Toroidal Localized Spoof Plasmons on Compact Metadisks

Abstract Localized spoof surface plasmons (LSSPs) have recently emerged as a new research frontier due to their unique properties and increasing applications. Despite the importance, most of the current researches only focus on electric/magnetic LSSPs. Very recent research has revealed that toroidal LSSPs, LSSPs modes with multipole toroidal moments, can be achieved at a point defect in a 2D groove metal array. However, this metamaterial shows the limitations of large volume and poor compatibility to photonic integrated circuits. To overcome the above challenges, here it is proposed and experimentally demonstrated compact planar metadisks based on split ring resonators to support the toroidal LSSPs at microwave frequencies. Additionally, it is experimentally demonstrated that the toroidal LSSPs resonance is very sensitive to the structure changes and the background medium. These might facilitate its utilization in the design and application of plasmonic deformation sensors and the refractive index sensors.


DOI: 10.1002/advs.201700487
ability to confine EM waves at a deep sub wavelength scale, SPPs provide solutions to overcome the diffraction limit and min iaturize the photonic components, [6] which is promising for various applications, such as miniaturized sensors, [7] photonic circuits, [8,9] light localization, [10,11] photo voltaics, [12] etc. Extending the concept of surface plasmon polaritons to longer wavelength regimes, such as microwave and terahertz frequencies, will be of great benefit to miniaturize the components of integrated circuits. [1] However, at these fre quency regions the noble metals behave like perfect electric conductors (PECs) and hence can only support surface wave with weak confinement. To increase the confinement, a concept of spoof SPPs has been proposed by Pendry et al. in 2004, where a special surface wave mode, propa gating on a periodically subwavelength structured PEC surface, has enhanced energy confinement and a dispersion similar with that of natural SPPs but at much lower frequencies. [13] Various methods have been developed to geometrically design the system of spoof SPPs, [14,15] which lead to potential applica tions in waveguiding, [16][17][18][19] sensing, [20,21] laser beams, [22] etc.
Depending on the geometry, the spoof surface plasmons can either be propagating spoof SPPs or localized spoof surface plasmons (LSSPs). [23,24] Currently, most of the studies focus on electric/magnetic LSSPs, where the LSSPs show multipole electric/magnetic dipole moments. [25][26][27][28][29] A toroidal multipole is another form of multipole which cannot be explained by the standard multimode expansion. [30] It is produced when currents flow on the surface of a torus along its meridian [31] and has great capability to exist in free space and interacts with light. Because of its unusual EM properties, the toroidal multipoles have attracted increasing attentions recently. [32][33][34][35][36][37] For example, it has been shown that the dynamic nonradiating charge current configurations could produce oscillating and propa gating vector potential without emitting EM radiation, which is known as the "anapole moment." [32][33][34][35] Despite its physical significance to the light-matter interaction, the research and experimental demonstration of the LSSPs with toroidal dipole moments is rare. Only recently, Kim et al. experimentally dem onstrated toroidal LSSPs at a point defect in a 2D groove metal array. [38] Despite the significance of the work, the large device volume of their structure makes the practical application chal lenging and difficult to integrate with photonic circuits.
In this work, to overcome the above challenge, we design compact planar metadisks based on split ring resonators Localized spoof surface plasmons (LSSPs) have recently emerged as a new research frontier due to their unique properties and increasing applications. Despite the importance, most of the current researches only focus on electric/ magnetic LSSPs. Very recent research has revealed that toroidal LSSPs, LSSPs modes with multipole toroidal moments, can be achieved at a point defect in a 2D groove metal array. However, this metamaterial shows the limitations of large volume and poor compatibility to photonic integrated circuits. To overcome the above challenges, here it is proposed and experimentally demonstrated compact planar metadisks based on split ring resonators to support the toroidal LSSPs at microwave frequencies. Additionally, it is experimentally demonstrated that the toroidal LSSPs resonance is very sensitive to the structure changes and the background medium. These might facilitate its utilization in the design and application of plasmonic deformation sensors and the refractive index sensors.

Metamaterials
Surface plasmon polaritons (SPPs) are a kind of electromag netic (EM) surface wave propagating at the interface between noble metals and dielectrics at optical frequencies. [1][2][3][4][5] With the (SRRs) to support toroidal LSSPs at microwave frequencies. We successfully observe the nearfield distributions of the toroidal LSSPs resonance mode, both in simulated and experimental results. We study the properties of the toroidal LSSPs and find it very sensitive to the structural parameters and the back ground medium. This might lead to potential application in plasmonic sensing and integra tion with the photonic integrated circuits.
