belgium h. benisty , a. lupu and a. degironhosting.umons.ac.be/php/ieeephotonicsbenelux... · 2015...

2015 IEEE Benelux Chapter,May 22nd, Mons, H. Benisty et al. 1

Functionalguidedphotonicswithparity‐time(PT)symmetryconcepts

H. Benisty1, A. Lupu2 and A. Degiron2

1Lab Charles Fabry, IOGS, Palaiseau, France

Institut d’Electronique Fondamentale, Univ. PSud, Orsay, France

IOGS

IEF

C2N

BELGIUM

LPN


WorkS inprogress


(serious)OUTLINEPT-symmetry brief history & basics

Quantum mech., Exceptional Point, Symmetry-breaking

PT-symmetry & plasmonics « I will survive » Electro-optics with gain&loss Early untold PT symmetry –(long-range plasmons) Example of metal & gain combination

- « PIROW » (plasmonic inverse-rib opt wg) & organics

Switching and PT–symmetry (*) Switching configurations below the Exceptional Point

Multimode waveguides management(**)

(*) A. Lupu, H. Benisty and A. Degiron, Opt. Express 21, 21651 (2013)(**) H. Benisty, A. Lupu, and A. Degiron, Phys. Rev. A 91, 053825 (2015)


P

Analogy inoptics

Hermitian operator H ♥ Real Eigenvalues

♥ Real Eigenvalues Hermitian operator

Non-Hermitian Hamiltonien

Coupled modes equations

C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998)

♥ Real Eigenvalues … as long as r’’ < s ♥ Real Eigenvalues … as long as g <

PT-Symmetric

T ≡ . . )

Gain [P sym] loss

ε"(x) = ‒ ε "(‒x)

gain losses

PT = PT


PT‐ symmetry :coupledWGs

Standard case

log10(T)-5-4-3-2-1012345

gain (cm-1)

dist

ance

L (µ

m)

0 100 200 300

0200

400

600

800abrupt behaviour

- g2

T11

T12coupling

L

1g1GAIN

LOSSP

Eigenvalues in complex plane

|T11|

Exceptional point(EP):singularity of

∂(eigenvalues)/∂(gain)

EP

Im() is antisymmetricε"(x) = ‒ ε "(‒x)

EP Re

Im

P


eigenstatebehaviourvs.« gain‐loss »

Symmetrybreaking

●Symmetry-breakingof eigenstates

12

AB

A

B("winner-takes-all")


PTsymmetryinOptics

• El Ganainy et al. (CREOL), « Theory of coupled optical PT-symmetric structures », Opt. Lett. 32, 2632 (2007)• Klaiman et al. PRL 2008; Guo et al. PRL 2009; … (topic starts to blow up)

• Ctyroky & Nolting 1996

• 2004-2005 : Kulishov/Greenberg/Poladian/Agarwal:Gratings with Δn= Δnrcos(Kz)+ iΔnicos(Kz+φ), «««nonreciprocity»»»

"unnamed"

"named"

Observedwithparametricgain/loss• Rüter et al. (Clausthal u. CREOL, Technion)« Observation of parity–time symmetry in optics », Nat. Phys. 6, 192 (2010)


PT‐ symmetry

PT-symmetry coupled waveguides PT-symmetry Bragg grating waveguide

Transverse PT-symmetry Longitudinal PT-symmetry

ε"(‒ x) = ‒ ε "(x)


PT‐ symmetry :« nonreciprocal R »

Not genuine nonreciprocity (no µ)

∆ε ~ cos(qx)+i sin(qx) = exp(iqx)

forbiddenallowed

-K K

q

q

π/2 shift of Re(ε)and Im(ε) modulations

Transition betweentwo dispersion branches

-K -K-q

K K-qNo -q! ω


Reciprocity ( @ Lorentz) =

symmetric S-matrix

YES


OUTLINEPT-symmetry brief history & basics








ixed losses :« Iwill survive »(a)

(b)

matched losses

fixed (metal) losses

log10(T)-5-4-3-2-1012345

gain (cm-1)

dist

ance

(µm

)

0 100 200 300

0200

400

600

800abrupt behaviour

0

200

400

600

800

1000

abrupt behaviour

gain (cm-1)

dist

ance

(µm

)

0 100 200 300

|T11|

|T11|

« passive- PT-structures »

« active- PT-structures »

e.g. Guo et al. PRL 2009

‐ g2

g1GAIN

LOSS

‐ g0

+gGAIN

FIXED LOSS

g0 and shouldbe"matched"

H. Benisty et al. Opt. Express, 19, 18004, 2011

EPremains

EP

g1=‐g2


PT−

+

_

Kogelnik 1970’s

Electro-optic tuningΔRe(n)

Device length L

Commutation loci

PT-sym, 2010’s

Gain / no gain

Fixed losses (Au) ??

Very few tunableΔRe(n) proposalsin plasmonics

We’d better tune ΔIm(n) !

What are the new diagrams ?


Substrate

BCB

Au

~4 μm~20 nm

~1 cm

Wideband mode (VIS-IR range)

Courtesy of A. Degiron


t

t

Co‐directionalcouplingbetweenplasmonicguideanddielectricguide

Degiron et al, New J. Phys. 2009(Duke U)

BCB

SiO2

Air

Two Eigenmodes

Detuning control by BCB thickness


Experimental waveguides

25

A combination of negative and positive lithography steps are used to fabricate plasmonic stripes coupled to SU8 waveguides, embedded in BCB polymer.A combination of negative and positive lithography steps are used to fabricate plasmonic stripes coupled to SU8 waveguides, embedded in BCB polymer.

CL = coupling length


___ Simulations▪ ▪ ▪ Experiments

Measurements vs. coupling length

Arbitrary BCB thickness

Optimized BCB thickness

BCBt=6.6 μm

BCBt=5.4 μm

26


Dephasing of beating is a first sign

0

0.5

1

0 0.5 10

0.7

1.4

0 0.5 10

25

50

0 0.5 1

Propagation distance

Tran

smis

sion

Propagation distance Propagation distance

T11

T12

g=0 g<gcrit g>>gcrit

Gain g

Losses -g

2

1

2

1

M

dzdi

2/2/

igig

M

Coupled Mode Theory

27


Applicationexample :Plasmonicmodulator

-30

-20

-10

0

10

20

30

0 0.2 0.4 0.6 0.8 1 1.2Normalized Material Gain

Pow

er (d

B)

SU8 WG

SP WG

•No electro-optic modulation in metals• PT -symmetry offers a plausible alternative to elaborate active devices.

•No electro-optic modulation in metals• PT -symmetry offers a plausible alternative to elaborate active devices.

Lupu et al., Opt. Express 2013

28


Moreminiatureplasmonics?Example ofPlasmonic Inverse‐Rib OpticalWG

JAP 2010, H. Benisty and M. BesbesE-field in 30-50 nm tip...(+JOSA 2012)

Like Oulton’s nanorod/spaser, but deterministic Gain brings just gain !

n~1.4n~2.0


Two coupled «PIROWs »:good?Again oneandanormal one

CanwehaveagoodEP?

H. Benisty and M. Besbes,

"Confinement and optical properties of the plasmonicinverse-rib waveguide,"

JOSA. B, vol. 29, pp. 818-826, 2012.

GAIN FIXED LOSSES

METAL

Something wrong ?


« Healing »ofTwo Coupled PIROWs

=-0.174

Asmall detuning compensate complex (Re&Im)couplingconstant IEEE J. Lightwave Technol., vol. 30, pp. 2675-2683, 2012. (H. B et al.)


ModelRealisation :Gainwith organics

Thermally evaporated “fvin” layer on glass substrate

Adjustable razor blades

Diverging LensCylindrical Lens

Sample

CCD(stripe lengthmeasurement)

Stripe quality (a) Without imaging (b) With imaging

Pump LASER Characteristics

Frequency Doubled Q-switched Nd:YVO4λ = 532 nm10 Hz, pulse duration < 500 ps

Pump Stripe Width : 320 µm

Variable Stripe Length (VSL) technique:+ Molecular film

Spectro(Ocean Optics)Spectro(Ocean Optics)Spectro(Ocean Optics)

(b)

(a)

“fvin”

H. Rabbani-Haghighi, S. Forget, S. Chénais et al. Appl. Phys. Lett. 95, 033305 (2009).

S.Chénais &S.Forgetteam,LPL,Paris13


E=0,41 mJ/cm2 → Gain= 50 cm‐1

Comparison : in a 5%‐doped DCM:PMMA of same thickness :

