# Multi-mode fiber radiance calculator

## About this calculator

This calculator computes the radiance of a laser beam propagating in a multi-mode or double-clad optical fiber. It can also be used for free space beams by replacing core diameter with focal spot diameter. Radiance is kind of a measure of beam quality with power included. At best radiance can only be conserved, not improved in optical components such pump combiners. Radiance is defined as

$R = \dfrac{P}{A\Omega}$

where $P$ is the optical power, $A$ is the cross-sectional area of the focal spot or the core area of the fiber, and $\Omega$ is the beam's divergence solid angle defined by its NA. This calculator computes $\Omega$ as

$\Omega = 2\pi \left(1-\cos\theta\right)$

where $\theta = \arcsin(\mathrm{NA})$ is the divergence angle. For small NA values, a useful approximation formula is

$\Omega = \pi \mathrm{NA}^2$