In order to design the toroidal LSSPs, we first consider a chain of SRRs as shown in Figure 1a. A single unit cell is depicted at the upper inset of Figure 1a, with a period of p = 5.44 mm. The brown region is the SRRs (copper with a conductivity of 5.7 × 10 7 S m −1 ) where a = 9 mm, s = w = 1.2 mm, t = 0.025 mm, and r 2 = 0.8 mm. The gray region is the FR4 substrate with a relative permittivity of 3.7 + 0.001 i at the frequency below 10.0 GHz. The height and width of the FR4 substrate is d = 4 mm, and l = 14 mm, respectively. It is well known that the single SRR can produce a magnetic dipole. [39] By arranging the SRRs in a chain, the induced magnetic dipoles of each SRRs will couple with the SRRs one by one, and in this way the spoof SPPs will be produced. The left inset of Figure 1c    and the distance between the SRRs and the center of the substrate is r 1 = 6 mm.
To calculate the localized EM modes in the SRR disks, the eigenmode solver of the commercially available software, Computer Simulation Technology (CST) Microwave Studio is employed. Figure 2a,b shows the magnetic and electric field intensity distri butions of the SRR disks. The direction of the fields is represented by the black arrows in the figures, where both magnetic and electric fields are strongly confined in a ringlike form at 4.16 GHz. Moreover, the magnetic field distributions exhibit a vortex with the field that threads all the SRRs, which is produced by the surface current oscillating on the SRRs. Also, the magnetic field is in a shape of torus, which is an important signature of the toroidal dipole moment as it provides a toroidal dipole along z direction.
To fully understand the physics behind this, we investigate the multipole responses in the SRR disks. The modes in the SRR disks are excited by putting a discrete port at the gap of one SRR, and the simulation is performed in the timedomain solver of CST. With the extracted surface cur rent around 4.16 GHz, the farfield scat tering power of electric dipole, magnetic dipole, toroidal dipole, electric quadrupole, and magnetic quadrupole are calculated according to multipole scattering theory. [40] The details of the calculations are shown in the Supporting Information. The radiation power magnitude of theses multipoles can be described as follows where c is the speed of light in the free space, ω is the angular frequency, α, β = x, y axes in our case, and  P,  M ,  T , Q αβ , and M αβ are the dipole moments of electric dipole, magnetic dipole, toroidal dipole, electric quadrupole, and magnetic quadrupole, respectively. The radiation powers as a function of the frequency are plotted in Figure 2c, where one can see that the toroidal dipole moment is larger than the other dipoles and multipolar components from 3.9 to 4.4 GHz. Especially, the radiation power of toroidal dipole moment is approximately two orders stronger than those of other multipole moments at 4.16 GHz. It is shown that the toroidal dipole moment is dominant around 4.16 GHz and the other resonances are suppressed by the toroidal dipolar resonance.
The variation of the radiation powers with different numbers of SRRs is an important property for the design consideration of the toroidal LSSPs. We calculate the radiation powers of dif ferent numbers of SRRs as a function of frequency. Figure 3a,b shows the dispersion of radiation powers of multipole moments in the SRR disks with 8 and 4 SRRs, respectively. It is clear that for the SRR disks with 8 SRRs, the toroidal dipole moment is dominant around 4.14 GHz, while for the SRR disks with 4 SRRs, the toroidal resonance shifts to 4.07 GHz. Figure 3c shows all the radiation powers of the toroidal dipole and reso nance frequency in different numbers of SRRs from 4 to 20. One can see that the toroidal resonance frequency blueshifts first and then redshifts when increasing the number of SRRs. This is because when increasing the numbers of SRRs from 4 to 12, the distance between two neighbor SRRs becomes small, the equivalent capacitance C slowly decreases due to the weaker edge effect, [41] while the equivalent inductance L almost stays the same when p > d. [  the resonance frequency increases. However, when increasing the number of SRRs from 12 to 20, two neighbor SRRs are very close, i.e., p<<d, the equivalent inductance L dramati cally increases due to the strong coupling effect. [41] Though the equivalent capacitance C still decreases, the equivalent inductance L plays the dominant role and the resonance frequency becomes lower. Note that the radiation power is monotonically increasing as the number of SRRs increases, this is because when number of SRRs increases, confinement of fields is stronger around SRRs, resulting in higher radia tion power. To understand the properties of toroidal LSSPs mode, we evaluate the modal volumes and Q factors with the formulas where ε is the dielectric constant, E is the electric field, ω 0 is resonance frequency, and Δω is 3dB resonant linewidth. [43] Figure 3d shows the calculated modal vol umes and Q factors for different numbers of SRRs. The modal volume decreases and the Q factor increases as the number of SRRs increases from 4 to 12. However, both the modal volume and Q factor become insen sitive to the number of SRRs when the number is larger than 12. This is because when two neighbor SRRs are very close; the field confinement is quite strong, which has little change when continually increasing the number of SRRs.
