1. Photonic Band Gap Materials: The “Semiconductors” of the future? C. M. Soukoulis Ames Lab. and Physics Dept. Iowa State University. and Research Center of Crete, FORTH - Heraklion, Crete

2. Collaborators Ames Laboratory, Iowa State University –Mike Sigalas (Agilent) –Gary Tuttle, W. Leung –Ekmel Ozbay (Turkey) –Rana Biswas –Mario Agio (Pavia), P. Markos (Slovakia) –E. Lidorikis (MIT), S. Foteinopoulou –C.T. Chan (Hong-Kong) –K.M. Ho Research Center of Crete –E. N. Economou –G. Kiriakidis, N. Katsarakis, M. Kafesaki –PCIC

3. Computational Methods Plane wave expansion method (PWE) C.T. Chan, K.M. Ho, E. Lidorikis, S. Foteinopoulou Transfer matrix method (TMM) M. Sigalas, I. El-Kady, P. Markos, S. Foteinopoulou Finite-difference-time-domain-method (FDTD) M. Agio, M. Kafesaki, E. Lidorikis, S. Foteinopoulou soukoulis@ameslab.gov soukouli@iesl.forth.gr http://cmpweb.ameslab.gov/personnel/soukoulis

4. PHOTONIC BAND GAP STRUCTURES: THE “SEMICONDUCTORS” OF THE FUTURE? Semiconductors Periodic crystal potential Atomic length scales Crystal structure given by nature Control electron flow 1950’s electronic revolution PBG Crystals Periodic variation of dielectric constant Length scale ~ Man-made structures Control e.m. wave propagation 1990’s optical fibers, lasers, PBGs --> photonics era

6. Fermi’s Golden Rule: hv Density of final states

7. Applications: Microwaves Efficient planar antennas Photonic Crystal Dielectric

8. Applications: Optical range Suppression of spontaneous emission Low-threshold lasers, single-mode LEDs, mirrors, optical filters

9. APPLICATIONS OF PBG MATERIALS: Frequency-selective, loss-less reflection Filters, switches, optical amplifiers Areas impacted: Automotive electronics - e.g., collision-avoidance radar (60-77 GHz) Electron cyclotron resonance heating for fusion plasma, diagnostic tool (60-200 GHz) Medical and biological application - e.g., microwave resonance therapy (40-80 GHz), imaging Wide bandwidth communication (60, 94 GHz) mm waveguides Fast electronics - interchip communication Remote sensing - e.g., monitoring atmospheric radiation; observational astronomy Lasers and optical devices - improved performance in efficiency and reduction of background noise Photocatalysis mm wave Infra-red visible

10. Outline Progress in fabricating 3D photonic crystals Layer-by-Layer structure (ISU) 3-cylinder structure (LIGA) Inverse opals and ordered silica matrices (many groups) Metallic photonic crystals Metallic and dielectric bends Photonic Crystal Waveguides and Bends (2D slabs or 3D PCs) Studies of the losses and effects of disorder

12. Three - cylinder Structure or Yablonovite Diamond like symmetry. PRL 65, 3152 (1990) and Euro. Phys. Lett. 16, 563 (1991) E. Yablonovitch

13. E. Yablonovitch et. al. PRL 67, 3380 (1991) 3-cylinder structure

14. Fabrication of 3-cylinder structure by LIGA technique Appl. Phys. Lett. 71, 1441 (1997) ISU, FORTH and Mainz

15. v=2.4 THz Appl. Phys. Lett. 71, 1441 (1997) experiment

16. Ho, Chan and Soukoulis, PRL 65, 3152 (1990) Diamond lattice gives the largest photonic band gap

17. Ho, Chan and Soukoulis, PRL 65, 3152 (1990) Diamond lattice

18. Photonic band gap formation A synergetic interplay between microscopic (Mie) and macroscopic (Bragg) resonances. Bragg scattering: 2d = m   /c = m  / d, m=1,2,… Mie resonance: 2r/ i = (m+1)/2, m=0,1,2,… oo Maximum reflection (m=0): Gap appears when:  (filling ratio) d ii r

19. Experimental band structure of a fcc lattice of air spheres Gap Fcc Airball(86%) n=3.5 Yablonovitch & Gmitter, PRL 63, 1950 (1989)

20. Ho, Chan and Soukoulis, PRL 65, 3152 (1990) FCC lattice has only a pseudogap

21. figure Density of States for a fcc structure of air spheres Ho, Chan and Soukoulis, PRL 65, 3152 (1990) Sozuer, Haus and Inguva, PRB 45, 13962 (1992) √ Busch and John, PRE 58, 3896 (1998)

