Exam 2 Review Chapters 6-8
Equations that will be given on the exam. All of the equations/constants from exam 1, plus the following:
Jones vectors
 A 

i 
 Be 
general, standard form: 

RCP: 1  1 
 i ( 90) 
2 e

LCP: 1  1 
 i ( 90) 
2 e

Jones matrices
linear polarizer:  cos 2 

cos 2   i sin 2 

 sin  cos   i sin  cos 

/2:  cos 2 sin 2 


 sin 2  cos 2 
sin  cos  

sin 2  
sin  cos   i sin  cos  


sin 2   i cos 2 

2
2T 2
ei0t  TE0eT
 (t  t0 ) 
1
2

a(t )  b(t ) 

e
 i ( t t0 )
2
( 0 )2 2
d

 a(t )b(t  t )dt 





1
 ( ) 

 2
E(t  t , r0 )
I
E0 e
det
1


 I ( )e
 i
d

( )dt  2 1  Re  ( ) 

I det ( )  2 I 1  Re  ( )
Quadratic dispersion
1
2
k  k0    0      0 
vg
1 1
 n  n   
0
vg c
1
  n  2n  
0
2c
Gaussian wavepacket, through thickness z:
E t , z  
 I ( )d



d
Re( k )
 r
d
 0


2 kimag (0 )r


FT  Sig 
2
Young
 2 0    I    I   

 kyh

   
 D

Pt source: I det (h)  2 I 0 1  cos

Extended source:
  2z
T   1 2
Fourier, Delta, Convolution
E0et
t 
I e

 sin  cos 

/4:
 d
vg  
Re( k )
 d
 0



 I ( y)dy

i  kz 0t 
1   
2 1/ 4
e
i
i   z
tan 1  
t
2
2 T 2  vg




2

e
1  z
t
2T 2  vg




2
1
 ( h)  e


ikyh 
D

I ( y)e

ikhy 
R
dy

I det (h)  2 I oneslit 1  Re  (h)
Michelson
I det ( )  2 I 0 (1  cos  ) (single )
Band of ’s:
Linear dispersion
Equations that you won’t need to know by heart. All of the equations listed for exam 1, plus the following:
 How the general Jones vector for elliptically polarized light relates to the angle of the ellipse (Eqn 6.12) and the
semi-major and semi-minor axes of the ellipse (Eqns 6.13 and 6.14)
 Ellipsometry equations
 Fourier transform of comb function
Equations/derivations/other stuff that you may need to know by heart. All of the items listed for exam 1, plus the
following (not an exhaustive list):
 Jones vectors for linearly polarized light
 Jones matrices for linear polarizers in x- and y-directions (although you can get them as special cases of the general
linear polarizer matrix which I will give you)
 Jones matrices for reflection and transmission
 How to get the Jones matrices for quarter- and half-wave plates for  = 45, from the general matrices that are given
 Group and phase velocity equations
 Definitions of Fourier and inverse Fourier transforms
 Parseval’s theorem
 Delta function definitions
 Sifting property of delta function
 Convolution theorems, without factors of sqrt(2)
 Definition of visibility
 V = ||
 Coherence time c = integral of ||2 dt (from – to +)
 Coherence length c = c  coherence time
 “Coherence slit separation” hc = integral of ||2 dh (from – to +)
Exam 2 Review