Laser Linewidth and Bandwidth Calculator

Laser linewidth represents the frequency range over which a laser emits its optical power, fundamentally governed by the Schawlow-Townes limit and modified by spontaneous emission and cavity characteristics. The primary governing equation for the spectral linewidth (deltanu) is expressed as:

deltanu = (π * plan * gammon^2 * nu) / P

Where plan is a derived scaling factor based on cavity coefficients (a1 / b1 * (1 / c1)), gammon represents the damping or decay factor, nu is the central optical frequency, and P denotes the output power. Additional variables evaluate the absolute wavelength boundaries (freq_max and freq_min) using the speed of light (speol) and the designated wavelength band (lambdaband).

Let us compute the laser linewidth for a helium-neon system operating under specific experimental conditions. Assume an optical output power (P) of 0.005 Watts, a central optical frequency (nu) of 4.74 x 10^14 Hz, a damping parameter (gammon) of 1.2 x 10^3, and a cavity scaling factor (plan) evaluated to 0.0015 based on coefficients a1, b1, and c1.

First, substitute these parameters into the core equation:

deltanu = (3.1416 * 0.0015 * (1.2 * 10^3)^2 * (4.74 * 10^14)) / 0.005

Evaluating the numerator gives approximately 3.225 x 10^7. Dividing this by the output power of 0.005 yields a spectral linewidth (deltanu) of roughly 6.45 x 10^9 Hz, or 6.45 GHz, illustrating how higher output power inversely compresses the fundamental emission width.

Ensure all input units are strictly converted to standard SI units (meters, hertz, watts) before running calculations to prevent scaling errors in exponential values. When evaluating high-coherence semiconductor or fiber lasers, verify that your damping factors accurately reflect thermal fluctuations and mechanical vibrations inside the resonant cavity.