1. NEGATIVE REFRACTION AND FOCUSING USING PHOTONIC CRYSTALS
DALHM Meeting
July 29,
FORTH, Heraklion, Crete

2. 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

3. 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,
Square Lattice of dielectric (alumina n=3.13) rods in air.
a = 4.79 mm.
ω= GHz
Guven - DALHM Meeting - July 2004 FORTH - Crete

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

5. Subwavelength Focusing
ω= 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

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

7. 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= GHz
Guven - DALHM Meeting - July 2004 FORTH - Crete

8. 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

9. Guven - DALHM Meeting - July 2004 FORTH - Crete

10. 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
Guven - DALHM Meeting - July 2004 FORTH - Crete

11. 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

12. 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

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

14. 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

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

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

17. 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)

18. 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

19. 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

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

21. 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

22. 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

23. 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

24. 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

25. Guven - DALHM Meeting - July 2004 FORTH - Crete
Outlook
Far:
Scaling down (Far-infrared and beyond?)
Going up: 3D?
Taken from:
Guven - DALHM Meeting - July 2004 FORTH - Crete