# Transform-limited pulse calculator

## About these calculators

The first calculator computes the transform-limited, i.e. minimum possible, pulse duration of a Gaussian or sech² pulse with a given spectral width either in wavelength or frequency domain. The second calculator computes the inverse of that, in other words, the minimum spectral width required to obtain a given pulse duration. In both cases, the calculation is based on the time-bandwidth product, which is a constant of the order of unity for transform-limited pulses and depends slightly on the pulse shape.

The time-bandwidth products of transform-limited Gaussian and sech² pulses are:

Since time-bandwidth product is defined as

where is the spectral width (in Hz) and is the pulse duration (in s), the transform-limited spectral width can be computed from pulse duration asand, conversely, pulse duration would beIf required, the spectral width can be converted from wavelength to frequency before the operation or from frequency to wavelength after the operation.