香港大学：Spontaneous Emission in 2D Arbitrary Inhomogeneous Environment

區图 Spontaneous Emission in2 D Arbitrary WILA ETVAY Inhomogeneous Environment Peng-Fei Qiao, Wei E I. Sha, Yongpin P Chen Wallace C H Choy, and Weng Cho Chew Department of Electrical and Electronic Engineering The University of Hong Kong Speaker: Y P Chen Sep14,2011

Spontaneous Emission in 2D Arbitrary Inhomogeneous Environment Peng-Fei Qiao, Wei E. I. Sha, Yongpin P. Chen, Wallace C. H. Choy, and Weng Cho Chew* Department of Electrical and Electronic Engineering The University of Hong Kong Speaker: Y.P. Chen Sep 14, 2011

Motivation Control of spontaneously emitted light lies at the heart of quantum optics. It is essential for diverse applications ranging from lasers, light-emitting diodes(LED), solar cells, and quantum information 8839 Active gain Purcell factor LED (photonic crystal cavity Laser (metallic microcavity M. Francardi et al. Appl. Phys. Lett C Walther et al. Science 327, 1495-1497(2010) 93,143102(2008)

Motivation Control of spontaneously emitted light lies at the heart of quantum optics. It is essential for diverse applications ranging from lasers, light-emitting diodes (LED), solar cells, and quantum information. C Walther et al. Science 327, 1495-1497 (2010) LED (photonic crystal cavity) Laser (metallic microcavity) M. Francardi et al. Appl. Phys. Lett. 93, 143102 (2008) Purcell factor

History hoton intensity Classical view: dNo dna AN2 dN1 W212 12 hV=E2-E Boltzmann statistics hV (E2-E1) hy hv hy kT hV SPONTANEOUS EMISSION STIMULATED EMISSION ABSORPTION II Spontaneous emission: an exited atom/molecule decay to the ground state and emits a photon

Classical View: Boltzmann statistics Photon intensity Spontaneous emission: an exited atom/molecule decay to the ground state and emits a photon History

Quantum Electrodynamics Theory The spontanoues emission of an atom can be a weak-coupling radiation process due to the vacuum fluctuations of electromagnetic field Spontaneous emission rate by Fermi golden rule y(ro, wo wWo E ∑p,(uxu)a-0) Mode expansion of dyadic green's function hOo G(xr1)=2∑吗(x(, l&. log, )Ig Ilok,)lg. ok 18. lo,) Representation by Greens tensor y(ro, wo) Local density of state(LDOs) Eohc2(p. Im G(ro, ro, wo)'pi p(r4)=∑luk26(4k-o) Purcell factor P(ro, wo) Im TrG(ro, ro, wo)I Im Tr G(ro, ro, wo)J) 70 Po(ro, wo) Im Tr Go(ro, ro, 0

Quantum Electrodynamics Theory Spontaneous emission rate by Fermi golden rule Mode expansion of dyadic green’s function Representation by Green’s tensor Local density of state (LDOS) Purcell factor The spontanoues emission of an atom can be a weak-coupling radiation process due to the vacuum fluctuations of electromagnetic field

Numerical solution of green's Function [Ge (to, to)]=0.25 Im(Gra(to, to)=0.125 Convergence D FDFD R99 0.05 6 log(PPw Position x/Ax Position: x GG 0 2-D free-space case(FDFD method) G(r, r)=G G yy 00G TM wave V2E2+kE2=-i0nJ=-65(x-m△n,y-n△)2=m△=m△p△△ V2H2+k3H2= G=E ZELl 0H2 TE wave H2+、-0 6 dr 1 88 Gyy=Ey-Ko 06(x-m△z,y-n△ 6(x-m△x,y-(m+05)Ay)6(x-m△xy-(n-05)△y) y

Numerical Solution of Green’s Function 2-D free-space case (FDFD method) TM wave TE wave convergence

Photonic Crystal a suitable modification of inhomogeneous environment is required so that the vacuum fluctuations controlling the se can be manipulated Photonic crystal(TM wave Photonic crystal(TE wave) 0.8 20×20 Array 20×20Aray 4×4Aray 0.6 4×4Aray x0.5 05 L0.3 0.1 PWE Method 0.1 FDFD Method FDFD Method 0 o PWE Method 10310·10-410-210°XMNX 0 Normalized SER 1010:10101010 Normalized SER SE Depends on the dispersion relation of photonic crystal (bandgap bandedge)

Photonic Crystal A suitable modification of inhomogeneous environment is required so that the vacuum fluctuations controlling the SE can be manipulated. Photonic crystal (TM wave) Photonic crystal (TE wave) SE Depends on the dispersion relation of photonic crystal (bandgap & bandedge)

Plasmonic Nano-Cavity Plasmonic cavity SE Depends on dispersion relation of SPP 250 Single-plate Double-plate 200 105 150 d/2 日 00500600700800 Wavelength(nm) A A 10 100 Double-plate Single-plate 50 00 500 600 700 800 0152025 Wavelength(nm) d(nm) 目1 150 100 Position x(nm) Position x (nm) 00-30 Position x(nm)

Plasmonic Nano-Cavity Plasmonic cavity SE Depends on dispersion relation of SPP

Photonic Yagi-Uda Nano-Antenna (Recent Work) Spontaneous emission can be redirected at any selected wavelength via tuning the compositions, sizes, and spatial locations of each element Dipole Director 100 ●●●●●● 100 1000 1200 Reflect selective wavelength (c) 0.5 n o -0.5 0.5 0.5 Y0.50 500 700 Wavelength (nm

Photonic Yagi-Uda Nano-Antenna (Recent Work) Spontaneous emission can be redirected at any selected wavelength via tuning the compositions, sizes, and spatial locations of each element. selective wavelength

Conclusion v The ldos determining the radiation dynamics of emitting source and se rate can be represented by the electric dyadic Greens function v The numerical solution of the electric Green s tensor has been obtained with the FdFd method by using proper approximations of the monopole and dipole sources Y The SE rate and direction can be manipulated in photonic and plasmonic nanostructures via engineering their dispersion relations, which is of a great help to emerging optoelectronics For more details, please see Pengfei Qiao, Wei E.l. Sha, Wallace C H Choy, and Weng Cho Chew, Phys. Rev. A 83, 043824, (2011)

Conclusion ✓ The LDOS determining the radiation dynamics of emitting source and SE rate can be represented by the electric dyadic Green’s function. ✓ The numerical solution of the electric Green’s tensor has been obtained with the FDFD method by using proper approximations of the monopole and dipole sources. ✓ The SE rate and direction can be manipulated in photonic and plasmonic nanostructures via engineering their dispersion relations, which is of a great help to emerging optoelectronics. For more details, please see Pengfei Qiao, Wei E.I. Sha, Wallace C.H. Choy, and Weng Cho Chew, Phys. Rev. A 83, 043824, (2011)