1. Complex numbers/phasors and amplitudes There was a question last time: since the Re part of a complex field is the physical one, why do we need the full phasor length as the physical field magnitude? The physical field is the Re part of E any time. But the phasor as usually drawn represents t=0. So Re[phasor] is the physical field only at t = 0. The maximum physical field strength (amplitude) won’t generally be seen t= 0, but instead whenever the phasor rotates across the real axis, given by the phase angle). So the phasor magnitude is the physical field amplitude.

2. Absorption filters (colored glass) Transmission vs :

3. short-pass filter Multilayer filters and Multilayer mirrors: much sharper and specialized features possible. Notch filter 3-notch filter long-pass filter

4. -Parallel components of E, B are equal at interfaces. -Have two directions in each material except the last. Phase shifts to the next boundary:

5. E’s are defined where their arrows start (except Eo). Match || parts at right side of j, left side of j+1 layers. P polarization:

6. H Two-layer example:

7. Multilayer method summary

8. P. If we choose a layer of effective thickness “  /2”, the matrix will ______: a) have zeros for its diagonal elements b) have zeros for its off-diagonal elements (Note: in multilayer technology, layers described as “  /2” or “  /4”, etc,  is that in the material, not vacuum. The effective thickness is.)

9. Physics 123 ideas If we choose the thickness to be “  /4”, the phases of these reflecting rays (due to thickness alone) are ________. a)All in phase b)Alternating phase

10. If we choose the thickness to be “ /4”, and we want a high R, we better choose the n’s to be ___________. Look at the phase of the first three reflections. a)(1.4, 1.5, 1.8) b)(1.5, 1.4, 1.8) Physics 123 ideas

11. Reflectance and coatings Air-Glass (multilayer theory works for zero layers, too!): Normal incidence Normal incidence R≈4% across visible for n G =1.5.

12. Anti-reflectance coatings Single /4 layer, Normal incidence Air-L-Glass (H) : Normal incidence R≈1% across visible for n G =1.5.

13. Anti-reflectance coatings Two /4 layers, normal incidence Air-L-H-Glass : More freedom to chose n’s, so usually better at some design, but but not so good at ’s away from the design. LH

14. Single /4 Anti-Reflectance Coating: AL Glass(H) light still bounces among lenses in camera, spreading glare Triple /4 coating : ALHLGlass(H)

15. High reflectance multilayers Air-(HL) N -Glass(H) /4 layers Better: Air-(HL) N -H-Glass

16. Computer design can optimize for any application, with different d’s, n’s and ordering One complication n: depends on.

17. What is different below for s polarization? a)We divide by n’s instead of multiply b)The cos’s go to sines c)The cos’s and n’s switch rows d)The cos’s move to the n’s row e)There are no cos’s P polarization: