Nonlinear devices of integrated optics – fundamentals and ...Sergiusz Patela Nonlinear integrated...

Nonlinear devices of integrated optics – fundamentals and

applications

Sergiusz PatelaWrocław University of Technology

Sergiusz Patela Nonlinear integrated optics

Definition

Whenever material response (electric polarisation, current density, magnetisation) is nonlinear function of electrical or magnetic field - nonlinearelectromagnetic phenomena appear.

Examples from classical electrodynamics: magnetisation curve for ferroelectric materials, Faraday effect (twist of polarisation plane in magnetic fields)

Examples of optical nonlinearities: optical harmonic generation, nonlinear refractive index changes.


Introduction

• Usually electrical field strength (E) of optical fields is much lower than internal atomic fields. In such case, there is a linear relation between electrical field strength (E) and dielectric displacement (D).

• Nonlinear effects will appear for optical power density of about 1 kW/cm2 (107 W/m2) .

• Nonlinear optical devices will operate with powers one order of magnitude higher.

• Due to a small cross section of optical waveguides, high optical power densities are available even for low-power optical beams.

EDrr

ε=


Power densities in optical waveguides

Optical power (P) 1 mW = 10-3 W

Single mode optical fibreMode field diameter (d) 10 µmCross-section area (S) 78,5*10-12 m2

Power density P/S = 1,3*107 W/m2 - enough power for observation of nonlinear optical effects

Strip waveguidewidth 5 µmThickness 1 µmCross sction area (S) 5* 10-12 m2

Power density P/S = 20*107 W/m2 – power density high enoug to build nonlinear photonic devices.


Nonlinear optical effects

The field of nonlinear optics is under strong development since 1960s. Research includes areas of:

• harmonic frequency generation• nonlinear spectroscopy (e.g. Raman)• Optical phase conjugation• Optical bistability• Optical switching


From the history of nonlinear optics ...

Pionearing work of P. A. Franken – a proof wihich is not there.

P.A. Franken, A.E. Hill, C.W. Peters, G. Weinreich, Phys. Rev. Lett., vol. 7, no. 4 (1961) pp. 118-119.

Fig. 1. A direct reproduction of the first plate in which there was an indication of second harmonic. The wavelength scale is in units 100 A. The arrow at 3472 A indicates the small but dense image produced by the second harmonic. The image of the primary beam at 6943 A is very large due to halation.


Constitutive equation (nonlinear optics)

PEEDrrrr

+ε=ε= 0

MHHBrrrr

+µ=µ= 0

NLPPPL

+=r

Constitutive equations of Maxwell’s equations set

NLL PPEEDrrrrr

++ε=ε= 0

EP LLrr

χε= 0

NLL PEPrrr

+χε= 0


Classification of optical nonlinear effects

Material response for optical beam propagation is characterised by polarisation vector and dielectric susceptibility tensor.

( ) ( ) ( ) ( )( )LL +χ++χ+χ+χε= nn EEEEEEEP 3210

If the atomic vibration amplitude is high enough, response is becoming nonlinear. Nonlinear response is described by higher order terms in the power series

( )EEP χε0=

linear effects

n.lin. 2-nd order

n.lin. 3-rd order


Nonlinear refractive index

220

220 2

1 EnnEnnn +=+= 220 Ennn ′+= Innn 20 ′′+=

20

22 42 ncnnn ′′

π=′=

( )( )ωω−ωω−χε

= ,,;4

3 32

02

cnn


Nonlinear optical materials - selecting criteria and figures of merit

Nonlinear second order figure of merit

( )ωω 222 nndM ijij =

where d-ij is nonlinear optical coefficient of the second order, and nω and n2ω are refractive indices for first and second order beams, respectively.

( )

λαχ 2

1

3 nM =

Nonlinear third order figure of merit

Saturated figure of merit

αλ

sat

satnM 2=

where n2sat is saturated third order refraction index


3rd order materials

Material λ Nonlinear refractive index n2

Response time τ

α n2/λα ∆nsat ∆nsat/λα

µm m2/W s 1/cm x10-8

GaAlAs r 1 10-8 10-8 104 1 0,1 0,1

GaAlAs nr 1 10-12 10-8 30 0,033 2x10-3 0,9

Sd CdSxSe1-x 1 10-14 10-11 3 0,003 5x10-5 0,3

PTS nr 1 >10-16 <10-12 <2 5x10-5 >10-3 >10

SiO2 1 10-20 10-14 10-5 10-3 >10-6 >1000


2nd order materials (SHG)

Material λ [nm] nω n2ω WJN

ωω 22

2

nn

deff

[x10-24 m2/V2]

Damage threshol

d [GW/c

m2]

Bandwidth [nm]

Kwarc 1064 1,5341 1,547 0,028 1,2 KDP 1058 1,4938 1,4705 0,029 1,0 200-1500 KD*P 1058 1,4978 1,4689 0,034 0,7 200-1500 ADP 1058 1,5066 1,4815 0,041 0,4 200-1200 LiNbO3 d31 1058 2,2322 2,2325 1,84 0,1 350-4500 LiNbO3 d33 1152 2,1506 2,2153 89,69 LiTaO3 1058 2,1366 2,2089 0,11 BBO 1064 1,657 1,5541 0,29 13 190-3500 KTP 1064 1,74-1,83 1,79-189 9,35 0,65 350-4500 LBO 1064 1,566-1,606 1,579-1,621 0,45 25 160-2600 KNbO3 1064 2,21-225 2,20-2,32 10,24 310-5500 LiJO3 1064 1,86 1,75 2,09 310-5500 ZnO 1058 1,95 2,048 0,4


