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.

Absorption filters (colored glass) Transmission vs :

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

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

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:

H Two-layer example:

Multilayer method summary

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.)

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

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

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.

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

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

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

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

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

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: