Putting Light to Work for You

1
Putting Light to Work for You

• Features of Signal Transfer

2
What have we learned?

• Any traveling sinusoidal wave may be described by
• y ym sin(kx ? wt f)
• f is the phase constant that determines where
  the wave starts.
• w 2pf 2p/T
• k 2p/l
• v l/T lf w/k
• Light always reflects with an angle of reflection
  equal to the angle of incidence (angles are
  measured to the normal).

3
What have we learned?

• When light travels into a denser medium from a
  rarer medium, it slows down and bends toward the
  normal.
• The amount light slows down in a medium is
  described by the index of refraction n c/v
• The amount light bends is found by Snells Law
• n1 sin q1 n2 sin q2
• When the angle of refraction is 90 degrees, the
  angle of incidence is equal to the critical angle
• sin qc n2/n1, where n1 is for the denser medium

4
What else have we learned?

• Light is trapped in an optical fiber if it
  strikes the sides of the fiber at angles greater
  than the critical angle for the core-cladding
  interface
• The core must have a higher index of refraction
  than the cladding for total internal reflection
  to occur.
• The numerical aperture (NA) of a fiber relates
  the maximum angle of incidence on the front of
  the fiber to the indices of refraction of the
  fiber
• NA n0 sin qm (n12 - n22)1/2.

5
Light in a waveguide

• Light that strikes the side of the fiber at an
  angle less than the critical angle qc will escape
• The angle that light strikes the side of the
  fiber depends on the angle q0 at which light
  enters the fiber the higher the angle at
  entrance, the lower the angle of incidence qi on
  the fiber wall

n2
n0
n1
qi
q0
6
Condition for TIR in waveguide

• Snells Law (and some geometry) says
• n0 sin q0 n1 sin (90 - qi) n1 cos qi
• If all of the beam is to stay within the
  waveguide, the angle of incidence on the wall
  must be greater than the critical angle
• sin qc n2/n1
• Then the angle at entrance must be obey
• n0 sin q0 lt n1cos qc

n2
n0
n1
qi
q0
7
Numerical Aperture

• n0 sin q0 lt n1cos qc
• Using some trig (and the critical angle
  relationship) we see that the minimum angle of
  entrance qm is found from
• n0 sin qm n1(1 - sin2 qc)1/2 n1
  (1-n22/n12)1/2 (n12 - n22)1/2.
• The function n0 sin qm is called the numerical
  aperture (NA) of the waveguide.
• A large NA means light can enter in a large cone
  and still stay within the waveguide.

8
Do the Fourier Series Exploration part of the
activity
9
Fourier Analysis

• Waves we want to send are not always sinusoidal
• BUT, Fourier showed that EVERY periodic function
  may be expressed as a sum of sine functions
• Each term in the sum has a frequency equal to an
  integer times the frequency of the original
  function.
• For example, a square wave is given by
• y(t) (4/p) (sin wt (1/3) sin 3wt (1/5) sin
  5wt (1/7) sin 7wt . . .)
• Visual aids are best, so we go to CUPS (youll
  use it in part of your activity today, so pay
  attention!)

10
Do the Before You part of the activity

• Continue to the Fourier Series Square Wave part

11
Fourier Transforms

• Waves we want to send are not always periodic
• BUT, Fourier showed that EVERY function may be
  expressed as an integral of sine functions
• Non-periodic function is similar to infinite
  period, or infintesimal frequency
• A sum over infintesimal steps (sin wt sin 2wt
  ) is an integral
• Visual aids are still best, so we again go to
  CUPS (youll use it in part of your activity
  today, so pay attention!)

12
Do the Fourier Transforms Pulses part of the
Activity
13
Why do we care about Fourier?

• We want to send signals from one
  computer/phone/etc. to another one.
• These signals will not be periodic if the message
  is to have any meaning.
• Each Fourier component is subject to different
  interactions as it travels
• Bandwidth is the range of frequencies that can
  travel through a medium
• Large bandwidths are hard to transfer reliably

14
Phase differences and interference

• Light rays taking different paths will travel
  different distances and be reflected a different
  number of times
• Both distance and reflection affect the how rays
  combine
• Rays will combine in different ways, sometimes
  adding and sometimes canceling

n2
n0
n1
qi
q0
15
Modes

• Certain combinations of rays produce a field that
  is uniform in amplitude throughout the length of
  the fiber
• These combinations are called modes and are
  similar to standing wave on a string
• Every path can be expressed as a sum of modes
  (like Fourier series)

n2
n0
n1
qi
q0
16
Reducing the number of Modes

• Different modes interact differently with the
  fiber, so modes will spread out, or disperse
• If the fiber is narrow, only a small range of q0
  will be able to enter, so the number of modes
  produced will decrease
• A small enough fiber can have only a single mode
• BUT, you will lose efficiency because not all the
  light from the source enters the fiber.

n2
n0
n1
qi
q0
17
Optical waveguides pros and cons

• Message remains private
• Flexibility
• Low Loss
• Insensitive to EM interference
• BUT
• Expensive to connect to every house
• Require electricity-to-light converters
• Either multi-modal, or less efficient

18
Dispersion

• Index of refraction is dependent on wavelength.
• Typical materials exhibit higher indices of
  refraction for lower wavelengths (higher
  energies)
• Thus violet light bends the most through a prism
  or water and appears on the outside of a rainbow.

19
Before the next class, . . .

• Read the Assignment on Describing Signals found
  on WebCT
• Read Chapter 4 from the handout from Grants book
  on Lightwave Transmission
• Do Reading Quiz 4 which will be posted on WebCT
  by Tuesday morning.
• Finish Homework 2, due Thursday
• Do Activity 04 Evaluation by Midnight Monday