22. Band structure for a close-packed fcc lattice of air spheres in silicon Busch and John, PRE 58, 3896 (1998)

23. DOS for a close-packed fcc lattice of air spheres in silicon Busch and John, PRE 58, 3896 (1998)

24.  /2  c DOS Air Spheres (  =1) in Dielectric (  =10) fcc arrangement with Air filling ratio ~ 74% supercell: 3  3  3, k-point sampling: 8  8  8, total grids: 72  72  72 Disorder In Position 0.30 0.015 0.85 0.040 1.60 0.085 2.40 0.135 : Average rms error in the dielectric constant  d:  D/R) at half peak d 0 : D/R at peak value  d/d 0 Lidorikis, Soukoulis

25.  /2  c DOS Air Spheres (  =1) in Dielectric (  =10) fcc arrangement with Air filling ratio ~ 74% supercell: 3  3  3, k-point sampling: 8  8  8, total grids: 72  72  72 Disorder In Radius 0.34 0.1 0.67 0.2 1.00 0.3 1.30 0.4 : Average rms error in dielectric const.  v:  V/V 0 )  v Lidorikis, Soukoulis

26. Carbon structures with 3d periodicity at optical wavelengths A. Zakhidov et. al. Science, 282, 897(1998)

27. On-chip natural asembly of silicon photonic bandgap structures Y. A. Vlasov et. al. Nature, 414, 289 (2001)

28. K. Busch and S. John, PRL 83, 967 (1999) Inversed opals infiltrated by liquid crystals

29. A. Blanco et. al. Nature 405, 437 (2002) Silicon inverted opals

30. Fabrication of photonic crystals by holographic lithography M.Campell et. al. Nature, 404, 53 (2000)

31. An easy-to-build structure with a full photonic band gap Iowa State layer-by-layer structure: Science News 144, 199 (1993); Solid State Comm. 89, 413 (1994) Phys. Rev. B 50, 1945 (1994)

32. Diameter of Rods Spacing of RodsMidgap Frequency Corresponding Wavelenth at Midgap 0.32 cm1.120 cm13 GHz 23 mm √ 0.20 cm0.711 cm20 GHz15 mm √ 0.08 cm0.284 cm50 GHz6 mm √ 340 micron1275 micron100 GHz3 mm √ 100 micron350 micron450 GHz0.66 mm √ 1.33 micron4.7430 THz10 micron 0.20 micron0.7112 x 10 14 Hz1.5 micron 667 Å2370 Å6 x 10 14 Hz5000 Å Iowa State University’s layer-by-layer structure Science News 144, 199 (1993); Solid State Comm. 89, 413 (1994) Phys. Rev. B 50, 1945 (1994) ? !! !!! ??

33. Iowa State University’s layer-by-layer structure Sandia National Laboratory.Iowa State University Ames Laboratory

34. Electro magnetic waves are incident on the side surface

35. Theory and experiment is in excellent agreement

36. An average attenuation of 16 dB per unit cell is obtained

37. Theoretical (dashed line) and experimental (solid line) transmission characteristics of the defect structure

38. The ISU layer by layer structure fabricated at Kyoto Univ. S. Noda et. al. Science, 289, 604 (2000)

40. S. Y. Lin et. al. Nature, 394, 251 (1998)

42. R. Biswas, ISU

44. Propagation along 90 bends in 3d dielectric structures M. Sigalas et. al. Microwave Opt. Techn. Lett. 23, 56 (1999) S. Noda, Kyoto Univ.

45. Metallic Structure

47. y x

48. Propagation along 90 bends in 3d metallic structures Transmission along the bend is more than 95% !! M. Sigalas et. al. Phys. Rev. B 60, 4426 (1999)

49. Agio and Soukoulis, PRE, 64, 055603R (2001)

50. Waveguide modes for widths of W1 and W3

52. Guided bends in Photonic Crystals: - Study of 60 o bends in W3 and W5 --Best the smoothest one in collaboration with PCIC groups

53. W3 taper+slit double bends Modal analysis for slit2 Field profile for a/ 

55. Studies of the out of plane losses

56. Kafesaki, Agio, Soukoulis, JOSA B (2002) Photonic Crystal Slabs

62. Comparison of 2D and 3D results 3D 2D 3D results can be derived by an effective 2D system with a slightly different f and an imaginary 

63. 2D and 3D gaps almost coincide in position and width.

64. Y-Splitters

65. Summary and Conclusions The layer-by-layer structure has been fabricated at telecom frequencies Inverse closed packed structures with high index materials ( TiO2, Si, Ge ) Doping of PBGs with active atoms and molecules will lead to new frontiers in microlasers, low threshold switches, random lasers Metallic PBGs. Connectivity is very important Photonic Crystal Waveguides and Bends ( 3d structures or dielectric slabs ) Tunable PBGs Detailed studies of disorder are very important

66. Summary: The “photon band structure” problem is solved Photonic gaps EXIST in diamond like structures Structure is optimized to give largest gap Localization of light in imminent Experimental Challenge Fabricate these new dielectric structures at optical wavelengths, then Applications of photonic gaps in physics and engineering may become possible.