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Light Propagation in Gbit LANS. John S. Abbott Engineering Associate -- Mathematics Corning Incorporated HPME01-024 Corning, NY 14831 abbottjs@corning.com talk at IMA 9 / 9 / 99 . Outline. 1. Problem characterizing high speed lasers predicting performance of links

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light propagation in gbit lans
Light Propagation in Gbit LANS

John S. Abbott

Engineering Associate -- Mathematics

Corning Incorporated

HPME01-024

Corning, NY 14831

abbottjs@corning.com

talk at IMA 9 / 9 / 99

outline
Outline

1. Problem

characterizing high speed lasers

predicting performance of links

2. Background for multimode fibers

3. Measurement data

4. Modeling results

5. Review of Problem

introduction
Introduction

To predict the performance of

a link using multimode fiber, we

need to know properties of both

fiber and laser.

The fiber’s properties (mode delays)

derive from the measured index

profile.

The laser’s properties (modal power

distribution) are equally important

and need to be estimated.

the problems of interest
The problems of interest

1. Predict the modal power distribution

P_m in a 100-500m length fiber for a

given laser -- for example, from the

nearfield intensity I(r ) on a short length.

2. Show that this can be used to predict

the bandwidth and performance of a

multimode fiber given its measured index

profile n(r ).

3. Determine limitations to this approach

or better methods

definition measurement of bandwidth
Definition/Measurement of Bandwidth

The bandwidth

is the frequency

where the FFT

of the

output pulse

drops to 1/2 of

its 0 frequency

value.

BW depends on

mode delays &

modal power

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

Different

Lasers

Different Fibers

laser bw source fiber tia2 2
Laser BW = Source + Fiber (TIA2.2)

Different

Lasers

Different Fibers

possible limitations
Possible limitations

1. The intensity distribution I(r ) on a short

length of fiber may not yet have settled into

an 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 over

time to reduce effects of modal interference.

one approach jsa 1998
One approach (JSA 1998 )

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

2. For a measured I(r ), determine the modal

power distribution P_m which best matches

I(r ) [in a least squares sense].

3. Comparison with experiments on short fibers

is somewhat encouraging but not satisfactory

example results least squares
Example Results -- least squares

Intensity I(r )

(parabolic distribution)

Calculated MPD

(equal power)

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

Calculated MPD

(negative value?)

Intensity data

second approach
Second approach

1. Assume the intensity distribution I(r ) is due to a Gaussian beam with

offset x and radius r, for which both I(r ) and P_m can be calculated explicitly. Again assume

2. For a measured I(r ), determine the best fit

offset Gaussian beam(r,x) whose P_m

best matches I(r ) [say in a least squares sense].

calculation of multimode bandwidth
Calculation of Multimode Bandwidth

The low frequency response of the system can be

modeled as the sum of delta functions corresponding

to the modes or mode groups:

where

(laser)

(fiber)

Thus the important parameters are

solving for tau m s
Solving for tau_m’s

The light propagation can be approximated by the

scalar wave equation, just as for single mode fiber:

where

is an eigenvalue and

calculation of multimode bandwidth 2
Calculation of Multimode Bandwidth (2)

The Fourier Transform of a sum of Delta functions

is easy to do:

So the amplitude is given by

calculation of tau m mode delay by perturbation method olshansky nolan abbott button
Calculation of tau_m = mode delay by Perturbation Method(Olshansky/Nolan/Abbott/Button)

Propagation

Parameter

Mode

Delay

(PMD)

conclusion
Conclusion

To predict the performance of

a link using multimode fiber, we

need to know properties of both

fiber and laser.

The fiber’s properties (mode delays)

derive from the measured index

profile.

The laser’s properties (modal power

distribution) are equally important

and need to be estimated.