1. dariusz.rozanski@szczesliwice.net Mode Group Diversity Multiplexing in Step Index and Graded Index Multimode Fibers Grzegorz Stępniak

2. 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

3. 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

4. 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 Graded index fiber

5. 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)

6. dariusz.rozanski@szczesliwice.net 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

7. 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

8. 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 indexStep index

9. 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 indexStep index

10. 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 indexStep index

11. 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 beam30  m FWHM Gaussian beam

12. dariusz.rozanski@szczesliwice.net 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

13. dariusz.rozanski@szczesliwice.net Near Fields at MMF output for various exciting beam tilts Graded indexStep index tilt 0 deg. tilt 9 deg.

14. dariusz.rozanski@szczesliwice.net Far Fields at MMF output for various exciting beam tilts tilt 0 deg. tilt 9 deg. Graded indexStep index

15. dariusz.rozanski@szczesliwice.net Exemplary signal recovery in two channel case Due to mode mixing and not perfect detector placement there is a linear crosstalk between the channels, that can be eliminated by inverting the crosstalk matrix In this case p1 and p2 are photodiode signals, and are original signals and C is the crosstalk matrix.

16. 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)