Spherical Wave Front

Optical Fiber & Wavelength Fundamentals

Light waves are transverse = Waves are perpendicular to the direction of wavesa.Nature of Light 1.

Wave: Focus of all waves with same phase

Light Effects such as reflection and refraction can be simplified with ray tracing geometry

Fiber-Optic Communication TechnologyWednesday, September 3, 2014 17:33

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A Train of planes traveling direction K

X: General portion Vector Wave Propagation vector

Wave-vector = k =

Wave Propagation Constant

Wavelength:

We define n (index of refraction) = c/vp 1

Light travels in free air (vacuum) @ 3x10^8 m/s upon entering a dielectric or non conducting material the velocity becomes up. (characteristic of material and < 3x10^8 m/s)

i.

Ex. n(air) = 1ii. n(water) = 1.33 n(diamond) = 2.42

Index of Refractiona.Basic Optical Laws and Definitions2.

: incidence angle : angle of refraction

Using Snell's law

Total interval reflection (Snell's)

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n1Sin(theta1) = n2Sin(theta2)N2/n1 = Sin(theta1)/Sin(theta2)

Since

Ex. n2 = 1

n2 = 1.5 (glass) {48 degreeAny light in incident @ is totally reflected back to glass -> results in

- Critical Angle- is the angle at which light has to enter the core for total refraction.

Total Internal Reflection

Fig. 2 Class 1

Xc : critical Propagation Angle Xc

And Since

Xc : Angle made by ray with centerline in order to have total relfection

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Trig.

2.3 Acceptance angle and numerical Aperture

: Acceptance angle

Only rays that enter edge of fiber core within 2(theta(a)) will be accepted within core

Snell's ->

In general

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In general

=

2.4 Line Width of an optical Source

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Optical Fiber: Dialectic waveguide -> Operates @ optical Frequencies -

Propagation of light within care can be described in terms of a set of electromagnetic waves called MODES

-

MODES -> are in fact the solution to the homogeneous wave equation in the fiber (DE)-

3.1 Fiber Types

Step. Index FiberVariation in the material of core -

Construction of Fiber Core: Ge dopped Silicate Glass (

Cladding: Pure Silicate Glass (

With

Buffer Coating: Plastic Material

Optical Fiber Modes and Configuration3.

Fig. 1 -> Fig 2

SMP : Simple Mode Fiber

Graded-Index Fiber Fig. 3 + Fig 4.

Multimode Graded- Index Fiber

Also Pulses are flattened at some point and will need to be reconstructed Much Larger Bandwidth (BW) than SMD (Single Mode Fiber)

Step-Index Fiber : NOTE: : Core - Cladding index Difference

Typical problem: Intermodal Dispersion

Modes in an Optical Waveguide

Fig. 5

n: order of modeModes have ,

Highest mode enters codes at Rule: The Smaller

Zero-order mode: Fundamental Mode

Normalized frequency parameters V

Calcular waveguide : V is large

Number of nodes:

Optical Fiber - Mode and ConfigurationWednesday, September 10, 2014 17:30

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Note: For SM operation

Ex. Find radius required for SM operation @ 1.3 nm of a fiber with NA = 0.12

Mode travel with a certain energy wave pattern. Not All modal energy is confined within the core-

Energy Patter Fig.6

Fig. 7

Fig. 8

Modal Properties

Fiber Losses

Posses Reduce BW-Efficiency -Data Rage-Capacity-

Def:1.

Fig. 9

Expressed in Decibels

Loss!

Fiber Losses Scatering -Radioactive-Core, Cladding-

Coupling-Modal-

Scattering or Rayleigh loss2.

Fig. 10

V = 2

Index

Arises from imperfections in the core during manufacturing process

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n: Core

KB: Boltzaman's Constraint

Isothermal Compressibility of material

(Tf = 1400 for silicon Glass )

Reduces of bend larger than fiver diameter -Microscopic bens within fiber during assembly -

Due to small bends in fiber-Radioactive Loss3.

Effective # of mode Neff that are guided by a curved fiber of radius a

= core-cladding index n2: Cladding

Globe's Equation

Expresses in terms of attenuation losses and For a mode if order (V, m) m: mode order

Core and cladding losses 4.

Or pulse spreading

Fig. 11

Modal Dispersion (MMF)5.

Dispersion : Detla (t) = sqrt(

If fiber of length L

Delta t =

Impose constraints on MMF performance (bit rate)

We define in this case delay-spread S

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Prof. L. AmaraDue. Sept. 17, 2014

For the Questions below, use the following Constants

A beam travels from water(n=1.3) to air( n=1.0) at angle =20 degrees. What was the angle of incidence?

1.

The numerical aperturea.The acceptance angle b.

A fiber is made of a core with an index of 1.4 and no cladding (Air Cladding). Find:2.

a.

b.

HW 1 Wednesday, September 17, 2014 10:33

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How long will it take to a light beam to reach the bottom of a lake 500m deep if the index of

refraction of water is 1.

Find Index of refraction of the other medium a.Find the Velocity of the ray in the other medium b.Find the angle of incident if the angle of refraction 2 is equal to 33c.

