Delayed self-heterodyne

An OSA cannot resolve a modern laser's linewidth: grating instruments stop at GHz-class resolution while lasers of interest sit at MHz, kHz, or below. Delayed self-heterodyne (DSH) sidesteps the problem by converting the optical linewidth into an RF measurement, using the laser as its own reference.

The arrangement: split the laser output into two arms. One arm passes through a long fiber delay; the other through an acousto-optic modulator that shifts its frequency by $f_{AOM}$ (40–200 MHz typical). Recombine the arms on a photodiode and examine the beat note at $f_{AOM}$ on an RF spectrum analyzer.

If the delay exceeds the laser's coherence time, the two arms are effectively independent sources with identical statistics, and the beat note is the self-convolution of the laser lineshape. For a Lorentzian laser line of width $\Delta\nu$, the beat is a Lorentzian of width $2\Delta\nu$: read the RF FWHM, divide by two.

The delay condition is the design decision. Coherence length in fiber is $L_c \approx c/(n\,\pi\,\Delta\nu)$ (about 6.6 km per 10 kHz of linewidth), and honest measurement wants delay several times $L_c$. Narrow lasers therefore demand tens of kilometers of spool, and at those lengths fiber loss, acoustic pickup, and 1/f noise all begin to shape the result. With insufficient delay the spectrum develops periodic coherence sidelobes and the naive width underestimates reality. The effect is recognizable and correctable by fitting, but a common source of optimistic datasheet numbers.

Two cautions. First, the Lorentzian-only arithmetic applies to white-frequency-noise broadening; real lasers carry 1/f noise that makes the measured width depend on measurement time and delay. Modern practice increasingly reports the frequency-noise PSD (from a discriminator or cross-correlation method) and quotes an intrinsic linewidth from its white floor. Second, isolate the laser well: DSH setups return reflections efficiently, and feedback narrows or destabilizes the very line being measured.