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Realization of Mathematical Operators Using Zeros and Poles of Transmission and Reflection Coefficients

Zangeneh Nejad, Farzad | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49589 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Khavasi, Amin; Rejaei, Behzad
  7. Abstract:
  8. Although digital computers have been developed enormously in recent years, analog computing is still of great importance in some specialized application. There are basically two different methods to perform analog computing: metasurface approach (MS) and Green’s function (GF) method. In this contribution, we have focused our attention to the second method. In this approach, the associated Green’s function of the operator of choice is directly performed using a multilayered slab. Despite the applicability of this method, there are two major drawbacks regarding it. The first one is that it is only feasible to perform operators whose Green’s functions have an odd symmetry in the spatial Fourier domain. Second, in this method, the values of thicknesses and refractive indices of the layers are calculated using an optimization method which not always results in practical values. In this contribution our aim is to overcome these two challenges. Two this end, by breaking the reflection symmetry of previously proposed multi-layered slab and by exploiting the Brewster effect, we first realize the operator of first order differentiation. We then developed the proposed Brewster differentiator to a half-wavelength dielectric slab which performs differentiation for both major polarizations. Motivated by the latter differentiator and by making use of unique features of promising graphene, we further design and demonstrate a tunable, planar, and highly miniaturized graphene-based differentiator. At the end of this contribution, we also introduce a new approach to perform integration using a well-known dielectric slab waveguide. Our approach is indeed based on the fact that the transmission coefficient of a dielectric slab waveguide has a pole at its mode excitation angle. Inspired by the latter integrator and by using graphene, we then design and demonstrate a tunable graphene based integrator
  9. Keywords:
  10. Graphene ; PLasmonic Structure ; Brewster Angle ; Green Function ; Analog Computers

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