Free Spectral Range Calculator

Estimate cavity and ring spacing with confidence. Switch units, export tables, and inspect plotted relationships. Designed for deeper resonator checks across practical calculation scenarios.

Calculator Inputs

Example Data Table

Type Length Group Index Center Wavelength FSR (GHz) Wavelength Spacing (pm)
Standing cavity 25 mm 1.4682 1550 nm 4.083810 32.727149
Standing cavity 50 mm 1.4682 1550 nm 2.041905 16.363574
Ring resonator 10 mm 1.9 1310 nm 15.778550 90.321053
Ring resonator 2 mm 2.1 1550 nm 71.379157 572.023810

Formula Used

General relation: FSR = 1 / round-trip time

Standing-wave cavity: FSR = c / (2 × ng × L)

Ring resonator: FSR = c / (ng × L)

Wavelength spacing approximation: Δλ ≈ λ² / (ng × Lrt)

Estimated mode order: m ≈ neff × Lrt / λ

In these relations, c is the speed of light, ng is the group index, L is the physical cavity length, Lrt is round-trip length, λ is the selected center wavelength, and neff is the optional effective index used for order estimation.

How to Use This Calculator

  1. Choose the resonator type. Use standing-wave for two-pass cavities and ring for one-loop resonators.
  2. Enter the physical cavity length and pick the matching unit.
  3. Enter the group index for the resonator medium or waveguide.
  4. Provide the center wavelength and its unit.
  5. Optionally enter an effective index to estimate resonance mode order.
  6. Press the calculate button to place the result summary above the form.
  7. Review frequency spacing, wavelength spacing, round-trip time, and the plotted trend.
  8. Use the CSV or PDF buttons to export the current result.

About Free Spectral Range

Free spectral range describes the spacing between neighboring resonances in a cavity or resonator. Engineers, physicists, and photonics students often use it when comparing resonator designs, checking laser mode spacing, or estimating how many resonances fit inside a wavelength band.

This calculator accepts standing-wave cavities and ring resonators because their round-trip paths differ. A standing cavity sends light forward and backward across the physical length, so the round-trip path is twice the listed length. A ring resonator uses a single closed loop, so the round-trip path equals the physical path length.

The most useful output is often frequency-domain FSR, shown here in hertz, megahertz, gigahertz, and terahertz. The page also estimates wavelength spacing around your chosen center wavelength. That wavelength result is an approximation that works best when the spacing is small compared with the center wavelength.

Group index strongly affects the result because FSR depends on round-trip group delay. Larger group index or longer path length lowers the spacing. Shorter resonators produce larger free spectral ranges, which is often useful when wider mode spacing is required.

The optional effective index field supports a rough longitudinal mode order estimate. That value is helpful for deeper checks, but the FSR itself is driven by group delay, so the group index remains the key input for spacing calculations.

FAQs

1. What is free spectral range?

Free spectral range is the spacing between neighboring resonant frequencies of a cavity or resonator. It is usually reported in hertz, but it can also be approximated as wavelength spacing near a chosen center wavelength.

2. Why does cavity length change the result?

Longer cavities take more time for one round trip. Because FSR equals the inverse of round-trip time, a longer resonator produces a smaller frequency spacing, while a shorter resonator produces a larger spacing.

3. Why is group index used instead of refractive index?

FSR depends on round-trip group delay. Group index captures that delay more accurately than ordinary refractive index when you want mode spacing in the frequency domain, especially in dispersive optical structures.

4. What is the difference between standing and ring resonators?

A standing-wave cavity uses a forward and backward pass over the physical length. A ring resonator uses one loop. That difference changes the round-trip path and therefore changes the computed free spectral range.

5. Is the wavelength spacing exact?

The wavelength spacing shown here is an approximation around the selected center wavelength. It is most reliable when the spacing is small compared with the chosen wavelength and dispersion does not vary sharply over the interval.

6. What does the effective index field do?

The optional effective index field estimates resonance order. It is not required for FSR. Leave it blank if you only need mode spacing and wavelength spacing.

7. Can I use this for fiber and integrated photonics?

Yes. The calculator can help with fiber cavities, Fabry-Perot structures, and ring-style resonators as long as you enter a suitable physical length, center wavelength, and group index for the device.

8. What do the export buttons save?

The CSV and PDF downloads save the current calculated summary. They make it easier to document design checks, compare setups, or share spacing calculations with students, teammates, or clients.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.