Calculator Inputs
Enter cavity dimensions, reflectivities, distributed losses, confinement factor, and optional emission cross section. The layout uses three columns on large screens, two on medium, and one on mobile.
Formula Used
The calculator separates distributed losses from mirror loss. It then computes modal threshold gain and converts it to material threshold gain through the optical confinement factor.
Where:
- L = cavity length
- R1, R2 = facet or mirror reflectivities
- αi = total internal distributed loss
- αm = mirror loss coefficient
- Γ = optical confinement factor
- σe = stimulated emission cross section
How to Use This Calculator
- Enter the resonator length and choose the correct length unit.
- Provide front and rear mirror reflectivities in percent.
- Enter absorption, scattering, diffraction, and other distributed losses.
- Input the optical confinement factor for the guided mode.
- Optionally add emission cross section to estimate threshold inversion density.
- Set a design margin if you want a more conservative target gain.
- Press the calculate button to display results above the form.
- Use the CSV and PDF buttons to export the generated summary.
Example Data Table
| Cavity Length | R1 | R2 | Total Internal Loss | Γ | σe | Modal Threshold Gain | Material Threshold Gain | Threshold Inversion |
|---|---|---|---|---|---|---|---|---|
| 300 µm | 32% | 95% | 10 cm-1 | 0.35 | 3 × 10-16 cm2 | 29.8455 cm-1 | 85.2727 cm-1 | 2.8424 × 1017 cm-3 |
Frequently Asked Questions
1. What does threshold gain mean in a laser cavity?
Threshold gain is the minimum gain needed for amplification to exactly balance mirror loss and internal loss. Below threshold, light decays. At threshold, the round-trip gain equals the round-trip loss.
2. Why are mirror reflectivities so important?
Reflectivities determine mirror loss. Lower reflectivity lets more light escape, which is useful for output coupling, but it also raises the gain needed for threshold. High reflectivity reduces threshold requirements.
3. What is the difference between modal and material gain?
Modal gain is the effective gain seen by the guided mode. Material gain is the gain provided by the active medium itself. They differ because the optical confinement factor is usually less than one.
4. When should I enter the emission cross section?
Enter it when you want an estimate of threshold inversion density. If you only need threshold gain, you can leave that field empty and the calculator will still compute the main design outputs.
5. Can I use dB units for loss inputs?
Yes. The calculator accepts cm^-1, m^-1, dB/cm, and dB/m. All values are internally converted to consistent SI units before the threshold calculations are performed.
6. Why does a shorter cavity often need higher threshold gain?
Mirror loss scales with 1 divided by cavity length. As the cavity becomes shorter, the same mirror reflectivities produce a larger loss coefficient, so the threshold gain rises.
7. What does the design margin change?
The design margin increases the reported target gain above the exact threshold value. It helps account for fabrication tolerance, temperature drift, aging, and modeling uncertainty during practical design work.
8. Is this suitable for semiconductor and solid-state lasers?
Yes, as a threshold estimate. The equations are broadly useful for many resonators, but detailed devices may also require wavelength dependence, spatial hole burning, carrier transport, or thermal modeling.