An Ultra-Wideband Band Pass Filter using Metal Insulator Metal Waveguide for Nanoscale Applications

A T-stub Square Ring Resonator (SRR) based UltraWide Band (UWB) Band Pass Filter (BPF) is studied and investigated in this paper. The proposed filter is based on coupled feed line connected to the T-stub SRR. Ultra-wideband characteristics can be realized by adjusting the T-stub lengths and coupling the gaps between both sides of waveguides and SRR. The characteristics of the T-stub SRR show that the miniaturized UWB BPF can be operated at THz frequencies. The proposed UWB filter is simulated and analyzed using the Finite Differential Time Domain (FDTD) solver-based Computer Simulation Technology (CST) studio suite. The resonance conditions are explained and the transmission performance of the filter agrees with the simulated and theoretical calculations. The proposed filter is best suitable for Electronic-Plasmonic Integrated Circuits (EPICs). Keywords-Metal-Insulator-Metal (MIM); ring resonator; coupled lines; Finite Differential Time Domain (FDTD); UltraWide Band (UWB); T-stub


INTRODUCTION
The light incident on a metal-insulator region produces a high-speed electromagnetic (EM) wave called Surface Plasmon Polarity (SPP) [1]. SPPs are known for overcoming the diffraction limit of the light at nanoscale wavelengths. Due to the low loss and high confinement of light at nanoscale range the Metal-Insulator-Metal (MIM) waveguide has been proposed by several researchers [2][3][4]. The subwavelength optical components that have been proposed when using MIM waveguide are reported in [5][6][7][8][9]. Several researchers worked on theories and experimentations of stub resonators like disk resonators [10], teeth-shaped resonators [11], rectangular [12], triangular [13], square [14], and circular [15] ring resonators. A Band Pass Filter (BPF) with symmetric side couple nano-disk resonators is analyzed for 1310nm and 1550nm in [16]. A concurrent dual band BPF is designed using slot waveguides and the performance is carried out at the resonant frequencies of 1300nm and 1600nm respectively in [17]. A tunable stepped impedance ring resonator for dual band BPF is designed and analysed at O and L bands in [18]. However, most of the investigations are carried out in single-, dual-and triple-band of operation for BPF. A limited work is carried out in Ultra-Wide Band (UWB) BPF where the bandwidth is limited, and the size of UWB filters is more. The optical bands used for transmission are O-band (1260-1360nm), E-band (1360-1460nm), S-band (1460-1530nm), C-band (1530-1565nm), and the L-band (1565-1625nm). The ring resonators are a fundamental component used in the Electronic-Photonic Integrated Circuits (EPICs). MIM and Insulator Metal-Insulator (IMI) are important geometries used in plasmonic waveguides. IMI waveguides carry light in longer propagation distances than MIM waveguides due to their cladding layers, but the MIM structures have higher confinement. Due to the high confinement and moderate propagation lengths, the MIM structures are efficiently used by EPICs. Authors in [19] designed a two-dimensional structure consisting of a MIM waveguide with a ring resonator, and two resonant peaks observed. This work is a further extension of the SRR for UWB applications.
Most of the existing resonators have symmetrical shapes. In this work, a nanoplasmonic T-stub loaded Square Ring Resonator (SRR) at optical bands is proposed. Most of the existing work was carried out on the design of single and dualoperating bands. In our proposed work, more than one band of frequencies are considered simultaneously (Ultra-Wide Band-UWB).
II. T-STUB SRR FILTER DESIGN SRR filter for dual band and SRR with stubs for triple band applications have been designed and their performance was investigated in our previous work [20]. In this paper, a T-stub SRR filter is designed which is suitable for UWB applications with compact dimensions. The methodology of the proposed filter design is illustrated with the flowchart shown in Figure 1. Firstly, the T-Stub SRR is designed using the Computer Simulation Technology (CST) studio suite. Simulations are carried out under Perfect Magnetic Layer (PML) boundary conditions for getting suitable transmission and reflection parameters. Figure 2 represents the proposed UWB filter designed using SRR. Four T-stubs are included at the four sides of the square ring representing the proposed T-stub SRR. The blue color in Figure 2 represents the metal and the gray color indicates the insulator. Silver is used as metal and silica is used as an insulator. The silver metal permittivity is calculated using the Drude model [21], i.e. ( ) ( ) 16 ) is the plasma frequency and γ p (=2. 73×10 13 ) is the collision frequency. SiO 2 ( 2.5 i ε = ) is used as an insulator and its permittivity is considered constant [21].   Two waveguides are situated on both sides of the T-stub SRR filter. The dimensions of the waveguide, T-stubs and SRR are tabulated in Table I. The basic properties of MIM waveguide like refractive index (N eff ), propagation length (PL) of SPP and calculated dispersion relation are defined in [17]. The proposed T-stub SRR filter is designed and analyzed using a commercially available Finite Differential Time Domain (FDTD) solver-based CST studio suite. PML boundary conditions with mesh size of 5nm×5nm were used in simulations. Two power monitors were included at the two ports of the filter (port 1 and port 2) to measure the incident power (P in ) and transmitted power (P out ). At port 1 (input port), part of the EM waves is reflected at the interface of the MIM waveguide and the remaining part of the EM waves is coupled to the SRR cavity with a small gap (g). The transmitting and reflecting EM waves in the SRR form standing waves and these are again coupled to the output port (port 2). The rectangular ring resonance condition is given by [12]:  Simulations were carried out for rectangular ring resonator observed the dual band operation [11]. Including the T-stubs on the four sides of the SRR forms the proposed UWB structure and operated O, E, S, and C bands simultaneously. The proposed filter is very useful for EPICs. The fabrication of MIM waveguide can be done by film deposition and photolithography techniques.

