Ultrashort Laser Pulse Phenomena, 2nd Edition

Nonlinear Refractive Index Effects 411

Non-uniform heating results in convection, turbulence, and a random noise in

the beam profile and amplification. In the case of dye laser amplifiers, a simple

but effective solution consists of using aqueous dye solutions cooled near 4

◦

C,

because (dn/dT)|

4

◦

C

≈ 0 at that temperature (or 11. 7

◦

C for heavy water). Pulse-

to-pulse fluctuations in the output of a Cu vapor laser pumped amplifier have

been considerably reduced by this technique [20].

In the case of solid-state amplifiers, a careful design of a cylindrically sym-

metric pump (and cooling) geometry is required to prevent thermal lensing from

causing beam distortion.

7.3.4. Combined Pulse Amplification and Chirping

The preceding section has established that self focusing sets a limit to the

maximum power that can be extracted from an amplifier chain. Within that limit,

SPM and subsequent compression can be combined with pulse amplification

[15, 17]. In the implementation of the process by Heist et al. [17] the pulse is

self-phase modulated through the nonlinear index of the solvent in the last stage

of the amplifier, for the purpose of subsequent pulse compression (Figure 7.9). If

the gain medium is not used at resonance, saturation can result in an even larger

phase modulation, which can be calculated with Eq. (7.17).

With the constraints set above for the absence of self-focusing, the pulse

propagation equation (1.194) is basically one-dimensional:

∂

∂z

˜

E =

1

2

ik





∂

2

∂t

2

˜

E + B

1

+ B

2

; (7.22)

Gain

SPM

Compression

Chirp

Figure 7.9 Block diagram showing the combination of pulse amplification, SPM, and compression.