Splitters And Couplers

Question 1

Diagram of Multimode Interferometer

Answer 1

Question 2

What makes up a 1x2 MMI?

Answer 2

A 1x2 Multimode Interferometer consists of:

• A single mode input waveguide
• A multimode waveguide section which can support a large number
  of guided modes
• 2 single mode output waveguides

Question 3

How does an MMI work?

Answer 3

• Light is coupled into the multimode region from the input waveguide and several
modes are excited in the multimode region.
• The modes will have a different propagation constant, so travel at different
speeds. The different mode will therefore have maxima and minima at different
lengths along the waveguide, and the modes will be out of phase.
• The interference of these out of phase modes will create an interference pattern,

The self-imaging point is given by

3L_π/(Nx4)

where L_π is the beat length

For 3db( 50:50) splitting ratio the output waveguides should be equidistantly positioned at
the length 3L<sub>π</sub>/8 from the input waveguide,

Question 4

What is the propagation constant of a mode in a MMI?

Answer 4

The propagation constant of each mode is approximated by:

β_v = k₀ n_e-((v+1)²πλ₀)/(4n_eW_e²)

where :

β = Propagation constant
ν = Mode number
k<sub>0</sub> = Wavenumber
n<sub>e</sub> = Effective index
λ<sub>0</sub> = Wavelength
W<sub>e</sub> = MMI effective width

Question 5

What is the beat length?

Answer 5

The beat length is the length over which a π phase
shift is realised between the first two guided modes:

Given by:

L_π = π/(β₀-β₁)

where L_π = Beat length

Question 6

What is the relationship between the effective MMI width W_e and the actual waveguide width?

Answer 6

the effective multimode waveguide width W_e is wider than the actual waveguide width because of modal penetration into the cladding).

Question 7

What is the Self Imaging?

Answer 7

“Self‐imaging is a property of multimode waveguides by which an input field profile is reproduced in single or multiple images at periodic intervals along the propagation direction of the guide”

-Soldano & Pennings, J. Lightwave Technology, 13, 4, 1995.

Question 8

What is the equation for self imaging point location

Answer 8

3L_π/(Nx4)

Where N is the number of points at a length. i.e. at N = 2, expect two self-imaging points.

Question 9

When does self-imaging occur?

Answer 9

Self imaging occurs when all of the modes in
the multimode waveguide arrive in phase at
the same point (i.e. constructive interference
occurs between the modes)

Question 10

Advantages of MMI

Answer 10

‐ Tolerant to fabrication error
‐ Can easily design 1xN splitter

Question 11

Disadvantages of MMI

Answer 11

‐ Difficult to achieve an arbitrary splitting ratio
‐ Insertion loss is more sensitive to wavelength than Y‐junction

Question 12

What is an edge coupler?

Answer 12

An edge coupler is a device that couples light from fibre to the chip using inplane/butt/ edge coupling.

Tapering is a vital component for these devices.