Design of a hybrid spoof plasmonic sub- terahertz ... - OSA Publishing

Vol. 25, No. 6 | 20 Mar 2017 | OPTICS EXPRESS 6860

Design of a hybrid spoof plasmonic subterahertz waveguide with low bending loss in a broad frequency band MOHAMMAD ALI KHOSROVANI MOGHADDAM AND MEHDI AHMADI-BOROUJENI

*

Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran * [email protected]

Abstract: The effect of dielectric cladding on the waveguiding characteristics of an array of metallic pillars on a metal plane in the sub-terahertz band is explored. Firstly, a 2D structure made up of a metallic grating of infinite lateral width with various dielectric overlays is analytically studied to get more insight into the problem. Then the ideas inferred from the 2D structure are applied to the realistic 3D structure that has a finite lateral width. It is shown that by proper design of the dielectric medium surrounding the metallic structure the modal field confinement can be enhanced in a broad frequency band resulting in a low bending loss. Especially, by integrating the pillars into a silicon channel of finite size and evacuating the spaces between them a highly confined spoof surface plasmon is supported and a considerable reduction in the bending loss over a broad bandwidth is observed. Due to small cross-sectional size, low bending loss and ease of fabrication, the proposed waveguide is a promising choice for millimeter-wave and terahertz integrated circuits; particularly those based on the silicon technology. © 2017 Optical Society of America OCIS codes: (130.2790) Guided waves; (230.7370) Waveguides; (130.5990) Semiconductors; (240.6680) Surface plasmons; (040.2235) Far infrared or terahertz; (050.6624) Subwavelength structures.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

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#285501 Journal © 2017

https://doi.org/10.1364/OE.25.006860 Received 30 Jan 2017; revised 11 Mar 2017; accepted 11 Mar 2017; published 15 Mar 2017


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1. Introduction Waveguides play an important role in the development of terahertz (THz) technology [1]. Besides being used for the guided transport of THz signals [2], they are building blocks of various devices such as sources [3], detectors [4], and passive components [5] and are also key components in some THz sensing and spectroscopy systems [6]. With the advent of commercial THz systems, the need for integrated THz circuits is felt necessitating the development of waveguides having high field confinement, low bending loss, and proper geometry for circuit realization. Periodic metallic structures capable of propagating confined surface waves, also referred to as spoof surface plasmons (SSP), are among the most promising waveguides for this purpose [5–10]. These waveguides support highly confined surface waves or SSP’s and their loss in the sub-THz regime is around 0.01~0.02 mm−1 [1,5]. Based on the idea of periodically altering the metal surface, various spoof plasmonic waveguides suitable for millimeter wave (mm-wave) and THz planar circuit realization have been proposed. A periodic array of metal tapes between two parallel metal plates, called parallel-plate ladder waveguide [11,12], an array of metallic pillars protruding out of a metallic surface, called Domino waveguide [13,14], a double-periodic metallic grating of domino-like elements for dual band operation [15], grooved metal strip [16], and a metallic surface with L-shaped grooves [17] are some examples. By the use of low-loss dielectrics, several hybrid metallic-dielectric structures for THz waveguiding are also proposed. In [18] a hybrid plasmonic waveguide composed of a plastic ribbon waveguide integrated with a metal grating is demonstrated for subwavelength confinement in the THz band. A periodic dielectric structure integrated with a graphene layer is also proposed as a tunable THz surface waveguide [19]. In order to localize certain frequencies at different locations on a domino waveguide, the space between metallic teeth is filled gradually with a dielectric [20]. Due to low-loss and low-dispersion characteristics of high-resistivity (HR) silicon in mm-wave and THz bands [21] and its available fabrication processes, planar silicon waveguides are another promising candidate for THz integrated circuits [22,23]. Highly-doped Si has also been used as a conductor in THz waveguides. As


