Laser Threshold Gain Calculator

A basic Fabry–Perot laser reaches threshold when round-trip gain equals round-trip loss. Using modal gain g and internal loss α_i:

• α_m = (1/(2L)) · ln(1/(R1·R2)) (mirror loss term)
• g_th = α_i + α_m (threshold modal gain)
• g_mat ≈ g_th / Γ (estimated material gain, if Γ is provided)

This model assumes a uniform gain region and uses intensity-based attenuation for the dB conversion.

1. Enter cavity length L and select its unit.
2. Provide the two mirror reflectivities R1 and R2.
3. Enter internal loss α_i in your preferred unit.
4. Optional: add confinement factor Γ to estimate material gain.
5. Choose an output unit, then press Calculate.
6. Use the CSV/PDF buttons to export the computed values.

Values are illustrative and rounded for readability.

1) What threshold gain represents

Threshold gain is the minimum modal gain needed for sustained oscillation in a laser cavity. At threshold, the optical field after one round trip returns with the same intensity it started with. This calculator reports that requirement as a gain coefficient, letting you compare designs using the same loss-and-length framework.

2) Mirror loss from cavity length

Mirror loss decreases when the cavity is longer because the logarithmic mirror term is divided by 2L. For example, keeping R1=R2=0.32, a 3 cm cavity needs noticeably less mirror gain than a 1 cm cavity. The tradeoff is that longer cavities can increase device size, absorption path length, and electrical resistance.

3) Reflectivity and output coupling

Reflectivity sets how much light stays in the cavity. Higher reflectivity reduces mirror loss and lowers the threshold gain, but it can also reduce the useful output power coupled out of the cavity. Many practical lasers intentionally use an asymmetric pair, such as a high-reflector and an output coupler, to balance threshold and extraction.

4) Internal loss sources

Internal loss α_i captures absorption, scattering, free-carrier loss, and waveguide leakage. In semiconductor ridge waveguides, rough sidewalls and imperfect confinement often dominate. In fiber or solid-state cavities, coating absorption and intracavity elements can contribute. Because internal loss adds directly to threshold gain, improving material quality can be as impactful as raising reflectivity.

5) Confinement factor and material gain

The confinement factor Γ expresses how much of the optical mode overlaps the gain medium. Modal gain relates to material gain by approximately g_mat≈g_th/Γ. A smaller Γ forces the active medium to provide more material gain for the same threshold, which can increase carrier density, heating, and linewidth broadening.

6) Units and conversions used

Loss and gain are often reported as 1/m, 1/cm, or dB/cm. This calculator converts dB units using the intensity relation α(dB/m)=4.343·α(1/m). Using consistent units matters when comparing data sheets, waveguide measurements, and cavity simulations.

7) Sensitivity to design changes

Small changes can shift threshold. Increasing R1 from 0.30 to 0.35 reduces the mirror term, while doubling α_i raises the threshold linearly. A quick workflow is to compute a baseline case, then vary one parameter at a time to see which lever offers the biggest reduction in required gain.

8) Practical checklist for use

Use measured reflectivities when possible, especially for coated mirrors. Enter cavity length as the optical path in the gain section, not the package length. Prefer internal loss extracted from waveguide cutback or cavity ring-down methods. Finally, export CSV or PDF results to keep a consistent record when iterating cavity geometries and coating choices.

1) Is the reported gain modal or material gain?

The main result is threshold modal gain. If you enter a confinement factor, the calculator also estimates the corresponding material gain using g_mat≈g_th/Γ.

2) What happens if I leave Γ blank?

The calculator still computes mirror loss and threshold modal gain. The material gain line will show a dash, because it depends on the confinement factor value.

3) Can I use dB/cm for internal loss?

Yes. Select dB/cm and enter your value. The tool converts to a linear attenuation coefficient using the standard intensity conversion and then combines it with the mirror loss.

4) Why must R1 and R2 be between 0 and 1?

Reflectivity is a fraction of reflected intensity. Values at 0 or 1 break the logarithm in the mirror-loss expression and are not physically usable for this simplified threshold model.

5) Does this include diffraction or coupling losses?

Not explicitly. Any additional round-trip loss should be included in α_i as an equivalent distributed loss, or treated with a more detailed cavity model.

6) How accurate is this threshold estimate?

It is a first-order design estimate. Real thresholds also depend on carrier dynamics, spatial hole burning, temperature, and nonuniform fields. It is best used for comparison and sanity checks.

7) What output unit should I choose?

Choose the unit that matches your measurements. Many waveguide loss results are in dB/cm, while simulations often use 1/m. The calculator keeps all outputs consistent with your selected unit.