\begin{document}$ {l_{{\rm{FC}}}}$\end{document} should satisfy \begin{document}$ {\rm{189}}\;{\text{μm}} > {l_{{\rm{FC}}}} > {\rm{119}}\;{\text{μm}}$\end{document}. This cavity length is too small to be measured with a ruler. To measure the cavity length, we introduce an optical method, in which Gouy phases of Hermite Gaussian transverse modes TEM00 and TEM10 are used. When the cavity length is scanned, resonant peaks and the corresponding scanning voltages are recorded. From theoretical derivation, the cavity length is related to the filter cavity piezo response to the scanning voltage \begin{document}$ {\varPsi '_{\rm{G}}}$\end{document}, the slope rate of piezo scanning voltage \begin{document}$ U'$\end{document}, and the time distance between TEM00 and TEM10 resonant peaks \begin{document}$ \Delta t$\end{document}. The finally measured cavity length is \begin{document}${l_{{\rm{FC}}}} = ({\rm{141}} \pm 28)~{\text{μm}}$\end{document}, which satisfies the design requirement. The measurement error mainly originates from inaccurate fitting of \begin{document}$ {\varPsi '_{\rm{G}}}$\end{document} and \begin{document}$ U'$\end{document}, and readout error of \begin{document}$ \Delta t$\end{document}. It is shown that the error of \begin{document}$ {\varPsi '_{\rm{G}}}$\end{document} is dominant since less data are used in the curve fitting. The measurement error is expected to be reduced if much more data of piezo response to scanning voltage are collected and used to fit \begin{document}$ {\varPsi '_{\rm{G}}}$\end{document} with higher order polynomials. The proposed measurement method of short cavity length needs neither wide tuning laser nor any peculiar instrument, and does not depend on any dispersion property of the cavity, and hence it has a certain generality. It can be hopefully used in many other optical systems, such as cavity quantum electrodynamics, where ultrashort cavity plays a central role."> - 必威体育下载

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Citation:

    Zhai Ze-Hui, Hao Wen-Jing, Liu Jian-Li, Duan Xi-Ya
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    • Abstract views:5880
    • PDF Downloads:83
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    Publishing process
    • Received Date:22 April 2020
    • Accepted Date:09 May 2020
    • Available Online:05 June 2020
    • Published Online:20 September 2020

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