An optical ray with 0 of 640nm traveling through another medium measures a wavelength of 27nm.

2.

`

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5.1 Internal DispersionFor MM System

Illustration -Fig. 1

Due to { Material Dispersion: Since is a function of n 's will travel at velocities-Wave Guide dispersion: dispersion constant(Core Radius) is function of

-

Minimum propagation delay in fiber

Ray 2 enters core at

Asume a pulse of width E entering fiber

Tdc - td0 is the time it takes for energy of the pulse t reach output of fiber

Ex: Train of laight pulses transmitted through 400m fiber

Also called chromatic dispersion - function of index of refraction

Light has many s -> is a function of n travel a (different) velocities ( du to type of material

. Ex. Silicate glass

Dispersion is related to (line width)

Units : picosecond /km/ nanoseconds

Fig. 2

2 extreme modes

5.1 Internal DispersionWednesday, September 17, 2014 17:36

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Bit rate Capacity (in bits/s) of a communication channel - - is obiosly impacted by dispersion-Depending of type of code (RZ, NRZ, Manchester, )-

or

Bw: Bandwidth -

Bit rate and Bandwidth 6.

6.1 Digital Formats

Fig. 3.

Baud rate = number of symbols per second = M

Binary system -> Bit rate = baud rate M = 2 -> {0,1}

Fig. 4

Illustration:

Bit rate vs. baud rate-

Now a 4-ary system with M - 4 symbols

{0 00 11 11 0

-

When transmitting a square wave, the receive signal is in fact a sine wave-

Fig. 7

Max Rate at which data can be transmitted - Capacity of channel -

-

For binary M=2 -> -

So

Shannon's Theorem

Fig. 8 Illustration:

6.2 BW and BT

Industry standard -

can be due to many effects

6.3 Effect of dispersion on Bit Rate

Step- index- Fiber-

Troy Maxwellj.troy66@yahoo.com

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BW is length dependent-Pulse spreads with Length -

6.4 Bandwidth - Length product (B.L)-

Ex. A BW= 42 MHz for 8 Km of fiber-

Expresses BW for a 3 KM Fiber

6.5 Electrical and optical Bandwidth

Fig. 9

Electrical System P is

Optical System P is

Fig. 10

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Channel Losses7.

Example:

Fiber Cable Attenuation = 5dB

Splice losses L dB(transmit)

Connector Losses: 3.5dB (transmit)

2.5db (receiver)

Total Channel loss =

Regenerative Repeater8.

Class 4Wednesday, September 24, 2014

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Pi input power-Po Output Power-Chanel Losses ( Will also include pulse Dispersion )-

Spacing of repeater

Inter symbol interference V or Overlapping of pulses at Receiver. This creates additional loss called ISI penalty or dispersion Equalization.

For a digit puse: bit error Rate (BER)

8.1. Temporal response (ISI)

Need NOTES!

Pulsavility

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Interval

Gaussian pulse ( Bell Shaped)

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In this case:

Now the Channel Losses

M System Wideband

Rise Time and Bandwidth -

System Rise time

Rise time of transmiting Circuit

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Impact of coding system on BW versus

Rise Time and BW ( and BW)

If (tav : pulse duration ->

For digital systems

Rise times Source (LED) = 8ns

Fiber (Intermodal) = 5ns

Pulse Broadening (intra-modal = 1ns.

Detector = 6ns

Ex1. Optical Fiber system over 8km without repeaters

Using NRZ , based on

Concept of Mode Coupling-

Mode Coupling by fiber bends

Transfer of power from one mode ((low order) and then (high order)

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Assume this is the dominant dispersion mechanism ISI ? (Dispersion equalization penalty) @

Without Mode Coupling total RMS pulse broadening a.

=

Ex: RMS pulse broadening from intermodal dispersion within a MM fiber is 0.6 ns/km

=

= 0.03dB

With mode coupling total RMS pulse broadeningb.

To Check if designed system is viable or not and also to find the location of repeaters -It is given by -Pi = Po+ -

8.2 Power budgeting Analysis

Pi: Input PowerPo: output power from fiberCL: channel losses

MaL = 7dB LED

9dB LD (laser Diode)

a : safety Margin

Now Pi = Po + (xfc + xj)L + Xcr + DL + Ma

Ex: System operating at

Mean power from LD ->

Cabe fiber Loss-> 1

Splice loss -> 0.3db

Connector loss (tc, Rc) -> 1dB each

Mean power refused at -> 55dBm

APD (avalanche photodiode) at 35

Max distance of link without repeater(BER =

Suppose a.

Power Budget Analysis

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losses LED to fiber 5dB

3 Connectors 1.5db each

Six splices 0.5dB each

10km of Fiber 0.6dB/km

Fiber to detector 6dB

Specs:

EX: System with

Led output power 0.1mW

Detector Sensitivity 0.1uW

5Mbs

Total Fiber Dispersion 4ns/KM

29.5dB

System is OK!!Since sensitivity of receiver is 0.1uW

Since power are in W

Next Dispersion EffectGoal: system without a repeater ->

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Close enough maybe system can be improved

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