To gain deeper insight into the dynamic picture of modes coupling and hybridization in the optoplasmonic structure in with the change of external control parameters, we traced the evolution of the optical powerflow through the gap of the Au nanodimer as a function of the excitation wavelength. In
, we compare the intensity spectrum in the dimer gap () with the corresponding spectra of the amplitude and phase of the Poynting vector at the gap center (). The amplitude of the three-dimensional (3D) real-valued Poynting vector
at a given point of space defines the local value of the optical power density. In turn, the Poynting vector phase can be defined in each coordinate plane as
, and characterizes the direction of the optical powerflow through this point. In particular,
) indicates either upward or downward energy flow through the dimer gap, respectively.
Fig. 3 Manipulation of optical powerflow through the nanoantenna gap with vortex nanogates. (a,b) Comparison of the intensity enhancement spectrum in the gap of microsphere-coupled Au dimer (a) with those of the Poynting vector amplitude and phase at the gap (more ...)
Comparison of the spectra in reveals a complex picture of alternating light flow through the dimer gap with the change of the wavelength. The direction of the powerflow reverses from the forward-moving at the frequencies both above and below the resonance to the backward-moving in a narrow range around the resonance wavelength. Essentially, the optoplasmonic structure driven across its hybridized photonic-plasmonic resonance operates as a photonic nanogate, which directs the optical powerflow through the nanosized channel (dimer gap). The gate can be open either ‘Up’ or ‘Down’, corresponding to either forward or backward powerflow, or ‘Closed’ at select wavelengths where the Poynting vector amplitude vanishes (resulting in no powerflow through the gap). It should be noted that the symmetrical coupled-dipole LSP resonance of the isolated nanoparticle dimer is characterized by the enhanced forward powerflow at the resonance frequency.
To better understand the physical processes underlying the operation of the optoplasmonic nanogate, in
we plot the spatial maps of the Poynting vector amplitude and powerflow through the nanodimer at select frequencies around the resonance. Here, each arrow points into the direction of the local powerflow, and its length is proportional to the local value of the power density. The complex 3D structure of the powerflow can be revealed by considering the 2D flow distributions in two perpendicular planes: one cutting along the dimer axis (y-z plane) and the other cutting through the center of the dimer gap (x-z plane) as shown in and , respectively. The powerflow distributions in the y-z plane feature enhanced(suppressed) flow through the dimer gap corresponding to the open (closed) nanogate state. The most revealing, however, is the evolution of the powerflow in the x-z plane, which features formation, evolution and disappearance of local areas of circulating powerflow—optical vortices [33
Fig. 4 Operation of the optoplasmonic vortex nanogate. (a-f) Single-frame excerpts from movies of the Poynting vector intensity |S| maps and the optical power flow through the nanoantenna gap at the frequencies around the photonic-plasmonic Fano resonance shown (more ...)
The physical origin of the optical vortex is the simple fact that the optical energy flows in the direction of the phase change. Therefore, phase singularities (occurring at points of zero field intensity) are always accompanied by the circulation of the optical energy [33
]. Free-space optical vortices occur in the interference field arising from the superposition of three or more partial waves, and can be controllably created by using “forked” holograms, lenses, spiral phase plates, and spatial light modulators. Electromagnetic fields diffracted by photonic and plasmonic nanostructures can also feature optical vortices resulting from the superposition of incident and refracted/reflected waves [58
]. In the considered optoplasmonic nanogate, optical vortices form around the phase singularities emerging in the interference field around the microcavity excited at the wavelength of its WG mode (shown in ). In fact, the well-known
phase-dependence of WG modes [60
] is a signature of the presence of phase singularities in their on-resonance electromagnetic field. In this context, the azimuthal mode index
gives the number of
phase cycles around the optical vortex formed around the microcavity center. However, high-strength vortices—i.e. those with
—are unstable, and typically break up into
vortices of strength
upon perturbation by an external field featuring no vortices (e.g., a constant field or a plane wave).
shows that under excitation by a plane wave with the wavelength approaching that of the hybridized photonic-plasmonic resonance, pairs of coupled counter-rotating optical vortices are formed inside the microcavity. This results in the enhanced backward powerflow just below the microcavity surface and reduces the E-field intensity generated in the gap of the Au nanoparticle dimer located above the surface (observed in ). Tuning of the excitation wavelength across the resonance leads to the nucleation of a pair of vortices of the opposite rotation direction in the Au dimer gap, which completely block the powerflow through the gap (). With the increase of the wavelength, these vortices drift apart from each other and closer to the microcavity surface, and their combined effect yields enhanced backward powerflow through the dimer gap (). Note that the nucleation and annihilation of vortices is accompanied by the formation and disappearance of the powerflow saddle points, in accordance with the topological charge conservation principle [58
]. In particular, a saddle point located just below the Au nanodimer is clearly visible in . Another saddle point accompanies the emergence of the vortex pair in the dimer gap. This point drifts up and down above the dimer, and its position defines the extent of the area with the enhanced backward powerflow (). If the wavelength is further increased, the vortices migrate from the microcavity surface into the microcavity material, which once again reverses the powerflow direction through the dimer gap. At the same time, oppositely-rotating vortices form in the outer evanescent-tail area, yielding the enhanced forward powerflow through the gap as shown in . This enhanced forward powerflow drives the intensity enhancement at the resonant peak observed in . When the excitation wavelength moves away from the resonance, the phase singularities approach and annihilate, resulting in a reduced powerflow through the gap, which leads to a reduction of the near-field intensity in the nanodimer gap.
Various configurations of coupled optical vortices appearing in and
resemble a complex switchable gearbox composed of multiple ‘vortex nanogears’, which can be dynamically rearranged by tuning the control parameters such as wavelength. The nanogears arrangement drives the local powerflow through the optoplasmonic nanogates, which can be reversibly switched into either ‘Open Up/Down’ or ‘Closed’ positions. The coupled vortex nanogears configurations corresponding to different regimes of the nanogate operation are schematically visualized in .