2. Chirped pulse amplification in broad spectral bandwidth laser media

The principle of CPA in broad gain bandwidth laser media (e.g., Ti:sapphire crystals) is presented in Figure 1. Femtosecond laser pulses generated by a large spectral bandwidth oscillator are temporally stretched with dispersive optical elements, in most cases diffraction gratings, up to few-hundred picoseconds or about one nanosecond pulse duration.

The Ti:sapphire laser is a four-level system as depicted by a simplified energy level diagram in Figure 1. Ti:sapphire crystals are optically pumped by nanosecond green lasers. By absorption of pump laser photons, the Ti atoms are raised from the ground energy level E1 to the spectral band E4. The excited atoms are rapidly transferred by nonradiative transitions from the absorption band E4 to the upper laser energy level E3. The spontaneous fluorescence lifetime of Ti atoms on the upper laser level is about 3 μs. The Ti atoms are accumulated on the upper laser level giving rise to a population inversion between E2 and E3 laser levels. Under these conditions, an input laser pulse with photon energy quanta corresponding to the energy difference between the E3 upper level and the E2 lower level is amplified by stimulated laser transitions between E3 and E2 levels. The generated laser radiation is coherently added to the input radiation.

Figure 1. Chirped pulse amplification (CPA) in Ti:sapphire laser crystals. Bν, amplified pulse frequency bandwidth; τp, temporally compressed pulse duration.

To get the population inversion between laser energy levels for laser amplification, we essentially need an efficient absorption of pump photons in Ti:sapphire crystals. The energy accumulated in the upper laser level can be the result of pumping with single or multiple pump laser beams. Angles between pump beams and seed pulse beam are noncritically defined and are practically imposed by the amplifier geometry.

Because the Ti atoms lifetime is in the range of few-μs, an acceptable delay between pump laser pulses and input stretched laser pulses is in the nanoseconds range. This temporal synchronization can be easily obtained with electronic devices.

Pulse duration of the recompressed pulse is inversely proportional to the optical frequency bandwidth which contains all phase-locked spectral components [20]. The highest amplification gain is obtained near the central wavelengths (790–800 nm) of the Ti:sapphire fluorescence spectrum, engendering the "gain narrowing" effect of the amplified laser pulse spectral band (Figure 2a). In the regenerative amplifiers and multi-pass amplifiers, with many passes through the laser amplifying media and high amplification factor, the effect of gain narrowing significantly contributes to the decrease of the spectral bandwidth of the amplified pulses (Figure 2b).

High-energy extraction efficiency can be obtained if laser amplifiers are working near the saturation regime, where the input laser pulse fluence is higher than the saturation fluence of the amplifying laser medium [20]. In this case, almost all accumulated energy on the upper level of the laser medium could be extracted and added to the input pulse energy [20]. The "red" spectral components travel in the leading edge of the temporally stretched pulse, whereas the "blue" spectral components are delayed in the trailing edge. In the amplifiers working near the saturation regime, due to the significant depletion of the upper laser-level population, the amplification factor of the "red" spectral components coming first in the amplifying medium is higher than that of the "blue" spectral components arriving on the trailing edge of the stretched pulse. The result is a redshift of the amplified laser pulse spectrum, associated with a spectrum narrowing (Figure 2b and c).

Stretched amplified pulses are recompressed in a temporal stretcher with diffraction gratings, where "red" spectral components are delayed compared to the "blue" components. Both "gain narrowing" and "redshifting" effects contribute to the increase of the amplified pulse duration after temporal recompression.

The amplified spontaneous emission (ASE), which takes place in the laser media as long as the population inversion between the upper and lower laser levels exists, deteriorates the picosecond intensity contrast of femtosecond laser systems. By all Ti:sapphire amplification, it is very difficult to attain more than 1011 intensity contrast of femtosecond pulses, as it is required in case of PW-class femtosecond laser systems.

3. Broadband optical parametric amplification

energy accumulation in the amplifying medium.

amplifiers.

Optical parametric amplification (OPA) is practically an instantaneous process without laser

Figure 2. Gain narrowing and redshifting in Ti:sapphire amplifiers. (a) Polarized fluorescence spectra and calculated gain line for an optical <sup>c</sup>-axis normal cut Ti:sapphire rod; =, <sup>c</sup>-axis parallel polarization; ┴, <sup>c</sup>-axis normal polarization. (b) Spectrum narrowing and redshifting after amplification in an all Ti:sapphire TW-class laser manufactured by Amplitude Technologies for the National Institute for Laser, Plasma, and Radiation Physics, Bucharest-Magurele; OSC: femtosecond oscillator spectrum; AMPL: spectrum after amplification. (c) Redshifting effect in nearly saturation operated Ti:sapphire

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By absorption of pump photons with ω<sup>p</sup> frequency, the crystal molecules leave from their ground energy level E1 to an excited intermediate higher energy level E2 (Figure 3a). While an excited molecule returns to its initial ground state, a photon with ω<sup>s</sup> signal frequency and

Dissipated heat in the active medium is given by the energy difference between the absorbed pump energy and the laser emitted energy. The thermal loading of the Ti:sapphire crystals produces beam wavefront distortions and phase dispersions of the spectral components of the large bandwidth laser pulses. It results in a poor beam focusing and an increase of the recompressed pulse duration.

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Figure 2. Gain narrowing and redshifting in Ti:sapphire amplifiers. (a) Polarized fluorescence spectra and calculated gain line for an optical <sup>c</sup>-axis normal cut Ti:sapphire rod; =, <sup>c</sup>-axis parallel polarization; ┴, <sup>c</sup>-axis normal polarization. (b) Spectrum narrowing and redshifting after amplification in an all Ti:sapphire TW-class laser manufactured by Amplitude Technologies for the National Institute for Laser, Plasma, and Radiation Physics, Bucharest-Magurele; OSC: femtosecond oscillator spectrum; AMPL: spectrum after amplification. (c) Redshifting effect in nearly saturation operated Ti:sapphire amplifiers.