III. RESULTS AND DISCUSSION
The reflection and transmission characteristics of the T-stub SRR are represented in Figure 3. The simulations were carried in the FDTD solver-based CST microwave studio suite under PML boundary conditions and mesh settings of 5nm×5nm. The simulation results of Figure 3 Figure 3(a) for varying L3, from 290 to 300 with a step size of 5nm. For increasing L3 the covering UWB is moved right as shown in Figure 3(a). The optimum length L3 is 295nm. The bandwidth observed is ~300nm by the T-stub SRR. By varying the optimum width W3 of the T-slot from 50nm to 60nm with a step size of 5nm, the UWB spectrum covers higher wavelengths i.e from 1240nm to 1570nm. However, the  Figure 3(b). By varying the gap g between the coupled waveguide and SRR, the operating UWB band shifts to the right (Figure 3(c)). The value of g varies from 2 to 4nm with a step size of 1nm. For the 2nm gap, the reflection coefficient is above -10dB for wavelengths from 1360nm to 1450nm, for 3nm the RC is less than -10dB throughout the bands, and for 4nm gap the bands are decreasing. Due to that, 3nm is considered the optimum gap of the proposed UWB filter. The bandwidth of the proposed UWB observed from the simulation results is ~300nm. The symmetrical MIM waveguides are located on both sides of the T-stub SRR, the electromagnetic wave in the T-stub SRR will form the stable resonance observed at three wavelengths shown in Figure 3. The proposed UWB filter is compared with existing filter models in terms of parameters like operating wavelength, Extinction Ratio (ER), Bandwidth (BW), Area (L×W) occupied by the filter, and application bands. The proposed filter provides an improved bandwidth of 310nm when compared with the bandwidth (150nm) of the filter presented in [23]. Even though the bandwidth is low for the proposed filter in comparison with the filter of [4] (320nm), it operates in four operating bands (O, S, C, and E). The proposed UWB T-stub SRR is giving better performance in terms of BW, filter size, and application bands as can be seen in Table II. The energy of the SPP wave at UWB wavelengths shows the stronger coupling of the T-stub SRR filter at 1264.94nm (237THz), 1362.69nm (220THz), and 1495.9nm (200.4THz) wavelengths as shown in Figure 3. According to the simulation, the odd mode analysis has given better results than the even mode analysis of the T-stub SRR filter.
IV. CONCLUSION In this paper, the T-stub SRR filter for ultra-wide band applications based on transmission characteristics was studied. The coupled line MIM plasmonic structure is composed of two straight waveguides and the T-stub SRR. Simulations were carried out using the FDTD based CST studio suite. The simulation results show that the T-stub SRR filter gives better performance in O, E, S, and C optical bands. The transmission is slightly smaller at bigger wavelengths when comparing with the transmission at smaller wavelengths. The proposed T-stub SRR is optimized for the parameters of L3 (length of the stub) and gap g between the MIM waveguide and SRR. The ER for the proposed T-Stub UWB filter is ~28.1 at 1252nm and ~17.5 at 1492nm respectively. The bandwidth for the UWB band is 310nm. The optimized parameters also show that the proposed filter is best suitable for optical UWB applications. A strong EM coupling was observed at the MIM waveguides and SRR throughout the UWB range. The proposed UWB is best suitable for EPICs for transmitting high speed data. These structures are fabricated using lithographic techniques.