Glossary entry

Free spectral range (FSR)

The frequency spacing between adjacent resonances of an optical resonator, c/(2 n_g L) for a Fabry-Perot cavity and c/(n_g L) for a ring, or λ²/(2 n_g L) in wavelength. It is the inverse of the round-trip time, so it is set by the group index and the length, and with the finesse it fixes the resonance linewidth. Formulas, the group-index subtlety, typical values, and how it is measured.

Optics fundamentals Integrated photonicsUpdated October 2026

The free spectral range is the spacing between the resonances of an optical cavity, the interval over which its transmission pattern repeats. It is the inverse of the cavity's round-trip time, because the resonance condition is that the round-trip phase advances by $2 π$ from one resonance to the next, and the round-trip time is set by the group index $n_{g}$ and the path length. For a Fabry-Perot cavity of length $L$ the round trip is $2 L$ , and for a ring resonator of circumference $L$ it is $L$ :

{F S R}_{ν} = \frac{c}{2 n_{g} L} (Fabry-Perot), \frac{c}{n_{g} L} (ring)

Spectrometers and datasheets often quote the FSR in wavelength, which follows from $Δ λ = λ^{2} Δ ν / c$ :

{F S R}_{λ} = \frac{λ_{0}^{2}}{2 n_{g} L} (Fabry-Perot), \frac{λ_{0}^{2}}{n_{g} L} (ring)

The frequency form is constant across the spectrum; the wavelength form grows as $λ^{2}$ , so a filter with a 100 GHz FSR has a 0.8 nm spacing at 1550 nm but 0.57 nm at 1310 nm. The Fabry-Perot Cavity Calculator gives both forms for any cavity together with the finesse, linewidth and Q that go with them, and the Ring Resonator Explorer does the same for rings.

Why the group index

The phase index sets where the resonances are, through $2 n L = m λ$ , but the spacing between them depends on how fast the round-trip phase changes with frequency, $d (2 π \cdot 2 n L ν / c) / d ν = 4 π L (n + ν d n / d ν) / c = 4 π L n_{g} / c$ . In a dispersive medium $n_{g}$ can differ from $n$ by a lot: about 3.6 against 3.2 in InGaAsP at 1550 nm, 4.18 against 2.446 for the effective indices of a 500 × 220 nm silicon strip (group index), 1.463 against 1.444 in fused silica. Using the phase index for the FSR of a silicon ring would overstate it by 71%. The dependence runs the other way as well: measuring the FSR of a known length is the standard way to measure the group index of a waveguide, and the FSR of a laser chip's Fabry-Perot fringes, divided into $c / 2 L$ , gives the group index of its active waveguide.

Typical values

Resonator	$L$	$n_{g}$	${F S R}_{ν}$	${F S R}_{λ}$ at 1550 nm
Silicon ring (500 × 220 nm strip), 10 µm radius	62.8 µm	4.18	1.14 THz	9.1 nm
Silicon ring, 100 µm round trip	100 µm	4.18	717 GHz	5.7 nm
Silicon nitride ring (1600 × 800 nm strip), 500 µm	500 µm	2.12	283 GHz	2.3 nm
Laser diode chip, 300 µm	300 µm	3.6	139 GHz	1.1 nm
Fused-silica etalon, 5 mm	5 mm	1.463	20.5 GHz	164 pm
Air-spaced etalon, 1 cm	1 cm	1.000	15.0 GHz	120 pm
Fiber Fabry-Perot, 10 cm	10 cm	1.468	1.02 GHz	8.2 pm
ULE reference cavity, 10 cm	10 cm	1.000	1.50 GHz	12 pm
Fiber ring cavity, 10 m	10 m	1.468	20.4 MHz	0.16 pm
VCSEL at 850 nm, one-wavelength spacer plus the penetration into both mirrors	about 1.1 µm	about 3.5	about 39 THz	about 94 nm (at 850 nm)

What the FSR decides

For a filter the FSR is the design parameter: a periodic filter passes every channel that sits on its comb, so an FSR equal to the channel spacing makes an interleaver and an FSR equal to $N$ times the spacing picks every $N$ th channel, which is how ring-based WDM demultiplexers are laid out, with the FSR chosen larger than the band so that only one resonance falls in it. For a laser the FSR is the longitudinal mode spacing, and its ratio to the gain bandwidth decides how many modes compete: a 300 µm chip with a 139 GHz spacing fits dozens of modes under a 5 THz gain curve and needs a grating to run single-mode, while a VCSEL's spacing of about 39 THz, some 94 nm at 850 nm, exceeds the gain bandwidth and leaves one. The VCSEL's cavity is longer than its one-wavelength spacer because the light penetrates about 0.43 µm into each Bragg mirror (distributed Bragg reflector). For a resonator's spectral resolution the FSR and the finesse together fix the linewidth, $Δ ν = F S R / F$ , and the FSR alone sets the unambiguous range of a scanning Fabry-Perot interferometer: features further apart than one FSR alias onto each other, so an analyzer is chosen with an FSR wider than the spectrum it is meant to show.

Measuring it

On an optical spectrum analyzer or a swept-laser transmission scan, the FSR is the spacing of the resonance peaks or dips, best taken as a fit to many resonances rather than one pair; on a laser the Fabry-Perot fringes below threshold give it directly. The measured FSR varies slowly with wavelength because $n_{g}$ does, and that variation is the group velocity dispersion of the cavity, which is how the dispersion of microresonators is measured for comb generation.

Common questions

What is the free spectral range?

The spacing between neighboring resonances of an optical cavity, in frequency or in wavelength. It equals the inverse of the round-trip time: $c / (2 n_{g} L)$ for a Fabry-Perot cavity of length $L$ and $c / (n_{g} L)$ for a ring of circumference $L$ .

How is the FSR of a ring resonator calculated?

From its circumference $L$ and group index $n_{g}$ : $F S R = c / (n_{g} L)$ in frequency, or $λ^{2} / (n_{g} L)$ in wavelength. A silicon ring of 10 µm radius, with $n_{g}$ = 4.18, has an FSR of 1.14 THz, 9.1 nm at 1550 nm.

Why does the FSR use the group index and not the phase index?

Because the spacing between resonances depends on how fast the round-trip phase changes with frequency, and that rate is set by the group index. The phase index sets where each resonance lies, the group index how far apart they are.

The finesse is the FSR divided by the resonance linewidth, and the Q is the resonance frequency divided by the linewidth, so $Q = (ν / F S R) F$ . A 10 µm-radius silicon ring with a loaded Q of $10^{5}$ has a linewidth of 1.93 GHz at 1550 nm and a finesse of 590 (quality factor).

References: B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019), chapter 11. A. E. Siegman, Lasers (University Science Books, 1986), chapter 11. W. Bogaerts et al., "Silicon microring resonators," Laser and Photonics Reviews 6, 47 (2012).