Wire Metamaterials-Based Microring Resonator in Subwavelength Structure
Ahmed A. Ali, Mohanned J. and A. H. Al-Janabi
 
Abstract
In this work we present the possibility of building a subwavelength microring resonator by manipulating the unite cell in the wire metamaterials. The proposed structure consist of mesh of copper wires. Firstly linear waveguide, bended waveguide as well as beam splitter were investigated at microwave range (737 MHZ), then the full structure of microring resonator were tested using commercial finite difference package CST Microwave.
Introduction
Natural materials are made up by lots and lots of small elements like atoms and molecules. Some of these materials are amorphous, others are crystalline [1]. Our main interest is in the interplay of waves and materials restricted to classical physics, the key parameter is a/λ, where a is the distance between elements in the material and λ is the free-space wavelength. Artificial materials in which atoms and molecules are replaced by macroscopic, man-made, elements [2]. All dimensions are bigger than those in natural materials. When the separation between the elements is comparable with the wavelength then we have the Bragg effect [3][4], and when the separation is much smaller than the wavelength then we can resort to effective-medium theory [4]. In the former case we have talked about photonic bandgap materials [5] and in the latter case about metamaterials [6].

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Generally, PCs are composed of periodic dielectric or metallo-dielectric nanostructures that have alternating low and high dielectric constant materials (refractive index) in one, two, and three dimensions, which affect the propagation of electromagnetic waves inside the structure [7]. Due to this periodicity, PCs exhibit a unique optical property, namely, a photonic band gap (PBG) where electromagnetic mode propagation is absolutely zero due to reflection. PBG is the range of frequencies that neither absorbs light nor allows light propagation. By introducing a defect (point or line or both) in these structures, the periodicity and thus the completeness of the band gap are broken and the propagation of light can be localized in the PBG region. Such an outcome allows realization of a wide variety of active and passive devices for signal processing such as, add-drop filters, power splitters, multiplexers and demultiplexers, triplexers, switches, directional couplers, bandstop filters, bandpass filters, and waveguides.
However, because of their wavelength-scale period, PCs result in large devices. This seriously restrains the range of applications, specifically in the low-frequency regimes where the wavelength is large. Metamaterials, on the contrary, possess spatial scales typically much smaller than the wavelength1
Since they were theoretically proposed by Pendry et al [8], and experimentally demonstrated by Smith et al.[9], metamaterials have attracted intensive research interest from microwave engineers and physicists in recent years because of their wide applications in super-lenses [6], [10], slow light [11], [12], optical switching [13], and wave guiding [14], [15]
Metamaterials are usually studied under the approach of the effective medium theory and experimentally measured from the far field [4]. They are mainly considered for their macroscopic properties owing to the subwavelength nature of their unit cells.
Recently, Fabrice Lemoult et al [16] have merged the wave guiding possibilities offered by PCs and the deep subwavelength nature of metamaterials by focusing on the propagation of waves in metamaterials made of resonant unit cells that are arranged on a deep subwavelength scale to go beyond the effective medium approximation. By manipulating the unit cell of the wire they were able to experimentally investigate the main components that can be used to control waves at the deep subwavelength scale: a cavity, a linear waveguide, bending as well as the beam splitter
Here we were be able to model their system first using the CST Microwave studio. Then we would expand the work to built a ring resonator used as add-drop filter or to built the field up to gain the nonlinear effect.
Firstly the frequency response for the system were measured for a mesh of 20*20 Copper wires with 0.3cm diameter and 1.2cm separation 40cm (a) and length by measuring the S21 between two discrete ports position on the opposite side of the system, as shown in the system configuration figure (1), then the result were compared with the same structure but with 37cm length as shown in figure (2).

figure (1) structure for the system under consideration, 20*20 Copper wires

Figure (2) S21 for the both wire lengths with the frequency selective line
The scanned bandwidth was about 300MHz from (600-900) MHz, then a certain frequency (737MHz) were selected on which the short wires (37cm) would have maximum transmission and the longer ones (40cm) wires would have the lower transmission (band gap region slightly above the resonance frequency of fn=nC/2L, were n: an integer C: speed of light, L:wire length). Linear waveguide were investigated by shorting a single raw of wires (37cm) inside the 20*20 mesh of (40cm) wires and recording the field propagation on the waveguide as shown in figure (3), profile of the signal inside the waveguide illustrated in the inset give the waveguide width of λ/32

Figure (3) subwavelength waveguide by shorting one row of the wires

It clearly shows the weak propagation on the system due to weak interference between our unit cell, wires here,. Anyhow the counter plot for the waveguide, shown in figure (4), clearly shows the resonance around the short wires and forbidden propagation around long ones.

Figure (4) subwavelength waveguide by shorting one row of the wires (contour view)
To enhance the coupling between the unit cells (wires here) and increase the waveguide efficiency two adjacent rows of wires were shortened. The field map for the latter case were presented in figure (5).

Figure (5) subwavelength waveguide by shorting two rows of the wires (showing good coupling)
Bended waveguide and beam splitter were simulated also as shown in figures (6 and 7) respectively.

Figure (6) subwavelength bended waveguide

Figure (7) subwavelength beam splitter
Finally, the complicated structure of microring resonator were molded as shown in figure (8)

Figure (8) subwavelength ring resonator
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