Anderson localization of photons and phonons for optomechanics Guillermo Arregui

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1 Anderson localization of photons and phonons for optomechanics Catalan Institute of Nanoscience and Nanotechnology (ICN2), Bellaterra, Spain Dept. de Física, Universitat Autonoma de Barcelona, Bellaterra, Spain

2 Optomechanical crystals

3 A corrugated silicon nanobeam cavity t w r h a=500 nm h=3a d=0.5a r=0.3a w=a t=0.44a d

4 A corrugated silicon nanobeam cavity t w r h a=500 nm h=3a d=0.5a r=0.3a w=a t=0.44a d

5 A corrugated silicon nanobeam cavity t w r h a=500 nm h=3a d=0.5a r=0.3a w=a t=0.44a d

6 The role of fabrication disorder

7 The role of fabrication disorder Typical fabrication disorder levels spoil the structure performance drastically

8 Disorder-induced localization Multiple scattering and interference leads to localization of photons and phonons (Anderson localization) g om /2π = 183 khz

9 Disorder-induced localization Photonic disorder-induced localization observed, but no mechanical modulation of the outcoupled light

10 Disorder-induced localization PD. García, R. Bericat-Vadell, G. Arregui, D Navarro-Urrios, M. Colombano, F. Alzina, CM. Sotomayor-Torres, Phys. Rev. B 95 (11), (2017)

11 Disorder-induced localization LOW DEGREE OF CO-LOCALIZATION PD. García, R. Bericat-Vadell, G. Arregui, D Navarro-Urrios, M. Colombano, F. Alzina, CM. Sotomayor-Torres, Phys. Rev. B 95 (11), (2017)

12 Guaranteeing co-localization Can we find a system that guarantees a higher degree of localization?

13 Guaranteeing co-localization Can we find a system that guarantees a higher degree of localization? GaAs/AlAs: DOUBLE MAGIC COINCIDENCE n 1 n 2 ~ Z 1 Z 2 n 1 n 2 ~ v 2 v 1

14 Guaranteeing co-localization Can we find a system that guarantees a higher degree of localization? GaAs/AlAs: DOUBLE MAGIC COINCIDENCE n 1 n 2 ~ Z 1 Z 2 n 1 n 2 ~ v 2 v 1 Automatic co-localization of photons and phonons in the Anderson-localization regime Precise control of disorder levels (MBE) Ideal structures for time-resolved experiments (ASOPS)

15 A perfect distributed Bragg reflector GaAs AlAs d GaAs = nm, d AlAs = 73,48 nm, N = 600

16 A mechanical and/or optical Lifshitz tail GaAs AlAs d GaAs = nm, d AlAs = 73,48 nm, N = 600

17 A mechanical and/or optical Lifshitz tail GaAs AlAs d GaAs = nm, d AlAs = 73,48 nm, N = 600

18 A mechanical and/or optical Lifshitz tail GaAs AlAs d GaAs = nm, d AlAs = 73,48 nm, N = 600

19 Co-localization of photon-phonon pairs GaAs AlAs Pairs of perfectly co-localized photons and phonons

20 Co-localization of photon-phonon pairs GaAs AlAs Pairs of perfectly co-localized photons and phonons

21 Co-localization of photon-phonon pairs GaAs AlAs

22 Optomechanical coupling

23 Optomechanical coupling

24 Optomechanical coupling The perfectly co-localized photon-phonon pairs push the distribution to higher values of the optomechanical coupling rate

25 Conclusions 1. Photon and phonon Anderson localization can be used as a new confinement strategy for cavity optomechanics experiments

26 Conclusions 1. Photon and phonon Anderson localization can be used as a new confinement strategy for cavity optomechanics experiments 2. Optomechanical interaction can be used to probe Anderson localization of phonons in the GHz range

27 Acknowlegdments Thank you! Wombat 2017, Besançon

28 Multilayers: Transfer Matrix Method Boundary conditions u i z = a i e iqiz iq + b i e iz with q i = ω v i ρ i, d i ρ i+1, d i+1 C i Displacement continuity u i d i = u i+1 0 C i+1 Stress continuity du i C i dz d du i+1 i = C i+1 dz 0 a i a i+1 b i b i+1 a i b i = (1 + Z i+1 Z i )e iq id i (1 Z i+1 Z i )e iq id i (1 Z i+1 Z i )e iq id i (1 + Z i+1 Z i )e iq id i a i+1 b i+1 M i = L i I i, i+1 L i = e iq id i 0 0 e iq id i I i,i+1 = (1 + Z i+1 Z i ) (1 Z i+1 Z i ) (1 Z i+1 Z i ) (1 + Z i+1 Z i )

29 Open acoustic resonator n 0, d 0 n 1, d 1 n 2, d 2 n 3, d 3 n i, d i n N 1, d N 1 n N, d N n N+1, d N+1 a 0 b 0 a N+1 b N+1 ρ 0, d 0 ρ 1, d 1 ρ 2, d 2 ρ 3, d 3 v 0 v 1 v 2 v 3 ρ i, d i v i ρ N 1, d N 1 v N 1 ρ N, d N v N ρ N+1, d N+1 v N+1 a 0 b 0 = M a N+1 b N+1 M (ω) = I 0,1 N i=1 M i Reflection/Transmission Spectrum a 0 = 1, b 0 = r, a N+1 = t, b N+1 = 0 r(ω) = 1 M 11 (ω) t(ω) = M 12(ω) M 11 (ω) Quasi-normal modes a 0 = 0, b 0 = 1, a N+1, b N+1 = 0 M 11 ω = 0 with ω ε C.

30 GaAs/AlAs: the double magic coincidence Analogy between optics and acoustics Z n v c n So, if i, Z i+1 Z i c ni v i = n i+1 n i = K M ac (ω) = M op (Kω) GaAs/AlAs: DOUBLE MAGIC COINCIDENCE Z 2 Z 1 ~ n 2 n 1 n 1 n 2 ~ v 2 v 1

31 Localization length GaAs AlAs log T = ξ L Dispersive localization length ξ OM coupling study in a narrow frequency band

32 Optomechanical coupling Moving boundaries Photoelastic g MB = ω o 2 N m=0 u z m ε m ε m+1 E(z m ) 2 L 0 ε(z) E(zm ) 2 ħ 2m eff ω m g PE = ω o 2 L 0 n 4 z p 12 (z) du(z) E(z dz m ) 2 L n 2 (z) E(z m ) 2 0 ħ 2m eff ω m