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Deriving Bandwidth Using Geometric OpticsPowerPoint Presentation

Deriving Bandwidth Using Geometric Optics

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Deriving Bandwidth Using Geometric Optics

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Deriving Bandwidth Using Geometric Optics

Prepared for

The Handbook of Fiber Optic Data Communication

Third Edition

Carolyn DeCusatis

The State University of New York, New Paltz

- Geometric Optics approximation
- Derivation of Numerical Aperture
- Derivation of Multipath Time Dispersion
- Maximum Bit Rate and Bandwidth-Distance Product

A Slab Waveguide

air

n2

q

n1>n2

f

n2

a

This is a 2 dimensional approximation

If α=0, the ray pictured would have been axial. (It isn’t.) The ray pictured here

is oblique, and goes bouncing down the slab.

The critical ray is the largest a that will propagate down the slab by total internal reflection.

air

n2

q

n1>n2

f

n2

a

φ= π/2-θ < π/2- θc

sin α = n1sin φ = n1cos θ

for critical rays:

sin α c = n1sin φ c = n1cos θ c

n1sin θ c = n2 therefore cos θ c=

therefore

sin αc= = NA= numerical aperture

n1>n2

sin αc= = NA= numerical aperture

The numerical aperture is the light gathering power of a microscope, or other lens system.

The acceptance cone is half the numerical aperture.

Time dispersion in unclad fiber is large.

The axial ray travels a distance l in

The oblique ray travels a distance l in

=

=

The arrival time difference is ΔT=

The multipath time dispersion is

=

And, to a good approximation, the maximum bit rate, B, is related to the multpath

time dispersion, which is related to the Bandwidth Δf

To a good approximation,

B ≈ 2Δf

,

And the bandwidth distance product is

(Δf)l≈

Fibre Channel distances when using multimode fiber optic cable

- Geometric Optics can be used to approximate the path of optical rays in a fiber
- Axial and oblique rays

- Numerical Aperture is the light gathering power of a fiber
- Acceptance angle is half the numerical aperture

- Tradeoff between numerical aperture and bandwidth-distance product