1. photonic band structure, Pi-Gang Luan & Wave Engineering Lab
Photonic crystals (I)
Bloch's theorem,
photonic band structure,
and energy flow
Pi-Gang Luan & Wave Engineering Lab
(欒丕綱 & 波動工程實驗室)
Institute of Optical Sciences
National Central University
(中央大學光電科學研究所)

2. Photonic/Sonic Crystals
1D Crystal
2D Crystal
3D Crystal

3. 3D Phononic Crystal?

4. Photonic/Sonic Band Structure

5. Applications

6. Photonic crystals as optical components P. Halevi et.al.
Appl. Phys. Lett.
75, 2725 (1999)
See also
Phys. Rev. Lett. 82, 719 (1999)

7. Periodic function, Fourier Series and Reciprocal Lattice

11. Lattice Bases vs. Reciprocal Lattice Bases (2D)
Square Lattice
Triangular Lattice

12. Binary System and Structure Factor (2D)

13. Example 1: Square Lattice, Circular Rods/Holes

14. Example 2: Triangular Lattice, Circular Rods/Holes

15. Example 3: Simple Cubic Lattice, Spheres

16. Bloch’s Theorem (Electron Systems):
Bloch’s Theorem and Brillouin zone
Bloch’s Theorem (Electron Systems):
First Brillouin Zone

17. Proving Bloch’s Theorem

18. Band Structure (Electron System)

19. Bloch’s Theorem and Photonic Band Structure

20. Energy Flow in Photonic Crystal
See Sakoda

21. Frequency Contours
Square Lattice

22. Two-Dimensional Inhomogeneous Wave Systems
Classical Waves
Unified Treatment

23. Binary System, Harmonic Waves
Scattered wave
Incident wave

24. Band Structure Calculation (2D, Scalar Wave)

26. Reduced Brillouin Zone and Dimensionless Frequency

27. Left: Photonic Band , Right: Transmission (20layers)
Photonic Band Gaps
Left: Photonic Band , Right: Transmission (20layers)