Numerical Simulation in Advanced Signal Analysis

**Chapter 1**

**Abstract**

**1. Introduction**

arbitrary pulse profiles.

Propagation

*Mounir Khelladi*

Femtosecond Laser Pulses:

Generation, Measurement and

In this contribution some basic properties of femtosecond laser pulse are summarized. In sections 2.1–2.5 the generation of femtosecond laser pulses via mode locking is described in simple physical terms. In section 2.6 we deal with measurement of ultrashort laser pulses. The characterization of ultrashort pulses with respect to amplitude and phase is therefore based on optical correlation techniques that make of the short pulse itself. In section 3 we start with the linear properties of ultrashort light pulses. However, due to the large bandwidth, the linear dispersion is responsible for dramatic effects. To describe and manage such dispersion effects a mathematical description of an ultrashort laser pulse is given first before we continue with methods how to change the temporal shape via the frequency domain. The chapter ends with a

paragraph of the wavelet representation of an ultrashort laser pulse.

characterization, dispersion, spectral phase, wavelet

**2. Ultrashort laser pulses generations**

amplifiers or optical parametric amplifiers.

**2.1 Titane sapphire oscillator**

**3**

**Keywords:** femtosecond laser pulse, ultrashort pulse, autocorrelation,

Propagation of ultrashort optical pulses in a linear optical medium consisting of free space [1–5], dispersive media [6, 7], diffractive optical elements [8–10], focusing elements [11] and apertures [12, 13] has been extensively studied analytically, though only a few isolated attempts have been made on numerical simulation. However, analytical methods have the limitations of not being able to handle

The central aim of this section is to give a concise introduction to nonlinear optics and to provide basic information about the most-widely used tunable femtosecond laser sources, in particular tunable Ti:sapphire oscillators and Ti:sapphire

In 1982, the first Ti:sapphire laser was built by Mouton [14]. The laser tunes from 680 nm to 1130 nm, which is the widest tuning range of any laser of its class1.
