Ultrashort Laser Pulse Phenomena, 2nd Edition

Pulse Amplitude and Phase Reconstruction 473

intensity autocorrelation. Obtaining such an intensity autocorrelation, however,

assumes that the beams coming from both arms of the correlator add construc-

tively toward the detector, destructively toward the source. Such a condition is

difficult to implement, because it requires subwavelength stability and accuracy

in controlling either arm. For this particular correlator, it is more convenient to

introduce a small tilt of either end mirror of the Michelson interferometer. Such

a tilt produces a pattern of parallel fringes at the output. Before the frequency

doubling crystal, we have thus generated a first-order correlation. The second

harmonic of such a first-order correlation is an interferometric correlation [22].

This arrangement has the advantage that one has complete control over the spac-

ing of the fringes, which can be adjusted to accommodate the spatial resolution

of the array detector used in this measurement. An example of an interferomet-

ric autocorrelation obtained with a fs UV pulse is shown in Fig. 9.7. For this

particular case, the nonlinearity is two-photon fluorescence in BaF

2

.

9.4. PULSE AMPLITUDE AND PHASE

RECONSTRUCTION

9.4.1. Introduction

Because the second-order autocorrelations are symmetric and do not provide

any information about the pulse asymmetry, either an additional measurement

or a new technique is required to determine the signal shape. We will start with

simple methods that complement the information of the autocorrelations, and pro-

ceed with an overview of various methods that have been introduced to provide

amplitude and phase information on fs signals. The ideal diagnostic instrument

is obviously one that would give a real time display of all pulse parameters.

Because of the ambiguity associated with an average over a large number of

pulses, a single-shot method is also desirable. The challenge in fs pulse char-

acterization is that a temporal resolution is needed that is faster than the pulse

itself. The solution, as sketched in Figure 9.8, is to apply a transfer function to

expand the signal. From the knowledge of the transfer function and the expanded

signal the shape of the original object is recovered.

As introduced in Chapter 1 a light pulse in the time domain is characterized

by its electric field

E(t) =

1

2

E(t)e

iϕ

0

e

iϕ(t)

e

iω



t

+ c. c. (9.29)

In this section we are concerned with the retrieval of the pulse envelope E(t) and

the time-dependent phase ϕ(t) only. The measurement and control of the absolute

phase ϕ

0

are described in Chapter 13.