Laser Cavity Mode Calculator

Introduction: laser cavity mode spacing and free spectral range

This laser cavity mode calculator estimates the free spectral range (FSR)—the frequency spacing between adjacent longitudinal resonator modes—for a simple two-mirror linear cavity. Enter the cavity length L (in cm) and a refractive index n for the medium inside the cavity, and the calculator converts that geometry into the spacing between successive resonances. That is useful when you want to see whether a laser cavity is likely to favor a single longitudinal mode or several closely spaced ones.

• FSR in frequency (Hz, commonly shown as MHz or GHz),
• and, if the implementation lists them, the family of allowed longitudinal mode frequencies (relative spacing and/or absolute values depending on how the page displays results).

Core physics and formulas for laser cavity modes

For a linear laser cavity of length L filled with a uniform medium of refractive index n, constructive interference requires the round-trip phase to equal an integer multiple of 2π. In practical terms, the cavity resonates only when the optical path length fits an integer number of half-wavelengths, so the physical mirror spacing and the refractive index both matter.

where:

• L is the physical mirror separation (entered in cm; internally convert to meters for SI),
• n is the refractive index (dimensionless), which may also be an effective index if the cavity contains more than one uniform section,
• λ is the vacuum wavelength corresponding to the resonant frequency,
• m is an integer mode number (longitudinal index).

In frequency form, adjacent longitudinal modes are separated by the free spectral range:

FSR (Δf) = c / (2 n L)

where c is the speed of light in vacuum (approximately 299,792,458 m/s). This relation is the main design rule for the page: shorten the cavity to spread the resonances apart, or increase the index to pack them closer together. In other words, the same laser geometry can move from widely spaced modes to tightly clustered modes just by changing the optical path length.

• Doubling L halves the FSR, so a longer resonator produces denser mode spacing.
• Increasing n decreases the FSR in the same proportion, because the optical path length grows even when the physical length does not.
• Short cavities (mm–cm) typically have FSR values in the GHz range; longer cavities drop into hundreds of MHz or lower.

From FSR to laser cavity mode frequencies

If you want absolute mode frequencies, one convenient expression is:

f_m = m · c / (2 n L)

In practice, many users care more about the spacing between neighboring resonances than about the absolute integer m, because m is very large at optical frequencies. For design and alignment work, the important question is usually how many cavity modes fit under the gain curve and how far apart those modes are once the cavity is locked to a particular length. The calculator therefore focuses on Δf and, optionally, relative mode positions.

How to interpret the laser cavity mode results

• FSR tells you how tightly the cavity modes are packed across the laser gain spectrum. If the gain bandwidth is much larger than the FSR, more than one longitudinal mode can fit under the same envelope, so the laser may run multimode unless you add a frequency-selective element.
• Single-frequency designs often push the FSR larger by shortening the cavity (smaller L) or by adding intracavity optics that suppress all but one resonance near threshold. If you are comparing two cavity layouts, the shorter one almost always gives the wider spacing.
• Changing n or L shifts the entire comb of cavity resonances. Temperature can change both L (thermal expansion) and n (thermo-optic effect), so a cavity that looks stable on paper can drift in practice if the bench warms up or the gain medium heats unevenly.

Worked example: a 25 cm air-spaced laser cavity

Example: L = 25 cm, n = 1.00 (air).

1. Convert length to meters: 25 cm = 0.25 m.
2. Compute FSR: Δf = c / (2 n L) = 299,792,458 / (2 × 1.00 × 0.25) Hz.
3. Denominator is 0.5, so Δf ≈ 599,584,916 Hz ≈ 599.6 MHz.

Interpretation: This air-spaced cavity supports allowed longitudinal resonances separated by about 600 MHz. That is a compact way to sanity-check the result: a 25 cm resonator should not produce gigahertz-scale spacing, but it also should not collapse into tens of megahertz unless the cavity is much longer. If you later replace the air path with a higher-index medium, the mode spacing shrinks because the optical path length grows even when the mirror spacing stays the same.

Quick comparison table for laser cavity FSR values

The table below shows how cavity length and refractive index change the free spectral range at a glance. It uses the simple Δf = c/(2nL) model, so it is best read as a design estimate rather than a complete resonator simulation.

Assumptions and limitations for laser cavity mode calculations (read this if results differ from a lab measurement)

This simple model is best for estimating longitudinal mode spacing before you account for mirror phase shifts, dispersion, or transverse structure.

• Linear two-mirror cavity, longitudinal modes only: This model describes the spacing of longitudinal resonances. Transverse mode structure (TEM modes), Gouy phase, and alignment effects are not included, so a real beam profile can show more structure than the calculator reports.
• Uniform refractive index: Assumes the intracavity medium has a single effective index n along the full length. Mixed media (e.g., part air + part crystal) require an effective optical length computed from the sum of n_iL_i.
• Phase index vs. group index: The simple formula uses a constant refractive index. In dispersive media, the spacing relevant to pulses and frequency combs can depend on group index n_g, not phase index n. If you’re working with broadband spectra, decide whether the phase index or the group index better matches your measurement.
• Mirror coating phase and penetration depth ignored: Real mirrors add wavelength-dependent phase shifts and effective penetration depth, slightly changing the effective cavity length and thus the FSR. That is often a small correction, but it matters when you are comparing against a precision measurement.
• c is the vacuum speed of light: The formula uses c and divides by n to account for propagation in the medium. If your “n” is already an effective/group index, this is usually correct; just be consistent about which index you are using.
• Length definition: L is treated as the physical mirror separation (or physical cavity length). For cavities with significant intracavity elements, the relevant value is often the optical length (nL) summed over sections.
• Unit sensitivity: This page expects L in centimeters. Entering meters by habit will produce an FSR that is 100× too small, so it is worth checking the unit before you trust the answer.

References for laser cavity mode spacing

• A. E. Siegman, Lasers, University Science Books — classic reference for resonators, cavity modes, and the connection between optical length and frequency spacing.
• O. Svelto, Principles of Lasers, Springer — clear treatment of longitudinal modes, gain bandwidth, and mode competition in practical laser systems.
• Saleh & Teich, Fundamentals of Photonics, Wiley — useful background on resonators, interference, and the frequency-domain view of cavity resonances.

How to use this laser cavity mode calculator

1. Enter Cavity Length L (cm) using the mirror spacing or effective cavity length you want to analyze.
2. Enter Refractive Index n for the intracavity medium, or use an effective index if the cavity includes more than one section.
3. Run the calculation, then compare the output against a nearby cavity length or refractive index so you can see how the laser cavity mode spacing shifts before you rely on the result.