Phase Matching using Bragg Reflector Waveguides Amr S. Helmy & Brian R. West Edward S. Rodgers Department of Electrical & Computer Engineering, University of Toronto Email:
[email protected] 1
2nd Order Nonlinearities; III-Vs vs. PPLN Point of Comparison
LiNbO3
GaAs/AlGaAs
d33 ≅ 30 pm.V-1
χxyz ≅ 100 s pm.V-1
0.4 – 4.8 μm
0.8 -17 μm
Phase-Matching Technologies
- Cerenkov PM - Natural Birefringence - QPM-Periodic Poling
- Birefringent Waveguides - QPM-Domain Amorphisation - QPM-Domain Reversal
Associated Losses
2
| x |≤
(core) , (cladding) ,
iKΛ k t e − A− B ⎛ c c ⎞ Dispersion Relation (TE): k c tan ⎜ , ⎟ = ik1 iKΛ e − A+ B ⎝ 2 ⎠
Λ= a + b
x
z
⎡ ⎤ i ⎛k k ⎞ A = e ik1a ⎢cos k 2b + ⎜⎜ 2 + 1 ⎟⎟ sin k 2b ⎥ , 2 ⎝ k1 k 2 ⎠ ⎣ ⎦
b, n2 tc
a, n1
y
⎡i ⎛k ⎤ k ⎞ B = e −ik1a ⎢ ⎜⎜ 2 − 1 ⎟⎟ sin k 2b ⎥, ⎣ 2 ⎝ k1 k 2 ⎠ ⎦ C = B * , D = A* , 11
λ/4 Bragg Reflection Waveguides k1a = k2b = π/2
kx eiKΛ + k1 / k 2 ⎛ kc tc ⎞ kc tan⎜ . ⎟ = ik1 iKΛ e + k 2 / k1 ⎝ 2 ⎠ ⎛ k2 KΛ = mπ − i ln⎜⎜ ⎝ k1
kc =
π tc
=
2π
λ
⎞ ⎟⎟ , ⎠
n −n 2 c
2 eff
kz
x
z
b, n2 tc
,
y
a, n1 12
λ/4 Bragg Reflection Waveguides
0
TE Modes
-5 0 5 Distance from Waveguide Core (μm)
Phase matched modes for an arbitrary structure
The modal index of both TIR and BRW Modal Effective Index
Normalized Intensity
1
3.3 3.2
TE Modes
3.1 3.0
BRW at 775 nm TIRW at 1550 nm
2.9 0.2
0.3
0.4
Core Thickness (μm) 13
λ/4 BRWs; Optimization Conversion efficiency will chiefly benefit from the spatial overlap in the core
E2ω(x)
Maximizing the power in core region is key
2ω
E ω (EE*)
ω
(EE*) [a.u.]
0.5
0
2ω
P2ω(x) = ε0d(x)[Eω(x)]2
1
E
Conversion efficiency depends on
Power at ω, Field at 2ω
-0.5
-1
-2
-1
0 x [μm]
1
2
14
λ/4 BRWs; Losses
Losses depend on the number of cladding periods Practically lossless structures can be achieved
Propagation Loss in QW-BRW
0
10
-2
10 Loss [dB/cm]
Waveguiding losses as a function of the number of Bragg pairs
-4
10
-6
10
-8
10
-10
10
5
10 15 20 Number of periods in each cladding
25
Circles = TE, Squares = TM Δ(Al(x)Ga(1-x)As)Clading = 0.3 (red), 0.4 (blue), 0.5 (green), 15
λ/4 BRWs; Tunability Thermal, electrooptic & carrier tuning 1550
BRWs are resonance based
The figure shows phase-matching using carrier tuning The core is the intrinsic region in a p-i-n junction
1545 PM wavelength [nm]
carrier and electrooptic effects for continuous tuning
Phase Matching Wavelength vs. Carrier Density in Core
1540 1535 1530 1525 1520 1515 1510 0
2
4 6 18 -3 carrier density [10 cm ]
8
10
16
λ/4 BRWs; 2D Waveguides TE
TM
Iterative process needed to design 2D Waveguides The λ/4 condition changes as the 1D & 2D to propagation constants are different
Transverse single mode condition restrict the 2D design This will govern the etch depth and ridge width 17
Summary We proposed Bragg reflection waveguides as a promising phase matching alternative We presented calculations showing practical structures are possible using the GaAs/AlGaAs system Propagation losses due to leakage can be in the 10-5 dB.cm-1 with < 10 Bragg reflector pairs Carrier tuning in p-i-n structures over 10s of eVs Excellent spatial overlap, with conversion efficiency that can be maximized through mode confinement in the core
Device growth and fabrication is underway 18
