Calculating Laser Diode Threshold Current

This solution explains how to calculate the threshold current ($I_{th}$) of a laser diode using its slope efficiency ($\eta_s$) and output power ($P_{out}$) at a given current ($I$). The method applies to diodes with piece-wise linear characteristics.

Laser Diode Power Equation

For a laser diode exhibiting linear behavior above threshold, the output optical power ($P_{out}$) is related to the operating current ($I$) and threshold current ($I_{th}$) by the slope efficiency ($\eta_s$):

$P_{out} = \eta_s \times (I - I_{th})$

Provided Data

• Slope Efficiency ($\eta_s$): 0.5 W/A
• Operating Current ($I$): 100 mA
• Output Power ($P_{out}$): 30 mW

Calculation Steps

1. Unit Conversion: Convert the given values to standard SI units (Amperes and Watts).

   • Current: $I = 100 \text{ mA} = 100 \times 10^{-3} \text{ A} = 0.1 \text{ A}$
   • Power: $P_{out} = 30 \text{ mW} = 30 \times 10^{-3} \text{ W} = 0.03 \text{ W}$
   • Slope Efficiency: $\eta_s = 0.5 \text{ W/A}$ (already in SI units)

2. Apply the Formula: Substitute the converted values into the power equation.

   $0.03 \text{ W} = 0.5 \text{ W/A} \times (0.1 \text{ A} - I_{th})$

3. Solve for $I_{th}$: Rearrange the equation to find the threshold current.

   • Divide the output power by the slope efficiency: $ \frac{P_{out}}{\eta_s} = I - I_{th} $ $ \frac{0.03 \text{ W}}{0.5 \text{ W/A}} = 0.1 \text{ A} - I_{th} $
   • Calculate the result: $ 0.06 \text{ A} = 0.1 \text{ A} - I_{th} $
   • Isolate $I_{th}$: $ I_{th} = 0.1 \text{ A} - 0.06 \text{ A} $ $ I_{th} = 0.04 \text{ A} $

4. Convert $I_{th}$ to mA: Convert the result from Amperes back to milliamperes.

   $I_{th} = 0.04 \text{ A} \times 1000 \text{ mA/A} = 40 \text{ mA}$

Therefore, the threshold current of the laser diode is 40 mA.