Guillermo Arregui

Anderson localization of photons and

phonons for optomechanics

Guillermo Arregui ImagineNano 2018, Bilbao

Catalan Institute of Nanoscience and Nanotechnology (ICN2), Bellaterra, Spain

Dept. de Física, Universitat Autonoma de Barcelona, Bellaterra, Spain

Optomechanical crystals

Guillermo Arregui ImagineNano 2018, Bilbao

A corrugated silicon nanobeam cavity

h

d

t

w

r

a=500 nm

h=3a

d=0.5a

r=0.3a

w=a

t=0.44a

Guillermo Arregui ImagineNano 2018, Bilbao

A corrugated silicon nanobeam cavity

h

d

t

w

r

a=500 nm

h=3a

d=0.5a

r=0.3a

w=a

t=0.44a

Guillermo Arregui ImagineNano 2018, Bilbao

h

d

t

w

r

a=500 nm

h=3a

d=0.5a

r=0.3a

w=a

t=0.44a

Guillermo Arregui ImagineNano 2018, Bilbao

A corrugated silicon nanobeam cavity

Guillermo Arregui ImagineNano 2018, Bilbao

The role of fabrication disorder

Guillermo Arregui ImagineNano 2018, Bilbao

The role of fabrication disorder

Typical fabrication disorder levels spoil the

structure performance drastically

Guillermo Arregui ImagineNano 2018, Bilbao

gom/2π = 183 kHz

Disorder-induced localization

Multiple scattering and interference leads to localization of photons

and phonons (Anderson localization)

Guillermo Arregui ImagineNano 2018, Bilbao

Disorder-induced localization

Photonic disorder-induced localization observed,

but no mechanical modulation of the outcoupled

light

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),

115129 (2017)

Guillermo Arregui ImagineNano 2018, Bilbao

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),

115129 (2017)

LOW DEGREE OF

CO-LOCALIZATION

Guillermo Arregui ImagineNano 2018, Bilbao

Guaranteeing co-localization…

Guillermo Arregui ImagineNano 2018, Bilbao

Can we find a system that guarantees a higher degree of localization ?

Guaranteeing co-localization…

GaAs/AlAs: “DOUBLE MAGIC COINCIDENCE”

𝑛1𝑛2~𝑍1𝑍2

𝑛1𝑛2~𝑣2𝑣1

Guillermo Arregui ImagineNano 2018, Bilbao

Can we find a system that guarantees a higher degree of localization ?

Guaranteeing co-localization…

GaAs/AlAs: “DOUBLE MAGIC COINCIDENCE”

𝑛1𝑛2~𝑍1𝑍2

𝑛1𝑛2~𝑣2𝑣1

Guillermo Arregui ImagineNano 2018, Bilbao

Can we find a system that guarantees a higher degree of localization ?

• 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)

A perfect distributed Bragg reflector

GaAsAlAs

Guillermo Arregui ImagineNano 2018, Bilbao

dGaAs = 61.88 nm , dAlAs = 73,48 nm , N = 600

A mechanical and/or optical Lifshitz tail

GaAsAlAs

Guillermo Arregui ImagineNano 2018, Bilbao

dGaAs = 61.88 nm , dAlAs = 73,48 nm , N = 600

A mechanical and/or optical Lifshitz tail

GaAsAlAs

Guillermo Arregui ImagineNano 2018, Bilbao

dGaAs = 61.88 nm , dAlAs = 73,48 nm , N = 600

A mechanical and/or optical Lifshitz tail

GaAsAlAs

Guillermo Arregui ImagineNano 2018, Bilbao

dGaAs = 61.88 nm , dAlAs = 73,48 nm , N = 600

Co-localization of photon-phonon pairs

GaAsAlAs

Pairs of perfectly co-localized photons and phonons

Guillermo Arregui ImagineNano 2018, Bilbao

Co-localization of photon-phonon pairs

GaAsAlAs

Pairs of perfectly co-localized photons and phonons

Guillermo Arregui ImagineNano 2018, Bilbao

Co-localization of photon-phonon pairs

GaAsAlAs

Guillermo Arregui ImagineNano 2018, Bilbao

Optomechanical coupling

Guillermo Arregui ImagineNano 2018, Bilbao

Optomechanical coupling

Guillermo Arregui ImagineNano 2018, Bilbao

Optomechanical coupling

The perfectly co-localized photon-phonon pairs push the distribution to

higher values of the optomechanical coupling rate

Guillermo Arregui ImagineNano 2018, Bilbao

Conclusions

Guillermo Arregui ImagineNano 2018, Bilbao

1. Photon and phonon Anderson localization can be used as a new

confinement strategy for cavity optomechanics experiments

Conclusions

Guillermo Arregui ImagineNano 2018, Bilbao

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

Acknowlegdments

Thank you!

