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

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

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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

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

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Proof Use reverse Fourier transform we have

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

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Field coupling

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

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

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Some practical structure of PC

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Superprism effect Group velocity effect Group velocity change sharply

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

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

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Antenna applications The experiment result :

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

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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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