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.
E phys  t   Re[ Ecomplex (t )]
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 :
Multilayer filters and Multilayer mirrors--based on interference: much sharper and
specialized features possible.
short-pass filter
Notch filter
3-notch filter
long-pass
filter
Multilayer method summary
M j ( p  pol )

cos  j

 C j (0)C j 1 (  j )  

nj
 i sin  j
cos  j

cos  j 
i sin  j

nj 


cos  j

M j ( p  pol )

cos  j

 C j (0)C j 1 (  j )  

nj
 i sin  j
cos  j

cos  j 
i sin  j

nj 


cos  j

 j  k j l j cos  j  n j kvac l j cos  j
(Note: in multilayer technology, layers described as “ /2”
or “ /4”, etc,  is that in the material, not vacuum. The
effective thickness is l j cos  j.)
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
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
Physics 123 ideas
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)
Reflectance and coatings
Air-Glass (multilayer theory works for zero layers, too!):
Normal incidence
 nG  nA 
R

 nG  nA 
Normal incidence
2
R≈4% across visible for nG=1.5.
Anti-reflectance coatings
Single /4 layer, Normal incidence
Air-L-Glass (H):
 na ng  nL 
R
 na ng  nL 2 


2
Normal incidence
2
R≈1% across visible for nG=1.5.
Anti-reflectance coatings
Two /4 layers, normal incidence
Air-L-H-Glass :
 n2 na  n n 
R 2
 n2 na  n n 


2
2
g 1
2
g 1
2
L
H
More freedom to chose n’s, so usually better at some design  , but
but not so good at ’s away from the design .
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 .