1 Sinusoidal Bragg Grating based on Hybrid Metal Insulator Metal Plasmonic Waveguide C. Sindhura, P. Sharma, V. D. Kumar Discipline of Electronics and Communication Engineering, PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, 482005, India E-mail: sindhurareddy234@gmail.com This is the first report on 3-D sinusoidal Bragg grating structure based on hybrid metal insulator metal (HMIM) plasmonic waveguide. The proposed structure has a gradual change in the refractive index rather than an abrupt change providing excellent filtering characteristics. The device is studied at an operating wavelength of 1.55 μm. The results are based on numerical simulations performed using the software CST MW studio suite. The transmission characteristics show more than 80% transmission in the passband and near zero transmission in the rejection band. The proposed structure reduces the scattering losses and a wide band gap of 0.387 μm is achieved. The proposed structure has a track length of 3.784 μm for 11 cells which is very less compared to previous reports allowing large-scale integration of photonic devices. A micro-cavity is also formed and its resonance is investigated by introducing a defect length of 0.217 μm in the periodic structure. A peak transmission of 50% and a narrow resonance bandwidth of 0.029 μm are achieved at 1.55μm resonance wavelength. The quality factor which defines the energy stored in the cavity is Q=53. 1. Introduction: The availability of nanofabrication techniques and high-performance computational resources opened up the applications of plasmonic devices in integrated photonics, all optical chips, solar cells, biosensors, etc. Though the plasmonic waveguides possess strong light confinement, the major limitation is that they suffer from large propagation losses [1]. Furthermore, two main kinds of the plasmonic waveguides are proposed. Metal-Insulator-Metal (MIM) and Insulator-Metal-Insulator (IMI). These waveguides suffer from the trade-off between propagation length and field confinement. The dielectric waveguides, in contrast, provide low losses but suffer from diffraction limit and are larger in size. Merging the guiding mechanisms of plasmonic and dielectric waveguides, various kinds of hybrid plasmonic waveguides are proposed, which provides a solution to the limitations faced by the conventional dielectric and standard plasmonic waveguides [2-4]. Few articles based on hybrid metal- insulator (HMI) plasmonic waveguides have been reported [5-6]. But, they are mostly 1-D structures which are practically not implementable. A study on plasmonic waveguide based on hybrid insulator-metal-insulator (HIMI) has been reported providing long range propagation and sub-wavelength confinement [7]. To further enhance the light confinement and to lessen the propagation losses, a multi-layered hybrid metal insulator metal (HMIM) plasmonic waveguide has been reported [8]. The components like bends, couplers, power dividers, ring resonators and logic gates have been reported earlier based on HMIM plasmonic waveguides [8-10]. However, there are only a few reports on Bragg reflectors and filters based on HMIM plasmonic waveguide [11], but more are needed to be explored. In literature, there are some reports on MIM plasmonic waveguides and graphene based Bragg reflectors, but they offer poor performance [12-15] and the explanation is as follows. A MIM based 2D Bragg grating structures have been reported in [12-14], which are not realistic as thickness is not finite. Besides MIM waveguides are prone to excessive ohmic loss and hybrid MIM waveguides are superior in this aspect [8-10]. The structure proposed in [16] is a MIM Sinusoidal Bragg grating, which gives better performance than rectangular ones proposed in [12-15], yet this is again a 2D structure. A Bragg structure based on HMI plasmonic waveguide with grating incorporated by periodically varying the thicknesses of dielectric layers has also been reported in [17]. Different from that a rectangular Bragg grating in a HMIM plasmonic waveguide has been reported recently which incorporates periodic variation of waveguide width [11]. Though this is a realistic 3D structure, it suffers poor transmission in passband due to abrupt changes in waveguide width, resulting in significant radiation losses. These losses could be mitigated by gradual width modulation of the hybrid plasmonic waveguide for realization of grating. With this motivation we propose and analyze a sinusoidal Bragg grating in a realistic HMIM plasmonic waveguide, which to best of our knowledge is the first report of its kind. The proposed structure is simulated using frequency domain solver of CST microwave (MW) studio suite, an electromagnetic computational tool which uses FEM (Finite Element Method) numerical method to solve electromagnetic equations. The perfectly matched layer (PML) absorbing boundary condition with a mesh density of 15 tetrahedrons per wavelengths is adopted and S-delta convergence test is performed to ensure accurate results. The proposed structure shows high transmission in the passband while nearly zero transmission within the band gap, thus having superior performance compared to the rectangular structure. Track length of the proposed sinusoidal Bragg gating is 3.784 μm for 11 cells which is very small compared to the previous literature [16], [17]. Further, a micro-cavity is also formed and investigated for the resonant mode within the band gap. The proposed sinusoidal Bragg gating is a realistic structure, compatible with semiconductor fabrication process and hence useful for future chip scale applications. Different layers of the waveguide can be deposited by some standard techniques like silver layer by metallization, silicon and silica layers by magnetron sputtering or PECVD (plasma enhanced chemical vapour deposition) process. Then e-beam lithography or focused ion beam can be used for patterning of the structure [2], [18-20]. 2. Principle and Design: The cross-sectional view of HMIM plasmonic waveguide is shown in the Fig. 1 a, where ‘Z’ is the direction of propagation. Silver is chosen for metal layer in the HMIM waveguide. The permittivity of metal is expressed by Drude model as [7]: = ∞ −   2  2 + (1) ReView by River Valley Technologies Micro Nano Letters 2018/07/27 14:42:38 IET Review Copy Only 2 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. 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