Photonic band gap effect, localization, and waveguiding in two-dimensional Quasicrystals

Transcription

1 Photonic band gap effect, localization, and waveguiding in two-dimensional Quasicrystals Mehmet Bayındır Ertugrul Cubukcu Irfan Bulu Ekmel Özbay M. Bayindir et al., Phys. Rev. B 63, 16114(R) (21) M. Bayindir et al., Europhysics Lett. 56, 41 (21) Department of Physics, Bilkent University, Turkey CLEO/QELS 21

2 Outline Review of recent works on quasiperiodic photonic crystals Dielectric and metallic Penrose photonic crystals Observation of photonic band gaps Defect characteristics Highly localized cavity modes within the stop bands Absence of translational symmetry tunning of the cavity frequency Guiding and bending of electromagnetic waves in planar waveguides Observation of waveguiding through coupled cavities The tight-binding approximation in classical waves Measurement and calculation of dispersion relation FDTD simulation of the coupled-cavity cavity waveguide (CCW) structures Summary

3 Photonic Band Gap Effects in Quasicrystals Octagonal quasicrystal quasicrystal Chan et al. Jin et al. Recent Works: Chan et al.,, PRL 8, 956 (1998): Existence of photonic band gap in octagonal quasicrystal,, defect characteristics Jin et al.,, APL 75, 1848 (1999): Observation of waveguiding in octagonal quasicrystal Cheng et al.,, PRB 59, 491 (1999): Defect characteristics and waveguiding Jin et al.,, PRB 61, 1762 (2): Cavities in dodecagonal and decagonal quasiperiodic Zoorob et al.,, Nature 44, 74 (2): Complete photonic bandgaps in 12-fold symmetric quasicrystals Zhang et al.,, PRB 63, 8115(R) (21): Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals Bayindir et al.,, PRB 63, 16114(R) (21): Photonic band gap effects, cavities, coupled-cavities, cavities, guiding and bending of EM waves in Penrose crystal

4 Two-dimensional Penrose Photonic Crystals Dielectric Crystal Specifications: Material = Alumina Radius = mm Length = 15 cm Filling factor.14 Refractive index = 3.1 Rhombic cell edges = 1.2 cm Metallic Crystal Specifications: Material = Copper Radius=3.1 mm Length=15 cm Filling factor.14 Rhombic cell edges=1.2 cm Experimental Setup

5 Dielectric Penrose Crystal: Transmission Spectra -1 Transmission (db) θ= o θ=3 o θ=6 o θ=9 o Photonic band gap θ The dielectric Penrose photonic crystal exhibits a stop band extending ending from 9.9 to 13.2 GHz for all incidence angles.

6 Metallic Penrose Crystal: Transmission Spectra Transmission (db) θ= o θ=3 o θ=6 o θ=9 o Plasma Frequency Photonic Band Gap θ The metallicity gap extends from zero frequency up to the plasma frequency ω p =14.9 GHz The photonic band gap due to the quasiperiodicity appears between 19.6 to 2.7 GHz

7 Dielectric Penrose Crystal: Defect Characteristics A B C FDTD Simulations Field patterns B Transmission (db) C B A C The strongly localized cavity modes were observed within the photonic band gap Higher cavity volume leads to shift the cavity mode to a lower frequency

8 Metallic Penrose Crystal: Defect Characteristics A Transmission (db) C B A B C The localized cavity modes were observed within both metallicity and photonic band gaps Higher cavity volume leads to shift the cavity mode to a lower frequency

9 Planar Dielectric Waveguides: Guiding and Bending Transmission (db) Guiding Band The metallicity gap extends from zero frequency up to the plasma frequency ω p =14.9 GHz The photonic band gap due to the quasiperiodicity appears between 19.6 to 2.7 GHz

10 Planar Dielectric Waveguides: Guiding and Bending Transmission (db) Bending Band The metallicity gap extends from zero frequency up to the plasma frequency ω p =14.9 GHz The photonic band gap due to the quasiperiodicity appears between 19.6 to 2.7 GHz

11 Propagation of Photons via Hopping: Tight-binding Picture Highly localized and weakly interacting cavity modes The tight-binding approximation [ E () r ] = ( Ω c) 2 ε ( r) E ( r) Ω inkλ () r = E e E ( r nλ) E n Ω ( 1 κ cos( k )) ω ( k) = Ω + Λ Ω v g ( k) = ω( k) = ΩΛκ sin( kλ) k τ ( k) = L v ( k) + 2πL p g c Photons can propagate along the localized cavity modes due to coupling c between them Dispersion relation, group velocity, and photon lifetime depend only a single tight-binding parameter κ that can be directly determined from experiments

12 Dielectric Coupled-Cavity Cavity Waveguides: Transmission and Phase Measurements Measurement Calculation Transmission (db) Defect Band kλ/π A defect band, waveguiding band, is formed within the photonic band b gap The measurement is in good agreement with the tight-binding model prediction.

13 Dielectric Coupled-Cavity Cavity Waveguides: FDTD Simulations Photons can propagate along highly localized coupled-cavity cavity modes throughout the waveguiding band

14 Summary We observed the photonic stop bands in dielectric and metallic PenroseP photonic crystals Strongly localized cavity modes were observed Tunning of the cavity frequency can be achieved due to absence of translational symmetry We observed guiding and bending of electromagnetic waves in planar ar waveguide structures Propagation of photons by hopping was observed in the coupled-cavity cavity structures Field patterns of various structures were obtained by using the FDTD code (FullWave( FullWave) Acknowledgements These works were supported by Turkish Department of Defense Grant No. KOBRA-1, and Thales JP8.4 NATO Grant No. SfP97197 National Science Foundation Grant No. INT