To experimentally verify the toroidal LSSPs mode, we fabricate a sample ( Figure 1b) and setup an experiment. In the experimental setup shown in the inset of Figure 4a, a dipole antenna is placed at the gap of one SRR of the SRR disks to excite the LSSPs modes. The discrete port is oscil lated along the radial direction of the cyl inder substrate. For the detection, another dipole antenna is placed 1 mm above the gap of the SRR to detect the electric field. Both antennas are connected to the vector network analyzer to get the reflection and transmission parameters. From Figure 4a, one can see that there is a dip or a reso nance near 4.16 GHz in both simulated and experimental results. This can be explained by the coupledmode theory (please see the Supporting Information). [44] Moreover, around 4.16 GHz the transmission curves experience resonances which are in accord ance with our expectation as shown in Figure 4b. All the compared simulated scattering parameters agree well with the experimental demonstration.
To scan near field around the metadisks, the detecting dipole antenna is fixed at the arm of a 3D movement platform. It is polarized along the z direction 2 mm above the SRR disks. The E z field distribution measured within 120 mm by 120 mm area experienced the toroidal LSSPs resonance at 4.17 GHz as shown in Figure 5b. The bright spots at the top side of the electric field distributions come from the excitation source. As a comparison, we simulate E z field distribution of the same setup at 4.17 GHz, see Figure 5a. The experimental and the simulated results show remarkable agreement. From Figure 5a,b, the black dashed lines show the edge of the SRR disks. From the field distributions, one can clearly see that the circulating E z field varies between nega tive and positive, which is a dipolelike EM field radiation pat tern. Besides, the location of the dipole is exactly at the center of the SRR disks, which is an important signature of the toroidal LSSPs mode.
We also study the impact of the structure and back ground parameters to the proposed toroidal LSSPs reso nator. Figure 6a shows the simulated reflection parameters of toroidal resonator as a function of thickness of the sub strate. A redshift of the toroidal LSSPs resonance is observed with increasing thickness of the substrate. For example, when the thickness of the substrate is t = 3 mm, the toroidal Adv. Sci. 2018, 5, 1700487  LSSPs resonance first appears at the frequency of 4.9 GHz. Increasing the thickness of the substrate from 3.5, 4, 4.5, and 5 mm, the toroidal LSSPs resonance is redshifted by 0.35, 0.65, 0.9, and 1.1 GHz, respectively, as shown in Figure 6b. Moreover, Figure 6c shows the simulated reflection parameters as a function of length of the SRRs. A redshift of the toroidal LSSP resonance is observed when increasing the length of SRRs (Figure 6d). Due to the sensitivity of the structure changes, the toroidal LSSPs reso nator may be used as a deformation sensor. Similarly, changing the permittivity of the background medium is simulated and dem onstrated experimentally. In the simulation, one can see a significant redshift at the reso nance frequency when relative permittivity of the background increases, see Figure 6e,f. A similar phenomenon is also experimentally demonstrated, by changing the background medium from air to oil (relative permittivity of 2.5), as shown in Figure 6f. The resonance frequency shifts from 4.17 GHz in the air to 3.7 GHz in the oil and the corresponding res onance frequency shift per refractive index [45] is 0.8 GHz/refractive index unit. There fore, the toroidal LSSPs resonator can work as a deformation sensor and to detect the refractive index changes of the surrounding medium.
In this work, we propose compact planar metadisks which support toroidal LSSPs at microwave frequency regime with strong compatibility with the photonic integrated circuits. The semianalytical results show that a dominant toroidal dipolar response can be observed from 3.9 to 4.4 GHz. We also per form the series of experiments and compare the transmission/reflection parameters and electric field distributions of the toroidal LSSPs mode with the simulation, which clearly indicates a toroidal dipole resonance around 4.17 GHz. Moreover, we numerically and experimentally demonstrate that the pro posed toroidal LSSPs resonator is sensitive to the structure changes and surroundings. Therefore, it can work as a plasmonic sensor to detect the deformation of the structure and the refractive index changes of the sur rounding medium. Besides, as the present metadisks show high symmetries, when using far field to excite the localized modes on the metadisks, the metadisks show sym metric responses at the toroidal dipole resonant frequency, making the excitations insensitive to the incident angles. Finally, the proposed compact metadisks can also be achieved at higher frequencies, such as terahertz and infrared frequencies, by properly downs caling of the present structure.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.