Ultrashort Laser Pulse Phenomena, 2nd Edition

6

Ultrashort Sources II: Examples

In the previous chapter the elements of passive mode-locking and their

function for pulse shaping were described in detail. Analytical and numerical

methods of characterizing mode-locked lasers were presented. Passive mode-

locking is indeed the most widely applied and successful technique to produce

pulses whose bandwidth approaches the limits imposed by the gain medium of

dye and solid-state lasers including fiber lasers. Passive mode-locking was the

technique of choice to produce sub 50-fs pulses in dye lasers and, today, is rou-

tinely applied in solid-state and fiber lasers. Sub 5-fs pulses have been obtained

from Ti:sapphire lasers without external pulse compression [1] using this method.

In this chapter we will review additional techniques of mode-locking and

discuss examples of mode-locked lasers. The purely active or synchronous mode-

locking will be covered first, followed by the hybrid passive–active technique.

Other techniques not discussed in the previous chapter are additive mode-locking,

methods based on second-order nonlinearities, and passive negative feedback. For

their important role as saturable absorbers we will review the relevant properties

of semiconductor materials. The later part of this chapter is devoted to specific

examples of popular lasers.

6.1. SYNCHRONOUS MODE-LOCKING

A simple method to generate short pulses is to excite the gain medium at a

repetition rate synchronized with the cavity mode spacing. This can be done by

using a pump that emits pulses at the round-trip rate of the cavity to be pumped.

One of the main advantages of synchronous mode-locking is that a much broader

341

342 Ultrashort Sources II: Examples

range of gain media can be used than in the case of passive mode-locking. This

includes semiconductor lasers and, for instance, laser dyes such as styryl 8, 9,

and 14, which have too short a lifetime to be practical in cw operation, but are

quite efficient when pumped with short pulses.

Ideally, the gain medium in a synchronously pumped laser should have a short

lifetime, so that the duration of the inversion is not larger than that of the pump

pulse. An extreme example is the case of optical parametric oscillators (OPO)

where the gain lives only for the time of the pump pulse.

Synchronous pumping is sometimes used in situations that do not meet this

criterion, just as starting mechanism. This is the case in some Ti:sapphire lasers,

where the gain medium has a longer lifetime than the cavity round-trip time, and

therefore synchronous pumping results in only a small modulation of the gain.

The small modulation of the gain coefficient α

g

(t) is sufficient to start the pulse

formation and compression mechanism by dispersion and SPM [2]. The initial

small gain modulation grows because of gain saturation by the modulated intra-

cavity radiation, resulting in a shortening of the function α

g

(t), and ultimately

ultrashort pulses.

The simple considerations that follow, neglecting the influence of saturation,

show the importance of cavity synchronism. If the laser cavity is slightly longer

than required for exact synchronism with the pump radiation (train of pulses),

stimulated emission and amplified spontaneous emission will constantly accu-

mulate at the leading edge of the pulse, resulting in pulse durations that could

be even longer than the pump pulse. Therefore, to avoid this situation, the cavity

length should be slightly shorter than that required for exact synchronism with

the pump radiation. Let us assume first perfect synchronism. The net gain factor

per round-trip is

G(t) = e

[α

g

(t)d

g

−L]

, (6.1)

where L is the natural logarithm of the loss per cavity round-trip. After n

round-trips, the initial spontaneous emission of intensity I

sp

has been amplified

sufficiently to saturate the gain α

g

, and thus the pulse intensity is approximately

I(t) ≈ I

sp

×



e

[α

g0

(t)d

g

−L]



n

= I

sp

×[G

0

(t)]

n

. The pulse is thus

√

n times narrower

than the unsaturated gain function G

0

(t).

For a cavity shorter than required for exact synchronism, in a frame of refer-

ence synchronous with the pulsed gain α

g

(t), the intracavity intensity of the j

th

round-trip is related to the previous one by:

I

j

(t) = I

j−1

(t + δ)e

[α

g

(t)d

g

−L]

, (6.2)

where δ is the mismatch between cavity round-trip time and the pump pulse

spacing. The net gain for the circulating pulse e

[α

g

(t)d

g

−L]

exists in the cavity for