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Physics 208A Presentation Oct. 18th, 2004 Artificial Magnetic Resonators and Potential Applications in Nonlinear Field Yongmin Liu Applied Science & Technology Outline I. Background of Metamaterials II. Artificial Magnetic Resonators at THz III. Potential Application in Nonlinearity IV. Summary What are Metamaterials? Artificially fabricated structures or media that exhibit electrodynamic properties not found in naturally occurring materials. * Dimension of the unit cell is less than the wavelength of excitation EM wave, thus the effective-media theorem can be applied. Why Metamaterials are Interesting? * We can design and control the properties of materials. Some novel properties, such as negative electric permittivity, negative magnetic permeability, negative refractive index etc. have been explored. Negative Permittivity The permittivity of metal is given by ep2 ( ) 1 ( i ) 2 ne 2 Plasma frequency: ep (typically in the UV region) 0 me where n is the electron density, and me is the electron mass 0 Damping factor: where is the electric conductivity In the visible region, () is negative for most metals. At lower frequencies, permittivity is imaginary. Negative Permittivity (cont’d) neff r 2 0ne2 n 2 , meff ln( a / r ) a 2 ep2 neff e 2 0 meff 6 radius of wire: r 1.0 10 m, lattice constant: a 5.0 103 m, n 5.675 1017 m 3 Negative with small loss in low frequencies can be achieved by metallic wire lattice ep 8.2GHz!! ep2 eff 1 ( i 0.1ep ) Pendry J.B. et al., Phys. Rev. Lett. 76, 4773 (1996) Negative Permeability Magnetism originates from 1) orbital motion of electrons 2) unpaired electron spins The magnetic response of most nature materials fades away in GHz region. Negative can be achieved by splitring resonator (SRR) Artificial magnetism can be realized by conducting, nonmagnetic split-ring resonators. The magnetic response is able to extend to THz, even higher frequency with large positive or negative permeability. Will discuss in detail later ! Left-handed Materials (LHM) with Negative Refractive Index (NIR) 2 n Refractive index: When < 0 and < 0 simultaneously, we have to choose n Maxwell’s equation: k E H , k H E n>0 ( > 0 , > 0) E k S H Right handed materials (RHM) n<0 ( < 0 , < 0) E k S H Left handed materials (LHM) LHM with NRI (cont’d) Exotic properties of LHM: 1. Snell’s law: RHM sin 1 n sin 2 k S LHM Negative refraction ! 2. Flat superlens Diffraction-limit (dmin~l) free ! Fourier Expansion of 2D object: E ( r, t ) ,k x ,k y Z ( ) ( E k x , k y exp ik z z ik x x ik y y it 2 2 2 2 Propagating waves: k z c k x k y , 2c 2 > k x2 k 2y , k z i k x2 k 2y 2c 2 , 2c 2 < k x2 k 2y . Evanescent waves: ) Veselago V.G. Sov. Phys.10, 509 (1968); Pendry J. B. PRL 85, 3966 (2000) LHM with NRI (cont’d) Artificially engineered metamaterials implements the concept of LHM! Photograph of LHM Shelby R. A. et al., Science 292, 77 (2001); Smith D. R. et al., Science 305, 788 (2004) Negative refraction by LHM prism LHM with NRI (cont’d) Imaging properties of LHM Electric field of a point source focused by a LHM slab Imaging experiment in microwave region Simulation of subwavelength imging by FDTD Houck A. A. et al. PRL 90, 137401 (2003); Kolinko P. et al. Opt Exp 11, 640 (2003) LHM with NRI (cont’d) Metamaterials open a new field in physics, engineering material science and optics! Negative refraction is among the Top 10 highlights of 2003 by Physicsweb http://physics.ucsd.edu/~drs/ Prof. Smith D.R. in UCSD Outline I. Background of Metamaterials II. Artificial Magnetic Resonators at THz III. Potential Application in Nonlinearity IV. Summary Artificial Magnetic Resonators at THz Concept: 1. The magnetic-flux induced current loop to form magnetic dipole. 2. The intrinsic conductance and inductance will cause strong paramagnetic or diamagnetic activity around the resonance frequency. 