Box 3.
Box 3.
Principle of Time-Resolved Nonlinear Optical Spectroscopy Experiments
In the generic experimental configuration for time-resolved
nonlinear optics experiments one, generally weak, laser pulse,
E1(t), propagating in the
direction k⃗1 is incident on the
sample at time t1. Pulse 1 alone would
probe the linear properties of the sample, and hence is called the
probe pulse. A second laser pulse,
E2(t), often called the
pump pulse, propagating in the direction
k⃗2 and delayed from the first
pulse by Δt = t2 −
t1, produces a further perturbation of
the sample. Because of the nonlinearities in semiconductors the
response of the sample to the total field
ET(t) =
E1(t) +
E2(t) is not the sum of the
responses to each field, the propagation of the probe pulse,
E1(t), is modified and
other fields are generated.
In general two types of measurements can be performed. They are called
pump/probe and coherent wave mixing experiments. In the first
category the small changes in sample transmission, T, seen
by the probe pulse and induced by the pump pulse are measured. In the
small signal regime, the differential transmission spectrum,
ΔT/T =
[T(E2) −
T(E2 =
0)]/T(E2 = 0),
reproduces the changes in the absorption spectrum of the sample,
α(ω), because ΔT/T ≈−Δα(ω)
× l, where l is the sample thickness. In the
second category, the two fields coherently interfere in the sample via
some nonlinearity. They generate several nonlinear polarization waves
that contain one contribution,
Ps(t,Δt),
emitting photons in background-free directions, for example
k⃗s =
2k⃗2 −
k⃗1. This type of experiment
measures a signal that is determined by the coherent nonlinear
polarization. For each delay, this signal can be time-resolved by use
of an ultrafast detection technique,
STR(t,Δt)∝|Ps(t,Δt)|2,
or it can be frequency resolved by a spectrometer
SFR(ω,Δt)∝|Ps(ω,Δt)|2.
In the case of atomic-like systems the profile of
STR(t,Δt) is a
step function followed by an exponentially decaying tail characterizing
the decoherence of the polarization. For this reason, the easiest and
most commonly used measurement technique, is to integrate the coherent
wave mixing signal with a slow detector, as Δt is varied.
This determines the so-called time-integrated signal,
STI(Δt), which, for
atomic systems, reproduces as a function of Δt the same
temporal behavior as
STR(t,Δt) vs.
t at any fixed Δt. As discussed in the text,
this is not the case for interacting systems like semiconductors.
Principle of Time-Resolved Nonlinear Optical Spectroscopy Experiments
In the generic experimental configuration for time-resolved
nonlinear optics experiments one, generally weak, laser pulse,
E1(t), propagating in the
direction k⃗1 is incident on the
sample at time t1. Pulse 1 alone would
probe the linear properties of the sample, and hence is called the
probe pulse. A second laser pulse,
E2(t), often called the
pump pulse, propagating in the direction
k⃗2 and delayed from the first
pulse by Δt = t2 −
t1, produces a further perturbation of
the sample. Because of the nonlinearities in semiconductors the
response of the sample to the total field
ET(t) =
E1(t) +
E2(t) is not the sum of the
responses to each field, the propagation of the probe pulse,
E1(t), is modified and
other fields are generated.
In general two types of measurements can be performed. They are called
pump/probe and coherent wave mixing experiments. In the first
category the small changes in sample transmission, T, seen
by the probe pulse and induced by the pump pulse are measured. In the
small signal regime, the differential transmission spectrum,
ΔT/T =
[T(E2) −
T(E2 =
0)]/T(E2 = 0),
reproduces the changes in the absorption spectrum of the sample,
α(ω), because ΔT/T ≈−Δα(ω)
× l, where l is the sample thickness. In the
second category, the two fields coherently interfere in the sample via
some nonlinearity. They generate several nonlinear polarization waves
that contain one contribution,
Ps(t,Δt),
emitting photons in background-free directions, for example
k⃗s =
2k⃗2 −
k⃗1. This type of experiment
measures a signal that is determined by the coherent nonlinear
polarization. For each delay, this signal can be time-resolved by use
of an ultrafast detection technique,
STR(t,Δt)∝|Ps(t,Δt)|2,
or it can be frequency resolved by a spectrometer
SFR(ω,Δt)∝|Ps(ω,Δt)|2.
In the case of atomic-like systems the profile of
STR(t,Δt) is a
step function followed by an exponentially decaying tail characterizing
the decoherence of the polarization. For this reason, the easiest and
most commonly used measurement technique, is to integrate the coherent
wave mixing signal with a slow detector, as Δt is varied.
This determines the so-called time-integrated signal,
STI(Δt), which, for
atomic systems, reproduces as a function of Δt the same
temporal behavior as
STR(t,Δt) vs.
t at any fixed Δt. As discussed in the text,
this is not the case for interacting systems like semiconductors.