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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 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 • The surface of the PC can be considered as a plane
The Floquet-Bloch theorem • Any function satisfying can be represented as • And • This is Floquet-Bloch transform
Proof • Use reverse Fourier transform we have
Field coupling • Consider a incident wave Eiand refraction wave Er and transmission wave Et • Dispersion relation:
Some practical structure of PC • The blue triangle in the figure is the first Brillouin’s zone
Brillouin’s zone • For 1D condition, Ɛ(x+a)=Ɛ(x) the first Brillouin’s zone is • Extend this concept to 3D
Superprism effect • Group velocity effect • Group velocity change sharply
Superprism effect • Chromatic dispersion effect • The amp also change with the freq
Antenna applications • We can use PC to control the propagation direction of antenna
Antenna applications • The experiment result :
More applications of PC • PCF(Photonic crystal fibers) • Invisible cloak
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