Glossary entry

Free spectral range (FSR)

The frequency or wavelength spacing between adjacent resonances of an optical cavity. Set by the round-trip group delay.

For a ring resonator of round-trip length $L$ and group index $n_g$ :

\text{FSR}_\nu \;=\; \frac{c}{n_g L}, \qquad \text{FSR}_\lambda \;=\; \frac{\lambda_0^2}{n_g L}.

For a Fabry–Pérot cavity of length $L$ , the round-trip path is $2L$ , so:

\text{FSR}_\nu \;=\; \frac{c}{2 n_g L}, \qquad \text{FSR}_\lambda \;=\; \frac{\lambda_0^2}{2 n_g L}.

The two formats are related by $\text{FSR}_\lambda = \text{FSR}_\nu \cdot \lambda_0^2 / c$ .

Typical FSRs at 1550 nm:

Resonator	$L$	$n_g$	$\text{FSR}_\lambda$
SOI ring, small	100 μm	4.3	5.6 nm
SOI ring, medium	500 μm	4.3	1.1 nm
SOI ring, large	1 mm	4.3	0.56 nm
SiN ring	500 μm	2.0	2.4 nm
Short fiber FP	1 cm	1.47	0.082 nm
Long fiber FP	1 m	1.47	0.82 pm
250 μm laser diode	250 μm	4.0	1.2 nm

FSR is the design parameter for WDM filters: matching FSR to channel spacing gives a periodic filter passing every $N$ th channel.

FSR and finesse together determine resonance linewidth: $\Delta\nu = \text{FSR} / \mathcal{F}$ . Both must be specified to fully characterize a resonator's spectral response.