dariusz.rozanski@szczesliwice.net

Mode Group Diversity Multiplexing in Step Index and Graded Index

Multimode Fibers

Grzegorz Stępniak

dariusz.rozanski@szczesliwice.net

Presentation outline

• Multimode fibers (MMF)

• Multiplexation methods in MMF

• MMF excitation with a Gaussian beam

• Far field, near field patterns for various excitations

• Exemplary system

• Summary

dariusz.rozanski@szczesliwice.net

Multimode Fibers

• The most common fiber for premises networks and data centers backbone • Greater core diameter, greater NA (difference between refraction indices of

the cladding and the core) than single mode fibers• In MMF light propagates in many modes• Different modes have different group velocities – modal dispersion, limited

bandwidth

dariusz.rozanski@szczesliwice.net

Step index fiber

Graded Index and Step Index Fibers

• In MMF fiber modes can be grouped into compound mode groups

• Modes within the same mode group have similar properties – propagation constants, group delays

• For mode, the mode group number is

• Graded index profile is assumed parabolic

LP

12 mGraded index fiber

dariusz.rozanski@szczesliwice.net

Multiplexation methods in MMF

• In telecommunications – a method of providing multiple data channels on one medium

• In MMF often a method of increasing the transmission rate

• Wavelength Division Multiplexing ((D)WDM) • Subcarrier Multiplexing (SCM)• Mode Group Diversity Multiplexing (MGDM)

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Mode Group Diversity Multiplexing

• Multiplexation that benefits from the multitude of modes in the fiber• Different mode groups excited with different information signals• Efficient launch and separation of mode groups at fiber output

necessary• Mode mixing is assumed to be low

dariusz.rozanski@szczesliwice.net

Calculations of coupling amplitudes in MMF

• MMF mode with spatial field (calculated using FEM)

• Input Gaussian beam with spatial field

• The coupling amplitude

• The power in the m-th mode group

LP),(, yx

)exp(}/)(exp{),( 222 yjkwyxAyxu

dxdyyxyxua ),(),( ,*

,

,

2, ),12(|| mawm

dariusz.rozanski@szczesliwice.net

Results: mode excitement vs. offset

Power in mode groups in MMF excited with a Gaussian beam. Tilt equals 0, beam FWHM 9 m, various curves correspond to different offsets. The MMF calculated is 62.5 m, NA=0.275 for 850 nm wavelength. Those parameters hold on in all subsequent calculations.

Graded index Step index

dariusz.rozanski@szczesliwice.net

Results: mode excitement vs. tilt

Power in mode groups in MMF excited with a Gaussian beam. Offset equals 0, beam FWHM 9 m, various curves correspond to different beam tilts.

Graded index Step index

dariusz.rozanski@szczesliwice.net

Results: mode excitement for fixed tilt – varying offset

Power in mode groups in MMF excited with a Gaussian beam. Tilt equals 6 deg., beam FWHM 9 m, various curves correspond to different beam offsets. RESULT: In step index fibers excitation is completely insensitive to offset. In graded index it depends on both: the offset and the tilt!

Graded index Step index

dariusz.rozanski@szczesliwice.net

Results: mode excitement in SI fibers – beam width dependence

Power in mode groups in SI MMF excited with a Gaussian beam. RESULT: With greater beam width possible separation of channels improves.

10 m FWHM Gaussian beam 30 m FWHM Gaussian beam

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MGDM separation of channels at fiber output

• Recovery of individual channels is possible due to their spatial/angular separation at the fiber output.

• Detection by spatially resolved photodiodes• Possible demultiplexing in:

– Near field– Far field

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Near Fields at MMF output for various exciting beam tilts

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

mode group number

Pow

er

0o

0o

0 10 20 30 40 50 600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

mode group number

Pow

er

0o

9o

Graded index Step index

tilt 0 deg.

tilt 9 deg.

dariusz.rozanski@szczesliwice.net

Far Fields at MMF output for various exciting beam tilts

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

mode group number

Pow

er

0o

0o

tilt 0 deg.

tilt 9 deg.

Graded index Step index

0 10 20 30 40 50 600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

mode group number

Pow

er

0o

9o

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Exemplary signal recovery in two channel case

2

1

2221

1211

2

1

x

x

cc

cc

p

p

Due to mode mixing and not perfect detector placementthere is a linear crosstalk between the channels,

that can be eliminated by inverting the crosstalk matrix

PCX 1In this case p1 and p2 are photodiode signals, and are original signals and C is the crosstalkmatrix.1x 2x

dariusz.rozanski@szczesliwice.net

Summary

• Possible realization of MG multiplexer with Gaussian beam excitation

• Far field analysis is the most suitable for demultiplexing• SI fiber is preferable: it is offset independent and

different mode groups can be easily recovered in the far field

• The drawbacks of SI that have not been considered in this work are:– higher group delay differences – lower bandwidth– higher mode mixing (possibly)