi }_{s}\right] $

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$L = \frac{{nd}}{{\cos i}} + {n_0}x - \frac{{{n_0}d}}{{\cos i}}\cos (q - i)$

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$ {n}_{0}\mathrm{sin}\theta =n\mathrm{sin}i $

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$L{\kern 1pt} = {n_0}x - {n_0}d\cos \theta + d\sqrt {{n^2} - {n_0}^2{{\sin }^2}\theta } $

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$ \begin{split} \Delta L =&\dfrac{\lambda }{{2\pi {n_{\rm{0}}}}}(\Delta {\phi _m} - \Delta {\phi _r}) =\Bigg[\sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}\theta } - {n_{\rm{0}}}\cos \theta - \\ & \sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}{\theta _{\rm{0}}}} + {n_{\rm{0}}}\cos {\theta _{\rm{0}}}\Bigg]{\kern 1pt} {\kern 1pt} \\ \end{split} $

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$\left. \begin{gathered} \Delta {L_1} = d\left[\sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}{\theta _1}} - {n_{\rm{0}}}\cos {\theta _1} - \sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}{\theta _{\rm{0}}}} + {n_{\rm{0}}}\cos {\theta _{\rm{0}}}\right]{\kern 1pt} {\kern 1pt} \\ \Delta {L_2} = d\left[\sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}{\theta _2}} - {n_{\rm{0}}}\cos {\theta _2} - \sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}{\theta _{\rm{0}}}} + {n_{\rm{0}}}\cos {\theta _{\rm{0}}}\right]{\kern 1pt} {\kern 1pt} \\ \Delta {L_3} = d\left[\sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}{\theta _3}} - {n_{\rm{0}}}\cos {\theta _3} - \sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}{\theta _{\rm{0}}}} + {n_{\rm{0}}}\cos {\theta _{\rm{0}}}\right]{\kern 1pt} {\kern 1pt} \\ {\rm{ }} \vdots \\ \Delta {L_x} = d\left[\sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}{\theta _x}} - {n_{\rm{0}}}\cos {\theta _x} - \sqrt {{n^{\rm{2}}} - {n_{\rm{0}}}^{\rm{2}}{{\sin }^{\rm{2}}}{\theta _{\rm{0}}}} + {n_{\rm{0}}}\cos {\theta _{\rm{0}}}\right]{\kern 1pt} {\kern 1pt} \\ \end{gathered} \right\} \Rightarrow n,d$

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