NEGATIVE REFRACTION AND FOCUSING USING PHOTONIC CRYSTALS DALHM Meeting July 29, 30 2004 FORTH, Heraklion, Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete outline Negative Refraction and Focusing studies on 2D photonic crystals so far: I. TM polarized lower band of a 2D dielectric photonic crystal. (E. Çubukçu, K. Aydın) II. TE polarized upper band of a 2D dielectric photonic crystal. (K. Güven, K. Aydın, Boratay Alıcı) III. Metallic-dielectric photonic crystal. (İ. Bulu, H. Çağlayan) Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete I. Cubukcu E., Aydin K., Ozbay E., Foteinopoulou S., and Soukoulis C. M., (2003) Nature, 423, 604; (2003) Phys. Rev. Lett. Vol. 91, 207401. Square Lattice of dielectric (alumina n=3.13) rods in air. a = 4.79 mm. ω=13.1-15.44 GHz Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete Refraction @ ω=13.7 GHz POLYSTRYLENE PELLETS PHOTONIC CRYSTAL Guven - DALHM Meeting - July 2004 FORTH - Crete

Subwavelength Focusing ω=13.698 GHz (λ=21.9 mm) dsrc=7.0 mm (0.3λ) Lateral intensity profile at d = 7.0 mm FWHM=0.21λ Guven - DALHM Meeting - July 2004 FORTH - Crete

Subwavelength resolution Two source configuration: dsrc=7.0 mm Δdsrc=λ/3 Top: two coherent sources (@ ω=13.698 GHz) Bottom: two incoherent sources (@ ω1=13.698 ω2=13.608 GHz) Fact: No sub-λ resolution even for n=15 (dash-dotted line)! Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete II. TE Polarized Upper Band of a 2D dielectric PC (submitted to Phys. Rev. B) Hexagonal crystal a=4.79 mm r=1.57 mm n=3.13 ω=41.0-46.3 GHz Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete Frequency surface and equal frequency contours of the 5th band in the full Brillouin zone Group Velocity and Phase Velocity are antiparallel. Thus: becomes negative Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete high order reflection occurs Propagation in the PC appears to be a single beam (mark 4), also supported by the presence of a single transmitted beam (mark 5) S. Foteinopoulou, and C. M. Soukoulis http://arxiv.org/cond-mat/0403542 Guven - DALHM Meeting - July 2004 FORTH - Crete

Effective refractive index calculation using Snell’s Law Incidence angle 150 300 450 neff (exp.) -0.52 -0.66 -0.86 neff (sim.) -0.72 -0.80 Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete Focusing of an omnidirectional source: dsrc/λ=2 dsrc/λ=4 Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete Intensity profiles in the focusing plane Experiment FDTD Simulation Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete Lateral Intensity Profiles at the respective focus locations for different source-PC distances: dsrc + dfocus≈constant Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete Flat Lens Behavior Guven - DALHM Meeting - July 2004 FORTH - Crete

Resolution of two sources? Guven - DALHM Meeting - July 2004 FORTH - Crete

I. Bulu, H. Caglayan, and E. Ozbay (submitted to Phys. Rev. B) Negative Refraction and Focusing using a 2D metallo-dielectric photonic crystal I. Bulu, H. Caglayan, and E. Ozbay (submitted to Phys. Rev. B)

Guven - DALHM Meeting - July 2004 FORTH - Crete Why metal-dielectric photonic crystal? The EFCs of metallic crystal are much smaller than the free space EFCs. All angle negative refraction requires (approximately) EFC between two media. A periodic dielectric perturbation to the metallic photonic crystal “flattens” the bands. Square lattice, a=1.1 cm, alumina (dielectric) and aluminum (metal) rods. Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete For the plotted free space EFS, at all incidence angles group velocities of the incident field and the refracted field fall into different sides of the surface normal vector. Conservation of the surface parallel component of the wave vector indicates that at the plotted frequency all incidence angles are negatively refracted. Guven - DALHM Meeting - July 2004 FORTH - Crete

Incidence: 35o Positively refracted, f=8.8 GHz Negatively refracted, f=9.77 GHz Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete within the frequency range of 9.1 GHz and 10.3 GHz waves are negatively refracted. as the angle of incidence increases so does the angle of refraction. Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete Focusing is observed away from the surface of the crystal. For source distances of 5 cm (top) and 7 cm (bottom) the focusing points are at 7.5 cm and 4.8 cm, respectively. Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete CONCLUSIONS Various photonic structures are employed for the investigation of negative refraction and focusing phenomena in the microwave regime: The two mechanisms giving rise to negative refraction is demonstrated experimentally. Focusing: Sub-λ resolution close to the interface (near field) and resolution on par with λ away from the interface (far field) is achieved. A solid framework of experiment and theory (band-structure analysis and FDTD simulations) is established. Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete Outlook Near: Optimized structure (The Quest for n=-1!, isotropic band structure) Enhanced transmission (better coupling at the interface. Surface corrugation analysis) Further investigation of metal-dielectric and all metal photonic crystals. Guven - DALHM Meeting - July 2004 FORTH - Crete

Guven - DALHM Meeting - July 2004 FORTH - Crete Outlook Far: Scaling down (Far-infrared and beyond?) Going up: 3D? Taken from: http://en.wikipedia.org/wiki/Electromagnetic_spectrum Guven - DALHM Meeting - July 2004 FORTH - Crete