Transcript Class08_review.ppt

Review
First Exam
What have we learned?
• Any traveling sinusoidal wave may be described by
y = ym sin(kx  wt + f)
• Light always reflects with an angle of reflection equal to
the angle of incidence (angles are measured to the normal).
• When light travels into a denser medium from a rarer
medium, it slows down and bends toward the normal.
• The Fourier spectrum of a wider pulse will be narrower
than that of a narrow pulse, so it has a smaller bandwidth.
• Your bandwidth B must be as large as the rate N at which
you transfer different amplitudes.
• The rise time of each pulse must be no more than 70% of
the duration of the pulse
Review (cont.)
• Any periodic function of frequency f0 can be expressed as a
sum over frequency of sinusoidal waves having frequencies
equal to nf0, where n is an integer. The sum is called the
Fourier series of the function, and a plot of amplitude
(coefficient of each sin/cos term) vs. frequency is called the
Fourier spectrum of the function.
• Any non-periodic function (so frequency f0 0) can be
expressed as an integral over frequency of sinusoidal waves
having frequencies. The integral is called the Fourier
transform of the function, and a plot of amplitude vs.
frequency is called the Fourier spectrum of the function.
• The Fourier spectrum of a wider pulse will be narrower than
that of a narrow pulse, so it has a smaller bandwidth.
What Else Have We Learned?
• Can represent binary data with pulses in a variety of ways
• 10110 could look like . . .
Notice that the NRZ
takes half the time of
the others for the
same pulse widths
Non-return-to-zero
(NRZ)
Return-to-zero
(RZ)
Bipolar Coding
Other schemes use
tricks to reduce
errors and BW
requirements.
Optical Waveguides Summary
• Dispersion means spreading
• Signals in a fiber will have several sources of dispersion:
– Chromatic:
• Material: index of refraction depends on wavelength (prism)
• Waveguide: some of wave travels through cladding with
different index of refraction (primarily single-mode) – leads to
wavelength-dependent effects
– Modal: different modes travel different paths and so
require different amounts of time to travel down fiber
(CUPS)
• Also have attenuation/loss due to scattering/absorption by
fiber material, which depends on wavelength/frequency
Optical Waveguide Summary
(cont.)
• Modes in a fiber are specific field
distributions that are independent of “z”, or
length traveled down the fiber
• Fields of modes look like harmonics of
standing waves
• Can make a single-mode fiber by:
– reducing diameter of fiber so smaller cone of
light enters
– reducing NA of fiber so smaller cone of light is
trapped
Interference of Waves
Amax
 If crests match
crests, then waves
Amax
interfere
constructively
 Crests will match 2Amax
if waves are one
wavelength, two
wavelengths, …
apart: path
difference = ml
wave 1
wave 2
sum
Destructive Interference
 If crests match troughs Amax
(180° out of phase),
then waves interfere
Amax
destructively
 Crests will match
troughs if waves are
one/half wavelength,
three/half wavelengths,
… apart: path
difference = (m+½)l
wave 1
wave 2
sum
What This Means for Light
 Light is electromagnetic radiation
 A light wave is oscillating electric and magnetic
fields
 The amplitude of the oscillation represents the
maximum electric (or magnetic) field and
determines the intensity of light
 Intensity depends on the square of the maximum
electric field: I = Emax2/(2cm0)
 Constructive interference produces brighter light;
destructive interference produces dimmer light.
Comparing Interference
2Emax
Emax
Medium amplitude
of electric field
yields medium
intensity light
Double amplitude
of electric field
yields quadruple
intensity (very
bright) light
Zero amplitude
of electric field
yields zero
intensity (no)
light
Coherent vs. Incoherent Light
• “Everyday light” is incoherent
• Laser light is an example of coherent light
• Simple wave equation describes coherent
waves
y = ym sin(kx  wt + f)
Diffraction Math
 The locations of successive minima are given by
a
1

sin q   m  l (m  0,  1,  2,...)
2
2

a sin q  nl (n  1,  2,  3.....)
 tan q = y/D
 for small angles, sin q ~ q ~ tan q = y/D
Diffraction by a circular aperture
 A circular aperture of diameter d
l
sin q  1.22 (1st minimum)
d
 Single slit of width a
sin q 
l
a
(1st minimum)
Resolvability
 Two objects are just resolved when the central
diffraction maximum of one object is at the first
minimum of the other. (Rayleigh’s criterion)
1.22l 1.22l
  sin

d
d
1
R
 As before, q approximately y/L
Comments on Resolvability
y
1.22 l
 
D
d
R
 If want to resolve objects closer to each
other (smaller y), need smaller wavelength
of light or larger aperature
 This is called the diffraction limit
Why Do We Care?
• CD-ROMS and other optical storage
devices
Before the next class, . . .
• Prepare for the First Exam!
– Exam on Thursday, Feb. 14.