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3D FDTD Code for Quantitative Study and Characterization of Biperiodic Photonic Crystal Waveguides. Proposal of the study on. By. School of Electrical and Computer Engineering Georgia Institute of Technology. Aliakbar Jafarpour. March 31 , 2005. Outline. Introduction (Photonic Crystals)

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proposal of the study on

3D FDTD Code for Quantitative Study and Characterization of Biperiodic Photonic Crystal Waveguides

Proposal of the study on

By

School of Electrical and Computer Engineering

Georgia Institute of Technology

Aliakbar Jafarpour

March 31, 2005

outline
Outline
  • Introduction (Photonic Crystals)
  • Motivation (Dispersion Issues)
  • Technical Approach (Biperiodicity)
  • Future Work and Concluding Remarks (3D Analysis)
outline1
Outline
  • Introduction (Photonic Crystals)
  • Motivation (Dispersion Issues)
  • Technical Approach (Biperiodicity)
  • Future Work and Concluding Remarks (3D Analysis)
wave phenomena at an interface i
Wave Phenomena at an Interface (I)
  • Homogeneous media
  • Angular dependence
  • Spectral dependence (dispersion): the prism effect

Refracted (Transmitted)

Reflected

Incident

Medium 1

Medium 2

wave phenomena at an interface ii
Wave Phenomena at an Interface (II)
  • Inhomogeneous media: lots of scattered wavelets
  • Transmission (forward-scattering) and reflection (back-scattering) in many directions

Reflected

Transmitted

Incident

Medium 1

Medium 2

wave phenomena at an interface iii
Wave Phenomena at an Interface (III)
  • Periodic media
  • Angular and spectral dependence (dispersion)
  • Diffraction: (guiding and bandgap)

Diffracted-

Diffracted-

Diffracted+

NO Diffracted+

Guiding

Bandgap

photonic crystals on wikipedia
Photonic Crystals on Wikipedia

http://en.wikipedia.org/wiki/Photonic_crystals

an introduction to photonic crystals 2
An Introduction to Photonic Crystals (2)
  • (2D) Periodic index of refraction
  • Optical counterparts of semiconductors
  • Photonic band gap (PBG) and light steering
outline2
Outline
  • Introduction (Photonic Crystals)
  • Motivation (Dispersion Issues)
  • Technical Approach (Biperiodicity)
  • Future Work and Concluding Remarks (3D Analysis)
photonic crystal waveguides

Mode Dispersion (TM)

Frequency, ωa/(2πc)

Phase Constant, ka/π

Photonic Crystal Waveguides
  • Removing a line of air holes
  • Modegap, nonlinear dispersion, and loss
outline3
Outline
  • Introduction (Photonic Crystals)
  • Motivation (Dispersion Issues)
  • Technical Approach (Biperiodicity)
  • Future Work and Concluding Remarks (3D Analysis)
biperiodic pcws

2r

a’

a

a

2r

Biperiodic PCWs
  • Periodic (1D)
  • Perturbing the periodicity
  • Analysis of non-periodic structures

A periodic PCW

Dispersion diagram of different PCWs

A biperiodic PCW

problems

Transmission Coefficient

Normalized Frequency, ωa/(2πc)

Problems
  • Experimental results
  • Low loss

A fabricated biperiodic PCW

proposed plan
Proposed Plan
  • Developing a 3D FDTD code
    • Test and debug
    • Incorporate sources
  • Calculating the loss of biperiodic and other photonic crystal waveguides
  • Comparing with experimental results
  • Incorporating nonlinearities
concluding remarks
Concluding Remarks
  • Time- and frequency-domain methods
  • Fabrication imperfections
  • Wideband characterization
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