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Superprism effect and EBG antenna applications

Superprism effect and EBG antenna applications. Reporter: 楊岡昀 Date:2010/5/20. Outlines. Floquet-Bloch transform Some practical structure of PC Superprism effect Antenna applications. Floquet-Bloch transform. Some hypotheses: Size of PC is much larger than the wavelength

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Superprism effect and EBG antenna applications

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  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 Eiand 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

  11. 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

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