7 Label-Free Pump–Probe Nanoscopy
179
7.2.2 Pump–Probe Signal Information
The pump–probe signal T is extracted from the total signal with a lock-in amplifier and its amplitude R = |T | can be retrieved, which is linearly dependent on
the applied powers and on the analyte concentration, as introduced in (1.2). With a
more advanced two-phase lock-in amplifier, the phase difference θ of the demodulated signal with respect to the reference pump modulation can also be recovered.
Two outputs, X = R cos θ (in-phase component) and Y = R sin θ (quadrature component), are obtained which represent the signal as a vector relative to the lock-in
reference oscillator. The modulus can be retrieved as R =
√
X 2 + Y 2 and the phase
as tan θ = Y /X .
Depending on the type of nonlinear absorption interaction, one of the two situations may occur, as sketched in Fig. 7.3a. The probe beam can experience a gain
in its transmission (or reflection), equivalent to an in-phase pump–probe signal
with amplitude > 0, θ = 0
◦
, X = R, Y = 0). This is the case of ground-state
depletion (GSD) and stimulated emission (SE) interactions. The probe beam can
alternatively experience a loss, equivalent to an anti-phase pump–probe signal with
amplitude < 0, θ = 180
◦
, X = −R, Y = 0. This is the case in two-photon absorption (TPA) and excited state absorption (ESA) interactions. This means that the type
of interaction can be distinguished by looking at the phase of the signal or at the sign
of the X component.
Varying the delay between pump and probe pulses (t in Fig. 7.3a), the
pump–probe signal intensity will vary according to the excited state relaxation
dynamics of the involved species. The obtained time-resolved spectra will feature
a maximum pump–probe signal when pump and probe pulses are overlapped, and
an exponential decrease with increasing delay. The extrapolation of a single- or
multiple-decay constant increases the molecular specificity of the technique, and
may help in the discrimination of different sample components. The time traces can
be analyzed in the time domain, performing multi-exponential fitting to derive the
characteristic decay constants. Alternatively, time-resolved spectra can be analyzed
in the frequency domain with the phasor analysis introduced for fluorescence lifetime
imaging [22], which provides an intuitive graphical view of the lifetimes without any
a priori assumption. It was proven that the application of the phasor analysis with
pump–probe imaging provides a robust method for efficiently distinguishing pigments in biological and in art samples [23], avoiding the fitting procedure which
typically requires high SNRs for a reliable separation of the different components.
Moreover, TPA and ESA processes, which cannot be distinguished with the phase
information, can be easily distinguished by looking at their temporal behavior. TPA is
an instantaneous process exhibiting a symmetric cross-correlation trace, while ESA
shows an instantaneous rise followed by a decay reflecting the characteristic lifetime
of the excited state [8].
179
7.2.2 Pump–Probe Signal Information
The pump–probe signal T is extracted from the total signal with a lock-in amplifier and its amplitude R = |T | can be retrieved, which is linearly dependent on
the applied powers and on the analyte concentration, as introduced in (1.2). With a
more advanced two-phase lock-in amplifier, the phase difference θ of the demodulated signal with respect to the reference pump modulation can also be recovered.
Two outputs, X = R cos θ (in-phase component) and Y = R sin θ (quadrature component), are obtained which represent the signal as a vector relative to the lock-in
reference oscillator. The modulus can be retrieved as R =
√
X 2 + Y 2 and the phase
as tan θ = Y /X .
Depending on the type of nonlinear absorption interaction, one of the two situations may occur, as sketched in Fig. 7.3a. The probe beam can experience a gain
in its transmission (or reflection), equivalent to an in-phase pump–probe signal
with amplitude > 0, θ = 0
◦
, X = R, Y = 0). This is the case of ground-state
depletion (GSD) and stimulated emission (SE) interactions. The probe beam can
alternatively experience a loss, equivalent to an anti-phase pump–probe signal with
amplitude < 0, θ = 180
◦
, X = −R, Y = 0. This is the case in two-photon absorption (TPA) and excited state absorption (ESA) interactions. This means that the type
of interaction can be distinguished by looking at the phase of the signal or at the sign
of the X component.
Varying the delay between pump and probe pulses (t in Fig. 7.3a), the
pump–probe signal intensity will vary according to the excited state relaxation
dynamics of the involved species. The obtained time-resolved spectra will feature
a maximum pump–probe signal when pump and probe pulses are overlapped, and
an exponential decrease with increasing delay. The extrapolation of a single- or
multiple-decay constant increases the molecular specificity of the technique, and
may help in the discrimination of different sample components. The time traces can
be analyzed in the time domain, performing multi-exponential fitting to derive the
characteristic decay constants. Alternatively, time-resolved spectra can be analyzed
in the frequency domain with the phasor analysis introduced for fluorescence lifetime
imaging [22], which provides an intuitive graphical view of the lifetimes without any
a priori assumption. It was proven that the application of the phasor analysis with
pump–probe imaging provides a robust method for efficiently distinguishing pigments in biological and in art samples [23], avoiding the fitting procedure which
typically requires high SNRs for a reliable separation of the different components.
Moreover, TPA and ESA processes, which cannot be distinguished with the phase
information, can be easily distinguished by looking at their temporal behavior. TPA is
an instantaneous process exhibiting a symmetric cross-correlation trace, while ESA
shows an instantaneous rise followed by a decay reflecting the characteristic lifetime
of the excited state [8].