Polarized Light Scattering

Topic 3 Part 3

Biophysics

More rigorous Treatment of Light Scattering

rEdVe)kk1(r

ekrE)r(E V

rkirki2

0��

.ˆˆ ..

• This is not a solution

•Polarizability per unt volume is a tensor (matrix)

• Transversality is ensured by k̂k1�

First Born and coupled dipole approximation

• The first born approximation assumes the electric field inside the particle is equal to the incident electric field.

• The coupled dipole approximation

'

..

.''V

0V

rkkirki2

s EredVr

ek)r(E o

�

jjN

1j

jrkirki2

s Eer

ekr(E

�

.) ..

ijijjjijjjN

ijij

rki0ii nnEbEae EE i0 ˆ).̂(.. ��

Stokes Vector and Mueller Matrices

2l

2r

22

2v

2h

2v

2h

EE

EE

EE

EE

V

U

Q

I

if V

U

Q

I

M

V

U

Q

I

44434241

34333231

24232221

14131211

MMMM

MMMM

MMMM

MMMM

M

Stokes vector completely describes intensity and polarization state of light.

Mueller matrix is a transformation matrix that is a property of material object

Check out examples of both

Significance of Muller matrix elements in absorption and

scattering

See notes for more description

1'

1'

'1

'1

LBLBCD

LBCBLD

LBCBLD

CDLDLD

e AM

A B

B C

D

E

h f

j g

h j k

f g k

Absorption Scattering

Measurement of Mueller matrix

• Do simple example – like detecting M14.

What kind of light do you put in?

• Use photoelasatic modulator taking advantage of modulation technique to

get good signal to noise.

)()(

)()(

Cos0Sin0

0100

Sin0Cos0

0001

= A Sin(wt)

Apparatus

Light source 90o Polarizer

Sample

Filter?

detector

PEM at 45o

PEM Quartz (strain)

Apply ac voltage – piezoelectric crystal

Do examples

Higher Order DNA Structure

www.library.csi.cuny.edu

Nucleosome

www.answers.com

www.plyojump.com/courses/biology/week06.html

30 nm fiber

Crystal Structure supports cross-linker model

(Nature 436, 138-141(7 July 2005)

http://cms.daegu.ac.kr/sgpark/molecular%20biology/VIBJI035.GIF

SolenoidCrosslinker

Nature Structural & Molecular Biology  12, 6 (2005)

Protein Scaffold

http://www.molbio.unige.ch/laemmli/images/Fig1.jpg

Function

Lampbrush chromosome

http://openlearn.open.ac.uk/file.php/2645/S377_1_041i.jpg

Polytene chromosomes from salivary gland cells of Drosophila larvae. Regions of condensed chromatin appear darkly stained whereas regions of de-condensed chromatin stain lightly.

www.bio.jhu.edu/~corces/Research2.html