Nanophotonics and Surface EM Waves: Size and Surface Effects - Prof. Pc Ku, Study notes of Electrical and Electronics Engineering

Download Nanophotonics and Surface EM Waves: Size and Surface Effects - Prof. Pc Ku and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! Lecture 9 – Light-Matter Interaction Part 3 Structure Dependence EECS 598-002 Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.Ku 2EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Schedule for the rest of the semester Introduction to light-matter interaction (1/26): How to determine ε(r)? The relationship to basic excitations. Basic excitations and measurement of ε(r). (1/31) Structure dependence of ε(r) overview (2/2) Surface effects (2/7 & 2/9): Surface EM wave Surface polaritons Size dependence Case studies (2/14 – 2/21): Quantum wells, wires, and dots Nanophotonics in microscopy Nanophotonics in plasmonics Dispersion engineering (2/23 – 3/9): Material dispersion Waveguide dispersion (photonic crystals) 5EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Plasmons in mesoscopic structures 2 2 0 Plasmon frequency: p ne m ω ε = Ref: J. B. Pendry et al., Phys. Rev. Lett. 76 (1996) 4773. If the structure consists of thin metal wires (r~1um) with air in the surroundings, we have (assuming wires are arranged into a cubic lattice of a period a): 2 2 2 2 0 ln 2 eff rn n a m m r e n a r π µ π π → → → Due to inductance Much lower ωp e.g. aluminum wires with r=1um, a=5mm: ωp 3622 THz->8.2 GHz. 6EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Negative refractive index Negative ε and negative µ negative n Ref: D. R. Smith et al., Phys. Rev. Lett. 84 (2000) 4184. J. B. Pendry et al., IEEE Trans. Micro. Theory & Tech., 47 (1999) 2075. 2 2 2 0 1eff F i ωµ ω ω ω = − − + Γ 7EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Subwavelength grating broadband mirror Ref: C. Mateus et al., Photon. Technol. Lett. 16 (2004) 1676. 10EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku TE polarized surface EM wave? If the electric field is TE polarized, we can show that the surface EM mode can not be supported. Homework 2 (Hint: Consider the boundary condition at the interface and show that the boundary condition can not be satisfied if the TE wave decays exponentially on both sides of the interface.) 11EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Electric field polarization The electric field has components both in parallel and in perpendicular to the x direction. Both transverse and longitudinal wave components exist in a surface EM wave. 12EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Dispersion relation of surface EM waves Dispersion relation = ω versus kx 2 2 2 1 1 2 2 2 2 2 2 2 1 2 1 2 ( ) ( ) x x x k i c k i c ck ω εα ω εα ε εω ε ε ⎧ + =⎪⎪ ⎨ ⎪ + =⎪⎩ + ⇒ = 15EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Attenuation Attenuation length L = the propagation distance at which the field intensity drops to 1/e. ( ) 22 1 2 2 2 1 2 2 1 1 2 2 2 2 2 1 2 2 1 2 2 1 12 1 2 2 2 1 1 2 2 3/ 2 1 Re( ) | | Im | | Im As a special case when real, ' '' and '' ' and ( ' '') 1 ' '' '' 1 2 '' '' x x x cL k c k i k i c cL ε ε ω ε ε ε ε ε ε ε ε ε ε ε ε ε ε εε ω ε ε ε ε εω ε ε ε ω ε +⎛ ⎞= ⎜ ⎟ +⎝ ⎠ = = + ⎛ ⎞+ ⇒ = ≈ +⎜ ⎟+ + ⎝ ⎠ ⎛ ⎞ ⇒ ≈ +⎜ ⎟ ⎝ ⎠ ⇒ = is very large 16EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Optical excitation of surface polaritons ω k Surface plasmon Photon in air Need to increase the k vector in order to radiatively excite the surface polaritons. 17EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Total internal reflection With light coming into the interface and experiencing total internal reflection, the kx component in the second media is larger than that in the free space. 2 0 sin sin ik θ θ 20EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Prism coupling technique glass metal air 21EECS 598-002 Nanophotonics and Nanoscale Fabrication by P.C.Ku Reading Prasad, chapters 2, 5 and 6.