anderson localization of photons and phonons for...
TRANSCRIPT
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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
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Optomechanical crystals
Guillermo Arregui ImagineNano 2018, Bilbao
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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
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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
![Page 5: Anderson localization of photons and phonons for optomechanicsphantomsfoundation.com/.../ImagineNano2018_Arregui.pdf · 2018. 3. 23. · Guillermo Arregui ImagineNano 2018, Bilbao](https://reader035.vdocuments.us/reader035/viewer/2022070302/6111c380b83f9166de7d3e52/html5/thumbnails/5.jpg)
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
![Page 6: Anderson localization of photons and phonons for optomechanicsphantomsfoundation.com/.../ImagineNano2018_Arregui.pdf · 2018. 3. 23. · Guillermo Arregui ImagineNano 2018, Bilbao](https://reader035.vdocuments.us/reader035/viewer/2022070302/6111c380b83f9166de7d3e52/html5/thumbnails/6.jpg)
Guillermo Arregui ImagineNano 2018, Bilbao
The role of fabrication disorder
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Guillermo Arregui ImagineNano 2018, Bilbao
The role of fabrication disorder
Typical fabrication disorder levels spoil the
structure performance drastically
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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)
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Guillermo Arregui ImagineNano 2018, Bilbao
Disorder-induced localization
Photonic disorder-induced localization observed,
but no mechanical modulation of the outcoupled
light
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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
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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
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Guaranteeing co-localization…
Guillermo Arregui ImagineNano 2018, Bilbao
Can we find a system that guarantees a higher degree of localization ?
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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 ?
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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)
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A perfect distributed Bragg reflector
GaAsAlAs
Guillermo Arregui ImagineNano 2018, Bilbao
dGaAs = 61.88 nm , dAlAs = 73,48 nm , N = 600
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A mechanical and/or optical Lifshitz tail
GaAsAlAs
Guillermo Arregui ImagineNano 2018, Bilbao
dGaAs = 61.88 nm , dAlAs = 73,48 nm , N = 600
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A mechanical and/or optical Lifshitz tail
GaAsAlAs
Guillermo Arregui ImagineNano 2018, Bilbao
dGaAs = 61.88 nm , dAlAs = 73,48 nm , N = 600
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A mechanical and/or optical Lifshitz tail
GaAsAlAs
Guillermo Arregui ImagineNano 2018, Bilbao
dGaAs = 61.88 nm , dAlAs = 73,48 nm , N = 600
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Co-localization of photon-phonon pairs
GaAsAlAs
Pairs of perfectly co-localized photons and phonons
Guillermo Arregui ImagineNano 2018, Bilbao
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Co-localization of photon-phonon pairs
GaAsAlAs
Pairs of perfectly co-localized photons and phonons
Guillermo Arregui ImagineNano 2018, Bilbao
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Co-localization of photon-phonon pairs
GaAsAlAs
Guillermo Arregui ImagineNano 2018, Bilbao
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Optomechanical coupling
Guillermo Arregui ImagineNano 2018, Bilbao
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Optomechanical coupling
Guillermo Arregui ImagineNano 2018, Bilbao
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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
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Conclusions
Guillermo Arregui ImagineNano 2018, Bilbao
1. Photon and phonon Anderson localization can be used as a new
confinement strategy for cavity optomechanics experiments
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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
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Acknowlegdments
Thank you!
Guillermo Arregui Wombat 2017, Besançon
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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
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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.
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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
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Localization length
𝑙𝑜𝑔 𝑇 = 𝜉𝐿GaAs
AlAs
Dispersive localization length 𝜉 OM coupling study in a narrow frequency band
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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