The Fabry-Perot Optical Cavity

Clean one microscope slide with isopropyl alcohol and let it dry. Hold it at a slight angle in the beam of a class-2 red laser pointer, about 2 m from a white wall. Wear the safety glasses; never look along the beam. You will see a set of nested rings or straight bars on the wall. That is the slide's two surfaces acting as a low-reflectivity Fabry-Perot etalon: R is only about 0.04 per surface, so the fringes are broad, but they are there. Measure the slide thickness with the caliper to 0.01 mm. Record it — it is the L in the free spectral range and it enters linearly.

Mount two front-surface mirrors on the optical bench carriers, facing each other, 100 mm apart. Set them parallel: walk the adjustment until the reflected spots from the laser overlap after several passes. Drill or leave a 2 mm gap at the edge so you can inject the beam at a shallow angle and watch the multiple reflections walk along the mirrors. Count them. The number of visible passes before the spot dies away is a direct, crude measurement of the round-trip loss: after N passes the intensity is R^(2N). Do not silver the mirrors or use back-surface household mirrors. A back-surface mirror gives you two reflections offset by the glass thickness and the fringes turn to mush.

Put the photodiode behind a 0.5 mm slit on a carrier and slide it across the fringe pattern, reading the current on the oscilloscope or the multimeter every millimetre. Plot intensity against position. Finesse is the fringe SPACING divided by the fringe WIDTH at half maximum. For your slide etalon expect a finesse near 0.7 — barely more than one, which is the honest answer for 4 % mirrors and exactly what the notebook predicts. Repeat with the two front-surface mirrors, which are around 90 % reflective. The finesse should climb to roughly 30. Same measurement, same instrument, one variable changed.

WHY OPEN AND NOT CLOSED. A closed cavity of volume V supports about 8 pi V nu^2 dnu / c^3 modes. At 500 nm in a 1 cm cube that is astronomically many, and an amplifier would try to oscillate on all of them at once. Removing the side walls means only rays that stay very nearly on-axis survive many round trips. The mode count collapses to a comb. STABILITY. Two flat mirrors is the hardest case to align, because any tilt walks the beam out sideways. Real lasers curve at least one mirror. The condition is 0 <= (1-L/R1)(1-L/R2) <= 1. A confocal cavity, where both radii equal the length, sits comfortably inside it and is far more forgiving to align. COMMON MISTAKES. Back-surface mirrors give doubled fringes. A dirty slide scatters more than it transmits. A laser pointer whose coherence length is under a millimetre will not produce fringes on a 1 mm etalon at all — if you see nothing, that is the likely cause, and it is the same coherence length that governs holography later in this batch. WHAT COMES NEXT. Every laser in this batch is an amplifier inside one of these. The amplifier decides the wavelength band; the cavity decides which frequencies inside that band are allowed and how much light leaks out per pass. Gain must exceed that leak. That inequality is the whole of laser physics and you have just measured its right-hand side.