Lect. 13: Dielectric Waveguide (2)

Optoelectronics (2012/2) W.-Y. Choi

E(y) profile: n1=1.5, n2=1.495, d=10m, =1m

TE1 TE2

Lect. 13: Dielectric Waveguide (2)

Optoelectronics (2012/2) W.-Y. Choi

E(y) profile: n1=1.5, n2=1.495, d=10m, =1m

TE1 TE2TE3

Lect. 13: Dielectric Waveguide (2)

Optoelectronics (2012/2) W.-Y. Choi

How much power is confined within the core

22

2

2

( )Power inside core

Total Power( )

dy

dy

y

y

E y dy

E y dy

How does change for different modes?

- Effective index: neff= /k0

d n1

n2

n2

- Confinement factor:

How does neff changes for different modes?

Lect. 13: Dielectric Waveguide (2)

Optoelectronics (2012/2) W.-Y. Choi

+ +( ) ~ ( )in m m

mE y a E y

n2

n1

n2

( )inE y

For , use the fact that ( )'s are orthogonal.m ma E y

Partitioning of input field into different guided modes.

( ) ( )in mE y E y dy ~ ( ) ( )n n mn

a E y E y dy 2 ( )m ma E y dy

2

( ) ( )

( )in m

mm

E y E y dya

E y dy

Dot product between Ein(y) and Em(y)Or projection of Ein(y) into basis Em(y)

(Sturm-Liouville theory)

( ) ( ) 0 if m nE y E y dy m n

Lect. 13: Dielectric Waveguide (2)

Optoelectronics (2012/2) W.-Y. Choi

b-V diagram for TE mode

V

b

12 2 20 1 2( )

(Normalized )V k d n n

k

d

n3

n1 core

cladding

n2

Asymmetric waveguide?

- Graphical solution

2 22 32 2

1 2

(Asymmetry factor)

n nan n

22

202 2

1 2

(Normalized )nk

bn n

For a given waveguide: V,a b from the diagram

Then, determine

- Numerical solution

Lect. 13: Dielectric Waveguide (2)

Optoelectronics (2012/2) W.-Y. Choi

m

Slope = c/n2

Slope = c/n1

TE1

cut-off

TE2

TE3

Schematic dispersion diagram, vs. for the slab waveguide for various TE m. modes.cut–off corresponds to V = /2. The group velocity vg at any is the slope of the vs. curve at that frequency.

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

- diagram

- For a given , phase velocity (=/) and group velocity (=d/d) can be determined.

- Group velocity determines the speed of information transfer

- Multi-mode waveguides suffers from dispersion since different modes have different group velocities

Lect. 13: Dielectric Waveguide (2)

Optoelectronics (2012/2) W.-Y. Choi

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