Engineering of light-matter interactions at nanoscale dimensions has been acknowledged as one of the primary branches of optical physics, and it has been verified that the strong interaction of an incident light with noble metal nanostructures at a certain optical frequency causes generation of surface plasmon resonance (SPRs), which correspond to the coherent oscillations of free electrons in the conduction band of the utilized subwavelength structures [1-6]. It is verified that the plasmonic properties of the metal structures in nanoscale can be characterized by classical electromagnetic theory, which provides analogous behavior to the atoms’ and molecules’ wave functions [7, 8]. On the other hand, near-field coupling between closely adjacent or neighbor nanoparticles has been considered as one of the important subfields of plasmonic notions [9-14]. Conventionally, robust plasmon resonance coupling can take place in adjacent metal nanoparticles which are known as a dimer, and a pair of particles is the simplest example of these nanostructures [15-18]. Prodan
Plasmonic nanostructures based on metallic nanoparticles have extensively been utilized in designing all-optical devices, which gives us opportunity to manipulate the plasmon resonance modes at particular frequencies [23-29]. Most of associated works prove that significant losses and dissipations appear during guiding of optical waves during electric plasmon propagation, and these destructive components cause dramatic limitations in the propagation distance. Liu
In this article, we employ Au nanoshells with Johnson-Christy constants to design heptamer clusters that are oriented in triphenylene molecular orientation [30, 31]. Utilizing the triphenylene structure and also extending the number shell heptamers in triphenylene molecular orientation, we designed a long range and efficient 1×4 Y-shape optical power splitter. Offset distance as a key part in designing of this device has been tailored numerically and the results presented. Finite-difference time-domain method (FDTD) as a simulation tool is used in our numerical approach to calculate the unique behavior of these proposed structures [34, 35]. Finally, we compare the optical properties and performance of our proposed nanoshell-based structure with an analogous splitter based on rod particles in the same orientation.
The rest of this work is organized as follows: In Section 2, the optical characteristics and plasmonic coupling modality between nanoshell and nanorod heptamers which are oriented in a triphenylene structure have been investigated numerically. Using the results of the accomplished modifications on the shells and rods dimensional sizes regarding to the extinction spectra and plasmon coupling intensity, we provided an efficient artificial blueprint of the shell heptamers to operate at the telecommunication spectrum. In Section 3, we studied the proposed 1×4 Y-splitters based on the examined heptamers composed of rods and shells that are situated as a triphenylene configuration. The optical properties of both of the splitters have been evaluated and the efficient and preferred solution is introduced.
In this section, the optical properties of Au nanorods and shells which are ordered as a triphenylene configuration are investigated briefly. First, we examine two traditional Au nanoparticles for heptamer structures to provide an accurate cluster that can be exploited at the telecommunication spectrum (λ~1550 nm). Figure 1 demonstrates the schematic diagram of the triphenylene nanostructure based on rod and shell heptamers. All of these particles are embedded in a glass host with a permittivity of ε~2.5. Considering structural modifications in the adjacent clusters, we evaluated the plasmon resonance and extinction spectral profile for this structure. To do this, an electric dipole source with transverse polarization direction has been applied which is located at 2R away from the first nanoparticles of the main heptamer (left heptamer). By locating plasmon resonance position at λ~1550 nm, based on the geometrical sizes of rod and shell particles, this distance is determined as 252 nm and 235 nm for rod and shell particles, respectively. Jung
[FIG. 1.] Three-dimensional schematics of plasmonic triphenylene nanostructures based on nanorod and nanoshell heptamers which are filled by and embedded in a glass dielectric substance as a host with a permittivity of ε~2.5. The chemical and physical characteristics of nanoparticles are completely identical in each one of the triphenylene structures. The geometrical sizes for shell heptamers are (inner radius, thickness, height)＝(Ri,T,H)＝(122.5 nm, 90.5 nm, 40 nm), for rod heptamers are (R,H)＝(126 nm, 40 nm). All of the proximal particles in each one of plasmonic triphenylene structures are adjusted to have 2 nm distance between every particle and the neighbor ones.
[FIG. 2.] Simulation results of the scattering cross-section diagrams for the Au rod and shell heptamers in plasmonic triphenylene nanostructures, (a) transverse mode excitation: the resonance of plasmon mode has occurred around the λ~1500 nm for nanorod, and the other minima relating to the Fano-like resonance, (b) longitudinal mode excitation: the resonance of plasmon mode has occurred around the λ~1450 nm and for nanorod, and the other minima relating to the Fano-like resonance.
[FIG. 3.] Two-dimensional snapshots of plasmonic triphenylene structures under transverse electric excitation by an electric dipole source with the amplitude of 1.15×10-8 mA (the polarization direction of the incident field is indicated by an arrow), (a) illuminating the rod heptamers by an incident electric dipole, and the excited plasmon modes have coupled and propagated through the heptamers, (b) the shell heptamers have excited by an incident transverse electric mode, (c) absorption (dissipative component) cross-section for Au nanoshell and nanorod heptamers in plasmonic triphenylene structure.
