Mode is a word laser jocks characterize a laser's beam quality. The Longitudinal Mode describes the beam longitudinally, along its direction, as opposed to the Transverse Mode, which describes the beam quality across its width.
Single Longitudinal Mode implies that there is only a single wavelength being emitted, which implies infinite coherence, or no need to match path lengths in holography! Its singularity can be measured by a Scanning Fabry-Perot Interferometer Spectrum Analyzer.
At the Home + Studio we have a Spectra-Physics 470 head, driven by a Jodon/Eldon box, wired up to a Kikusui Oscilloscope. The driver sends a sine wave of current into the head's piezo-electric donut, to which one of the mirrors of the resonating cavity is attached. As the volage sweeps through its range, the cavity expands and contracts, causing constructive or destructive interference depending on how the resonator is spaced. If the spacing is a multiple of the laser's lambda, then a bright flash is focused on the interferometer's photodetector, which tranlates to a blip on the oscilloscope. On the right of this image, the scope traces are shown, the bottom one being a single longitudinal mode. The left shows what effect the multiple modes have on the coherence length in a hologram.
