Optics I: Introduction

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Optics I Introduction
Prof. Rick Trebino Georgia Tech www.physics.gatech
.edu/frog/lectures

• A short, arbitrary, condensed history of optics
• Maxwell's equations
• The wave equation
• Cool things that happen to light
• Total internal reflection
• Interference
• Diffraction
• The laser
• Nonlinear optics
• Ultrafast optics
• The Fourier transform and its key role in optics

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The History of Optics
What is light and what can be done with it?
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Optics in Ancient History
A mirror was discovered in workers' quarters
nearthe tomb of PharaohSesostris II (1900
BCE). Ancient Greeks (500-300 BCE)
Burning glass mentioned by Aristophanes (424
BCE) Law of reflection Catoptrics by
Euclid (300 BCE) Refraction in water
mentioned by Plato in The Republic
Euclid thought that the eye emits rays that
reflect off objects.
Pyramid of Sesostris II(also known as Senusret
II)
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Ancient Greeks Ancient light weapons
Early Greek and Roman historians report that
Archimedes equipped several hundred people with
metal mirrors to focus sunlight onto Roman
warships in the battle of Syracuse (213 -211 BCE).
And despite a failed attempt by the Discovery
Channels Myth Busters to replicate the feat, in
2005 MIT undergrads set up 127 mirrors in a
courtyard to test the idea
This story is probably apocryphal.
This story is not apocryphal!
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Optics in the Middle Ages Alhazen
Arab scientist Alhazen (1000 AD) studied
spherical and parabolic mirrors. Alhazen
correctly proposed that the eyes passively
receive light reflected from objects, rather
than emanating light raysthemselves. He also
explained the lawsof reflection and refraction
by the slower movement of light through denser
substances.
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Optics in early 17th-century Europe

• Hans Lippershey applied for a patent on the
  Galilean telescope in 1608.
• Galileo (1564-1642) used one to look at our moon,
  Jupiter and its moons, and the sun.

Two of Galileos telescopes
Galileos drawings of the moon
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Johannes Kepler

• Discovered total internal reflection
• Showed why telescopes work
• Developed a first-order theory of
• geometrical optics
• Discovered the small-angle approximation to the
  law of refraction

Johannes Kepler (15711630)
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Willibrord Snell
Willibrord Snell discovered the Law of
Refraction, now named after him.
Willibrord Snell (1591-1626)
ni is the refractive index of each medium.
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17th-century Optics
Descartes reasoned that light must be like sound.
So he modeled light as pressure variations in a
medium (aether).
Rene Descartes (1596-1659)

• Robert Hooke (1635-1703) studied colored
  interference between thin films and developed the
  first wave theory of light.

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Christiaan Huygens

• Huygens extended the wave theory of
• optics.
• He realized that light slowed down on
• entering dense media.
• He explained polarization and
• double refraction.
• Huygens principle
• says that a wave
• propagates as if
  the wave-front were
• composed of an ar-
• ray of point sources
• each emitting a
• spherical wave.

Christiaan Huygens (1629-1695)
Double refraction
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Isaac Newton

• "I procured me a triangular glass prism to try
  therewith the celebrated phenomena of colours."
  (Newton, 1665)

Isaac Newton (1642-1727)
After remaining ambivalent for many years, he
eventually concluded that it was evidence for a
particle theory of light.
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18th and 19th century OpticsEuler, Young, and
Fresnel

• Leonhard Euler (1707-1783) further developed the
  wave theory and designed achromatic lenses by
  combining lenses of different materials.

Thomas Young (1773-1829) explained interference
and colored fringes and showed that light was a
transverse wave. Augustin Fresnel (1788-1827)
did experiments to establish the wave theory and
derived expressions for reflected and transmitted
waves.
Augustin Fresnel
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James Clerk Maxwell
Maxwell unified electricity and magnetism with
his now famous equations and showed that light is
an electromagnetic wave.
James Clerk Maxwell (1831-1879)

• where is the electric field, is the
  magnetic field, and c is the velocity of light.

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Maxwells equations simplify to the wave equation
for the electric field.

• which has a simple sine-wave solution

where
The same is true for the magnetic field.
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Light is an electromagnetic wave.

• The electric (E) and magnetic (B) fields are in
  phase.