FDTD parameters descriptions and settings are listed in this table for investigating the optical properties of the 1×4 Y-splitter numerically
Parameters and settings of employed dipole sources are listed in this table
In this section, we demonstrate a new application of Au rods and shells heptamers which are oriented in a triphenylene structure. Figure 4 shows the schematic diagram of a Y-shape splitter which includes an input port and four output ports (1×4 Y-splitter). The most important point here is that due to the symmetry in physical configuration of the proposed Y-splitters composed of rod and shell heptamers, the momentum of the electric dipole of an incident magnetic plasmon resonance is insignificant and almost zero, which verifies the dark mode existence in this guidance regime. In addition, it has been strongly verified that that elucidated dark mode is extremely infrequent during utilization of a plane wave source in normal mode, which corresponds to the deviation of the employed nanoshells and rods sizes in all of the arranged heptamers [8, 31]. Here, we applied this mode in FDTD simulation settings, especially when using the electric dipole source which includes localized fields. Considering investigated plasmonic triphenylene structures composed of rod and shell heptamers and extending the number of clusters in the propagation direction (
[FIG. 4.] (a) Three-dimensional schematics of four-branch Y-splitters plasmonic triphenylene nanostructures based on nanorod heptamers, (b) Three-dimensional schematics of four-branch Y-splitters plasmonic triphenylene nanostructures based on nanoshell heptamers. The chemical and physical characteristics of nanoshells are completely similar through the device.
Continuing using the mentioned magnetic dipole sources which are indicated by arrows in Figs. 5(a) and 5(b), the magnetic field is distributed along the plasmon waveguide by coupling between shared or mutual particles of the heptamers in both 1×4 rod and shell-based Y-splitters. These depictions are two-dimensional (
[FIG. 5.] Illuminating both of the 1×4 Y-splitters that are based on rod and shell nanoclusters arrays by magnetic dipole source, (a) four-branch Y-splitter based on bulk Au nanorod heptamers that are extended in the propagation axis (x-axis) and magnetic dipole source with an amplitude of 1.12×10-20 m2A is located at the center of first and main heptamer and the nanoparticle of this heptamer has omitted, (b) four-branch Y-splitter based on bulk Au nanoshell heptamers with examined dimensions that are extended in the propagation axis (x-axis) and magnetic dipole source with an amplitude of 1.12×10-20 m2A is located at the center of first and main heptamer and the nanoparticle of this heptamer has been omitted.
[FIG. 6.] Real-time averaged power variations along the splitting direction (y-axis), (a) the power variations for both of the small and big dividing units of the splitter based on rod heptamers have been illustrated and this diagram is utilized in transported power calculations, (b) the power variations for both of the small and big dividing units of the splitter based on shell heptamers have illustrated and this diagram has utilized in transported power calculations, (c) this diagram compares the decaying length of the magnetic transverse mode distribution along the propagation direction (x-axis). The real-time averaged power decays for both of the latest splitters as 3.8 μm and 4.4 μm for the configurations based on rod and shell heptamers, respectively.
Owning a large decay distance of optical power along a plasmonic nanostructure is one of the prominent purposes that can be improved by using more complex configurations and accurately adjusted nanoparticles. Therefore, considering studied structures, we would want to quantify and evaluate the decaying length of the propagated and coupled magnetic plasmon resonance along the branches (propagation direction in the
For the final examination, we measured the effect of offset distance (splitter arm spacing) as a significant parameter on the operation quality of the proposed device. Ahmadivand
[FIG. 7.] The influence of offset distance variations on the decaying length of magnetic power, (a) setting the arm spacing to 1400 nm and 1500 nm for the four-branch Y-splitter of nanorod heptamers leads to obtaining the power decay lengths of 3.8 μm and 3.25 μm, respectively, (b) setting the arm spacing to 1450 nm and 1520 nm for the four-branch Y-splitter of nanoshell heptamers leads to increasing the offset distance and directly reduces the propagation length of the distributed magnetic fields refers to 4.4 μm and 4.01 μm decay length, respectively, (c) this diagram evaluates controlled modifications in the offset distance of the shell-based splitter from 1600 nm to 1450 nm for the biggest splitting section over the decaying length (x-axis).
In this work, we studied the magnetic plasmon resonance coupling and guiding through the nanorod and shell heptamers arrays ordered in a triphenylene structure. Extending the number of proposed nanoparticles clusters, we designed a long-range and enhanced 1×4 Y-shape splitter to employ at the telecom spectrum. To provide exact results, we evaluated the spectral response of the two similar configurations composed of two different nanoparticles (rod and shell) clusters in triphenylene molecular fashion. Therefore, we calculated the plasmon resonance quality and the influence of lossy components on the splitter performance at the telecom spectrum (λ~1550 nm). Simulations results proved that the splitter based on shell heptamers shows efficient behavior during magnetic plasmon resonance propagation along the structure with 23.9% power ratio at each one of four branches, the decay length of 4.4 μm, and 1450 nm offset distance. The effects of dissipative and lossy factors on the device operation have been investigated numerically based on an FDTD method. Ultimately, we proposed an enhanced structure composed of Au nanoshell heptamers that is able to provide longer optical power propagation at the desired spectrum with lower impact of losses. This work opens new paths to utilize recommended theory in designing various efficient plasmonic devices that are able to function at the NIR efficiently.