Making Optical Meta-Materials for Fun and Applications Gennady Shvets, The University of Texas at Austin Saturday Physics Workshop, April 22, 2006

What is a MetaMaterial? Originates from a Greek word  : "after/beyond" Example: metaphysics ("beyond nature"): a branch of philosophy concerned with giving a general and fundamental account of the way the world is. (Wilkepidia) Metamaterials are artificially engineered materials possessing properties (e.g., mechanical, optical, electrical) that are not encountered in naturally occurring materials. The emphasis of this talk in on unusual electromagnetic properties such as dielectric permittivity , magnetic permeability , and refractive index n.

What is a MetaMaterial? Material properties are determined by the properties of the sub-units plus their spatial distribution. For a <<   effective medium theory. For a ~  photonic effects. What about meso- scale materials: bigger than atom but smaller than the wavelength??

MetaMaterials for fun: fundamental physics on small scale The physics of "small-scale" lies at the heart of the metamaterial advantage. The physics at small scale is different than bulk physics and, from a performance standpoint, often significantly better. Quantum confinement, exchange-biased ferromagnetism, and effective media responses are all examples of how the physics at small-scale can result in enhanced electromagnetic properties. Example: unit cell of a microwave metamaterial consisting of a split-ring resonator and metal wires

MetaMaterials for profit: applications Endoscope for MRI: using the power of metamaterials for medical imaging (Wiltshire et. al., Science'01)

MetaMaterials for profit: applications Can one make a "perfect magnetic conductor"? Yes! Shown is the "High Impedance" (Z=E/H) surface that suppresses magnetic field Application: low-lying patch antennas that would not work on a conducting substrate.

Elecromagnetic Spectrum We may think that radio waves are completely different physical objects or events than gamma- rays. They are produced in very different ways, and we detect them in different ways. Radio waves, visible light, X-rays, and all the other parts of the electromagnetic spectrum are fundamentally the same thing. They are all electromagnetic radiation!

Microscopes: the Engines of Discovery Van Leeuwenhooke (1676): discovered bacteria, blood cells What if the imaged specimen is a sub-wavelength grating?

Difficult to resolve sub- features L >> d/2  Small features (or large wavenumbers) of the object are lost because of the exponential evanescence of short-wavelength waves

Getting up close: from far to near field E.H. Synge, "A suggested method for extending the microscopic resolution into the ultramicroscopic region" Phil. Mag. 6, 356 (1928) U. Durig, D. W. Pohl, and Rohrer, “Near-field Optical Scanning Microscopy” (1986) E. Betzig et. al., “Near-field scanning optical microscopy (NSOM)” (1986)

Getting too close may not be possible! Buried (sub-surface) features Amplify evanescent waves?

What is a dielectric permittivity? External field polarizes dielectric  field inside dielectric is smaller that outside  ratio is called dielectric permittivity  In most materials  (e.g.,  = 12 for Si,  = 2.25 for glass) Permittivity depends on frequency: long lookup tables! Not without exceptions:  < 0 in metals (visible, IR,…)

What is a magnetic permeability? External B-field magnetizes material More complex mechanisms: electron and nuclear spins Field inside can be smaller, or larger, or much larger In most materials  There are exceptions (ferrites), but only at microwave frequencies

How waves propagate (or not)? Propagation of electromagnetic waves in medium is determined by e and m of the medium (J. C. Maxwell): In most natural materials   waves propagate Sometimes either  < 0, or  < 0  no propagation

In vacuum “right-hand rule” relates E, H, and k. Note: normally  > 0 and  > 0 E H k Consequence: phase velocity (along k) and group velocity (along the Poynting ExH vector) are in the same direction In NIMs group and phase velocity are in opposite directions Positive Index Medium Negative Index Medium Basic properties of Negative Index Waves

Positive Index Medium Negative Index Medium Positive/Negative Index Interface What happens for the oblique incidence?

