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Improvement and Expansion of Characteristic Green’s Function-Complex Images Method for Extraction of Green’s Function of Finite Dielectric Structures

Torabi, Abdorreza | 2014

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 46074 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Shishegar, Amir Ahmad; Faraji-Dana, Reza
  7. Abstract:
  8. Finite dielctric structures are commonly used in optical devices, Microwave Integrated Circuitc (MICs) and printed antennas. To analyze these structures, full-wave analysis methods cannot be employed easily. They need huge computer resources and are time-consuming especially for electrically large structures. On the other hand, asymptotic techniques may not be exact enough for these structures. In this thesis, MPIE technique is chosen as an accurate and efficient technique for analyzing these structres. To use this technique, the magnetic vector potential and electric scalar potential are required. Uniform and closed-form spatial Green's function for finite dielectric structures is derived by using a combination of the characteristic Green's function (CGF)and rational function fitting method (RFFM). Employing the concept of quasi leaky waves, CGF-RFFM represents both of the discrete and continuous spectrum contributions efficiently by using the modified VECTFIT algorithm. An error of less than 0.2% is achieved compared with the direct numerical integration of the spectral integral. The derived Green's function is exact for separable structures while it is approximate for non-separable structures like truncated dielectric substrates where the corner regions are replaced by fictitious materials. To obtain more accurate results , mode conversions due to the surface waves (SWs)incident on the the end-facet are considered by employing the scattering matrix in the formulation for structures supporting several guided modes. The main advantage of this method lies in its speed as well as accuracy. Excellent agreements with the rigorous method of moments (MoM)are shown in several examples. Morover to obtain more exact spatial Green’s function, a closed-form spatial Green's function for a truncated dielectric slab is derived by using a combination of the CGF and perfectly matched layer (PML) method. The original structure is terminated by PML that is backed by perfect electric conductor (PEC) in semi-infinite layer at the top and/or bottom. The eigenmodes of the closed structure by PML construct the continuous spectrum contribution of the original structure efficiently. Generalized scattering matrix (GSM) of truncating surface which contains possible conversions between all modes is computed with mode-matching method. It is demonstrated that by importing GSM in CGF formulation, more exact results for non-separable structures can be obtained. The source and observation points dependence is analytically available in derived expression and allows very efficient computation and storage of the spatial Green's function. Very close to the source , where the large number of modes must be considered, Shank's transform is used to preserve the efficiency of the method. The main advantage of the method lies in its accuracy and low dependency of the result to the PML parameters. Furthermore, a novel method for computation of guided mode reflectivity from optical waveguide end-facet is presented. The method is based on the characteristic Green's function technique formulation. By separability assumption of the structure, a uniform and closed-form expression of spatial Green's function is obtained. Derived expression consists of discrete and continuous spectrum contributions which denote guided and radiation modes effects, respectively.Having a full wave solution efficient optimization procedure is then used to calculate the exact reflection coefficients of guided modes at the end-facets. To find mode coupling coefficients, CGF-CI formulation is modified to incorporate coupling matrix of abruptly terminated waveguides. The main advantage of this method lies in its simple implementation as well as accuracy for any refractive index contrast .
  9. Keywords:
  10. Complex Images Method ; Finite Difference Time Domain (FDTD) ; Charactristic Green's Function (CGF) ; Fimte Dielectric Structure ; Rational Functions Fitting Method (RFFM) ; Perfectly Watched Layer

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