METAMATERIALS and NEGATIVE REFRACTION
Nandita Aggarwal
Laboratory of Applied Optics
Ecole Polytechnique de Federal Lausanne
Presentation Overview
Introduction to negative refraction
Theoretical explanation
Experimental verification
Different structures as metamaterials• SRR structure• S-SRR structure• EX-SRR structure• Omega type structure
Negative refraction in optical regime
Applications• Super lenses• High directive Antennas• Cloak invisibility
References
Reversing light : Negative refraction
Time reversal
Negative Refraction
(Reversal of spatial evolution of phase)
Time reversal and negative refraction
Disobeying Snell’s Law: Left handed materials
Light makes negative angle with the normal
Poynting vector has the opposite sign to the wave vector
Theoretical Explanation in brief
Assumption: Wavelength used > spacing and size of the unit cell.
Composite can be assumed homogeneous.
µ(eff.) and ε(eff.) are structure dependent.
Experimental Verification
Al plates separation: 1.2 cm
Radius of circular plates: 15 cm
Detector was rotated around the circumference of circle in 1.5 degree steps
LHM material (Prism)Unit cell : 5mmOperating wavelength : 3cm (8-12 GHz)
Experimental Verification
Refractive index of teflon : 1.4 +- 0.1
Refractive index of LHM : -2.7 +-0.1
• Split Ring Resonators + Metallic Wires
• S shaped Split Ring Resonators
• Extended S shape Split Ring Resonator
• Fish scale
• Omega type
Different Structures as Metamaterials
Split Ring Resonator + Metallic Wires
Dispersion curve for the parallel polariraztion. Dashed line shows the SRR with wires placed uniformly between them.
Split Ring Resonator
S shaped Split Ring Resonators
Effective permeability for the S-SRR structure in the case of F1 = F2 = F = 0.3
S shaped Split Ring Resonators
Two unit cells of a periodic arrayed structure (a) A broken rods array, (b) A capacitance-enlarged rods array, (c) A ‘S’- shaped rods array
S shaped Split Ring Resonators
The real part of the effective permittivity measured for configuration (b) and (c) with the change in value of h.
Extended S-shaped Split Ring Resonators
The ES-SRR structure with a period of 2 rings in the z direction and its analytical model
Extended S-shaped Split Ring Resonators
Extended S-Shaped SRR Normal S-Shaped SRR
Effective Permeability Vs. Frequency
Omega type structuresSnell refraction experimental results
3-D result with the three axes representing detected power in mW, Frequency in GHz and angle in degrees.
2-D curve extracted at 12.6 GHz from 3-D results.
Negative refraction in optical regime
Detailed history of development of magnetic resonance frequency as a function of time
Superlens
The electric component of the field will be given by some 2D fourier expansion:
Propagating waves:
Evanescent waves:
Diffraction limit of the lens:
Superlens
• With this new lens, both propagating and evanescent waves contribute to the resoltuion of the image
• Enhancement of evanescent waves i.e. amplification (though evanescent waves carry no energy still the results are surprising) of these waves was proven by Sir John Pendry in 2000.
Negative Refraction Makes a Perfect Lens
Superlens
Perfect Lensing in Action
A slab of negative material effectively removes an equal thickness of space for
(A) The far field
(B) The near field , translating the object into a perfect image
Highly Directive Antennas
Geometrical interpretation of the emission of a source inside slab of metamaterial having optical index close to zero
Construction in reciprocal space
Cloaking
"I still think it is a distant concept, but this latest structure does show clearly there is a potential for cloaking -- in the science fiction sense – to become science fact at some point," says Smith.
Invisible Man become a reality?
Cloaking
Snapshots of time-dependent , steady-state electric field patterns.Cu cyllinder is cloakedA: Simulation of cloak with exact material propertiesB: Simulation with reduced material propertiesC: Experimental measurment of bare conducting cyllinder D: Experimental measurments of cloaked conducting cyllinder
References
1. J.B Pendry Physics review Letters, Vol. 85, no. 18 (3966-3969)
2. John B. Pendry and David R. Smith DRS&JBP (final).doc, Physics
Today
3. Costas M. Soukoulis, Stefan Linden, Science, Vol 315, (47-49)
4. H.S Chen et al. PIER 51, 231-247, 2005
5. D. Schurig, J.J. Mock, Science, Vol 314 (977-979); 2006