#### Transcript Document

```Optical Design of Waveguides
for Operation in the Visible and
Infrared
Mustafa Yorulmaz
Bilkent University,
Physics Department
May 25, 2007
Bilkent University, Physics Department
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Outline
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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
Wave-fronts and raypaths
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AC /   2  2AB /   2q
q  0,1,2,...
The angle of inclination is discrete, only
AC  AB  2d sin 
sin  m  m
May 25, 2007

2d
m  1,2,..
a limited number of angles are permitted
for constructive interference.
Bilkent University, Physics Department
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The number of modes of a waveguide
is limited
It is derived that the angle of inclination is discrete:
sin  m  m

2d
since
sin m  1
 M  2d /  
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 singlemode 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
Field distributions for TE guided modes in a
dielectric waveguide.
The condition for total internal reflection:
  cos1 (n2 / n1 )
The condition for constructive interference:
2

2d sin   2 r  2m
May 25, 2007
Bilkent University, Physics Department
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Optical coupling
Light propagates in a waveguide in the form of modes, the complex amplitude of the
Electric field is the superposition of these modes:
E( y, z)   amum ( y) exp( j m z)
m
αm is amplitude, um(y) is transverse distribution
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.
l 

 s( y)u ( y)dy
l

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
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.
Rib
waveguide
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:
f ' ( x) 
May 25, 2007
Bilkent University, Physics Department
f ( x  x)  f ( x)
x
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Simulation program
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Waveguide Mode Solver by Hilmi Volkan Demir and Vijit Sabnis
Finite difference method (FDM)
Solving the polarised solutions of the wave equation.
Geometry of rib-waveguide structure
Cell structure of finite difference scheme
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
Rib-waveguide structure presented in *
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
Parameters of rib-waveguide structure
presented in *
-Active region overlap
integral is 0.99
-It lacks of MQWs
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
Rib-waveguide structure presented in **
Our simulation result to the structure presented in **
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
Parameters of rib-waveguide 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
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Rib-width > 1mm 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 @1550nm
Layer
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
-MQWs are designed as ten periods of
AlN(1.2nm)/GaN(1.4nm) layers.
AlN (barrier)
1.2
1
-The rib has a width of 2.5µm
GaN (well)
1.4
10
AlN (barrier)
1.2
10
GaN
300
GaN
760
Sapphire
1000
Rib-Width
2500
Side-Width
5000
Our rib-waveguide design structure for IR region,
-Rib-width is 2.5 um > 1um
-Single mode operation
-Circular mode profile
Rib-Height
1531.6
Parameters of our rib-waveguide structure for IR region
May 25, 2007
E-field distribution of this structure
-Power coupling efficiency is 0.078
-Active region overlap integral is 0.05
Bilkent University, Physics Department
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Our design @440nm
Layer
Thickness (nm)
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
Loop
Our rib-waveguide design structure for IR region,
E-field distribution of this structure
-MQWs are designed as five periods of
In35Ga65N(4nm)/GaN(4nm) layers.
-Rib-width is 1.5 um > 1um
-Single mode operation
-Circular mode profile
-Power coupling efficiency is 0.074
-Active region overlap integral is 0.13
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
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Having MQWs
Satisfying single mode operation
Rib width > 1mm (@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
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Different way for confining and enhancing light: Guiding light in lowindex 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
•h
Geometry 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
The contours of E-field amplitude and Efield lines that are shown in***.
3D surface plot of E-field amplitudes presented in ***
Our simulation results to the
structure presented in ***
Parameters and geometry of slot-waveguide structure presented 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.
*** 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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Our-slot waveguide design for operation
@ 1550nm
nc
1
ns
1
nh
2.031
wh
400nm
ws
50nm
h
400nm
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 slotwaveguide
May 25, 2007
Bilkent University, Physics Department
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Thanks..
Questions?
May 25, 2007
Bilkent University, Physics Department
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