Organic materials

ADP = NH4H2PO4

KDP = KH2PO4 MNA = 2-metylo-4-nitroanilinaNPP = N-(4-nitrofenyl)-(L)- prolinol PNP = 2-( N-prolinol)- 5-nitropyrydyna

MBANP = 2-(α - metylo- benzyloamino)-5-nitropyrydyna

DAN = 4-(N, N-dimetylo- amino)-3- acetamido- nitrobenzen COANP = 2-cyclooctyl- amino-5- nitropyrydyna

MAP = 3-methyl-(2,4- dinitrofenylo)- amino-propanol

POM = 1-tlenek 3-metylo-4-nitro- pyrydyny

MN

A

NP

P

PN

P

LiN

bO3 d

33

CO

AN

P

DA

N

MA

P LiJO

3

LiN

bO3 d

31

Moc

znik

ADP

K

DP

Kw

arc

10-2 10-1 1 101 102 103 104

d2 /n3 (x 10-24 m2 /V2)


Is it possible to build all-optical transmission or data processing systems?


Technology enablers

1. Materials – available in good quality, large quantity, for the right prize

2. Existence of production scale technology

3. Existence of packaging and interconnection technologies (industry compatible)

4. Proven agreement with standards and quality requirements


Simple all optical M-Z interferometer

Active area

Strip waveguide

Y splitter

GaAs Substrate

GaAsAlxGa1-xAs

Modulating signal: laser or fiber

Modulated output signal

Input sinal λ=1.3 µm

Modulation efficiency versus modulating signal power

1 2 3 4 5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

M [%]

P opt [mW]


Simple functional devices (nonlinear prism and grating couplers)

Laser Ar +

beam expander

gray filter beam

splitter

prism coupler

detector

Pwy

Pwe

detector

Corning 7059 waveguide

Schott GG495 glass filter


Prism coupler - limiting action

TE0

TM0

0,5 dB/cm

1,7 dB/cm

P out

[mW

]

1

2

3

4

100 200 300 400 500 600P in [mW]


Optical bistability

700 800

a Pwy

Pwe900

[j.w.]

Optical bistability obtained with the prism coupler


Phase adjustment condition for nonlinear optical phenomena

0.2 0.4 0.6 0.8 1

t [um]

1.5

1.6

1.7

1.8

1.9

2

Neff

0.2 0.4 0.6 0.8 1t [um]

1.45

1.5

1.55

1.6

1.65


SHG

P r o m ie ń d io d ylas e r o w e j(λ = 0 ,8 4 µ m ) Ś w ia t ło w ó d

p as k o w y

P od ło ż e L iN b O 3

P r o m ie ń d r u g ie jh a r m o n ic z n e jλ = 0 ,4 2 µ m

D io d a la s e ro w aλ = 0 ,8 4 µm

H + :L iN b O 3

L iN b O 3

λ 2 = 0 ,4 2 µm

5 1 0 5 0 1 0 0

P 0 ,8 4 [m W ]

P 0 ,4 2[m W ]

0 ,0 1

0 ,0 5

0 ,1

0 ,5

1 ,0

strip waveguide

laser beam

substrateSHG beam

laser diode


Nonlinear optical switches (optically controllable switches)

1. Nonlinear optical loop mirror (NOLM)

2. Non-Linear Amplifying Optical Loop Mirror (NALM)

3. Nonlinear directional coupler

4. Nonlinear Mach-Zehnder interferometer


Optical XOR gate

Optical power guided in a and b branches, controls transmission of pulses from the branch c. Electrodes adjust working point of the device (initial phase shift between the branchess = π).

TE

TE

TM

polarisertransm. TM

a

c

b

Function XOR:A B Q0 0 01 0 10 1 11 1 0

U(π)


0

0,05

0,1

0,15

0,2

0,25

0 0,5 1 1,5 2

Nonlinear beam deflector

nc

nf

ns Λs

βs βcs

wo

θcθs(Ic)(λc)

(λs)Steering

beam

Deflected beam

z

Input power Pc [W]

Def

lect

ion

of o

utpu

t bea

m


Nonlinear directional coupler

t t

t

Channel 1

Channel 2

Bar state

Cross stateA dashed line depicts operation of a linear device.


Nonlinear Bragg grating

nfo + n2I

Ef

nsδ

L

d

Eb

Bragg condition: 2 Λ = ν λ , ν = 1, 2, 3, ...where: λ = λo/nwaveguideefficient reflection only for λo = 2 Λ nwaveg. /ν


Nonlinear optical loop mirror (NOLM)

The device consists of a fused fiber coupler (splitter) with two of its arms connected to an unbroken loop of fiber. The device makes use of the phenomenon of “Nonlinear Kerr Effect”. The two counter propagating light beams are nonlinearly phase-shifted by different amount. The phase shift is power-dependent.

Applications: noise limiter, optical gate, optical signal processing (digital)

Coupler ≠ 50%, ⇒ complete coupling not possible


The Non-Linear Amplifying Optical Loop Mirror (NALM)

Coupler = 50%, ⇒ complete coupling is possible


The NOLM as a Logic Gate

Demultiplexing of a TDM Data Stream. A control pulse is used to select a channel from an incominghigh-speed TDM data streem.

NOLM Configured as an AND Logic Gate

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