1. Superprism effect and EBG antenna applications Reporter: 楊岡昀 Date:2010/5/20

2. Outlines Floquet-Bloch transform Some practical structure of PC Superprism effect Antenna applications

3. Floquet-Bloch transform Some hypotheses: Size of PC is much larger than the wavelength The surface of the PC can be considered as a plane

4. The Floquet-Bloch theorem Any function satisfying can be represented as And This is Floquet-Bloch transform

5. Proof Use reverse Fourier transform we have

6. Field coupling Consider a incident wave Ei and refraction wave Er and transmission wave Et Dispersion relation:

7. Field coupling

8. Some practical structure of PC The blue triangle in the figure is the first Brillouin’s zone

9. Brillouin’s zone For 1D condition, Ɛ(x+a)=Ɛ(x) the first Brillouin’s zone is Extend this concept to 3D

10. Some practical structure of PC

12. Superprism effect Group velocity effect Group velocity change sharply

13. Superprism effect Chromatic dispersion effect The amp also change with the freq

14. Antenna applications We can use PC to control the propagation direction of antenna

15. Antenna applications The experiment result :

16. More applications of PC PCF(Photonic crystal fibers) Invisible cloak

17. References METAMATERIALS Physics and Engineering Explorations, NADER ENGHETA/RICHARD W. ZIOLKOWSKI Semiconductor Physics and Devices, D.A. Neamen Handout of the lesson 光子晶體 (Photonic Crystals), which is held by Professor 邱奕鵬