Theoretical investigations on Optical Metamaterials Jianji Yang Supervisor : Christophe Sauvan Nanophotonics and Electromagnetism Group Laboratoire Charles Fabry de l’Institut d’Optique Collaborators: Stéphane Collin, Jean Luc Pelouard Laboratoire de Photonique et de Nanostructures (LPN)

2 Metamaterials (MMs) MMs: Engineered materials possessing properties that are not available in nature, especially negative permeability and negative refractive index. Potential applications : Imaging, Invisibility Cloaking, Sensors, Photon Management, Nonlinear Optics, Antennas, Wave Absorber… Example: Negative Index “Perfect” Lens J. Pendry, " Negative Refraction Makes a Perfect Lens ", Phys. Rev. Lett. 85, 3966 (2000).

3 Concept of Effective Parameters homogenization Effective Parameters: It is a significant challenge to homogenize metamaterials, i.e. to determine the effective material parameters. Crucial Parameters: effective refractive index n eff, effective permittivity ɛ eff and effective permittivity µ eff … metamaterial r t r t n eff, ɛ eff, µ eff ɛ eff <0, µ eff <0 n eff <0

4 Negative index in the microwaves Magnetic Response H Split Ring Resonator (SRR) Collection of SRR forms effective magnetic medium. Electric Response Metallic Wires ε m <0 Collection of conducting wires forms an effective metal with a controllable plasma frequency. Pendry, J. B., et al., 47, 2075, IEEE Trans. Microw. Theory Tech. (1999) Pendry, J. B., et al., 76, 4773, Phys. Rev. Lett. (1996) Γ: dissipation factor F: fractional factor ω P : controllable plasma frequency

5 Split-ring resonators (SRRs) based metamaterial, functioning in microwave spectrum. R. A. Shelby et al., Vol. 292, pp , Science (2001). 5mm Negative index in the microwaves

6 Moving to Optical Spectrum Fishnet metamaterials, functioning in near-infrared spectrum. J. Valentine et al., 455, , Nature (2008). Fishnet Metamaterial Conceptual Difficulties: high dissipation of metals, saturation of magnetic resonance… Fabrication Difficulties: difficulty of scaling-down and stacking-up… Current Loop 1m1m

7 Fishnet: important fundamental mode Measurement agrees well with calculated fundamental Bloch mode. J. Valentine et al., 455, , Nature (2008). measurement fundamental Bloch mode Quartz Fishnet Prism Air Incident Beam Output Beam n <0 α Prism Measurement

8 J. Yang et a l., Appl. Phys. Lett. 97, (2010) Fishnet: important fundamental mode Single Bloch Mode Approximation (SBMA) fundamental Bloch mode mediates the light transport in fishnet metamaterials. SBMA Rigorous T λ (μm)λ (μm) R t Fishnet r air n eff Fundamental Bloch Mode

9 Microscopic Model: basic waveguide modes TE 01 : least attenuated mode of a rectangular hole gap-SPP : least attenuated mode of a planar SPP waveguide gap-SPP TE 01 Metal layer Dielectric layer J. Yang et al., (submitted)

10 Elementary Scattering Coefficients ρ gap-SPP α α τ Incident TE 01 H.T. Liu and P. Lalanne, 452, , Nature (2008) α α t sp r sp TE 01 gap-SPP Incident gap-SPP ρ, τ : reflectivity and transmissivity of TE 01 r sp, t sp : reflectivity and transmissivity of gap-SPP α : coupling coefficient between gap-SPP and TE 01

11 Coupled Mode Formalism Analytical Model Dispersion relation A m = τ A m+1 + ρ B m + α C n + α D n+1 B m = τ B m-1 + ρ A m s + α C n + α D n+1 C n = t sp C n+1 + r sp D n + α B m+1 + α A m D n = t sp D n+1 + r sp C n + α B m+1 + α A m A m+1 B m+1 AmAm BmBm C n+1 D n+1 CnCn DnDn

12 Microscopic Model Microscopic model Fishnet mode (exact) A m+1 B m+1 AmAm BmBm C n+1 D n+1 CnCn DnDn

13 Resonance of gap-SPP Current Loop Gap-SPP mode shows resonance around 2  m, via the coupling with TE 01 mode, this resonance influences the light transport significantly.

14 Conclusion: We have studied the optical fishnet metamaterials theoretically. In particular we investigate the important fundamental Bloch mode of fishnet structure, and we also formulate the construction of this mode from a relatively microscopic point of view. In the future, we will investigate other types of plasmonic structures, especially some potentially applicable designs.

15 Thank you !