Chapter 5: Wave Optics

How to explain the effects due to interference, diffraction, and

polarization of light?

How do lasers work?

Wave Optics

•Effects due to interference, diffraction, and polarization can not be explained by geometric optics.

•Wave nature of light was demonstrated by Young’s double slit experiment (1820).

In phase waves lead to constructive

interference

Out of phase waves lead to destructive

interference

Two Wave Interference

•What causes two identical waves to become “in-phase” or “out-of-phase”?

Path difference between the two waves!

•Waves are in-phase when

P = 0, , 2, 3, …, n

•Waves are out-of-phase when

P = /2, 3/2, 5/2, …, (n+1/2)

http://www.physics.northwestern.edu/ugrad/vpl/waves/superposition2.html

Path difference P = (r2 – r1)

Example: Two Wave Interference

Path difference = 1 wavelength

Path difference = 1/2 wavelength

Two Wave Interference (Contd.)

Condition for constructive interference:

L

y

d

n

n = 0, 1, 2, …

Two Wave Interference Pattern

n=0

Intensity

n=2n=1

y

www.Colorado.EDU/physics/2000/schroedinger/two-slit2.html

Thin Film Interference (Soap Bubbles)

The phase difference of rays reflected from the top and bottom surfaces depends on the thickness and refractive index of the film, the angle at which the light strikes the film surface and the wavelength of the light.

Thin Film Interference (Antireflection coating)

The substrate (glass, quartz, etc.) is coated with a thin layer of material so that reflections from the outer surface of the film and the outer surface of the substrate cancel each other by destructive interference.

Multiple Wave Interference – Diffraction Grating

•Constructive interference occurs only when all waves are in-phase.

•Path difference between any two successive waves must be n.

•Condition for interference maxima is,

•Interference pattern has

sharp peaks.

nSind

2 slits 16 slits8 slits

http://www.microscopy.fsu.edu/primer/java/imageformation/gratingdiffraction/index.html

Diffraction Grating (Contd.)

•Gratings have hundreds of slits per cm.

•Applications in spectroscopy, crystallography etc.

Diffraction pattern from a crystalline solid

Diffraction of light from a CD

Iridescence: A diffraction phenomenon

Review Problem

A grating has 5000 lines/cm. A second order maximum is observed at 300. What is the wavelength of light?

500 nm

LASER: Light Amplification by Stimulated Emission of Light

•Stimulated emission process was predicted by Einstein in 1916. First laser developed in 1959.

•“Photons” and atoms can interact via the following processes.

Absorption: Atom can absorb a photon and become excited.

Spontaneous emission: Atom in excited state will spontaneously emit a photon and occupy a lower energy state.

Stimulated emission: Atom in excited state is stimulated by a photon to emit another photon and occupy a lower energy state. Emitted photon has the same wavelength, phase, and direction as the stimulating photon.

http://www.colorado.edu/physics/2000/lasers/lasers2.html

Stimulated Emission

•Stimulated emission is more likely under “population inversion”.

•Pumping: Process by which energy is supplied to excite more atoms to achieve population inversion.

Atoms can be pumped by photon absorption, collisions, electric current…etc.

http://www.colorado.edu/physics/2000/lasers/lasers3.html

PUMP

Normal condition: Thermal equilibrium

Population inversion achieved by “pumping”

Laser Operation in a 3 Level System

http://www.phys.hawaii.edu/%7Eteb/optics/java/laser/index.html

Excited

Reservoir

Ground

Excited

Reservoir

Ground

1. Pumping: Excites atoms to highest level.

2. Fast radiative decay to reservoir creates population inversion between reservoir and ground states.

Excited

Reservoir

Ground

3. Seed photon stimulates emission and light is amplified! Laser light

Light Amplification

•Light is amplified in a “resonant cavity” between two mirrors.

•Photons from stimulated emission bounce between mirrors knocking out more photons. Light is “amplified”!

http://www.colorado.edu/physics/2000/lasers/lasers4.html

Active MediumLaser Light

90% Reflecting Mirror

100% Reflecting Mirror

Properties of Laser Light

•High Power Density: At the focus, lasers can be thousands of times more intense than the sun!

•Sunlight ~ 1300 W/m2

•Laser ~ 106 W/m2

•High Spectral purity: Light is emitted in a narrow band of wavelengths. This is due to the atomic processes in the “active medium”.

•Small beam divergence: All photons travel in the same direction. Typical beam divergence ~ 2 x 10-5 degrees/m.

•Coherence: All the emitted photons

bear a constant phase relationship

with each other in both time and space.

Types of Lasers

•Solid state lasers, gas lasers, dye Lasers, semiconductor (diode) lasers.

Laser Type Wavelength (nm)

Free Electron UV, X-ray??

Excimer: Argon fluoride 193

Nitrogen 337

Argon Ion (blue) 488

Argon Ion (green) 514

Helium Neon 633

Rhodamine 6G Dye (tunable) 570 - 650

Ruby (CrAlO3) 694

Nd:YAG 1064

Carbon Dioxide 10600

http://www.microscopy.fsu.edu/primer/lightandcolor/java.html

Holography (3D Imaging)

Conventional Photography Holography

Relative intensities are recorded on film

Interference pattern is recorded on film

“Phase” information about waves is lost

“Phase” information is retained in the interference

pattern

Film3D Object

Holography (2 Step Process)

RecordingReconstruction

Interference pattern is recorded on film.Need high resolution (slow) film, long

exposure and vibration free set up.

Interference pattern acts as a diffraction grating so different orders of maxima and minima

reconstruct the image.

Polarization

•Light is a “transverse” electromagnetic wave.

•Polarization is the orientation of the electric field.

Note:•Natural light is “randomly” polarized.•Eye cannot distinguish different polarizations.

Production of Polarized Light

•Selective Absorption:

•Note: Optically “active” materials can change the polarization direction. Example: Sugar solution, DNA, liquid crystals…etc.

Production of Polarized Light (Contd.)

•Reflection:

http://www.colorado.edu/physics/2000/applets/polarized.html

Production of Polarized Light

•Scattering:

Light scattered in a perpendicular direction

is partially polarized!

Polarized Light: Some Applications

•Mineral characterization.

•Stress / strain fields (visual inspection of windshields).

•Polarization microscopy.

•Sunglasses / camera filters.

•LCD displays.

•Polarized art?

http://micro.magnet.fsu.edu/primer/virtual/polarizing/index.html

http://www.colorado.edu/physics/2000/index.pl