Unusual refractive properties of NIMs Light enters n > 0 material  deflection Light enters n < 0 material  focusing (“Veselago Lens”) Surface waves make Veselago’s lens a super-lens! (Pendry, 2000)

Straw in a negative index water empty glass regular water, n = 1.3 “negative” water, n = -1.3

Magnification in a NIM: dropping ball n = 1 regular material, n = 1 negative index material, n = -1 n = -1 From Dolling et. al., Opt. Lett’06

Negative Index Materials to the Rescue:  = -1,  = -1  n = -1 L/2 L L/2 Super-lens prevents image degradation  beats the diffraction limit established by Abbe

How to Make a Negative-Index Material In microwave range: use “perfectly” conducting components to simulate  < 0 and  < 0, Smith et.al., (2000) Metal poles:  = 1 –  p 2 /  2 < 0 Split-ring resonators, Pendry’99: “geometric” resonance at  M Challenges: (a) moving to optical frequencies (infrared, visible, UV) (b) simplifying the structure (  < 0 and  < 0 from same element)

Another Example a  -wave NIM Basic Elements of a NIM: (a) Split ring resonator: just a well designed inductor resonating at  << c/L  gives  < 0 (b) Metal wires (continuous or cut): r << L to ensure that  < 0 for  << c/L

Applications of Negative-Index Materials: Miniaturizing Everything! Artist’s rendition of a sub-wavelength antenna embedded in a negative index shell Nano-cavities, nano-waveguides,…if you can make optical NIM

Making a better short focus lens n=+3 To make a short-focus lens, one needs a positive-index material with a much larger index n=-1

Optical magnetism: from SRR’s to nanorods Simplify the structure: (a) easy fabrication (b)  from same element Grigorenko et.al., Nature’05 Dolling et. al., Opt.Lett.’05 Shalaev et. al., Opt.Lett.’05 Zhang et.al., PRL ’05 NIMs in 2005: Many interesting designs but nothing works so far: unit size comparable to the wavelength 

The high cost of simplification: from meta-material to antennas Plasmonic Nano-ringsPlasmonic strips and rods Shvets, PRB’03 Shvets&Urzhumov, PRL’04 Alu,Salandrino, Engheta, archive’05 Meta-material: size << /2n Photonic crystals: size = /2n Cannot use SRR’s or other microwave tricks: how to miniaturize?? Plasmonics!

Engineering  : resonantly-induced magnetic dipole moments in a nanoparticle Use proximity effect in a lattice: electric octupole resonance has finite magnetic dipole moment for finite size particles! Goal: Use radiation in doubly-negative band for sub- wavelength imaging  plasmonic superlens electrostatic potential magnetic field: resonance at  = -5.3

Sub-wavelength imaging with SPC Magnetic field behind plane wave illuminated double-slit: D = /5, separation 2D Blue   p = 0.6, X = -0.2 Red   p = 0.6, X = 0.8 no damping Black  same as red, but with damping Dotted   p = (outside of the left-handed band) Nanostructured super-lens Hot spots at the super-lens Electric field lineouts Shvets, Urzhumov, PRL 93, (2004)

“Poor Man’s Super-Lens”:  Inserting a slab of matched material with negative  (and, one day,  ) can prevent image degradation Super-lensing is a highly resonant phenomenon: frequency-dependent permittivities must match Recent UV results: Fang et.al, Science ’05, Melville and Blaikie, Opt. Expr. ’05 We have demonstrated super-lensing in IR and (a) proved its resonant nature, (b) demonstrated a new application: sub-surface imaging

Superlens in mid-IR: sub-surface imaging SiO 2 /SiC/SiO 2 superlens with a metallic pattern (0.5  m slits in Ag film separated by 3  m on the bottom side) was imaged from the top using NSOM Sub-surface imaging of sub- features at 800 nm depth accomplished at  m (CO 2 laser) using a superlens  opens the way to applications of super-lensing to sub-surface imaging of integrated circuits pattern on bottom NSOM image from top with Taubner and Hillenbrandt (MPQ/Munich)

=10.26  m =10.70  m =10.85  m Resonant phenomenon  in narrow frequency range Hi-Fi image  multiple diffraction orders amplified Summary of 1-D periodic array imaging through a super-lens super-imaging at  m regular imaging at 9.47  m Fang et. al., Science ‘05

=10.62  m amplitude images =11.03  m phase images SEM image small hole: 500nm Sub-surface imaging of isolated holes =10.85  m =9.27  m Resolution of /20 Increased range of frequencies for imaging  amplitude or phase Higher resolution with phase imaging  less sensitive to topography

Conclusions Optical meta-materials have been shown to have remarkable applications: Can be used to engineer exotic meta-media: Negative Index Materials  plasmonic approach to making a sub- NIM NIMs and negative  materials can be used to overcome diffraction limit and construct a super-lens A super-lens enables ultra-deep sub-surface imaging using NSOM probe Very new field  lots of work to do (theory and experiments)