PHYS 408 Applied Optics (Lecture 6) JAN-APRIL 2016 EDITION JEFF YOUNG AMPEL RM 113

Logistics Homework #1: -Will post solutions and next assignment this weekend -degree of difficulty? Labs: -due at end of last session -try to take all data next week

Quick review of key points from last lecture Point-like dipoles have a very characteristic radiation pattern that can be derived using the vector potential A(r). The radiation is fundamentally a spherical wave, with angular modulation of the E and H vectors’ amplitudes. There is no radiation along the axis of the dipole, and most of the power is radiated with a polarizaiton aligned with the dipole, in the equatorial plane. Did anyone figure out the circles in the plot?

New Module: Light encounters with Optical Elements What happens when one of our plane waves strikes a flat interface between two media with different dielectric constants? k in krkr ktkt z x What is the boundary condition for field components parallel to surface?  in rr tt n=n 2 n=n 1 Write down the relevant equations, starting with the general expressions for the 3 waves

Set up the problem Why, given E inc, can we assume this form? How do we use the boundary conditions?

Use continuity of E field across boundary Simplify the k’s…

Conclusion “Phase matching” the 3 wavefronts.

Fresnel equations (you will derive) Where k // is the conserved in-plane wavevector Show that n 1 r s 2 cos(  1 ) + n 2 t s 2 cos(  2 )=1 What does this mean for

Thin film optics What do you think the amplitude of the transmitted wave would be if the incident wave had amplitude 1? d z x What do you notice about the transmitted wave?

What about power conservation now? Reflected wave? If power was conserved at the single interface, it wouldn’t be here. Wherein lies the problem?

Multiple reflections In reality, there are an infinite number of reflections and transmissions of a harmonic beam that encounters a series of parallel dielectric discontinuities

Two quite different approaches to solving problem In assignment you evaluate the series directly In class we will solve it in a different way