Example Data Table
| Case | Method | Inputs | Output (g_net) |
|---|---|---|---|
| A | Power ratio | Pin=1 mW, Pout=4 mW, L=1 cm | ≈ 1.386 1/cm |
| B | Cross-sections | σe=3e−20 m², σa=1e−20 m², Ne=2e24 1/m³, Na=1e24 1/m³ | ≈ 0.500 1/cm |
| C | Modal relation | Γ=0.85, g_material=35 1/cm, αi=5 1/cm | ≈ 24.75 1/cm |
Formula Used
1) Power ratio along an active length
Assuming exponential amplification along length L:
g_net = ln(Pout / Pin) / L
Gain in decibels: Gain(dB) = 10·log10(Pout/Pin).
2) Cross-sections and population densities
A simple material-gain model using emission and absorption:
g_material = σe·Ne − σa·Na
3) Modal gain relation with confinement and loss
Relates waveguide (modal) gain to material gain:
g_modal = Γ·g_material − αi
This calculator can solve for any missing variable.
How to Use This Calculator
- Select a calculation method that matches your measurements.
- Choose the output unit for gain coefficients.
- Enter all required inputs; keep units consistent.
- Enable Γ and αi only when you need modal corrections.
- Click Calculate to display results above the form.
- Use Download CSV or PDF to export computed values.
1) What the gain coefficient represents
The optical gain coefficient, g, quantifies how optical power changes per unit length inside an active medium. Positive g indicates amplification, while negative values indicate attenuation. It is commonly reported in 1/cm or 1/m and links device physics to measurable power change.
2) Using power-ratio data for quick estimation
When you can measure input and output power across a known interaction length, the exponential model gives g = ln(Pout/Pin)/L. For example, a 4× power increase over 1 cm yields about 1.386 1/cm. This method is practical for amplifiers and pumped sections. It also works for segmented measurements along a chip.
3) Interpreting gain in decibels and per-length form
Lab instruments often present gain in dB, but device models frequently use per-length coefficients. The calculator reports both forms so you can compare specifications: Gain(dB)=10·log10(Pout/Pin), and g scales with length. Short devices can show large dB/cm values without high total dB.
4) Material gain from cross-sections and populations
For many gain media, a first-order estimate uses g_material = σe·Ne − σa·Na. Typical stimulated emission cross-sections may fall around 10−21 to 10−19 m², while carrier or ion densities can reach 1024 to 1026 1/m³. As inversion grows, emission dominates absorption and g becomes positive. This is a useful screening model before detailed spectroscopy.
5) Confinement factor and waveguide realities
In guided devices, only a fraction of the optical mode overlaps the active region. The confinement factor Γ (often 0.3–0.9 in integrated photonics) scales material gain to modal gain. This is why two devices with the same material parameters can deliver different net gain. Use simulated mode profiles when Γ is uncertain.
6) Accounting for internal loss and net performance
Internal loss αi represents distributed absorption, scattering, and free-carrier effects. The modal relation g_modal = Γ·g_material − αi helps separate “how good the material is” from “how lossy the structure is.” In many waveguides, αi of a few 1/cm is a meaningful design driver. Reporting αi alongside Γ improves comparisons across platforms.
7) Diagnosing negative or unexpected results
A negative g can be valid: insufficient pump, poor inversion, coupling losses included in the measurement, or an overestimated interaction length can all reduce the inferred coefficient. Compare the loss-corrected modal result to the raw power-ratio result to see whether losses dominate the measurement.
8) Reporting results for design and validation
For professional reporting, record Pin, Pout, length, units, and whether Γ and αi were applied. State the method used, then provide g in a consistent unit (1/cm is common for short devices, 1/m for longer paths). Include uncertainty notes, such as power-meter accuracy and facet coupling repeatability. Exporting CSV and PDF supports traceable lab documentation.
1) What is the difference between material gain and modal gain?
Material gain describes the active medium itself. Modal gain is what the guided optical mode experiences after confinement (Γ) and internal losses (αi) are included.
2) When should I use the power ratio method?
Use it when you have Pin, Pout, and the effective interaction length, and coupling losses are minimized or separately accounted for.
3) Why can my calculated gain be negative?
Negative gain may indicate net loss, weak pumping, absorption exceeding emission, or that external coupling losses were included in Pout/Pin.
4) Which output unit should I choose?
Choose 1/cm for short devices like chips and waveguides, and 1/m for longer paths like fiber or long free-space cells.
5) What does the confinement factor Γ change?
Γ scales material gain to the fraction of optical power overlapping the active region. Lower Γ reduces modal gain even if material gain is high.
6) What does internal loss αi represent?
αi models distributed attenuation from scattering, absorption, and carrier-related effects inside the structure. It subtracts directly from the modal gain.
7) How do I relate dB gain to a gain coefficient?
Convert dB to a power ratio, then use g = ln(Pout/Pin)/L. The calculator reports both dB and per-length gain together.
Accurate inputs and units produce dependable optical gain results.