Objective
To demonstrate 2-dimensional (2D) strong confinement and guiding of terahertz (THz) waves in the deep subwavelength scale using a magnetic metamaterial and its application to THz-integrated device.

Background
THz technology is now drawing increasing attention due to its applications in biochemical sensing, security detection, and high-speed communication. To realize such applications, an easily accessible guided mode with highly localized electromagnetic (EM) fields below the diffraction limit is required. Surface plasmon polaritons (SPPs), the surface modes present at metal-dielectric interfaces, have the potential to overcome the diffraction limit. However, in the THz region where metal resembles a perfect electric conductor (PEC), such plasmonic structures cannot be used, because the EM fields of SPP hardly penetrate into the metal, instead extend hundreds of wavelengths into the dielectric medium. Therefore, strong confinement and guiding of THz waves in the deep subwavelength scale (< l/10) remains a major challenge and alternative approaches are highly desired. In this work, we propose a novel THz waveguide utilizing a magnetic metamaterial in conjunction with a parallel-metal-plate waveguide for 2D strong confinement and guiding of THz waves in the deep subwavelength scale. The proposed waveguiding system inherently has no cutoff for any core width and height, paving the way toward the deep subwavelength transport of THz waves for aforementioned THz-integrated device applications.

Results
Figure 1(a) shows the proposed structure of a subwavelength THz waveguide by incorporating a negative permeability metamaterial (NPM) as claddings between the two parallel metal plates. The metal plates, which provide the electric boundary condition, confine the electric field within a deep subwavelength gap (electric-field-mediated confinement). On the other hand, a gap in a NPM provides the magnetic boundary condition for magnetic-field-mediated confinement along the y direction. As a result, the proposed structure inherently has no cutoff for any core width and height, thus realizing 2D strong confinement in the deep subwavelength core. Figures 1(b) and 1(c) shows an array of metal-dielectric-metal magnetic resonators to realize the metamaterial that exhibits isotropic negative permeability in the y and z directions. Each magnetic resonator consists of a high-dielectric material (e1) sandwiched between two metal plates, and the resonators are arranged in a three-dimensional array. Another low-dielectric material (e2) is used to separate the resonators in the x direction.

The waveguiding performance of the proposed structure was numerically investigated using a finite-difference time-domain (FDTD) method. Figures 2(a) and 2(b) show Ex distributions in the y-z plane and in the x-y plane at 0.77 THz at which the metamaterial claddings exhibit mz < -1.0. The symmetric Ex profile of the coupled MPPs excited at each interface is clearly observed and strong confinement in the deep subwavelength core is achieved. For the considered configuration and operating frequency, a large kz = 4.6k0 (k0 = w/c is the wave number in vacuum) is obtained, while a low group velocity of c/21.8 is achieved with a modest propagation loss (2.5 dB/l). Similar confinement and waveguiding properties are also found for the magnetic field Hy shown in Figs. 2(c) and 2(d). Following the confinement of the electric and magnetic fields, the EM energy flow in the waveguide is strictly concentrated in the core.

Fig. 1. (a) Schematic of the gap MPP waveguide. (b) An array of magnetic resonators is used to form a metamaterial that exhibits isotropic negative permeability in the y and z directions, and (c) a single metal-dielectric-metal magnetic resonator with the dimensions indicated.

Fig. 2. Electric field Ex distributions at 0.77 THz in the (a) y-z and (b) x-y planes. (e) and (f) Corresponding magnetic field Hy in both planes. The structures of the waveguide are indicated by the black lines.

Fig. 3. Electric field Ex distributions in the y-z plane of waveguides with (a) a 90º bend and (b) a splitter at 0.77 THz. The claddings in (a) and (b) are represented by an isotropic effective medium with m = -7.79 + 0.86i.

We also demonstrated that the subwavelength waveguiding can be realized even in the presence of a sharp bend in the waveguide. Figures 3(a) and 3(b) show Ex distributions in the y-z plane of waveguides with a 90º bend and a splitter. The subwavelength radiation is guided around the bend and splitter experiencing a very low reflection. Surprisingly, almost 96.5% impinging energy is transferred through the deep subwavelength sharp bend. This is due to the improved impedance matching when the waveguide is sufficiently small compared to the wavelength and the bend can be considered as a junction between two transmission lines with the same characteristic impedance. These unique wave-confining features based on unconventional EM configurations may also have great potential for optical applications, such as biomedical imaging, nanolithography, and ultrasmall optical-integrated circuit.

Representative Papers
A. Ishikawa, et al., Phys. Rev. Lett. 102, 043904 (2009). view pdf