PT-symmetric photonics: hidden reefs on the route toward ...
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PT-symmetric photonics: hidden reefs on the route toward practical applications
A. Lupu 1, H. Benisty 3, A.Lavrinenko 4, N.Dubrovina 1, A. Ramdane 2
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Heraklion 2016-06-17 - Anatole LUPU
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Using PT-symmetry for switching applications
Locally PT-symmetric Bragg gratings
PT-symmetry: a new platform for active optical devices
Summary and conclusions
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PT-symmetry genuine feature: Functional role of losses
PT-symmetric directional coupler PT-symmetric Bragg grating
Gain-loss modulated PT-symmetric structures functionalities : Switching and tunability Spatial (modal) non-reciprocity Active tailoring of the grating spectral response and dispersion
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Re Im
∆β∆β∆β∆βeff detuning
∆β∆β ∆β∆βef
f/ κκ κκ
critical point
L1
L2
PT coupled WGs detuning variation Transmission variation
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Re Im
∆β∆β∆β∆βeff detuning
∆β∆β ∆β∆βef
f/ κκ κκ
critical point
L1
L2
Transmission variation
Bar -> Cross: T11=1, T12=0 -> T11=0, T12=1 Cross -> Bar: T11=1, T12=0 -> T11=0, T12=1
g1
χχχχ2
1 1
0
G1
X2
1 0
10 0
g1
χχχχ2
1 0
1
G1
X2
1 1
00 0
Can we obtain binary switching in a non conservative layout?
Binary switching operation
PT coupled WGs detuning variation
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T11= 1(bar)
T12= 0(cross)
T11 + T12= 1 (energy conservative states)
What is the minimal gain ×××× length product for switching?
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∆
( ) 22 2 2
im 2 2im
tan 1LL
ππ − ∆ = − −∆
( )1 1 2 2 1 2im2 2
ig ii
β β χ β βδ+ − − −= = + ∆
1 2im 2
g χ+∆ =
L=2Lc
-g1=χχχχ2
κκκκGAIN
LOSS
g1
χχχχ2
Detuning
∆∆∆∆im= imaginary detuning !
CMT solution
18.6dB
1 2im 2 0.67
2 c
gL L
χ π+∆ = ≈
A. Lupu, H. Benisty. et al, Opt. Exp. 2013
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Advantages : Compatibility with III-V laser sources fabrication technology Emulation of electro-refractive index variation in plasmonics and metameterials
III-V technology electro-optical switch Operation principle
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Hybrid plasmonic/dielectric PTSS design Fixed losses switching operation
T11=0T12=1
T11>1T12=0
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( )( ) ( ) ( )
( ) ( ) ( )1 2
cos sin sinexp
2sin cos sin
i iz z z
gM z z
i iz z z
δ κχ
κ δ
Ω − Ω Ω − Ω Ω= Ω Ω + Ω
Ω Ω gain losses
Coupled modes equations Transfer matrix Gauge transformation
Gauge transformation doesn’t affect the zeros of PTSS !
Hybrid plasmonic/dielectric PTSS design Fixed losses switching operation
T11=0T12=1
T11>1T12=0
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Nominal coupling length L=2Lc
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Optimal coupling length L>2Lc
Nominal coupling length L=2Lc
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PTSS design
Effective index variation
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Switching operation (L=2.1Lc)
T11=0T12=1
T11=1T12=0
T11 ≈≈≈≈ 0T12 ≈≈≈≈ 1
T11≈≈≈≈1T12 ≈≈≈≈ 0
T11 ≈≈≈≈ 0T12 ≈≈≈≈ 1
T11≈≈≈≈1T12 ≈≈≈≈ 1
∆∆∆∆N=0.00001
∆∆∆∆N=0.0001
∆∆∆∆N=0.001
PTSS design
Effective index variation
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Grating assisted PTSS
PTSS off PTSS on
Gain
Loss
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Grating assisted PTSS
PTSS off PTSS on
Grating assisted PTSS switching
∆∆∆∆N=0.00001
∆∆∆∆N=0.0001
∆∆∆∆N=0.001
Gain
Loss
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Using PT-symmetry for switching applications
Locally PT-symmetric Bragg gratings
PT-symmetry: a new platform for active optical devices
Summary and conclusions
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PT-symmetric Bragg grating
Z. Lin et al, Phys. Rev. Lett 106, 213901 (2011)
Unidirectional reflectivity
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PT-symmetric Bragg grating
Z. Lin et al, Phys. Rev. Lett 106, 213901 (2011)
Low reflectivity High reflectivity
Unidirectional reflectivity
PT-symmetric Bragg mirror
L. Feng et al, Opt. Express 22, 1760–1767 (2014)
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Coupling profile Conventional Bragg grating spectral response
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Inter-waveguides spacing variation: co- and contra-directional couplers
