Complex numbers/phasors and amplitudes Student question: 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 at each time. At some time the phasor will rotate across the real axis, and the amplitude will peak. So the phasor magnitude is the physical field amplitude.

Absorption filters (colored glass) Transmission vs :

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

Multilayer method summary

P. If we choose a layer of effective thickness “  /2”, the matrix M 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.