http://en.wikipedia.org/wiki/Group_velocity

Announcements See email on exam results and scoring. Will return at end of class.

Reading Quiz Which quantities can be greater than c? a) vphase b) signal propagation speeds c) image propagation speeds

Reading Quiz Group velocity is given by (you can check units) a. b. c.

Ellipsometry: finding n, k or thicknesses, roughness… 3 starts linear, angle a linear polarizer, angle q 1 2 does something Wikipedia http://www.gaertnerscientific.com/ellipsometers/l116sf.htm

Superposition of Waves Single frequency light has infinite extent in time (mathematical, not physical) Any light with information (e.g. pulsing) has to contain a spread in frequencies. Any light created in the universe has more than one frequency (it had a beginning).

Superposition of Waves Addition of two waves, equal magnitude:

Superposition of Waves Phase velocity speed of single frequency wave Group velocity (this definition not valid when absorption is strong) speed of “envelope”, pulse, signal, image, energy, information

Dispersion due to n(w) Wave speed depends on w kRe (w)=n(w) w/c Dispersion: when vphase is not constant: k(w) and w(k) are not linear: vphase =c/n(w) n w

Does group velocity exceed c? kRe (w)=n(w) w/c k/w =1/c Look at slope for vg : Where our definition is valid (low absorption), w

“Things” that go faster than the speed of light Waves on beach move at v<c (duh) The point on the beach that is getting hit moves to the left at v/sin(q), which could be anything greater than v. But that speed is a mathematical thing, not a physical one.

If in some strange system, then the group velocity is

If in some strange system, the group velocity is

Energy and superimposed plane waves Practicing simple addition of waves (Phscs 123) You add two waves, of amplitude E1 and 2E1. Same polarization. In some places they add constructively, and some places destructively. E1 by itself corresponds to intensity I1 . The brightest intensities seen in the interference pattern are: 3I1 4I1 6I1 9I1 25I1

You add two coherent 1-D waves, of intensities I1 and 9I1 You add two coherent 1-D waves, of intensities I1 and 9I1. In some places they add constructively, and some places destructively. The dimmest intensities seen in the interference pattern are: 2I1 3I1 4I1 6I1 8I1

We can write Find in terms of I did it I tried

What color(s) do the surfaces of these red plastic objects reflect?

From an optics perspective, what’s the biggest difference between what’s inside the two red plastics?

Interference/diffraction (“structural”) colors in nature: iridescence http://www.webexhibits.org/causesofcolor/15A.html

Opals are natural 3-d diffraction gratings or “photonic crystals”

What’s missing in the albino peacock?

Opals

Photonic Crystals: 3-D diffraction grating

Nocturnal animals have layer of cells behind retina with multilayer mirrors that reflect unabsorbed light back through it!

Cameleon http://www.youtube.com/watch?v=7Yxq_G05cHU

Change colors for camouflage, mood Outer layer: cells that can concentrate red or yellow pigment in center (cells almost clear), or spread them over cell (colored) Middle layer: sacks of photonic crystal plates, reflecting blue Inner layer: cells that can concentrate melanin (black) in center (cells almost clear), or spread them over cell (black) Only 1 and 3 controlled by nerves?

Chromatophore organ

Iridophores (photonic crystals) and chromatophores (pigment organs)

Chameleon colours 'switched by crystals' - http://www. bbc. co Latest Chameleon colours 'switched by crystals' - http://www.bbc.co.uk/news/science-environment-31819588