Multi-mode fiber radiance calculator

Input

Output

μm²

sr

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=PAΩR = \dfrac{P}{A\Omega}

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

Ω=2π(1cosθ)\Omega = 2\pi \left(1-\cos\theta\right)

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

Ω=πNA2\Omega = \pi \mathrm{NA}^2