2r a H _+ _+ _+ + _ _+ _+ Pendry J.B. et al, IEEE MTT 47, 2075 (1999) Artificial Magnetic Resonators at THz (cont’d) Current distribution of SRR simulated by Microwave Studio Artificial Magnetic Resonators at THz (cont’d) H-field of SRR simulated by Microwave Studio Artificial Magnetic Resonators at THz r 2 eff 1 a2 1 2i 3 2 0r 0 2Cr 3 Resonance frequency: 0 3 2 0Cr 3 Magnetic plasma frequency: mp 3 2 0Cr 3 (1 r 2 / a 2 ) Typical value: r 2.0 103 m a 5.0 103 m, d 1.0 104 m f 0 2.94GHz, f mp 4.17GHz Pendry J.B. et al, IEEE MTT 47, 2075 (1999) Dispersion of eff with frequency Artificial Magnetic Resonators at THz (cont’d) Sample 50um Cu S: space W: width L :length G: gap Au/Ti quartz L:26m, S:10m, W:4m d=L+S, G: 2m, :1.5x103W Ye T.J. et al., Science 303, 1494 (2004) Artificial Magnetic Resonators at THz (cont’d) IR I0 =30o Die Simulation (THz) Experiment (THz) D1 1.22 1.27±0.07 D2 0.88 0.96±0.05 D3 0.91 0.85±0.15 Experimentally and theoretically ellipsometric results Artificial Magnetic Resonators at THz (cont’d) 3.0 2.5 Re(Mue) 2.0 1.5 1.0 0.5 0.0 LSR300 LSR350 LSR400 -0.5 -1.0 -1.5 0 10000 20000 30000 40000 50000 60000 Frequency (GHz) k (cm-1) f (THz) λ/a LSR400 1100 33.00 2.52525 LSR350 1282 38.46 2.47629 LSR300 1490 44.70 2.48571 Near-infrared (45THz) magnetic resonance is achieved by novel design. Final goal is visible region. Outline I. Background of Metamaterials II. Artificial Magnetic Resonators at THz III. Potential Application in Nonlinearity IV. Summary Potential Application in Nonlinearity Extremely high intensity is the key to nonlinear phenomena! Brabec T et al., Rev. Mod. Phys. 72, 545 (2000) Potential Application in Nonlinearity (cont’d) When resonance takes place, the energy is strongly localized inside the small resonators. Local fields can be many orders higher than that in free space. For a capacitor of 1nm 1nm 1nm , one single photon can create an electric field about 108V/cm. Localized E-filed with 103 times larger than the external field. Potential Application in Nonlinearity (cont’d) Embed the magnetic resonator into dielectric matrix whose permittivity is intensity-dependent. Two aspects of the nonlinear response: 1) The strong localized field changes the dielectric permittivity, since D D (|E|2) 2) Nonlinear eigenfrequency adjusts correspondingly due to the change of capacitance. External H fieldIntensity of the local E fieldValue of permittivity Capacitance Eigenfrequency Potential Application in Nonlinearity (cont’d) Effect nonlinear permittivity: eff (| E |2 ) D (| E |2 ) p2 (1 i ) Effective permeability: (a 2 / d 2 ) 2 eff ( H ) 1 2 02NL i where 2 0 NL dg c 2 (H ) ( ) a h D (| E g ( H ) |2 ) 2 2 2 Consider Kerr nonlinearity: D (| E | ) D 0 | E | / Ec Ec is a characteristic electric field, and 1corresponds to focusing or defocusing nonlinearity respectively. Zharov A.A. et al., PRL 91, 037401 (2003) Potential Application in Nonlinearity (cont’d) (1 X 2 )[( X 2 W 2 ) 2 W 2 2 ] | H | A E X6 W / 0 , X 0 NL / 0 , 0 is the eigenfrequency in linear limit 2 Transition of eff from – to + 2 2 c Jump of eff due to external H field Outline I. Background of Metamaterials II. Artificial Magnetic Resonators at THz III. Potential Application in Nonlinearity IV. Summary Summary The unprecedented properties associated with metamaterials, such as negative refraction, superlensing etc. are reviewed. The principle of achieving negative permeability, which is critical in realizing LHM is interpreted. Magnetic resonators with resonance frequency above THz is successfully demonstrated. The strong localized field inside the resonator can cause nonlinear effect. As one example, the hysteresis-type dependence of the magnetic permeability on the field intensity is theoretically studied. It is the right time to start the new topic--nonlinear effects in metamaterials. The engineering of nonlinear composite materials will open a number of applications such as swithers, frequnecy multipliers etc.