Gain= 40 cm‐1

Gainwith organics can be high&fast

nanosec. pump‐probe gain

S.Chénais &S.Forgetteam,LPL,Paris13


BarandCrossperfectswitchstatesinideal(gain=loss)PT‐symmetriccoupler(PTSC)

Bar Cross perfect switch Cross Bar perfect switch

Smallest length SwitchNot good Switch

dB dB

T11 T12T11 T12

g1

2

1 1

0

g1

2

1 0

10 0

g1

2

1 0

1

g1

2

1 1

00 0

T11

T12

T11

T12


2

2 2 2im 2 2

im

tan 1LL

im 0.67 2.103L

CMTsolution

Whatisthenewconceptreplacing“Vπ”?

Realindexmodulation Imaginaryindexmodulation

Δ(Im)replacesΔ(Re)

Δ(Im)=|g|+|χ|(the« sum »ofgainandloss)

Sorathershortcouplersarepossible

[#¤@§§](*)

(*)Copyrighted


FLAVOURSOFIMPERFECTPT ‐SYMMETRY

Losses2

gaing1

2=g1

2 =g1or

2:fixed,variableg1


1exp 2 cg L

Positive role of losses : less gain needed Unbalanced coupler penalty

29

1 2im 2 0.67

2 cgL L

Remarkable feature

Switching possible with less gain and more losses, provided @0.67π met

UnbalancedPTSC:positiveroleoflosses!


OpticalMemoryconfiguration

Kulishov 2005

Concept remains to be proven…


Multimodetransmission

without crosstalk ! short datacom


m=1,2,3,... How to select one mode (at given ω)?

ByGrating (+Lens)?ByMMIvariant?Bygrating variants ?

Castro et al.Liu, Miller and Fan, S.H. Cheng, (2012) et al.

Modeselection recipes ?

?Confined hologram ?


Three flavours ofPT‐symmetry

Periodicity(bounded)

& PT-symmetry

propagation

propagation

PT-symmetryPeriodicitypropagation& PT-symmetry

Kulishov« pseudo -nonreciprocal… »

Simple case

New case


-0.02-0.01

00.01

0.020.03

0.040.05

0.06

1000

2000

3000

4000

5000

6000

2.80

2.70

2.60

0 0.1 0.2 0.3 0.4 0.5

| ΔεI |

Re(n

eff)

zeros

#1

#6 #7

0.1 0.2 0.3 0.4 0.50-0.02

0

0.02

0.04

0.06

| ΔεI |Im

(nef

f)

Modesby1DTMMcalculation

ΔεI

Phys. Rev. A 91, 053825 (2015)


5 10 15 20 25 30 35 40

5

10

15

20

25

30

35

40

10-4

10-2.2

10-3

eige

nvec

tori

ndex

1

31

61

1 31 61

1 12 24 36

|<ψ | ΔεI |ψ >|²

2nd order perturbationtheory explains modeclusters

Phys. Rev. A 91, 053825 (2015)


9 stripes gain/loss pattern

0 4 8

1.2

1.199

1.198

|ΔωI| 104

Im(ω

)10

4

(a) 5

0

-50 4 8

|ΔωI| 104

(b)

Re(ω

)loss mode

gain mode

gain&loss

modes

0 72 144

-3.14

0

3.14

0

1

2

Transverse coordinate x

Ampli

tude

(a.u.

)Ph

ase

loss modegain mode

(d)

(e)

0 5 10 15n°4

0 5 10 150

0.51

-101

n°5

0 5 10 150

0.51

-101

n°6

Only modes#4and#5gotobroken sym


Fieldevolution with PT‐sym/just‐sym stripes

……

PT‐sym P‐only‐sym4 gainlobes

P‐only‐sym4 loss lobes


Work not(notyet)inprogress


CONCLUSION

PT–symmetry

« Hologram » of gain and losses

Many Emerging features @ Exceptional Point.

Several avenues for worthwile photonic devices

Plasmonics Replace Electro-optics by Gain&LossGood switching conditions existbelow Sym.-Breaking point.

Transverse mode management

belgium h. benisty , a. lupu and a. degironhosting.umons.ac.be/php/ieeephotonicsbenelux... · 2015...

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