Chirp Pulse Amplification

Laser amplifier gain (being rather sloppy, but roughly correct):

The stored energy density (J/cm2) Est is related to the pump energy Epump modified by :

1. The overlap of the pump spectrum to the absorption spectrum of the material

2. The intrinsic efficiency of the material

3. The laser material excited state storage time relative to the pump pulse length.

4. Saturation effects for very high pump energy densities.

The small signal gain is G = exp(Est/Esat), where Esat is a characteristic of the material.

The maximum extractable energy of course Est * Area. (when (G-1)*Ein >> Est)

If Est >> Esat, the gain becomes very large, and amplified spontaneous emission will extract all of the stored energy in the laser rod into unusable output.

If Est << Esat, the gain will be very low, and will not exceed the absorption and other losses in the laser.

For efficient operation, lasers must operate with stored and input energy densities roughly comparable their saturation energy density.

Saturation energy density of common laser materials

Optical damage

Surface damage: Laser pulse causes local heating at the surface. Local temperatures cause thermal (fracture, decomposition, or melting) damage.

Thermal diffusion causes the energy damage threshold to vary as approximately the square root of the pulse length. For a 1 nanosecond pulse, damage thresholds are typically one to a few Joules per square centimeter (for many pulses).

Bulk damage: Typically bulk damage in high peak power laser systems is caused by non linear self focussing of the input laser beam.

Inhomogeneities in the input beam can cause small scale focussing and beam break-up through the same mechanism. Typically this beam breakup is the limit to allowable peak power density in a laser system. Depending on the laser material, and the size of the inhomegenity of the input beam, peak power densities of 10-100GW/cm2 are allowable.

Minimum Pulse Length: The combination of maximum allowable peak powers, peak energy densities (as a function of pulse length) and required energy densities for reasonable gain, the minimum pulse length which can be effectively amplified is around 100psec. (In low gain systems pulses down to 10psec can probably be amplified).

Laser crystal size limits

It is possible to increase the output peak power of a laser system by increasing the size of the optics. In addition to the obvious problem of increased system cost, this approach will not work for high repetition rate systems. We present arguments for conventional rod type lasers. Other geometries (such as slab lasers) are substantially more resistant to these effects, but do not avoid them completely. There are two thermal effects which limit the size of the laser of the laser optics:

Thermal Fracture: Some of the pump energy deposited in the laser rod is converted to waste heat. For laser pumped systems, this may be <50% of the stored energy, for lamp pumped systems, it is typically several times the stored energy. This is a major advantage of diode pumped lasers over lamp pumped systems, however diodes are still too expensive for high energy laser.

Thermal fracture stress is proportional to the dissipated thermal power per unit length. For laser materials with good thermal properties (like Nd:YAG and Ti:Sapphire), about 40W/cm can be dissipated.

Thermal Focussing: The index of refraction of laser materials varies with temperature. The variation of temperature across the rod causes the beam to be focussed or defocused. The focal length F = KA/Pth, K a constant, A the rod cross section area, and Pth the thermal power dissipated in the rod. If the thermal focal length becomes comparable to the length of the rod, stable beam propogation is difficult. This effectively limits the allowable rod length.

Thermal Birefringence: The anisotripic thermal stress in a laser rod causes a de-polarization of a polarized input beam. This causes a substantial loss of output power, and degradation of output beam quality. Various compensation schemes can reduce this effect .

The combination of thermal effects limits the maximum rod cross section area for high average power applications. For 120Hz lasers, the maximum rod area (for Nd:YAG) is about 0.25 square centimeters. This limits the maximum peak output power to less than about 10GW.

Chirp Pulse Amplification

The peak power limit can be avoided by amplifying a long optical pulse to high energy, and then compressing the pulse.

The dispersive stretching system is usually constructed from either an optical fiber, or a pair of diffraction gratings. A fiber can provide a larger dispersion, but its higher order dispersion cannot be exactly corrected with the compression grating.

The dispersive compression system is usually constructed from a pair of diffraction gratings

Note that in the dispersive expander, the Fourier transform of the pulse shape can be controlled with a spatial light modulator (intensity and phase control are required). This allows compensation for finite bandwidth in the amplifier system, and for some errors in the compression and expansion.

In Ti:Sapphire laser systems, CPA can be used to produce pulses typically around 100fsec, but under some conditions as short at a few femptoseconds. Low repetition rate, 1J, 100fsec laser systems can be constructed on a table top - 10TW peak power output.

Page by Josef Frisch frisch@slac.stanford.edu 04/22/2002

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