Ultrashort Laser Pulse Phenomena, 2nd Edition

414 Femtosecond Pulse Amplification

Stretcher Amplifier Compressor

Figure 7.11 Block diagram of chirped pulse amplification.

linear, two essential conditions have to be met by the amplifier:

• the amplifier bandwidth exceeds that of the pulse to be amplified; and

• the amplifier is not saturated.

It is only if these two conditions are met that the original pulse duration can

be restored by the conjugated dispersion line. It is not unusual to operate an

amplifier in the wings of its gain profile, where the first condition is best met.

For instance, Ti:sapphire, with its peak amplification factor close to 800 nm,

is used as an amplifier for 1.06 µm, because of its flat gain profile in that

wavelength range. A pulse energy of 1 mJ has been obtained in such a Ti:sapphire

amplifier chain, corresponding to a gain of 10

7

. Further linear amplification

with Ti:sapphire requires rods of too large a diameter to be economical. With

Nd:glass as a gain medium pulse energies as large as 20 J were obtained [5].

Because of the bandwidth limitation in the last 10

4

factor of amplification,

the recompressed pulse has a duration of 400 fs, a fivefold stretch from the

original 80 fs.

7.5. AMPLIFIER DESIGN

7.5.1. Gain Media and Pump Pulses

Parameters of gain media crucial for the amplification of fs pulses are:

• The interaction cross section. For a given amplifier volume (inverted vol-

ume) this parameter determines the small signal gain and the maximum

Amplifier Design 415

possible energy per unit area that can be extracted from the system. The

latter is limited by gain saturation.

• The energy storage time of the active medium. If there is no ASE, this time

is determined by the lifetime of the upper laser level T

10

and indicates (a)

how long gain is available after pump pulse excitation for τ

pump

< (<)T

g

or

(b) how fast a stationary gain is reached if τ

pump

> (>)T

g

. The corresponding

response time can be significantly shorter if ASE occurs, it is then roughly

given by:

T

ASE

=

ω

ASE

I

ASE

(L)σ

ASE

. (7.25)

When short pump pulses are used, the latter quantity provides a measure

of the maximum jitter allowable between pump and signal pulse without

perturbing the reproducibility of amplification.

• The spectral width of the gain profile ω

g

= (ω

g

/λ

g

)λ

g

and the nature

of the line broadening. The minimum pulse duration (or maximum pulse

bandwidth) that can be maintained by the amplification process is of the

order of 2π/ω

g

(or ω

g

).

These parameters were given in Table 7.1 for typical materials used as gain

media in fs amplifiers. The wavelength and bandwidth of the seed pulse dic-

tates the choice of the gain medium. Presently, it is only in the near infrared

that a selection can be made among various types of gain media, dyes, and

solid-state materials for fs pulse amplification. At pulse durations of the order

of 10

−14

s gain narrowing effects of single dyes dominate [3] leading to pulse

broadening. These difficulties can be overcome by using a mixture of several

dyes with different transition frequencies providing optimum amplification for

a broad input spectrum [22]. The achievable energies with dye amplifiers are

on the order of 1 mJ. This value is determined by the saturation energy den-

sity and the dye volume that can be uniformly pumped with available pump

lasers.

Shorter pulses and higher energies can, in principle, be extracted from cer-

tain solid-state amplifiers. With the additional advantage of compactness, such

systems are attractive candidates for producing pulses in the TW and PW range.

These systems are typically limited to the red and near infrared spectral range.

At certain wavelengths in the UV (Table 7.1) excimer gases can be used for

fs pulse amplification (see for example, Glownia et al. [11], Szatmari et al. [12],

Watanabe et al. [23], Taylor et al. [24], Heist et al. [25], and Mossavi

et al. [26]). The interaction cross-section being similar to that of dyes, the satura-

tion energy density of excimer gain media is also of the order of millijoules/cm

2

.