Download Week4-figs

Trivia Question
Which “Big Bang Theory” character is from
New Jersey?
(a) Raj Koothrappali
(b) Bernadette Rostenkowski
(c) Howard Wolowitz
(d) Sheldon Cooper
(e) Amy Farrah Fowler
(f) Leonard Hofstadter a b c d e f
(g) Penny
g
The grand overview of Optics/Photonics
Historical Development: Ray Optics → Wave Optics → EM Optics
→ Quantum Optics.
• Ray Optics is an approximation of Wave Optics in which wavelength
short compared to other dimensions (focal lengths, diameter of optical
components, etc.) so that Diffraction can be ignored.
•
• Wave Optics – Is needed to describe phenomena such as
INTERFERENCE, DIFFRACTION, Phase and Group velocities
The Electromagnetic Spectrum
  c
Postulates of Wave Optics
• Light travels as waves with a speed of light in a vacuum
given by co.
• Speed of lightc in a medium determined by refractive
0
n 1
index n c  n
• Optical wave is expressed mathematically as a
wavefunction y(r,t) which satisfies the wave equation:
2
1

y
2y  2 2  0
c t
• Principle of superposition: y (r, t)  y (r, t)  y (r, t)
1
2
• Refractive index n(r) can vary with position as long as
variations occur of distances long compared to
wavelength.
Postulates of Wave Optics
• Optical Intensity (optical power/ unit area) [W/cm2] is
proportional to average of square of waveform. Average
over times much longer then duration of optical cycle 1/ν.
I (r , t )  2 y 2 (r , t )
• Optical power (Watts) calculated as power flowing
through area perpendicular to direction of propagating
wave.
P(t )   I (r , t ) dA
A
• Optical energy: Integrate optical power over some period
of time. (Energy/ time=Watts)
Animation of transverse waves:
http://phet.colorado.edu/sims/wave-on-astring/wave-on-a-string_en.html
USE IE as browser.
y  f ( x, t )
Wave Function
S
t0
t1
t2
t3
Shape the same at some
later time.
t4
V→
( x  x ')
V
t 4  t0
X position
x’
General Wave Function
x
x '  x Vt
y ( x, t )  f ( x  vt )
When waves collide
Animation of transverse waves:
http://phet.colorado.edu/sims/wave-on-astring/wave-on-a-string_en.html
USE IE as browser.
Perform animation with low tension (so speed of
waves is low) and put too pulses of wave separated
by some time. What happens when waves overlap
after reflection?
In phase, out of phase, partially out of phase waves
2
1
Out of phase
1
0.5
Ai
Ai
Bi
Bi
0
Ai
0
Ai
Bi
1
Bi
 0.5
In phase
2
0
20
40
60
xi
80
100
1
0
20
40
60
xi
Partially out of
Phase
80
100
Electric fields as Phasors (similar to E field as phasors in Phys 121)
When waves collide – Superposition of waves
Animation of transverse waves:
http://phet.colorado.edu/sims/wave-on-astring/wave-on-a-string_en.html
USE IE as browser.
Perform animation with normal tension, but oscillate
the one end. Reflected waves form a standing wave
with incoming wave.
When waves collide – Superposition of waves
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=19
Illustrates principle of Superposition
Illustrates standing waves
Illustrates “beats”
Illustrates effect of phase difference
between the waves
Illustrates effect of waves of different
amplitudes
Illustrates concept of # of
wavelengths in optical path length.
Beat Wave
Group Velocity versus Phase velocity
• For animation below, GREEN dot follows position of
GROUP of waves. Note: follows speed at which the
envelope of wave motion travels.
• RED dot follows constant PHASE within the wave.
• Note that PHASE and GROUP velocity in general
are DIFFERENT.
• Which speed determines Velocity at which
INFORMATION can be transmitted?
• Which velocity can be LARGER than speed of light?
15
Group Velocity