5 Coherent Nonlinear Processes in Metal-Semiconductor …
109
optical properties of the coupled system are well explained within the framework
of a coupled oscillator model discussed above. Since in this case, it is an ensemble of molecules interacting with multiple SPP modes, the dipole coupling is given
by NMS = 2
µ eff (r) · E SPP (r)d
3 r . Here, µ eff ∝
√
N denotes an effective dipole
moment density and N is the exciton number. E SPP (r) gives the average strength
of the local SPP vacuum electric field fluctuations at position r [23, 25–27]. The
simulated reflectivity spectra obtained using the coupled oscillator model and Bloch
equations are shown in Fig. 5.2b [25–27]. The experimentally obtained and calculated reflectivity spectra near the anti-crossing and the dispersion relations of the
coupled modes are compared in Fig. 5.2c and d, respectively.
At the zero exciton-SPP detuning (∼ 30
◦ ), both polaritons contain 50% exciton
and SPP fractions however, the collective polariton modes display strikingly different
amplitudes and widths under resonant condition. The difference can arise due to the
co-operative damping arising due to the inherent damping of excitons and SPPs [26,
35, 36]. The difference in the damping of the collective modes is known as sub- and
super-radiance. Such co-operative damping has been observed in many strongly coupled systems like trapped ions, QDs, and SPPs [8, 26, 35, 36, 40]. The experimental
results strongly suggest that the optical properties of the hybrid systems are largely
governed by the interplay between the coherent as well as the incoherent energy
exchange processes between excitons and SPPs. Even though excitons and SPPs
are fundamentally very different, the co-operative damping opens up possibility of
tailoring the polariton dynamics. Since the radiative damping of SPPs is much faster
compared to excitons, the co-operative damping effects are relatively weaker. If both
subsystems are resonant and have equal radiative damping rates ( exc = SPP ), one
of the polariton mode will decay with very fast rate, whereas another will not decay
at all. In other words, one of the modes is transformed into a perfectly dark mode
(with zero decay rate), which is completely decoupled from the environment [8, 26,
35]. Thus, co-operative damping can lead to enhancement or total suppression of
spontaneous emission or population trapping induced completely by vacuum field
fluctuations. Such a tailoring of polariton dynamics is promising for developing
quantum plasmonic devices [41–44].
5.3 Polariton Dynamics
We now turn to nonlinear response of the metal-J-aggregate hybrid nanostructure. As
mentioned in the earlier section, in an ensemble of emitters interacting with multiple
SPP modes, the Rabi frequency is independent of the number of photons present
in each mode. Hence one might think that metal-J-aggregate hybrid structures are
not likely to exhibit any nonlinear response. On the other hand, exciton and SPP are
fundamentally different with exciton exhibiting a strong optical nonlinearity. Since
polaritons are formed due to mixture of excitons and SPPs, polaritons also exhibit
nonlinearity like exciton. In this section we discuss experiments performed to investigate incoherent as well coherent polariton dynamics using nonlinear spectroscopy.
109
optical properties of the coupled system are well explained within the framework
of a coupled oscillator model discussed above. Since in this case, it is an ensemble of molecules interacting with multiple SPP modes, the dipole coupling is given
by NMS = 2
µ eff (r) · E SPP (r)d
3 r . Here, µ eff ∝
√
N denotes an effective dipole
moment density and N is the exciton number. E SPP (r) gives the average strength
of the local SPP vacuum electric field fluctuations at position r [23, 25–27]. The
simulated reflectivity spectra obtained using the coupled oscillator model and Bloch
equations are shown in Fig. 5.2b [25–27]. The experimentally obtained and calculated reflectivity spectra near the anti-crossing and the dispersion relations of the
coupled modes are compared in Fig. 5.2c and d, respectively.
At the zero exciton-SPP detuning (∼ 30
◦ ), both polaritons contain 50% exciton
and SPP fractions however, the collective polariton modes display strikingly different
amplitudes and widths under resonant condition. The difference can arise due to the
co-operative damping arising due to the inherent damping of excitons and SPPs [26,
35, 36]. The difference in the damping of the collective modes is known as sub- and
super-radiance. Such co-operative damping has been observed in many strongly coupled systems like trapped ions, QDs, and SPPs [8, 26, 35, 36, 40]. The experimental
results strongly suggest that the optical properties of the hybrid systems are largely
governed by the interplay between the coherent as well as the incoherent energy
exchange processes between excitons and SPPs. Even though excitons and SPPs
are fundamentally very different, the co-operative damping opens up possibility of
tailoring the polariton dynamics. Since the radiative damping of SPPs is much faster
compared to excitons, the co-operative damping effects are relatively weaker. If both
subsystems are resonant and have equal radiative damping rates ( exc = SPP ), one
of the polariton mode will decay with very fast rate, whereas another will not decay
at all. In other words, one of the modes is transformed into a perfectly dark mode
(with zero decay rate), which is completely decoupled from the environment [8, 26,
35]. Thus, co-operative damping can lead to enhancement or total suppression of
spontaneous emission or population trapping induced completely by vacuum field
fluctuations. Such a tailoring of polariton dynamics is promising for developing
quantum plasmonic devices [41–44].
5.3 Polariton Dynamics
We now turn to nonlinear response of the metal-J-aggregate hybrid nanostructure. As
mentioned in the earlier section, in an ensemble of emitters interacting with multiple
SPP modes, the Rabi frequency is independent of the number of photons present
in each mode. Hence one might think that metal-J-aggregate hybrid structures are
not likely to exhibit any nonlinear response. On the other hand, exciton and SPP are
fundamentally different with exciton exhibiting a strong optical nonlinearity. Since
polaritons are formed due to mixture of excitons and SPPs, polaritons also exhibit
nonlinearity like exciton. In this section we discuss experiments performed to investigate incoherent as well coherent polariton dynamics using nonlinear spectroscopy.