Laser Linewidth and Bandwidth Calculator

Laser linewidth is the width of a laser optical spectrum around its center frequency. A perfectly monochromatic source would occupy one frequency, but every real laser has finite spectral width caused by spontaneous emission, cavity fluctuations, technical noise, temperature drift, and measurement time. This calculator connects frequency linewidth with wavelength bandwidth, coherence time, coherence length, center frequency, and optical quality factor using standard narrowband relationships. Center frequency is the speed of light divided by center wavelength. For a linewidth much smaller than the optical carrier frequency, wavelength bandwidth is approximately wavelength squared times frequency linewidth divided by the speed of light. The calculator reports this very small width in picometers. The approximation is excellent for ordinary lasers because their linewidth is typically many orders of magnitude below their hundreds-of-terahertz carrier frequency. For a Lorentzian spectrum, first-order field coherence decays exponentially. A commonly used coherence time is one divided by pi times the full-width-at-half-maximum frequency linewidth. Multiplying that time by the vacuum speed of light gives coherence length. Different references may omit pi, use a Gaussian spectral shape, define a half width, or account for propagation inside a material. Those conventions produce different numerical factors, so always compare definitions as well as values. The optical quality factor is center frequency divided by frequency linewidth. A narrow-linewidth laser has a high quality factor and a long coherence length, making it valuable in interferometry, coherent communication, precision metrology, spectroscopy, frequency standards, and sensing. Broader sources have shorter coherence and may be preferred when interference artifacts or speckle need to be reduced. Use a linewidth measured over the time scale relevant to the application. Fast intrinsic linewidth measurements can look much narrower than long observations that include drift and acoustic or electrical noise. The wavelength-bandwidth conversion also assumes vacuum wavelength; refractive index and dispersion matter inside media. This calculator gives a consistent set of idealized spectral quantities for planning and comparison, while a complete system analysis should identify spectral line shape, measurement bandwidth, environmental stability, and whether the quoted linewidth is instantaneous, integrated, or instrument limited.