The electric field, the magnetic field, and the
propagation direction are all perpendicular. But
it was still thought that light was a vibration
of some sort of medium, aether, just as sound
waves are vibrations in air.
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Michelson Morley

• Michelson and Morley attempted to measure the
  earth's velocity with respect to the aether and
  found it to be zero, no matter the direction
  (despite the earths motion), effectively
  disproving the existence of the aether.

Edward Morley (1838-1923)
Albert Michelson (1852-1931)
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Albert Einstein

• Einstein showed that light

is a phenomenon of empty space has a velocity
thats constant, independent of observer
velocity is both a wave and a particle
Albert Einstein (1879-1955)
Excited medium
and undergoes stimulated emission, the basis of
the laser.
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The interaction of light and matter

• Light excites atoms, which then emit more light.

Electric field at atom
Electron cloud
Emitted electric field
On resonance (the light frequency is the same as
that of the atom)
The crucial issue is the relative phase of the
incident light and this re-emitted light. If
these two waves are 180 out of phase,
destructive interference occurs, and the beam
will be attenuatedabsorption. If theyre 90
out of phase the speed of light
changesrefraction.
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Absorption of light varies massively.
Water is clear in the visible, but not in other
spectral regions.
Notice that the penetration depth varies by over
ten orders of magnitude!
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Variation of the refractive index with wavelength
(dispersion) causes the beautiful prismatic
effects we know and love.
Prisms disperse white light into its various
colors.
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Rainbows result from refraction andreflection of
sunlight in water droplets.

• Note that there can be two rainbows, and the top
  one is inverted.

There are many interesting optics effects in real
life
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An interesting question is what happensto light
when it encounters a surface.

• At an oblique angle, light can be completely
  transmitted
• or completely reflected (it depends on its
  polarization).
• Total internal reflection is the basis of optical
  fibers,
• a billion dollar industry.

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Light beams can interfere with each other Two
point sources
Different separations. Note the different
patterns. Constructive vs. destructive
interference
The idea is central to many laser techniques,
such as holography, ultrafast photography, and
acousto-optic modulators. Tests of quantum
mechanics also use it.
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Light beams can be intentionally made to
interfere with each other.

• Using a partially reflecting mirror, we can split
  a beam into two.

If we then combine the two beams, their relative
phase matters. The above Sagnac Interferometer
measures rotation.
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Often, they do so by themselves.
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Fourier decomposing functions plays a big role in
optics.

• Here, we write a square wave as a sum of sine
  waves of different frequency.

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The Fourier transform is perhaps the most
important equation in science.

• It converts a function of time to one of
  frequency

and converting back uses almost the same formula
The spectrum of a light wave will be given by
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Diffraction

• Light bends around corners. This is called
  diffraction.

The light pattern emerging from a single small
rectangular opening
The diffraction pattern far away is the (2D)
Fourier transform of the slit transmission vs.
position.
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Light is not only a wave, but also a particle.

• Photographs taken in dimmer light look grainier.

Very very dim
Very dim
Dim
Bright
Very bright
Very very bright
When we detect very weak light, we find that its
made up of particles. We call them photons.
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The Laser

• A laser is a medium that stores energy,
  surrounded by two mirrors.
• Photons entering the medium undergo stimulated
  emission. As a
• result, the intensity exiting from the medium
  exceeds that entering it.
• A partially reflecting output mirror lets some
  light out.

A laser will lase if the beam increases in
intensity during a round trip that is, if I3
I0.
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Electromagnetism is linear The principle of
Superposition holds.

• If E1(x,y,z,t) and E2(x,y,z,t) are solutions to
  Maxwells equations,
• then E1(x,y,z,t) E2(x,y,z,t) is also a
  solution.

This means that light beams pass through each
other without affecting each other.
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Nonlinear Optics produces many exotic effects.

• Sending high-intensity infrared laser light into
  a crystal yielded this display of green light

Nonlinear optics allows us to change the color of
a light beam, to change its shape in space and
time, and to test the fundamental principles of
quantum mechanics.
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Ultrashort laser pulses are theshortest events
ever created.

• This pulse is only 4.5 x 10-15 seconds long, that
  is, 4.5 femtoseconds

How do we measure such a short event?
We must use the event to
measure itself.
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• Light is, in short, the most refined
• form of matter.
  

Louis de Broglie