Laser Cavity Mode Calculator

What this calculator does

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. Using the cavity’s physical length L (entered in cm) and a refractive index n for the intracavity medium, it computes:

• 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 a linear cavity of length L filled with a uniform medium of refractive index n, constructive interference requires that the round-trip phase equals an integer multiple of 2π. A common way to express the resonance condition is:

where:

• L is the physical mirror separation (entered in cm; internally convert to meters for SI),
• n is the refractive index (dimensionless),
• 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). The scaling is simple and very useful in design:

• Doubling L halves the FSR.
• Increasing n decreases the FSR in the same proportion.
• Short cavities (mm–cm) typically have FSR values in the GHz range; longer cavities drop into hundreds of MHz or lower.

From FSR to 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 spacing (FSR) than the absolute integer m, because m is very large at optical frequencies. For example, at 1064 nm and a 25 cm air cavity, m is on the order of hundreds of thousands. The calculator therefore focuses on Δf and (optionally) relative mode positions.

How to interpret the results

• FSR tells you how densely the cavity modes lie in frequency. If your gain bandwidth is wide compared with the FSR, many longitudinal modes can lase simultaneously (multi-mode operation) unless additional mode selection is used.
• Single-frequency designs often push FSR larger by shortening the cavity (smaller L) or using intracavity elements that effectively limit which mode can reach threshold.
• Changing n or L shifts the entire comb of cavity resonances. Temperature can change both L (thermal expansion) and n (thermo-optic effect), producing measurable frequency drift.

Worked example

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: The cavity supports allowed longitudinal resonances spaced by about 600 MHz. If the laser’s gain bandwidth spans several GHz (common for many gain media), multiple longitudinal modes could fit under the gain curve unless something restricts them.

Quick comparison table (typical FSR values)

The table below illustrates how FSR changes with length and refractive index. Values are approximate and assume the simple Δf = c/(2nL) model.

Assumptions and limitations (read this if results differ from a lab measurement)

• 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.
• 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 (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, consider whether n should represent n_g at your wavelength.
• 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.
• 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.
• 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.

References (for further reading)

• A. E. Siegman, Lasers, University Science Books.
• O. Svelto, Principles of Lasers, Springer.
• Saleh & Teich, Fundamentals of Photonics, Wiley.