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Migration of Eigenmodes in Photonic and Quantum-Well Structures

Hosseinnia, Amir Hossein | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41013 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Mehrany, Khashayar; Rashidian, Bizhan
  7. Abstract:
  8. Mode extraction in photonic and quantum-well structures requires solving transcendental equations and applying complex root searching methods, which incurs a diversity of numerical obstacles. In this thesis, the most effective methods for derivation of complex roots in such equations are investigated and analyzed. Thus the complex modes of an arbitrary one-dimensional photonic structure are extracted with highly adjustable precision and accuracy. The improper modes, i.e. solutions of the improper dispersion equation, are also studied and extracted by exploiting numerical methods. After this step, the migration of modes caused by changing the physical parameters of the structure is investigated and then the effects of making such changes are numerically studied. Using block-diagrams to interpret the photonic mode migration pattern, a novel method is proposed to predict the mode migration path of photonic modes leaving their initial position in the reciprocal space. In the second part of the thesis, more emphasis is put on photonic crystal analysis methods. Thanks to the feasibility of numerical methods previously used for slab waveguides in periodic waveguides, a new method is also proposed to determine modes in photonic crystal based guiding structures and coupled resonators. Basically, the method relies on analyzing the reflection and transmission coefficients of the structure. Results of the proposed method are validated by using the standard methods, against which the superiority of the proposed method is demonstrated.

  9. Keywords:
  10. Waveguides ; Photonic Crystal ; Quantum Wells ; Transcendental Equation ; Eigen Mode Determination ; Mode Migration

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