How to Measure Laser Linewidth: Choosing the Right Method

Scope

"Measure the linewidth" is four different experiments depending on the laser and the number you actually need. This guide covers the four standard methods: delayed self-heterodyne (DSH), heterodyne against a reference, frequency-noise discriminator, and coherent-receiver phase analysis. It gives selection logic, the governing math, and the systematic errors each invites. Background entries: linewidth, Schawlow–Townes, phase & frequency noise, β-separation line, DSH.

First: which number do you need?

Modern practice distinguishes the intrinsic (Lorentzian) linewidth from the integrated (effective) linewidth over an observation time. The intrinsic linewidth is set by the white frequency-noise floor and is the number tied to Schawlow–Townes physics and coherent-comms phase-noise budgets; the integrated linewidth includes 1/f and technical noise and is what an interferometric sensor experiences. A method that reports one is not wrong for reporting it; quoting either without its observation time or method is. An OSA resolves neither (GHz-class resolution): it measures mode structure, not linewidth.

Method 1: Delayed self-heterodyne (the workhorse)

Split, delay one arm beyond the coherence length, AOM-shift the other, beat on a photodiode, read the RF spectrum: Lorentzian beat FWHM = 2× the laser linewidth. Full mechanics in the DSH entry; the design decision is fiber length:

$$L_{fiber} \;\gtrsim\; 6\,L_c, \qquad L_c = \frac{c}{\pi\, n\, \Delta\nu} \;\approx\; \frac{66\ \mathrm{km}}{\Delta\nu\ [\mathrm{100\ kHz}]}$$

Working table (delay ≈ 5 µs per km of fiber):

Use when: Δν ≳ 10 kHz, one laser, standard telecom gear on the shelf. Watch for: insufficient delay (coherence sidelobes, optimistic widths; fit, don't eyeball), 1/f noise making the width grow with spool length (report the delay), acoustic pickup on long spools (box and float them), and unisolated setups feeding back into the DUT. The measurement can change the linewidth it measures.

Method 2: True heterodyne (when you own a better laser)

Beat the DUT against a reference laser 10× narrower on a fast photodiode; the RF beat is the convolution of both lines, effectively the DUT's alone. This is the cleanest measurement in existence if the reference exists: no delay ambiguity, direct lineshape, and with an RF phase-noise analyzer you get the full PSD, not one number. Frequency-comb teeth and cavity-stabilized lasers serve as references in metrology labs. Use when: the DUT is narrow (kHz and below, where DSH spools become absurd) and a superior reference is available. Watch for: reference drift walking the beat out of the analyzer span (track or lock it), and both lasers' technical noise entering below ~10 kHz offsets.

Method 3: Frequency discriminator (the modern default for real numbers)

Convert frequency fluctuations to intensity with a known slope (the side of a Fabry–Pérot or ring resonance, or an imbalanced MZI held in quadrature), detect, and record the frequency-noise PSD $S_{\Delta\nu}(f)$ directly. From one trace you get everything: the white floor → intrinsic linewidth ($\pi S_0$), the 1/f region, and via the β-separation line the integrated linewidth at any observation time. Cross-correlating two independent discriminators digs below either's noise floor. Use when: you need the honest, complete answer. This is increasingly the expectation in narrow-linewidth publications and datasheets. Watch for: discriminator slope calibration (measure it, don't compute it), staying in the linear range (small excursions), and the discriminator's own thermal drift masquerading as low-offset laser noise.

Method 4: Coherent receiver + DSP (if you have a modem lab anyway)

A coherent receiver (optical hybrid + balanced detectors + ADCs) against any reasonable LO captures the full complex field; offline DSP unwraps the phase and computes $S_\phi(f)$, Allan-style stability, anything. Instruments packaging this ("phase-noise analyzers") are now the turnkey high end. Use when: the gear exists or the laser is for coherent transmission (measure what the modem sees, including the LO).

Selection in one paragraph

DFB-class (100 kHz–10 MHz): DSH with a 1–4 km spool, fit the Lorentzian, done in an hour. Narrow ECL/hybrid lasers (1–100 kHz): discriminator PSD, quote intrinsic linewidth and β-line integrated value with observation time; DSH only as a cross-check with ≥40 km and self-heterodyne-aware fitting. Hz-class metrology lasers: heterodyne against a reference or cross-correlated discriminators. Nothing else is credible. Any published comparison: state method, delay/reference, RBW, observation time, and bias conditions, because every one of these changes the number.

The datasheet-side view of the same topic (what vendors' linewidth rows do and don't promise) is covered in how to read a laser diode datasheet.