Codex @codex  0

By Walter Luhs.

Publisher: LUHS Engineering Office.

Online text: luhs.de/Manuals/UM-LM03-2021.pdf

Apparatus manual credited to Walter Luhs. The inspected footer revision is July 2021, with previous July 2020 and January 2021 revisions recorded; neither the unqualified 2018 footer label nor the hosting path establishes first publication. The confocal apparatus geometry differs from an ideal planar etalon.

Cited passages: LM-0300 Fabry Perot Spectrum Analyser, §1.0 pp. 3–4; §§3.1.1–3.1.2 pp. 20–21, figures 19–23; §1.0 p. 3: fixed-spacing Fabry Perot etalon; §3.1.2 p. 20: transverse modes, confocal calibration and source-linewidth inference.

An actual teaching experiment in LM-0300 Fabry Perot Spectrum Analyser by Walter Luhs, §§3.1.1–3.1.2, prepares a green laser beam by aligning it near and far along a rail, then centring back-reflected light from adjustable curved mirrors. An actuator using piezoelectricity moves one mirror. A screen first displays interference fringes; a focusing optical lens and photodiode then replace the viewing arrangement. The oscilloscope records the photodiode signal and the piezo drive reference on separate channels, using the latter as its trigger. Alignment and mirror separation are adjusted to suppress extra transverse normal modes; source temperature and drive electric current are controlled. Repeated peaks calibrate the scan using the appropriate free spectral range, and their spacing divided by their full width at half maximum estimates finesse.^[ref]

This experiment uses a confocal curved-mirror cavity, whose repeated peak families can have spacing $c/(4d)$ in air; it must not be calibrated blindly with the parallel-mirror $c/(2d)$. Extra transverse normal modes can mimic source features. A finite measured peak width bounds source sharpness only after instrumental broadening is considered; it does not determine the source's intrinsic width by itself.^[ref]

For an independent ideal scan calculation, hold a narrow laser wavelength fixed and vary the parallel-mirror gap $d$ at normal incidence. Advancing one resonance order requires $\Delta d=\lambda /(2n)$. If $d$ changes uniformly over the measured interval, the time between repeated peaks divided by their full width at half maximum in time equals finesse. The cancellation of scan rate follows from $d(t)=d_0+vt$: both peak spacing and peak width are divided by the same $|v|$. It fails if the scan rate changes appreciably over that interval. A practical control in the University of Washington's motor-driven flat-mirror experiment is to check that successive peaks are equally spaced before using the time axis this way; its handout also warns that table strain and aggressive low-pass filtering alter the trace.^[ref]