1. Ultrashort Pulse

2. Pulse Wave

## Every function

can be represented by the summation of individual

## frequency components

, the so called

## Fourier Series

. With a set of given single frequencies a new time signal can be generated.

On the other hand by

## sampling

a time signal with respect to its frequency components, the

## source frequencies

of the time signal can be revealed. This process is known under the term

## Fourier Transformation

and widely used in engineering and science.

The

## interactive visualization

on this pages exemplifies the Fourier Transformation and its characteristic parameters. The Graphs show; the resulting or starting time signal (top), the single frequency terms (bottom-left) and the spectral representation of the frequency components (bottom-right). The blue lines in the spectrum indicate the individual frequencies (

## Delta Dirac Functions

); the connecting dark line is (spline-) interpolated.

The temporal spread of an **optical ultrashort pulse** lies in the range of picoseconds and below. In order to reach such short time regions, a broad spectrum of **phase matched** frequency terms is required. This is commonly achieved in **mode-locked lasers**. The relevant parameters responsible for the pulse shape are **Δ frequency**, **center frequency**, and **bandwidth** (frequency spacing); they can be adjusted with the control panel above.

In case of ideal mode-locking and zero dispersion the smallest possible pulse width (

## Fourier Limited Pulse Width

) can be modeled as a fourier series of the individual frequency components.