Light Propagation in Gbit LANS

John S. AbbottEngineering Associate -- MathematicsCorning Incorporated

HPME01-024Corning, NY 14831abbottjs@corning.com

talk at IMA 9 / 9 / 99

Outline

1. Problemcharacterizing high speed laserspredicting performance of links

2. Background for multimode fibers3. Measurement data4. Modeling results5. Review of Problem

IntroductionTo predict the performance of a link using multimode fiber, weneed to know properties of bothfiber and laser.

The fiber’s properties (mode delays)derive from the measured indexprofile.

The laser’s properties (modal powerdistribution) are equally importantand need to be estimated.

The problems of interest

1. Predict the modal power distributionP_m in a 100-500m length fiber for agiven laser -- for example, from the nearfield intensity I(r ) on a short length.

2. Show that this can be used to predictthe bandwidth and performance of a multimode fiber given its measured indexprofile n(r ).

3. Determine limitations to this approachor better methods

Definition/Measurement of Bandwidth

The bandwidthis the frequencywhere the FFT of the output pulsedrops to 1/2 of its 0 frequencyvalue.

BW depends onmode delays &modal power

Laser BW = Source + FiberThe bandwidth depends on both laser and fiber.

Different Fibers

Dif

fere

nt

Las

ers

Laser BW = Source + Fiber (TIA2.2)

Different Fibers

Dif

fere

nt

Las

ers

Possible limitations

1. The intensity distribution I(r ) on a shortlength of fiber may not yet have settled intoan excitation of individual propagating modes.Some think a continuum of modes is initially propagated and that these gradually evolve through destructive interference into a finite number of propagating modes.

2. Related modal noise/mode interaction effects -- current measurement technique is to‘shake’ the fiber under test and average overtime to reduce effects of modal interference.

One approach (JSA 1998 )

1. Assume the intensity distribution I(r ) is given by

2. For a measured I(r ), determine the modalpower distribution P_m which best matches I(r ) [in a least squares sense].

3. Comparison with experiments on short fibersis somewhat encouraging but not satisfactory

Example Results -- least squares

Intensity I(r )(parabolic distribution)

Calculated MPD(equal power)

Example Results -- least squares(using real data)

Intensity data Calculated MPD

Example Results -- least squares(using real data -- example 2)

Intensity dataCalculated MPD(negative value?)

Second approach

1. Assume the intensity distribution I(r ) is due to a Gaussian beam with offset x and radius , for which both I(r ) and P_m can be calculated explicitly. Again assume

2. For a measured I(r ), determine the best fitoffset Gaussian beam(,x) whose P_m best matches I(r ) [say in a least squares sense].

Calculation of Multimode Bandwidth

The low frequency response of the system can bemodeled as the sum of delta functions correspondingto the modes or mode groups:

where

Thus the important parameters are (laser)

(fiber)

Solving for tau_m’sThe light propagation can be approximated by thescalar wave equation, just as for single mode fiber:

where is an eigenvalue and

Calculation of Multimode Bandwidth (2)

The Fourier Transform of a sum of Delta functionsis easy to do:

So the amplitude is given by

Calculation of tau_m = mode delay by Perturbation Method (Olshansky/Nolan/Abbott/Button)

(PMD)

Mode Delay

PropagationParameter

Application of modeling mode delays -- DMD measurement

ConclusionTo predict the performance of a link using multimode fiber, weneed to know properties of bothfiber and laser.

The fiber’s properties (mode delays)derive from the measured indexprofile.

The laser’s properties (modal powerdistribution) are equally importantand need to be estimated.