nonlinear devices of integrated optics – fundamentals and
TRANSCRIPT
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.
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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=
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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.
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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
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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.
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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
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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
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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
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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
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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
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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
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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)
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Is it possible to build all-optical transmission or data processing systems?
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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
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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]
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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
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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]
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Optical bistability
700 800
a Pwy
Pwe900
[j.w.]
Optical bistability obtained with the prism coupler
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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
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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
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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
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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)
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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
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Nonlinear directional coupler
t t
t
Channel 1
Channel 2
Bar state
Cross stateA dashed line depicts operation of a linear device.
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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
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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
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The Non-Linear Amplifying Optical Loop Mirror (NALM)
Coupler = 50%, ⇒ complete coupling is possible