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Optics (Physics 452000 - Fall 2020) : Prof. R. R. Alfano Problem Set 6

This document contains an optics problem set with 8 questions covering topics like: 1) Calculating the time for an electron to travel around a Bohr orbit 2) Properties of ruby and emerald lasers 3) Definitions of polarization terms 4) Jones matrices for half wave and quarter wave plates 5) Using Jones matrices to determine output fields 6) Combining polarization components with wave plates 7) Representing elliptically polarized light with Jones vectors

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73 views2 pages

Optics (Physics 452000 - Fall 2020) : Prof. R. R. Alfano Problem Set 6

This document contains an optics problem set with 8 questions covering topics like: 1) Calculating the time for an electron to travel around a Bohr orbit 2) Properties of ruby and emerald lasers 3) Definitions of polarization terms 4) Jones matrices for half wave and quarter wave plates 5) Using Jones matrices to determine output fields 6) Combining polarization components with wave plates 7) Representing elliptically polarized light with Jones vectors

Uploaded by

Simon Savitt
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Optics (Physics 452000 - Fall 2020)

Prof. R. R. Alfano
Problem Set 6

1 How many attoseconds does an electron need to travel


around a Bohr orbit path?
v2 e
Use: F = ma, a = r
, E= 4πo r2
, F = eÊ

2 a) Why is ruby red and emerald green?; b) what are their


emission wavelengths?; c) What are their bandwidths in
emission?; d) What are their host material and laser ions?
3 Give a definition for the following terms from the web:
a) Faraday rotator
b) Optical activity
c) Circular Dichroism
d) Chirality

4 What are the Jones matrix for a half wave plate and a
quarter wave plate?
5 Using the following Jones matrix for λ/4 plate
 
1 0
Jλ/4 = , Eout = JEin
0 −i  
1
a) What is the output, Eout field, for linear polarized as input?
  −1
1
b) What is the output, Eout field, for RH as input?
−i

1
6 Using the following Jones matrix for λ/2 plate
 
1 0
Jλ/2 = , Eout = JEin
0 −1  
1
a) What is the output, Eout field, for linear polarized as input?
  1
1
b) What is the output, Eout field, for LH as input?
i

7 Combination of polarization
 
Ex
a) What is the output field of λ/2 followed by a λ/4 and then, followed by λ/2 for Ein =
  Ey
1
?
1

8 Note the following Jones Matrix


   
Eox Eox eiφx
E= = ,
Eoy Eoy eiφy
 
A
E= counterclockwise rotation
iB
 
A
E= elliptical polarized light
B + iC
√  
Eox = A, Eoy = B 2 + C 2 , and  = tan−1 B C

Equation of the ellipse:


 2  2
Ex Ey   
Ey
+ − 2 EEox
x
Eoy
cos = sin2 
Eox Eoy
φy − φx = 
 
3
Using the following Jones vector: ?
2+i
a) Show that  = 26.6o
b) Show that α = 35.8o , inclination angle.

2 2
tan 2α = (2Eox Eoy cos)/(Eox − Eoy )
c) Show that it represents elliptically polarized light with the ellipse equations as follows:

(Ex2 /9) + (Ey2 /5) − 0.267Ex Ey = 0.2

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