Optical Design of Waveguides for Operation in the Visible and Infrared

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


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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


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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


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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.


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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.


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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)


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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

)()(

)('


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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


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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).


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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



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).


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Challenges for Design

Rib-width > 1m for fabrication Single mode Having MQWs Circular mode profile Material overlap integral Coupling Efficiency


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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


GaN 50

AlN (barrier) 1.2 1

GaN (well) 1.4 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



Parameters of our rib-waveguide structure for IR region

Our rib-waveguide design structure for IR region, E-field distribution of this structure


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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


GaN (barrier) 4 5

In35Ga65N 50

GaN (barrier) 4 1


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



Our rib-waveguide design structure for IR region, E-field distribution of this structure

Parameters of our rib-waveguide structure for IR region


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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)


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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] .


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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.


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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


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Optical Design of Waveguides for Operation in the Visible and Infrared