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M. Kauranen et al.
6.4 Early Work
6.4.1 Basic Results
The L-shaped nanoparticles for SHG were originally introduced for autocorrelation
measurements of the plasmon dephasing time in metal nanoparticles [36]. The motivation for our studies, on the other hand, has been to prepare arrays of nanoparticles
with tailorable nonlinear properties. Our very first results already showed that the
efficiency of SHG depends sensitively on how the individual particles are ordered in
the array [37].
Subsequent work, however, soon showed that the expected selection rules between
the allowed and forbidden signals are not well obeyed. The forbidden signals were
then traced to the broken symmetry of the actual samples compared to the ideal,
which could arise from small-scale defects or the deviations of the overall shape
from the ideal. The broken symmetry was found to lead to relatively strong SHG
responses for tensor components forbidden by the ideal symmetry [25, 38, 39]. This
was explained by the fact that small defects can attract very strong spatially confined
fields which can modify local electric-field distribution and significantly affect the
second-order response [40, 41]. In most cases, the forbidden signals were related
to chiral symmetry breaking, i.e., the loss of mirror symmetry with respect to y
axis (Fig. 6.1). More specifically, the SHG signals from nanoparticles with defects
revealed strong chirality even from an array designed to be achiral [25].
6.4.2 Multipole Effects
Various multipole sources of radiation can be distinguished in the far-field by measuring their polarization dependent angular emission patterns. In the case of coherent SHG, however, strong signals are detected only in the transmitted and reflected
directions, preventing the measurement of the full radiation pattern. The radiative
properties of the various multipoles in the two opposite directions lead to differences in interference between electric dipoles and higher multipoles. In particular,
the polarization-dependent SHG response allows different multipolar contributions
to SHG signal to be distinguished [42].
Experimental evidence of multipole interference in the second-harmonic radiation
from an array of metallic L-shaped nanoparticles (length 200 nm, width 100 nm,
period 400 nm) suggested that the contribution of higher multipoles was up to 20 %
of the total emitted SH field amplitude [42]. The NRT approach was used in order
to confirm previous results and to separate the dipolar and higher multipole parts of
all in-plane tensor components. The results showed that the nonlinear response was
dominated by a tensor component associated with chiral symmetry breaking of the
sample [41]. The same tensor component exhibited strong multipole character. The
relation between chiral symmetry breaking and strong multipole effects was due to
M. Kauranen et al.
6.4 Early Work
6.4.1 Basic Results
The L-shaped nanoparticles for SHG were originally introduced for autocorrelation
measurements of the plasmon dephasing time in metal nanoparticles [36]. The motivation for our studies, on the other hand, has been to prepare arrays of nanoparticles
with tailorable nonlinear properties. Our very first results already showed that the
efficiency of SHG depends sensitively on how the individual particles are ordered in
the array [37].
Subsequent work, however, soon showed that the expected selection rules between
the allowed and forbidden signals are not well obeyed. The forbidden signals were
then traced to the broken symmetry of the actual samples compared to the ideal,
which could arise from small-scale defects or the deviations of the overall shape
from the ideal. The broken symmetry was found to lead to relatively strong SHG
responses for tensor components forbidden by the ideal symmetry [25, 38, 39]. This
was explained by the fact that small defects can attract very strong spatially confined
fields which can modify local electric-field distribution and significantly affect the
second-order response [40, 41]. In most cases, the forbidden signals were related
to chiral symmetry breaking, i.e., the loss of mirror symmetry with respect to y
axis (Fig. 6.1). More specifically, the SHG signals from nanoparticles with defects
revealed strong chirality even from an array designed to be achiral [25].
6.4.2 Multipole Effects
Various multipole sources of radiation can be distinguished in the far-field by measuring their polarization dependent angular emission patterns. In the case of coherent SHG, however, strong signals are detected only in the transmitted and reflected
directions, preventing the measurement of the full radiation pattern. The radiative
properties of the various multipoles in the two opposite directions lead to differences in interference between electric dipoles and higher multipoles. In particular,
the polarization-dependent SHG response allows different multipolar contributions
to SHG signal to be distinguished [42].
Experimental evidence of multipole interference in the second-harmonic radiation
from an array of metallic L-shaped nanoparticles (length 200 nm, width 100 nm,
period 400 nm) suggested that the contribution of higher multipoles was up to 20 %
of the total emitted SH field amplitude [42]. The NRT approach was used in order
to confirm previous results and to separate the dipolar and higher multipole parts of
all in-plane tensor components. The results showed that the nonlinear response was
dominated by a tensor component associated with chiral symmetry breaking of the
sample [41]. The same tensor component exhibited strong multipole character. The
relation between chiral symmetry breaking and strong multipole effects was due to