Guillermo Arregui Wombat 2017, Besançon

Multilayers: Transfer Matrix Method

ρ𝑖 , 𝑑𝑖𝐶𝑖

Displacement continuity 𝑢𝑖 𝑑𝑖 = 𝑢𝑖+1 0ρ𝑖+1 , 𝑑𝑖+1𝐶𝑖+1

Stress continuity 𝐶𝑖𝑑𝑢𝑖𝑑𝑧𝑑𝑖 = 𝐶𝑖+1

𝑑𝑢𝑖+1𝑑𝑧0

𝑢𝑖 𝑧 = 𝑎𝑖𝑒𝑖𝑞𝑖𝑧 + 𝑏𝑖𝑒

−𝑖𝑞𝑖𝑧 𝑤𝑖𝑡ℎ 𝑞𝑖 =𝜔

𝑣𝑖

𝑎𝑖𝑏𝑖=

(1 +𝑍𝑖+1𝑍𝑖)𝑒−𝑖𝑞𝑖𝑑𝑖 (1 −

𝑍𝑖+1𝑍𝑖)𝑒−𝑖𝑞𝑖𝑑𝑖

(1 −𝑍𝑖+1𝑍𝑖)𝑒𝑖𝑞𝑖𝑑𝑖 (1 +

𝑍𝑖+1𝑍𝑖)𝑒𝑖𝑞𝑖𝑑𝑖

𝑎𝑖+1𝑏𝑖+1

𝑳𝑖 =𝑒−𝑖𝑞𝑖𝑑𝑖 0

0 𝑒𝑖𝑞𝑖𝑑𝑖𝑰𝑖,𝑖+1 =

(1 +𝑍𝑖+1𝑍𝑖) (1 −

𝑍𝑖+1𝑍𝑖)

(1 −𝑍𝑖+1𝑍𝑖) (1 +

𝑍𝑖+1𝑍𝑖)

𝑎𝑖

𝑏𝑖

𝑎𝑖+1

𝑏𝑖+1

𝑀𝑖 = 𝑳𝑖 ⋅ 𝑰𝑖, 𝑖+1

Boundary conditions

Open acoustic resonator

𝑛1 , 𝑑1 𝑛2 , 𝑑2 𝑛3 , 𝑑3 𝑛𝑖 , 𝑑𝑖 𝑛𝑁−1 , 𝑑𝑁−1 𝑛𝑁 , 𝑑𝑁𝑛0 , 𝑑0 𝑛𝑁+1 , 𝑑𝑁+1

… …

ρ0 , 𝑑0𝑣0

ρ1 , 𝑑1𝑣1

ρ2 , 𝑑2𝑣2

ρ3 , 𝑑3𝑣3

ρ𝑖 , 𝑑𝑖𝑣𝑖

ρ𝑁−1 , 𝑑𝑁−1𝑣𝑁−1

ρ𝑁 , 𝑑𝑁𝑣𝑁

ρ𝑁+1 , 𝑑𝑁+1𝑣𝑁+1

𝑎0𝑏0= 𝑴 ⋅

𝑎𝑁+1𝑏𝑁+1

𝑎0

𝑏0

𝑎𝑁+1

𝑏𝑁+1

𝑴 (𝜔) = 𝑰0,1 ⋅

𝑖=1

𝑁

𝑴𝑖

Reflection/Transmission Spectrum 𝑎0 = 1 , 𝑏0 = 𝑟 , 𝑎𝑁+1 = 𝑡 , 𝑏𝑁+1 = 0

Quasi-normal modes 𝑎0 = 0 , 𝑏0 = 1 , 𝑎𝑁+1, 𝑏𝑁+1 = 0

𝑟(𝜔) =1

𝑀11(𝜔)𝑡(𝜔) =

𝑀12(𝜔)

𝑀11(𝜔)

𝑀11 𝜔 = 0 𝑤𝑖𝑡ℎ 𝜔 𝜖 ℂ.

GaAs/AlAs: the double magic coincidence

Analogy between optics and acoustics𝑍 → 𝑛

𝑣 →𝑐

𝑛

So, if ∀𝑖,𝑍𝑖+1𝑍𝑖=𝑛𝑖+1𝑛𝑖

𝑐 𝑛𝑖𝑣𝑖= 𝐾

𝑀𝑎𝑐(𝜔) = 𝑀𝑜𝑝(𝐾𝜔)

GaAs/AlAs: DOUBLE MAGIC COINCIDENCE

𝑛1𝑛2~𝑣2𝑣1

𝑍2𝑍1~𝑛2𝑛1

Localization length

𝑙𝑜𝑔 𝑇 = 𝜉𝐿GaAs

AlAs

Dispersive localization length 𝜉 OM coupling study in a narrow frequency band

Optomechanical coupling

Moving boundaries

𝑔𝑀𝐵 = −𝜔𝑜2

𝑚=0𝑁 𝑢 𝑧𝑚 𝜖𝑚 − 𝜖𝑚+1 𝐸(𝑧𝑚)

2

0𝐿𝜖(𝑧) 𝐸(𝑧𝑚)

2

ℏ

2𝑚𝑒𝑓𝑓𝜔𝑚𝑔𝑃𝐸 =𝜔𝑜2

0𝐿𝑛4 𝑧 𝑝12(𝑧)

𝑑𝑢(𝑧)𝑑𝑧𝐸(𝑧𝑚)

2

0𝐿𝑛2(𝑧) 𝐸(𝑧𝑚)

2

ℏ

2𝑚𝑒𝑓𝑓𝜔𝑚

Photoelastic