Post on 24-Dec-2015
May 25, 2007 Bilkent University, Physics Department
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Optical Design of Waveguides for Operation in the Visible and InfraredMustafa Yorulmaz
Bilkent University,
Physics Department
May 25, 2007 Bilkent University, Physics Department
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Outline
Waveguide theory Simulation Methodology State-of-the-art of rib-waveguides Our rib-waveguide designs State-of-the art of slot-waveguides Our slot-waveguide design Achievements
May 25, 2007 Bilkent University, Physics Department
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Planar mirror waveguides
qABAC 2/22/2
The picture shows the wave-fronts in addition to the ray model. In order to have constructive interference, the twice reflected wave must be in phase with the incident wave:
,...2,1,0qsin2dABAC
dmm 2
sin ,..2,1m
The angle of inclination is discrete, only a limited number of angles are permitted for constructive interference.
Wave-fronts and raypaths
May 25, 2007 Bilkent University, Physics Department
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The number of modes of a waveguide is limited
dmm 2
sin
It is derived that the angle of inclination is discrete:
since 1sin m /2dM
The total number of modes is M, which is a function of waveguide thickness and the wavelength.
If 2d/λ<1 no modes available thus λmax=2d or fmin=c/2d (cut-off frequency).If M=1, i.e. 1<2d/λ<2 then the wave guide is called single-mode
Example: If d=0.5μ, the cut-off wavelength is 1μ. The waveguide is single-mode for wavelengths down to 0.5μ, and multi-mode for lower wavelength operations.
May 25, 2007 Bilkent University, Physics Department
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Planar Dielectric Waveguides
The condition for total internal reflection:
)/(cos 121 nn
The condition for constructive interference:
md r
22sin22
Field distributions for TE guided modes in a dielectric waveguide.
May 25, 2007 Bilkent University, Physics Department
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Optical coupling
m
mmm zjyuazyE )exp()(),(
The amplitude of different modes depend on the light source used to “excite” the waveguide. If the source has a distribution that matches perfectly that of a specific mode, only that mode is excited. A source of arbitrary distribution excites different modes by different amounts.
Light propagates in a waveguide in the form of modes, the complex amplitude of the Electric field is the superposition of these modes:
αm is amplitude, um(y) is transverse distribution
dyyuys ll )()(
The amplitude of the lth mode is found by the overlap integral of the lth mode and the light distributions s(y)
May 25, 2007 Bilkent University, Physics Department
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Simulation methodology
Rib waveguide
The geometrical structure and the piecewise constant n(x,y) profile, makes analytical solutions of field distributions very difficult. Numerical methods provide reliable approximate solutions.
Finite Difference Method: the structure is divided into cells so that inside the cell the refractive index is constant. The differential operator is replaced by:
x
xfxxfxf
)()(
)('
May 25, 2007 Bilkent University, Physics Department
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Simulation program
Waveguide Mode Solver by Hilmi Volkan Demir and Vijit Sabnis Finite difference method (FDM) Solving the polarised solutions of the wave equation.
Cell structure of finite difference schemeGeometry of rib-waveguide structure
Inputs and outputs of the simulation program
May 25, 2007 Bilkent University, Physics Department
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Structure of their design and our simulation results to their structure Layer Thickness (nm)
Air 3000
Gan 3000
Al0.088Ga0.912N 4000
Sapphire 6000
Rib-Width 3000
Side-Width 5000
Rib-Height 2800
-Single mode
-Power coupling efficiency is 0.81
-Active region overlap integral is 0.99
-It lacks of MQWs
Rib-waveguide structure presented in * Parameters of rib-waveguide structure presented in *
Our simulation result to the structure presented in *
* R. Hui, Y. Wan, J. Li, S. X. Jin, J. Y. Lin, and H. X. Jiang, “III-nitride-based planar lightwave circuits for long wavelength optical communications,” IEEE J. Quantum Electron. 41, 100-110 (2005).
May 25, 2007 Bilkent University, Physics Department
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Structure of their design and our simulation results to their structure
Layer Thickness (nm) Loop
Air 1000
Al20Ga80N 20
Al20Ga80N 5
GaN 2.4 30
Al20Ga80N 20 30
GaN 1000
GaN 30
Sapphire 1000
Rib-Width 500
Side-Width 5000
Rib-Height 750
-It has MQWs
-E-field distribution doesn’t project on active layer
-It has a rib-widht smaller than 1um
-Power coupling efficiency is 0.6
-Active region overlap integral is 0.001
Rib-waveguide structure presented in **
Parameters of rib-waveguide structure presented in **
Our simulation result to the structure presented in **
** T. N. Oder, J. Y. Lin and H. X. Jiang, “Propagation Properties of Light in AlGaN/GaN Quantum Well Waveguides.” Appl. Phy. Lett. 79, 2511 (2001).
