Ultrashort Laser Pulse Phenomena, 2nd Edition

Zero Area Pulse Propagation 515

Recent advances in fs photon echo spectroscopy of molecules and solids are

summarized in papers by Ashbury et al. [20] and Dao et al. [21].

In summary, the photon echo method is quite powerful and useful for the

determination of relaxation times longer than the pulse duration. It has been one

of the most commonly used.

10.9. ZERO AREA PULSE PROPAGATION

The photon echo experiment is based on a sequence of two nonoverlapping

pulses whose relative phase is unimportant. An essential feature of coherent exci-

tation is that the excitation depends on the phase of the applied signal. We saw in

Chapter 4 that a sequence of two pulses 180

◦

out-of-phase applied at resonance

to a two-level system, will return that system to the ground state. There will be

no energy loss for this particular pulse sequence, while there will be maximum

absorption if the pulses are in phase. The contrast in absorption for the in phase

pulse sequence—as opposed to the sequence of pulses out-of-phase—can be

used as a measure of coherent interaction, and to determine T

2

. The experimen-

tal setup consists essentially of a Michelson or a Mach–Zehnder interferometer

(Figure 10.16) to produce a zero area pulse.

The measurement is particularly simple and clear in the case of a single homo-

geneously broadened line. A linear (i.e., with a small area pulse) measurement

provides all the information needed in that case. The zero area pulse sequence

has a zero spectral Fourier component at the average pulse frequency. The linear

absorption for that pulse sequence—when applied at resonance with the line—

is proportional to the spectral overlap of the line and the pulse spectrum. For

T

2

=∞, the infinitely narrow line coincides with the node of the spectrum

of the zero area pulse, and there is no absorption. The smaller T

2

, the broader

the line and its overlap with the pulse spectrum. With decreasing T

2

, the ratio of

BS

1

BS

2









Figure 10.16 Michelson or Mach–Zehnder interferometers for the generation of zero area pulses.

The beam splitters BS

1

and BS

2

should be identical, to produce a zero area pulse. The field envelopes

of the pulses are shown.

516 Measurement Techniques of Femtosecond Spectroscopy

absorption for an out-of-phase (zero area) pulse sequence to the absorption for an

in phase pulse sequence will also decrease. An illustration of such a measurement

in Li vapor is shown in Figure 10.17. The energy of the second harmonic of the

transmitted pulse sequence is plotted as function of the delay between the two

components of the pulse.

In the time domain the experiment can be explained as follows. The first signal

emerging out of the interferometer of Fig. 10.16 excites the resonant transition

in lithium vapor. The induced dipoles reradiate a field which opposes the applied

field, and therefore cause absorption. The energy stored in the medium will be

restituted to the second signal emerging out of the interferometer if the latter is

180

◦

out-of-phase with the first pulse (the reradiated field adds in phase with the

applied electromagnetic signal). Maximum absorption occurs for in phase pulse

sequences. The signal versus delay should therefore show an interference pattern

with a periodicity in delay equal to the light period.

The constructive–destructive interferences that extend beyond the region of

pulse overlap decay with the collision time of the resonant sodium atoms with a

buffer gas (Ar, 1000 torr pressure). SH detection was used in that particular exam-

ple [22]. By using SH detection, the transition between the region corresponding

to pulse interferences, and coherent interaction effects, can easily be identified.

010

8

6

4

2

0

20

Delay (ps)

Ar pressure: 1000 torr

Second harmonic intensity

30 40

Figure 10.17 SH detection of the transmission of a zero area pulse sequence consisting of two

delayed pulses through lithium vapor in the presence of argon as buffer gas. The vertical lines

indicate the contrast between in-phase and out-of-phase transmission. The second harmonic of the

transmitted zero area pulse sequence versus delay is recorded. The advantage of the SH detection is

that the first portion of the curve is approximately the interferometric autocorrelation of the pulse.

The transmission corresponding to out-of-phase pulse sequence is the lower envelope near zero delay

(weaker pulse because of destructive interference) and becomes the upper envelope for larger delays

(larger transmission on resonance for out-of-phase pulse sequences).