A Theoretical study on Negative Refractive Index Metamaterials

A Theoretical study on Negative Refractive Index Metamaterials (Review) Madhurrya P. Talukdar Tezpur University

Contents • Introduction • Negative refraction • Electromagnetic Wave propagation • How to make NIM • Conclusion

Introduction Invisibility Camouflage Stealth technology Vacuum property (most effective)

Possible types of materials: • μ>0, Є>0, being most known materials, natural or otherwise. • μ>0, Є<0, being materials not well investigated. • μ<0, Є>0, also being materials not well investigated • μ<0, Є<0, where these materials do not exist naturally(Metamaterials)

Metamaterials Man-made materials First introduced theoretically by Victor Veselago in 1967 Consists of Artificially structured units (meta-atoms) Meta atoms composed of two or more conventional materials

Negative refraction: empty glass regular water, n = 1. 3 “negative” water, n = -1. 3

Group velocity vg is in the opposite direction to the wave (or phase) velocity, vp The structural array of metamaterials must be smaller than the EM wavelength used. To achieve negative refraction MM’s must interact with the magnetic component of light. * ‘Probing the Magnetic Field of Light at Optical Frequencies’ Brussi et. al VOL 326 SCIENCE

Electromagnetic wave propagation and cloaking Theory Transformation optics is a simple approach to design MM’s (Pendry et. al)

What happens to light in NIM? Light enters n > 0 material deflection Light enters n < 0 material focusing (“Veselago Lens”)

Cloaking Fermat’s principle states light rays take the shortest optical paths in dielectric media When n is spatially varying shortest optical paths are usually curved. Fig: bending of light around a cloaked object (Leonhart 2006)

“Optical cloaking” for invisibility: Plasmonics and metamaterials T. Ebbesen et al. , Nature 391, 667 (1998). W. Cai et al. , “Optical cloaking with metamaterial, ” Nat. Photonics 1, 224 (2007). G. Gay et al. , Phys. Rev. Lett. 96, 213901 (2006). G. Abajo et al. , “Tunneling mechanism of light transmission through metallic films, ” Phys. Rev. Lett. 95, 067403 (2005). W. Barnes et al. , Phys. Rev. Lett. 92, 107401 (2004). A. Alu & N. Engheta, Phys. Rev. E 72, 016623 (2005).

How to make NIM? In microwave range: use “perfectly” conducting components to simulate e < 0 and m < 0, Smith et. al. , (2000) Metal poles: e = 1 – wp 2/w 2 < 0 Split-ring resonators, Pendry’ 99: “geometric” resonance at w. M

Split Ring Resonators

At frequency> resonant frequency the real part of μ of the SRR becomes negative. Combining the negative permeability with negative dielectric constant of another material to produce negative refractive index metamaterials. Challenges: (a) moving to optical frequencies (infrared, visible, UV) (b) simplifying the structure (e < 0 and m < 0 from same element)

Conclusion 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-l NIMs and negative e materials can be used to overcome diffraction limit and construct a super-lens A super-lens enables ultra-deep sub-surface imaging Very new field lots of work to do (theory and experiments)

References 1. Veselago, V. G. Sov. Phys. Usp. 10, 509 -514(1968). 2. Pendry, J. B. Phys. Rev. Lett. 85, 3966 -3969(2000) 3. Pendry, J. B. , Schurig, D. & Smith, D. R. Science 312, 1780 -1782(2006). 4. D. L. Mills and E. Burstein, Rep. Prog. Phys. 37, 817 (1974). 5. R. E. Camley and D. L. Mills, Phys. Rev. B 26, 1280 6. A. Hartstein, E. Burstein, A. A. Maradudin, R. Brewer, and R. F. Wallis, J. Phys. C 6, 1266 (1973). 7. D. R. Smith, D. C. Vier, Willie Padilla, Syrus C. Nemat-Nasser, and S. Schultz, Appl. Phys. Lett. 75, 1425 (1999). 8. C. R. Simovski, Physical Optics. 107, 766 -793. 9. D. R. Smith, D. C. Vier, Willie Padilla, Syrus C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 -4187(2000) 10. Pendry, J. B. , A. J. Holden, W. J. Stewart, and I. Youngs, Physical Review Letters, Vol. 76, 4773 -4776, (1996). 11. Pendry, J. B. , A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. on Microwave Theory and Techniques, Vol. 47, 2075 -2084, (1999). 12. C. Sabah, H. G. Roskos, Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 18 -21, 2009. 13. A. Grbic and G. V. Eleftheriades, J. App. Phys. 98, 43106 (2005) 14. D. R. Smith, J. Opt. soc. Am. B 21, 1032 (2004) 15. D. R. Smith, J. B. Pendry, J. Opt. Soc. Am. B 23 391 (2006). 16. P. K. L. Drude, Theory of Optics(Longmans, London, 1902; ONTI, Moscow, 1935) 17. I. E. Tamm, Z. Phys. 76, 849 (1932). 18. C. R. Simovski, Metamaterials 1, 62 (2007) 19. C. R. Simovski, Metamaterials 2, 342 (2008) 20. C. R. Simovski , Phys. Rev. B 62, 13718 (2000)

for your attention. .