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Polarized Light Scattering

Polarized Light Scattering. Biophysics. More rigorous Treatment of Light Scattering. This is not a solution Polarizability per unt volume is a tensor (matrix) Transversality is ensured by. Transversality condition. is the transversality condition. E is perpendicular to. Example: If.

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Polarized Light Scattering

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  1. Polarized Light Scattering Biophysics

  2. More rigorous Treatment of Light Scattering • This is not a solution • Polarizability per unt volume is a tensor (matrix) • Transversality is ensured by

  3. Transversality condition is the transversality condition E is perpendicular to Example: If show

  4. 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

  5. Linearly Polarized Light

  6. Circularly Polarized Light • E (x,t) = E0 (j ± i k) ei(kx-wt) • Ey = Re(E0 ei(kx-wt)) = E0cos(kx-wt) • Ez = Re(± i E0 ei(kx-wt)) =- ± E0sin(kx-wt) • At a particular position x (say x = 0) get • The electric field sweeps out a circle

  7. Elliptically and Unpolarized Light • Elliptical • E (x,t) = (E1 j +i E2 k) ei(kx-wt), with E1 not equal to E2. • Unpolarized light • E always perpendicular to B but changes direction fast, on order of 10 ns or greater.

  8. Polarizers • Transmit light parallel to polarization axis • Unpolarized: I  Io/2 • Circular: I  Io/2 • Linear: I = Iocos2(q) • [Remember I a E2] • Birefringence

  9. Stokes Vector and Mueller Matrices 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

  10. Example of Stokes Vectors • What do these (below) represent? How would we represent right circularly polarized light

  11. Examples of Muller Matrices Linear Polarizer Circular polarizer Retarder at ±45o where d is the strain

  12. Examples: Show that a vertical, horizontal, circular polarizer do what they are supposed to for incident un- and linearly polarized lights. Show that a vertical polarizer + 90 degree retarder at 45o can act as a circular polarizer, with the polarizer first. Work out in class. (See Maple).

  13. Significance of Muller matrix elements in absorption and scattering See notes for more description Absorption Scattering

  14. Mueller Matrix Elements Each element describes a change in polarization Eg. Ir = (M11 + M14) Io IL = (M11 - M14) Io  M14 = ½(Ir – IL)/Io

  15. 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. d = A Sin(wt)

  16. 90o Polarizer Light source Sample PEM at 45o Filter? detector PEM Quartz (strain) Apply ac voltage – piezoelectric crystal Apparatus Do examples www.youtube.com/watch?v=Z40AsPaktzw

  17. We can expand the cosine and sine terms as Bessel Functions: Cos(Asin(wt)) = J0(A) + 2J2(A)cos(2wt) + 2J4(A)cos(4wt) + … Sin(Asin(wt))= 2J1(A)sin(wt) + 2J3(A)sin(3wt) + … So if no final filter is used, The DC current is M11 The 1f signal is M14/M11 The 2f signal is M12/M11

  18. Higher Order DNA Structure www.library.csi.cuny.edu

  19. Nucleosome www.answers.com www.plyojump.com/courses/biology/week06.html

  20. 30 nm fiber Crosslinker Solenoid Crystal Structure supports cross-linker model (Nature436, 138-141(7 July 2005) http://cms.daegu.ac.kr/sgpark/molecular%20biology/VIBJI035.GIF Nature Structural & Molecular Biology12, 6 (2005)

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

  22. 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.

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