Ultrashort Laser Pulse Phenomena, 2nd Edition

Data Deconvolutions 493

to material parameters such as occupation numbers, carrier density, and molecular

orientation. In this chapter we discuss a selection of fs experimental techniques,

many of them originally developed for ps and ns spectroscopy.

The obvious temporal limitation of the pump–probe technique is the duration

of the pump and probe. The medium preparation should be completed before

the material can be probed. If the physics of the interaction is well understood,

a theoretical modeling (deconvolution) can provide some interpretation of data

corresponding to partial temporal overlap of pump and probe.

A compromise often must be sought between spectral and temporal resolution.

Either the probe or the pump pulse has to select a specific spectral feature. To

excite the desired transition, rather than an adjacent one, the excitation spectrum

(i.e., the pulse spectral width ω

p

, augmented by the Rabi frequency κE or

power broadening of the transition, if needed) should not exceed the separation

between lines . The spectral resolution imposes therefore a limit to the temporal

resolution, because the pulse duration should not be less than τ

p

≈ 1/( + κE).

10.2. DATA DECONVOLUTIONS

In most fs time-resolved experiments, a signal S(τ

d

) is measured as a function

of position or delay τ

d

of a reference probe pulse of intensity I

ref

(t). We will

consider the large class of measurements where the measured quantity is propor-

tional to the product of a gating function I

g

times the physical quantity f (t)to

be analyzed. The gate I

g

(t) is a direct function of the reference intensity I

ref

(t).

Because—as pointed out in the previous chapter—the detection electronics has

no fs resolution, the measured signal will be the time integral:

S(τ

d

) =



∞

−∞

I

g

(t − τ

d

)f (t)dt. (10.1)

Deconvolution procedures should thus be applied to retrieve the physical quan-

tity f (t) from the measurement S(τ

d

). A typical example is a measurement of

time resolved fluorescence by upconversion. As detailed in Section 10.7, the

detected upconversion radiation results from mixing the signal (fluorescence)

and the reference pulse in a nonlinear crystal. Therefore, in that particular case,

the gate function is the reference pulse itself I

g

(t) = I

ref

(t). It is often assumed

that the gating function in the correlation product [Eq. (10.1)] is much shorter

than the fastest transient of the signal and thus can be approximated by a δ func-

tion. With that simplifying assumption, the signal is directly proportional to the

physical parameter to be measured: S(τ

d

) ∝ f (τ

d

). There are, however, fast

events—such as the rise of fluorescence—for which this simplifying assumption

is not valid. The exact temporal dependence f (τ

d

) can be extracted from the data