Ultrashort Laser Pulse Phenomena, 2nd Edition

10

Measurement Techniques of

Femtosecond Spectroscopy

10.1. INTRODUCTION

Femtosecond pulses are an ideal tool to investigate ultrafast processes of var-

ious origins. There is usually more than one parameter that varies with time in

any particular experiment. One of these parameters will often be the position.

As an example of the types of time dependence that have to be distinguished, let

us consider the example of an apple falling from a tree (Figure 10.1). A photo-

graph taken with a sufficiently short exposure time can freeze the motion of the

falling apple as it reaches the position x. We can compare this picture with one

of the apple still on the tree, which provides some information about the aging

process. To establish either the law of motion x(t) or the temporal behavior of

aging, we need to know exactly the time elapsed from the moment the apple

was shaken loose from the tree to the moment the photograph was taken. The

standard experimental technique is to trigger the fall (for instance, ignite a small

explosion) and simultaneously start a clock that synchronizes the shutter of the

camera. By triggering the event, we do not have to wait days for the apple to

fall down.

A pump–probe femtosecond experiment has analogies as well as fundamen-

tal differences with the falling apple measurement. The basic analogy is that a

powerful light pulse—usually labeled the “pump pulse” or “excitation pulse”—

interacts with the sample and excites it into a nonequilibrium state (Figure 10.2).

The sample thereafter relaxes toward a new equilibrium state. This process can

be mapped by sending a second (much weaker) pulse, called a probe or test

491

492 Measurement Techniques of Femtosecond Spectroscopy

x

x

t

Figure 10.1 The falling apple and the aging apple.

Probe

Pump

Sample

D

0Delay

S

S

Delay

Figure 10.2 Schematic representation of a pump–probe experiment in ultrafast spectroscopy. The

pump and probe pulses can be obtained from a single source and delayed with respect to each other

in a Michelson or a Mach–Zehnder interferometer, for example.

(pulse), onto the sample. The probe is the analog of the snapshot photograph,

aimed at detecting a change of optical properties without disturbing the object

under investigation. The difference with the falling apple is that the speed of

light is infinite compared to the velocity of the apple, whereas the propagation

time of the probe radiation through the sample can be long compared with the

event to be observed. Therefore, the geometry of interaction, the angle between

probe and pump, the interaction length, and the group velocities in the sample

are essential parameters in femtosecond pump–probe experiments.

In a typical pump–probe experiment, the delayed weak pulse probes the

change of an optical property S, such as transmission or reflection, induced

by the pump. Repeating the experiments for various delays τ

d

provides the func-

tion S(τ

d

). Depending on the actual light–matter interaction, S(τ

d

) is related