Sub-wavelength electromagnetic structures
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1 Sub-wavelength electromagnetic structures Shanhui Fan, Z. Ruan, L. Verselegers, P. Catrysse, Z. Yu, J. Shin, J. T. Shen, G. Veronis Ginzton Laboratory, Stanford University
2 Outline Waveguide Meta-material Resonator metal metal Ag air Ag 50 nm
3 Single-Interface Plasmons ω Light line: ω = k c n d E λ sp << λ Deep UV ω sp Surface Plasmon H E k = 2π λ H
4 Metallic Slot Waveguides air (n=1) λ = 0.6µm λ = 1.0µm metal metal SiO 2 (n=1.5) λ = 1.5µm λ = 10µm Broad-band nanoscale manipulation of light G. Veronis and S. Fan, Optics Letters, 30, 3359 (2005). G. Veronis and S. Fan, Journal of Lightwave Technology, 25, 2511 (2007).
5 High-Performance Nano-Components High-efficiency bends Ag air Near-ideal splitters Ag 50 nm G. Veronis and S. Fan, APL 87, (2005) Strong-coupling between dielectric and plasmonic waveguides Ultrahigh-density packing of slot waveguides Opt. Exp. 15, 1211 (2007) Opt. Exp. 16, 2129 (2008)
6 Enhancing THz Generation Conventional nonlinear optical approach suffers from length-scale mismatch between THz and Optical waves. ω 1, ω 2 Polyethylene Ω = ω 1 - ω 2 LiNbO 3 Quartz Infra-red THz C. Staus, et al. Optics Express 16, (2008)
7 Slot Waveguide For Optimal THz and Optical Guiding λ = 200 µm λ = 2.02 µm metal GaAs x (µm) x (µm) THz guiding by the metal slot Optical guiding by the dielectric strip Phase-matching Balancing material and waveguide dispersion Z. Ruan et al, Optics Express 17, (2009)
8 Outline Waveguide Meta-material Resonator metal metal Ag air Ag 50 nm
9 Sub-wavelength states determine material properties Si refractive index n si ~ nm atom size << wavelength
10 An example of creating effective dielectric E Sub-wavelength TEM-like modes Wavelength ε = d a 2, µ = 1, L = a d L L d a J. T. Shen, P. Catrysse, S. Fan, Physical Review Letters, 94, (2005)
11 Transmission spectrum Incident light Incident light E
12 Guiding of electromagnetic wave on a PEC slab n = d/a = 16 Wavevector ( 2π / d)
13 Towards 3D isotropic high-index meta-material ε = 20.0, µ = 0.098, n = 1.4 B. Wood and J. B. Pendry, Journal of Physics B, Condensed Matter, 19, (2007)
14 3D Isotropic High-Index Materials ε = 20.0, µ = ε = 18.3, µ = J. Shin, J. T. Shen, and S. Fan, Physical Review Letters 102, (2009). Recent experiment: Choi et al, Nature 470, 369 (2011).
15 Outline Waveguide Meta-material Resonator metal metal Ag air Ag 50 nm
16 Cross-section of an object Total scattered power P s Incident wave Power per unit area I 0 Total absorbed power P a Scattering Cross Section A s = P s I 0 Absorption Cross Section A s = P s I 0
17 Cross-section of an object Incident wave Measures how large an object is seen by externally incident wave. Practically important. Key motivation of many nano-antenna is to have EM cross-section to be much larger than the geometric cross-section.
18 What is the maximal scattering cross-section achievable for a sub-wavelength object? atom EM cross-section On resonance: 2λ π For 2D 3λ 2 2π For 3D >> Atom Size
19 What about a meta-atom? λ = 1.4 micron < λ 2 2π Smaller than the single-channel limit of the atom. Husnik et al, Nature Photonics 2, 614 (2008).
20 Partial-wave expansion exp[ik r] m = 0 m = 1 m = 2 = σ total = m σ m
21 Maximizing single channel contribution Incoming wave a m In general b m a m No scattering when Outgoing wave b m b m = a m Maximum scattering (on resonance) when b m = a m Maximal contribution from single channel σ m = 2λ π
22 Condition for super-scatterer σ total = Atom: resonant only at a single angular momentum channel No contribution from non-resonant channels m σ m atom σ total 2λ π EM cross-section Meta-atom: Create resonances at the same wavelength, at large numbers of angular momentum channels σ total >> 2λ π
23 Multiple resonances at the same wavelength β dielectric metal β ( ω m ) 2πr = 2mπ
24 metal dielectric Super light scattering from sub-wavelength scatterer Size of scatterer: 0.32λ Scattering cross-section: 8 * 2λ / π Far beyond the single-channel limit!
25 Compared to a simple plasmonic scatterer Z. Ruan and S. Fan, Physical Review Letters 105, (2010).
26 A single resonance: sub-wavelength metal slit E Perfect metal Fabry-Perot Resonance
27 Transmission Cross Section σ T Incident light power density F inc [W/m] λ π Total transmission power P T [W] σ T ( ω ) = P T F inc [m] L. Verslegers, Z. Yu, P. Catrysse, S. Fan, J. Opt. Soc. Am. B 27, (2010)
28 EIT and Super Scattering 0 o Metal 60 o L. Verslegers, Z. Yu, Z. Ruan, P. Catrysse, S. Fan, Physical Review Letters 108, (2012)
29 Super and sub-radiant states Broad resonance (superradiant) Narrow resonance (subradiant) Intensity Frequency Intensity Frequency
30 Orthogonal Radiation Patterns Broad resonance (superradiant) Narrow resonance (subradiant) Low Q High Q
31 Super-scattering Spectrum of transmission cross-section Peak cross section is a sum of contribution from individual resonance. Thus cross-section is not constraint by the upper limit of single resonance cross-section Z. Ruan and S. Fan, Physical Review Letters 105, (2010)
32 Optical Analogue to Electromagnetically Induced Transparency Perfect overlap of radiation pattern between two resonances Complete destructive interference at resonance. Broad resonance (superradiant) Narrow resonance (subradiant) Perfect EIT 150
33 General Situations Broad resonance (superradiant) Narrow resonance (subradiant)
34 General Situations Incident angle influences the excitation of the two eigenmodes and thus the amplitude and magnitude of the intereference L. Verslegers, Z. Yu, Z. Ruan, P. Catrysse, S. Fan, Physical Review Letters 108, (2012)
35 Summary Waveguide Meta-material Resonator metal metal Ag air Ag 50 nm
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