an example, a 1D array of V-shaped grooves etched on a highly-doped silicon substrate is proposed for THz surface plasmon propagation [24]. Spoof plasmonic waveguides can provide subwavelength confinement in a limited bandwidth where a low bending (radiation) loss is achievable. But, obtaining a low bending loss in a wide bandwidth remains a challenge. As presented in [13], bend loss is 10% for the bending radius of one wavelength, but it increases drastically when the bending radius becomes smaller compared to a wavelength. In this paper, we show that by using a hybrid plasmonic structure, i.e., a hybrid metallic-dielectric periodic structure, low bending loss is achievable in a broader bandwidth as compared to conventional all-metallic structures. Benefitting from the mentioned features of both HR silicon and the periodic metallic structures, we propose a periodic array of metallic pillars embedded in a silicon ridge for highly-confined transfer of mm-wave and THz waves with low bending losses over a bandwidth of nearly one octave. In order to enhance the field confinement of the mentioned periodic metallic waveguide, we study two modifications: burying the metallic pillars in a silicon layer of finite size and filling the spaces between the pillars, i.e. the grooves, with air. It should be stressed that these two modifications can readily be implemented by the available fabrication processes; such as planar dielectric waveguide technology, deep reactive ion etching (DRIE), electroplating, and micromachining [22–26]. Hence, an important advantage of the proposed structure from a practical point of view is its compatibility with common planar fabrication processes, particularly those related to the silicon technology. The metallic pillars can be realized by highly-doped silicon and the surrounding dielectric structure can be micro-machined or etched HR silicon. Therefore, the proposed waveguide is a potential candidate for mm-wave and terahertz integrated devices and circuits. The outline of this paper is as follows. First, we analyze a 2D hybrid metallic-dielectric grating having an infinite lateral width to investigate the effect of different configurations of the dielectric coating on its guiding characteristics. Main ideas for the design of the final structure are inferred from this analysis. Then, applying the results of the 2D analysis to the design of a finite lateral width structure, we investigate its waveguiding performance and assess its confinement and bending loss at different frequencies. Finally, we study the performance of sharp waveguide bends based on the proposed structure using a full-wave simulation. 2. Analysis of the 2D structure The proposed waveguide is composed of a periodic set of metallic box-shaped pillars, also called dominos, on a metal plate as illustrated in Fig. 1. The outermost region covering the whole structure is assumed to be filled with a relative dielectric constant of ε1 while the intermediate region overlaying the pillars and the grooves are filled with dielectrics of relative permittivity ε2 and ε3, respectively. The dielectric structure is assumed to be composed of only air and HR silicon. By using a customized dielectric cladding made up of HR silicon and air, we achieve more degrees of freedom in the design of the waveguide without increasing its attenuation constant considerably.

Fig. 1. (a) Perspective view, (b) front view and (c) side view of proposed hybrid plasmonic waveguide based on an array of metallic pillars (gray regions) on a metal plate embedded in a dielectric cladding composed of regions with dielectric constants ε1, ε2, and ε3.


The waveguiding properties of the mentioned metallic structure are dependent on the geometrical parameters, such as height, period, lateral width, and the spacing of metal pillars that are defined by h, d, l and a, respectively. Parameters h2 and l2 denote the height and width of the intermediate dielectric layer covering the metallic pillars as depicted in Fig. 1. The proposed structure has a finite lateral width. However, to shed some light on the problem and to facilitate the design procedure we start from the analysis of a 2D structure having an infinite lateral width, i.e., the structure with no variation along the y-axis and l = l2 →∞. In the different regions of the 2D structure, the electromagnetic fields of the spoof surface plasmon propagating in the x-direction can be expanded into transverse-magnetic (TM) Bloch waves. In the outermost semi-infinite region, the transverse component of the magnetic field can be written as: H1 y =

∞

A

n

n =−∞

exp ( − jk xn x ) exp[α1n ( z + h1 )]

(1)

where h1 = h2-h. In the intermediate overlaying layer (-h1