Find the optical gain at threshold of a laser diode having following parametric values R1 = R2 = 0.42,   α = 5cm-1 and L = 560 µm

To find the optical gain at the threshold of a laser diode, we use the threshold gain formula for a Fabry-Perot cavity laser. The formula for the threshold gain \( g_{th} \) is given by:

\[
g_{th} = \frac{1}{L} \ln \left( \frac{1}{R_1 R_2} \right) + \alpha
\]

where:
- \( R_1 = 0.42 \) and \( R_2 = 0.42 \) are the reflectivities of the laser mirrors,
- \( \alpha = 5 \, \text{cm}^{-1} \) is the internal loss coefficient,
- \( L = 560 \, \mu\text{m} = 0.056 \, \text{cm} \) is the cavity length.

### Step-by-Step Solution

1. **Calculate the mirror loss term:**

\[
\ln \left( \frac{1}{R_1 R_2} \right) = \ln \left( \frac{1}{0.42 \times 0.42} \right)
\]

2. **Convert the cavity length \( L \) to centimeters:**

\[
L = 560 \, \mu\text{

Learn how to calculate the optical gain at threshold for a laser diode using the threshold gain formula for a Fabry-Perot cavity laser. Includes specific values such as R1 = 0.42, R2 = 0.42, α = 5 cm-1, and L = 560 µm. Suitable for advanced college-level students and professionals.

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