Thin crystals are used in different applications with femtosecond pulses:

• Harmonic generation (SHG, SFG);
• Optical parametric generation and amplification (OPG, OPA);
• Difference frequency generation (DFG);
• Pulse width measurements by auto and cross correlation;
• THz frequency generation (in GaSe crystal);
• Polarization entangled photon pairs generation.

The propagation of a ultrashort optical pulses through the crystal results in a delay of the pulses because of Group Velocities Mismatch (GVM), a duration broadening because of Group Delay Dispersion (GDD) and a frequency chirp. Unfortunately those effects forces to limit nonlinear crystal thickness in frequency generation schemes. For two collinearly propagating pulses with different group velocities their quasistatic interaction length (Lqs) is defined as distance over which they separate by a path equal to the one of the pulses duration (or to the desired pulse duration):

where GVM is the group velocity mismatch and   is the duration of the pulse. GVM calculations are presented for the most popular Type 1 phase matching applications for different crystals in Table 1.Optimal BBO, LBO, KDP and LiIO3 crystal thicknesses which are limited by GVM for Type 1 SHG of 800 nm at different fundamental pulse duration are presented in the Table 2. Also effective coefficients and phase matching angles at room temperature (20°C) are calculated. If longer crystal will be used this will cause second harmonic pulse broadening to the duration longer than fundamental pulse duration (or desired pulse duration). Group delay dispersion (GDD) has an important impact on the propagation of pulses, because a pulse always has certain spectral width, so that dispersion will cause its frequency components to propagate with different velocities. In case of crystals where we have normal dispersion when refractive index decreases with increasing wavelength this leads to a lower group velocity of higher-frequency components, and thus to a positive chirp.The frequency dependence of the group velocity also has an influence on the pulse duration. If the pulse is initially unchirped, dispersion in a crystal will always increase its duration. This is called dispersive pulse broadening. For an originally unchirped Gaussian pulse with the duration  ₀, the pulse duration is increased according to:

where L - thickness of the crystal in mm; D  - second order group delay dispersion or dispersion parameter. Table 3 gives D parameter for Type 1 phase matching SHG @ 800 nm for 800 nm pulse with „o“ polarization and 400 nm pulse with „e“ polarization in different crystals. 

Table 1. Group velocity mismatch between shortest and longest wave pulse for Type 1 phase matching