May 25, 2007 Bilkent University, Physics Department
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Challenges for Design
Rib-width > 1m for fabrication Single mode Having MQWs Circular mode profile Material overlap integral Coupling Efficiency
May 25, 2007 Bilkent University, Physics Department
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Our design @1550nmLayer Thickness (nm) Loop
Air 1000
GaN 1200
AlN (barrier) 1.2 1
GaN (well) 1.4 10
AlN (barrier) 1.2 10
GaN 50
AlN (barrier) 1.2 1
GaN (well) 1.4 10
AlN (barrier) 1.2 10
GaN 50
AlN (barrier) 1.2 1
GaN (well) 1.4 10
AlN (barrier) 1.2 10
GaN 300
GaN 760
Sapphire 1000
Rib-Width 2500
Side-Width 5000
Rib-Height 1531.6
-MQWs are designed as ten periods of AlN(1.2nm)/GaN(1.4nm) layers.
-The rib has a width of 2.5µm
-Rib-width is 2.5 um > 1um
-Single mode operation
-Made of MWQs
-Circular mode profile
-Power coupling efficiency is 0.078
-Active region overlap integral is 0.05
Parameters of our rib-waveguide structure for IR region
Our rib-waveguide design structure for IR region, E-field distribution of this structure
May 25, 2007 Bilkent University, Physics Department
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Our design @440nmLayer Thickness (nm) Loop
Air 1000
GaN 1240
Al10Ga90N 10
GaN (barrier) 4 1
In35Ga65N (well) 4 5
GaN (barrier) 4 5
In35Ga65N 50
GaN (barrier) 4 1
In35Ga65N (well) 4 5
GaN (barrier) 4 5
In35Ga65N 50
GaN (barrier) 4 1
In35Ga65N (well) 4 5
GaN (barrier) 4 5
GaN 300
GaN 560
Sapphire 1000
Rib-Width 1500
Side-Width 5000
Rib-Height 1632
-MQWs are designed as five periods of In35Ga65N(4nm)/GaN(4nm) layers.
-Rib-width is 1.5 um > 1um
-Single mode operation
-Made of MWQs
-Circular mode profile
-Power coupling efficiency is 0.074
-Active region overlap integral is 0.13
Our rib-waveguide design structure for IR region, E-field distribution of this structure
Parameters of our rib-waveguide structure for IR region
May 25, 2007 Bilkent University, Physics Department
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Achievements with our rib-waveguide designs Having MQWs Satisfying single mode operation Rib width > 1m (@440nm and @1550nm) Power coupling ~ 0.7-0.8 (@440nm and
@1550nm) Material Overlap > 0.1 (@440nm)
May 25, 2007 Bilkent University, Physics Department
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New type of waveguide design: Slot-waveguide Different way for confining and enhancing light: Guiding light in low-
index materials According to the Maxwell’s laws that the electric field must undergo
a large discontinuity with much higher amplitude in the low index side to satisfy the continuity of the normal component of electric flux density for a high-index-contrast interface. So that, this discontinuity is used to strongly enhance and confine light in a nanometer-wide region of low index material
Parameters
•nc
•ns
•nh
•wh
•ws
•hGeometry of slot-waveguide structure presented ***
*** V. Almeida, Q. Xu, C. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209 (2004) . [ISI] .
May 25, 2007 Bilkent University, Physics Department
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Verification of paper for slot-waveguide design
nc 1.44
ns 1.44
nh 3.48
wh 180nm
ws 50nm
h 300nm
Parameters and geometry of slot-waveguide structure presented in *** The contours of E-field amplitude and E-field lines that are shown in***.
3D surface plot of E-field amplitudes presented in ***
*** V. Almeida, Q. Xu, C. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209 (2004) . [ISI] .
Our
sim
ulat
ion
resu
lts t
o th
e st
ruct
ure
pres
ente
d in
***
-In this study, we confirm the result of paper [***] and we also calculate power coupling efficiency and active region overlap integral of their structure. They are 0.63 and 0.65 respectively.
May 25, 2007 Bilkent University, Physics Department
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Our-slot waveguide design for operation @ 1550nm
nc 1
ns 1
nh 2.031
wh 400nm
ws 50nm
h 400nm
-We obtained our slot-waveguide-design made of AlN
-Single-mode operation
-At nano-meter scale
-Important for future integration of waveguides in optoelectronic and photonic devices
-Power coupling efficiency is 0.8 and active region overlap integral is 0.48 of this slot-waveguide
May 25, 2007 Bilkent University, Physics Department
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Thanks..
Questions?