1. Planar gradient meta-surface to focus EM waves in reflection geometry
Xin Li1, Shiyi Xiao1, Qiong He1, Bengeng Cai2, Tiejun Cui2, Lei Zhou1*
1State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai, , China
2 State Key Laboratory of Millimeter Waves and Institute of Target Characteristics and Identification, Southeast University, Nanjing , China
Backgrounds:
III. FDTD & Experimental Verification
PROBLEMS !
Metamaterials are used to focus plane waves to point image in transmission geometry1,2,3.
Energy loss due to reflection at surface caused by impedance mismatch.
Using high impedance surface as basic structure
Sandwich structure: metallic H-shape + dielectric slab + metal
Magnetic resonance
Different Ly in a super cell
Hyperbolic φ
Motivation:
Planar lens in reflection geometry
Fig. 1 Various structures to focus PWs in transmission geometry
I. Concept – Radiation of A Surface Current
Fig. 5 (a) φ dependence on Ly (b) φ distribution in a super cell.
Fig. 6 Fabricated sample
Electric field at different z planes
Fig. 2 Scheme of planar lens focusing
Surface current distribution
Fig. 4 Electric field at (a) z=f (b) z=2f
FIG. 7 (a) Scheme for experiment setup. (b) Electric field of FDTD simulation. (c) Corresponding experiment result.
(d) Electric field distribution at focal plane of FDTD simulation (green line) and experiment (purple circle).
Field enhancement~3
Half peak width~
: focus
II. How to Realize Such A Surface Current?
added phase term to compensate propagation phase difference
Oblique incidence
Applying dyadic Green’s function
For a homogeneous system:
Polarization current for TE wave
Radiated electric field
Reflected electric field
Numerical calculation ( )
whereφis reflection phase
FIG. 8 FDTD simulations for oblique incidence (a) 10° (b) 20° (c) 30° (d) 45° or
By LDA, the system must be inhomogeneous
with position-dependentφ
Conclusions:
Criterion for focusing: surface current with hyperbolic φ(x)
Design samples and employ both FDTD simulation and experiment to verify our idea
Ultra-thin device, works for oblique incidence
Different focuses based on different parameters
Such a hyperbolic profile ofφ(x) can be realized by carefully designed gradient meta-surface
Fig. 3 Numerical calculated radiated electric field
[1] L. Verslegers, et al., Nano Lett. 9, 235 (2009)
[2] L. Lin, et al., Nano Lett. 10, 1936 (2010)
[3] O. Paul, et al., Appl. Phys. Lett. 96, (2010)