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