1. Artificial Magnetic Resonators and Potential Applications in Nonlinear Field Yongmin Liu Applied Science & Technology Physics 208A Presentation Oct. 18 th, 2004

2. Outline I.Background of Metamaterials II.Artificial Magnetic Resonators at THz III.Potential Application in Nonlinearity IV.Summary

3. 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.

4. Negative Permittivity The permittivity of metal is given by Plasma frequency: where n is the electron density, and m e is the electron mass Damping factor: where  is the electric conductivity In the visible region,  is negative for most metals. At lower frequencies, permittivity is imaginary. (typically in the UV region)

5. Negative  with small loss in low frequencies can be achieved by metallic wire lattice Pendry J.B. et al., Phys. Rev. Lett. 76, 4773 (1996) Negative Permittivity (cont’d) lattice constant: radius of wire:

6. Negative  can be achieved by split- ring resonator (SRR) 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. 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 !

7. Left-handed Materials (LHM) with Negative Refractive Index (NIR) When  and  simultaneously, we have to choose Refractive index: E H k S Right handed materials (RHM) E H kS Left handed materials (LHM) n > 0  n < 0  Maxwell’s equation:

8. LHM with NRI (cont’d) 1. Snell’s law: Exotic properties of LHM: Negative refraction ! 2. Flat superlens Diffraction-limit (  min  ) free ! Veselago V.G. Sov. Phys.10, 509 (1968); Pendry J. B. PRL 85, 3966 (2000) S k LHM RHM Fourier Expansion of 2D object: Propagating waves: Evanescent waves: Z

9. 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

10. LHM with NRI (cont’d) Imaging properties of LHM Houck A. A. et al. PRL 90, 137401 (2003); Kolinko P. et al. Opt Exp 11, 640 (2003) Simulation of subwavelength imging by FDTD Imaging experiment in microwave region Electric field of a point source focused by a LHM slab

11. http://physics.ucsd.edu/~drs/ Prof. Smith D.R. in UCSD 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

12. Outline I.Background of Metamaterials II.Artificial Magnetic Resonators at THz III.Potential Application in Nonlinearity IV.Summary

13. 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. Artificial Magnetic Resonators at THz + + + _ _ _ H a 2r Pendry J.B. et al, IEEE MTT 47, 2075 (1999)

14. Artificial Magnetic Resonators at THz (cont’d) Current distribution of SRR simulated by Microwave Studio

15. Artificial Magnetic Resonators at THz (cont’d) H-field of SRR simulated by Microwave Studio

16. Resonance frequency: Magnetic plasma frequency: Typical value: Artificial Magnetic Resonators at THz Pendry J.B. et al, IEEE MTT 47, 2075 (1999) Dispersion of  eff with frequency

17. 50um Sample L :length G: gap S: space W: width quartz Cu Au/Ti L:26m, S:10m, W:4m d=L+S, G: 2m,  :1.5x10 3  Artificial Magnetic Resonators at THz (cont’d) Ye T.J. et al., Science 303, 1494 (2004)

18. Die Simulation (THz) Experiment (THz) D1 1.221.27±0.07 D2 0.880.96±0.05 D3 0.910.85±0.15  =30 o IRIR I0I0 Artificial Magnetic Resonators at THz (cont’d) Experimentally and theoretically ellipsometric results

19. Artificial Magnetic Resonators at THz (cont’d) k (cm-1)f (THz)λ/a LSR400110033.002.52525 LSR350128238.462.47629 LSR300149044.702.48571 Near-infrared (45THz) magnetic resonance is achieved by novel design. Final goal is visible region.

20. Outline I.Background of Metamaterials II.Artificial Magnetic Resonators at THz III.Potential Application in Nonlinearity IV.Summary

21. Potential Application in Nonlinearity Extremely high intensity is the key to nonlinear phenomena! Brabec T et al., Rev. Mod. Phys. 72, 545 (2000)

22. 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, one single photon can create an electric field about 10 8 V/cm. Localized E-filed with 10 3 times larger than the external field.

23. 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 field  Intensity of the local E field  Value of permittivity  Capacitance  Eigenfrequency

24. Potential Application in Nonlinearity (cont’d) Effect nonlinear permittivity: Effective permeability: where Consider Kerr nonlinearity: E c is a characteristic electric field, and corresponds to focusing or defocusing nonlinearity respectively. Zharov A.A. et al., PRL 91, 037401 (2003)

25. Potential Application in Nonlinearity (cont’d)   is the eigenfrequency in linear limit Jump of  eff due to external H field Transition of  eff from – to +

26. Outline I.Background of Metamaterials II.Artificial Magnetic Resonators at THz III.Potential Application in Nonlinearity IV.Summary

27. 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.