Refractive index contrast modulation: photo-imprinted Bragg gratings
rugated Bragg mirrors
Grating duty ratio variation: co- and contra-directional couplers
surface corrugated Bragg gratings
Bragg mirrors
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Front side incidence (high reflection) Rear side incidence (low reflection)
( ) 2 /0( ) i zn z n f z ne π Λ= + ∆
Hamming type apodization of complex index profile
( ) 1 0.852cos(2 / ) f z z Lπ= +
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Pseudo PT-symmetric apodization of complex index profile
Spectral maps (Are=0.852)
( ) ( ) ( )( )0 Re Im( ) cos 2 / sin 2 /n z n f z A z L iA z Lπ π= + +
A. Lupu, H. Benisty, A. Lavrinenko, JTSQE 2016
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Single mode amplifier (ARe=-0.95; AIm=0.95)
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Single mode amplifier (ARe=-0.95; AIm=0.95)
Single mode DFB laser (ARe=0.95; AIm=-0.95)
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Basic Duty Cycle Off-Resonance
Concatenated Gratings Phase Shifted Pair Gratings
H. Sakata, Opt. Lett., 17, (1992)
D.-B. Kim et al., Photon. Technol. Lett, 10, (1998) D. Wiesmann et al., Photon. Technol. Lett., 12, (2000)
A. Lupu, et al., OFC/IOOC (1999)
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Spectral maps (supersymmetric BDC)
Duty cycle modulation schemes
A. Lupu, H. Benisty, A. Lavrinenko, JTSQE 2016
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Spectral maps (superperiod ORM)
Grating period modulation schemes
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A. Lupu, H. Benisty, A. Lavrinenko, JTSQE 2016
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Grating period modulation
Spectral response
Cm=0.5 Cm=0.7
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Hamming type apodization of complex index profile
No antireflection coating
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Hamming type apodization of complex index profile
No antireflection coating Antireflection coating
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No antireflection coating
Complex index modulationARe=-0.85; Aloss=0; Again=0.85
Complex index modulationARe=-0.85; Aloss=0; Again=-0.85
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No antireflection coating
Complex index modulationARe=-0.85; Aloss=0; Again=0.85
Complex index modulationARe=-0.85; Aloss=0; Again=-0.85
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Using PT-symmetry for switching applications
Locally PT-symmetric Bragg gratings
PT-symmetry: a new platform for active optical devices
Summary and conclusions
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Coupler non-reciprocity
Buffer memory application
g1=0
χχχχ2=0
1 1Deactivated memory state
Feedback loop
g1
χχχχ2
1
>11
Activated memory state
Feedback loopSee also: M. Kulishov, et al, “Trapping light in a ring resonator using a grating assisted coupler with asymmetric transmission,”Opt. Express 13, 3567 (2005)
L=2Lc
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Contra-directional
Drop
In Thru
Add
C. Elachi, C. Yeh, Opt. Comm. 7, 201 (1973)
Contra-directionalanti-symmetric
Drop
In Thru
Add
Frustrated coupling
Perrone et al, J. Lightwave Technol. 19, 1943 (2001) A. Ankiewicz et al, 31, 2151 (1997)K. Muhieddine et al, Opt. Express 18, 23183 (2010) A. Lupu et al, Opt. Express 19, 1246 (2011)
J.-L. Archambault et al, Opt. Lett. 19,180 (1994)
Co-directional
Add
In Thru
Drop
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Vertical PTSBG directional coupler
Switch operation principle
Gain off state
Gain on state
A. Lupu, H. Benisty, et al., PNFA 2014
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A new platform for active optical devices
Coherent perfect absorber Buffer memory
Unidirectional DFB laserTunable add-drop
Binary phase modulator (0=>π)π)π)π)
Reconfigurable spatial DMUX
PT-symmetric switch
Single mode amplifier
H. Benisty, A. Lupu, A. Degiron, Phys Rev. A 91, 053825 (2015)
A. Lupu, H. Benisty. et al, Opt. Exp. 2013 H. Benisty… A. Lupu, et al., Opt. Exp. 2011
A. Lupu, et al., PNFA 2014
A. Lupu, H. Benisty, et al., PNFA 2014
A. Lupu, H. Benisty, A. Lavrinenko, JTSQE 2016
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Perfect Bar and Cross switch states in a non-conservative layout
Impact of material and technological imperfections
Tailoring spectral properties PT-symmetric Bragg gratings
Proposal of a new platform for active optical devices
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Theory Experiment
Mind the gap!