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Lecture on Photonic Crystals

Lecture on Photonic Crystals. 陳啟昌 副教授 國立中央大學 光電科學與工程系. Butterfly crystals. Phys Rev E.67.021907,2003. Spine of sea mouse.

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Lecture on Photonic Crystals

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  1. Lecture on Photonic Crystals 陳啟昌 副教授 國立中央大學 光電科學與工程系

  2. Butterfly crystals Phys Rev E.67.021907,2003

  3. Spine of sea mouse The sea mouse may not look like a mouse, but its hairs are photonic marvels. As the angle of incident light changes, the photonic crystal structure of the spines tunes their reflectance, making new colors appear.

  4. Opal Optics and Photonics News, p.38, Feb, 2003

  5. Famous People Eli Yablonovitch UCLA (Bell Communication Research) Reduction of spontaneous emission Sajeev John University of Toronto (Princeton University) Localization of light

  6. Properties of EM waves 反射(Reflection) 折射(Refraction) 繞射(Diffraction) 干射(Interference) 色散(Dispersion) 極化(Polarization) 波動(wave) 粒子(particle, photon)

  7. Definition of Polarization Plane of incidence Ei Er Br Bi ni Interface qi qr nt Bt qt Et TM TE: transverse electric mode(┴), E perpendicular to PoI TM: transverse magnetic mode(//), E parallel to PoI Brewster’s angle=polarization angle qi+qt=90o r//=0 Application: Test of polarizer

  8. Design of high-reflection coating n1 t1 n2 t2 n1 t1 n2 t2 ns l n0 N pairs Transmission n1t1=l/4 n2t2=l/4 l

  9. 1D, 2D and 3D photonic crystals 1D 2D 3D Transmission Photonic bandgap w

  10. Dispersion relation of bulk materials bulk Refractive index of AlxGa1-xN bulk l(nm)=1240/Ephoton(eV)

  11. k and wavelength :Propagation vector k: the magnitude of , propagation number=2p/l

  12. Dispersion relation w=w(k) of waveguide vg2 Slab vg=Dw/Dk n=c/vg vg1 Helmholtz equation:

  13. Band structure of 1D photonic crystal 1D P. C. w p/a -p/a Photonic bandgap k

  14. Reciprocal lattice vector First Brillouin Zone First Brillouin Zone Reciprocal lattice vectors provide a nature basis for optical wavevectors

  15. Ey Ex y Ey x z Band structure of 2D photonic crystal Ex

  16. Electronic band structure and photonic band structure Acta Materialia vol. p.5823, 2003

  17. Crystal Structures Body Centered Cubic Face Centered Cubic Buckyballs C60 Diamond

  18. Diamond, Zinc Blende, FCC, BCC crystal structures ZB Diamond FCC BCC

  19. kz P F L ky D D H G S G N kx First Brillouin zone of 3-D crystal structures kz L L U G Q S ky D S X Z W kx K Body Centered Cubic Face Centered Cubic The centre of the zone, which is characterised by the wave vector , is always denoted by . The points X and L lie at the surface of the first Brillouin zone. It is seen, for example, that the line  connecting  and X is directed along the crystallographic direction {100} and the line  connecting  and L is directed along the crystallographic direction {111}.

  20. Scaling law a/l

  21. Defect states Defects Defect states Transmission Defect state Ed Energy

  22. Tools for PBG structure design Finite-Difference Time-domain Method (FDTD) Propagation of electromagnetic field

  23. Tools for PBG structure design Finite-Difference Time-domain Method (FDTD) Mode pattern

  24. Tools for PBG structure design Finite-Difference Time-domain Method (FDTD) Transmission or reflection spectrum

  25. Tools for PBG structure design FDTD method Maxwell equations Yee lattice K. S. Yee, IEEE Trans. Antennas Propagat. Vol. AP-14, p. 302, 1966.

  26. Tools for PBG structure design Plane Wave Expansion Method (PWE) Band structure calculation

  27. Tools for PBG structure design Plane Wave Expansion Method (PWE) Defect mode of photonic crystal structure

  28. Tools for PBG structure design Plane Wave Expansion Method (PWE) Mode patterns

  29. Tools for PBG structure design Multiple Scattering Theory (MST) Data from Prof. Z. Ye Propagation of electromagnetic field

  30. Slab waveguides Effective index neff n1 x Helmholtz equation n2 (1)Finite-difference method n3 (2)Marcatili’s method

  31. neff of SOI structure and cut-off thickness neff nair=1 t nSi=3.46 nSiO2=1.46 t (mm)

  32. Photoresist Spin coating Substrate Patterning Dry Etching Stripper Fabrication techniques e-beam photolithography

  33. E-beam writer in NCU Raith 150 Acceleration voltage: 200-30keV

  34. E-beam photolithography 中央大學光電中心李建階老師提供

  35. Focused Ion Beam Ga source

  36. Collaboration with Dr. M-P Bernal Université de Franche-Comté (France) Using FIB milling PC structure fabricated by FIB in LiNbO3 Period=720nm Radius=200nm 12min , square Period=1mm Radius=300nm 10min , hexagonal

  37. PC fiber

  38. Photonic Crystal Research in NCU FDTD PWE MST E-beam photolithography microspheres PC Waveguides Engineering Theory 葉真 欒丕綱 Design Fabrication 陳啟昌 張正陽 詹益仁 張正陽 李建階 陳暉 綦振瀛 Single photon light source Characterization 陳啟昌 徐子民 張正陽

  39. 4吋Si與III-V製程 Equipments Fabrication for 4” Si and III-V

  40. Equipments

  41. Artificial opal and Inversed opal Nanotechnology 16, 1440, 2005 Applied Surface Science, vol. 217/1-4, pp 281-288, 2003. Desalination, vol. 200, 97, 2006

  42. Output 2 Output 1 Input 1 beamsplitter Input 2 Photonic crystal beam splitters Type II Type I Air holes Dielectric rods Applied Optics, vol.43, p.4188, 2004 US patent: 6,879,432B1, 2004. Optics Communications vol. 259, p.873, 2006

  43. PC directional couplers Conventional waveguides Output port for 1.31mm Output port for 1.55mm PC waveguides Input port Tile 45 degree Top view Optics Express, vol. 13, p.38, 2005.

  44. SHOW-ODR with wafer bonding 1dB/cm (C+L band) for TE and TM modes Large operation bandwidth: C+L band Low propagation loss Low polarization dependent loss Low material dispersion Low non-linearity Low material absorption Micro-fluidic channel Optics Express, vol. 12, p. 6589, 2004. IEEE Photonic Technology Letters, vol.17, 2592, 2005 IEEE J. MEMS 15, 584, 2006

  45. Reflection Coupling between conventional waveguides and PC waveguides Air holes Fabrication in Friedrich Schiller University Jena, Germany PC lens PC taper Opt. Express. Vol. 14, 10759, 2006

  46. GaN photonic crystals ~60nm GaN Appl. Phys. Lett. vol. 89, 071116, 2006 also selected to be published in Virtual Journal of Nanoscale Science & Technology, September 4, 2006 Volume 14, Issue 10

  47. Directional emission from PC waveguides Optics Express vol. 14, 2423, 2006

  48. Transmission spectrum of photonic crystal waveguides with and without microspheres TM TE Optics Express vol. 12, p. 3934, 2004

  49. Partial bandgap or Negative refraction Phys. Rev. B 70, 113101,2004

  50. New PC book in chinese

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