Ellipsometry: finding n,  or thicknesses, roughness… Wikipedia /ellipsometers/l116sf.htm starts linear, angle  does something linear polarizer, angle 

Any light with information (e.g. pulsing) has to contain more than one frequency. Superposition of Waves 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 phase oscillations Group velocity speed of “envelope”, pulse, signal, image, energy, information (this definition not valid when absorption is strong)

n  Dispersion due to n(  )  k Re (  =n(  c Dispersion is when v phase is not constant: k(  or  (k  are not linear: Wave speed depends on  v phase =c/n( 

Does group velocity exceed c? k Re (  =n(  c  Look at slope for v g : Where our definition is valid (low absorption), k/  c 

If in some strange system, then the group velocity is a) b) c) d)

If in some strange system, the group velocity is a) b) c) d)

Energyand superimposed plane waves Energy and superimposed plane waves Two restrictions for this result to be true: ____________

Energyand superimposed plane waves Energy and superimposed plane waves Practicing simple addition of waves You add two 1-D waves, of amplitude E 1 and 2E 1. In some places they add constructively, and some places destructively. E 1 by itself corresponds to intensity I 1. The brightest intensities seen in the interference pattern are: a)3I 1 b)4I 1 c)6I 1 d)9I 1 e)25I 1

You add two coherent 1-D waves, of amplitude I 1 and 9I 1. In some places they add constructively, and some places destructively. The dimmest intensities seen in the interference pattern are: a)2I 1 b)3I 1 c)4I 1 d)6I 1 e)8I 1

Show that and find in terms of a)I did it b)I tried