# 6.9 Polarization

 Page 1 / 1
We discuss the polarization of light waves.

## Polarization

Recall that we can add waves so lets take a plane wave traveling in the z direction and break it into components. ${\stackrel{⃗}{E}}_{x}={E}_{0x}{\mathrm{cos}}\left(kz-\omega t\right)\stackrel{̂}{ı}$ ${\stackrel{⃗}{E}}_{y}={E}_{0y}{\mathrm{cos}}\left(kz-\omega t+\delta \right)\stackrel{̂}{}$ Where $\delta$ is some arbitrary phase between the two components. The electric field for the wave is $\stackrel{⃗}{E}={\stackrel{⃗}{E}}_{x}+{\stackrel{⃗}{E}}_{y}$ Now there are a number of different cases that arise.

If $\delta =0,\phantom{\rule{thickmathspace}{0ex}}2\pi ,\phantom{\rule{thickmathspace}{0ex}}4\pi ,\dots$ Then we can write the field as $\stackrel{⃗}{E}=\left({E}_{0x}\stackrel{̂}{ı}+{E}_{0y}\stackrel{̂}{}\right){\mathrm{cos}}\left(kz-\omega t\right)$

Polarization of light for thecase $\stackrel{⃗}{E}=\left({E}_{0x}\stackrel{̂}{ı}+{E}_{0y}\stackrel{̂}{}\right){\mathrm{cos}}\left(kz-\omega t\right)$

The field is linearly polarized, that is the E field lies along a straight line.

Likewise If $\delta =\pi ,\phantom{\rule{thickmathspace}{0ex}}3\pi ,\phantom{\rule{thickmathspace}{0ex}}5\pi ,\dots$ Then again it is linearly polarized, but is now "flipped" $\stackrel{⃗}{E}=\left({E}_{0x}\stackrel{̂}{i}-{E}_{0y}\stackrel{̂}{j}\right){\mathrm{cos}}\left(kz-\omega t\right)$

Polarization of light for thecase $\stackrel{⃗}{E}=\left({E}_{0x}\stackrel{̂}{ı}-{E}_{0y}\stackrel{̂}{}\right){\mathrm{cos}}\left(kz-\omega t\right)$

Circularly polarized light is a particularly interest example. Let $\delta =-\pi /2$ and ${E}_{0x}={E}_{0y}={E}_{0}$

Then ${\stackrel{⃗}{E}}_{x}={E}_{0}{\mathrm{cos}}\left(kz-\omega t\right)\stackrel{̂}{ı}$ ${\stackrel{⃗}{E}}_{y}={E}_{0}{\mathrm{cos}}\left(kz-\omega t-\pi /2\right)\stackrel{̂}{}$ ${\stackrel{⃗}{E}}_{y}={E}_{0}{\mathrm{sin}}\left(kz-\omega t\right)\stackrel{̂}{}$ or $\stackrel{⃗}{E}={E}_{0}\left[{\mathrm{cos}}\left(kz-\omega t\right)\stackrel{̂}{ı}+{\mathrm{sin}}\left(kz-\omega t\right)\stackrel{̂}{}\right]$

The direction of $\stackrel{⃗}{E}$ is changing with time. For example consider the case at $z=0$ . Then

$\stackrel{⃗}{E}={E}_{0}\left[{\mathrm{cos}}\left(-\omega t\right)\stackrel{̂}{ı}+{\mathrm{sin}}\left(-\omega t\right)\stackrel{̂}{}\right]$

$\stackrel{⃗}{E}={E}_{0}\left[{\mathrm{cos}}\left(\omega t\right)\stackrel{̂}{ı}-{\mathrm{sin}}\left(\omega t\right)\stackrel{̂}{}\right]$

In this case the electric field undergoes uniform circular rotation. For light coming out of the page, it will have the motion shown in thefigure

Polarization of light for thecase $\stackrel{⃗}{E}={E}_{0}\left[{\mathrm{cos}}\left(\omega t\right)\stackrel{̂}{ı}-{\mathrm{sin}}\left(\omega t\right)\stackrel{̂}{}\right]\text{.}$ I, and most physicists would call the Left Hand Circular polarization (LHC). The thumb points in thedirection of the light ray and the fingers curve in the direction of rotation. (This is known as the Angular momentum convention, optical scientists will usethe "Optical" convention which is opposite - we will stick to the angular momentum convention.)

Suppose $\delta =\pi /2$ then you get $\stackrel{⃗}{E}={E}_{0}\left[{\mathrm{cos}}\left(kz-\omega t\right)\stackrel{̂}{ı}-{\mathrm{sin}}\left(kz-\omega t\right)\stackrel{̂}{}\right]$ This now has the opposite rotation, it is Right Handed.

The most general case of polarization has $\delta$ arbitrary and ${E}_{0x}\ne {E}_{0y}$ and is elliptically polarized.

Ellipticalpolarization

## Natural light

Natural light is emitted with the $\stackrel{⃗}{E}$ field in a mixture of random directions. This in unpolarized light. At any particular instant $\stackrel{⃗}{E}$ has a particular direction, but that direction changes rapidly and randomly.

## Malus' law

A polarizer is a device that takes incident natural light and transmits polarized light. For example a linear polarizer will take incident light andselect only that component of the light that has its $\stackrel{⃗}{E}$ field lined up along the transmission axis. Suppose there is a linear polarizer that transmits light along a particular axis. This is followed by asecond linear polarizer that has its transmission axis at a different angle with $\theta$ being the angle between the transmission axes. Since $I\sim {E}^{2}$ then at the second polarizer $I\left(\theta \right)=I\left(0\right){{\mathrm{cos}}}^{2}\theta$ where $I\left(0\right)$ is the Irradiance of the light hitting the second polarizer.

Lets consider unpolarized light hitting a linear polarizer. Then half the Irradiance will get through. If this is followed by a second polarizer at ${90}^{0}$ then no light will pass through the second polarizer. Now what happens if a third polarizer is placed between them?

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!