ECE 4300
Homework 1
September 3, 2008
Due: Wednesday, September 10, in class This will be graded S/U. You may work with others on this assignment, but by turning in this homework, and signing your name to it, you are saying that you have done the
Classical Electrodynamics
Physics 6561 Homework 12. Ocially due: In class on Tuesday, 12/2
Due to the Thanksgiving holiday we will accept homeworks without the need for additional explanation until Friday, 12/5 at 2pm. There will be an envelope on the boa
Optic Axis, the normal to the lens through the center
Height of ray is the distance from the endpoint of the ray to the axis
Paraxial Approximation: Slope < 15 degrees, tan theta = theta
Abcd matrix:
|A B|
|C D|
Move distance l over, abcd matrix is 1 l 0
Cornell University Department of Physics
Classical Electrodynamics P561
Second Exam - solutions by Johannes Heinonen November 29, 2007
1. Multipole moments
a) The charge density can be written as = 0 4Y00 (, ) + 1 So we get the sperical multipole moments
Classical Electrodynamics
Physics 6561 Homework 13. Due: Ocially due: Friday, 12/05 at 2pm in the envelope next to my door.
Note: This is the last homework set. I will accept homework without the need for additional explanation until the exam, that is Thu
Classical Electrodynamics
Physics 6561 Homework 11. Due: In class on Tuesday, 11/25
0. Reading assignment Read the sections in Jackson we did not have time to cover in class: 7.9, 8.1, the second half of 8.5 starting from page 364, 8.6, 8.7, 8.8.
1. TEM w
Classical Electrodynamics
Physics 6561 Homework 10. Due: In class on Tuesday, 11/18
0. Reading assignment Read the parts of chapter 7 in Jackson we did not have time to cover in class: 7.5.E, 7.6, 7.7. 1. Reection and refraction through multiple layers (a
Classical Electrodynamics
Physics 6561 Homework 9. Due: In class on Tuesday, 11/11
1. General polarization of plane waves Prove the statement in class (and Jackson p300) that a generic plane wave of the form E (x, t) = (E+
+
+ E
)e
ikxit
is elliptically
Classical Electrodynamics
Physics 6561 Homework 8. Due: In class on Tuesday, 11/4. NOTE: original problem 3 has been moved to next set and replaced with dierent problem.
1. Dirac quantization for two particles Problem 6.17 from Jackson on page 290. 2. Cau
Classical Electrodynamics
Physics 6561 Homework 7. Due: In class on Tuesday, 10/28.
1. Generic properties of the multipole expansion a. Problem 4.4 from Jackson. b. Problem 4.5 from Jackson 2. Magnetostatics Problem 5.10 from Jackson. 3. The Dirac string
Classical Electrodynamics
Physics 6561 Homework 6. Greens functions. Due: In class on Tuesday, 10/21.
1. Problem 3.1 from Jackson. 2. Problem 3.13 from Jackson (this is the continuation of 3.1, and is problem 3.12 in the second edition). 3. Problem 3.17 f
Cornell University Department of Physics
Classical Electrodynamics P561
Second Exam November 29, 2007
You have 3 hours to work on the exam. This is an open notes open Jackson exam (but no other book or printed material may be used): you can use any of yo
Beam Diffraction
Plane Wave propagating in a k vector direction, extends from neg inf to inf.
E(z,t) = Eoe^(j*(kz-wt)
|k| = spatial freq rads/cm
Can use plane waves to describe real waves. Superimpose different plane waves.
Have the same wavelength
E(y) =
ECE 4300
Lasersand Optoelectronics
Fall 2015
Homework 2
Due next Friday, September 11, in class.
Problem 1. Gaussian Beams
A laser beam is characterized at one particular point in space as having a complex beam
parameter, q(z), equal to q=j5 + 50 cm. The
ECE 4300
Lasersand Optoelectronics
Fall 2015
Homework 3
Due Friday, September 25, in class.
Problem 1. Spatial modes
Consider a two mirror laser cavity consisting of a plane mirror (R=) and a curved mirror with
R=100 cm.
a. Make a plot of the size of the
ECE 4300
Lasersand Optoelectronics
Fall 2015
Homework 1
Due next Friday, September 4, in class.
Problem 1. Ray matrices and the thick lens
I have no doubt you can find the solution to this problem somewhere, but you need to grind
through deriving an ABCD
ECE 4300
Lasersand Optoelectronics
Fall 2015
Homework 5
Due Monday, October 26, in class.
Problem 1. Frequency and wavelength conversions
The table below lists the central line and linewidth of various sources, sometimes in Hz and
sometimes in wavelength.
ECE 4300
Lasers and Optoelectronics
Fall 2015
Homework 6
Due Friday, November 6, in class.
Problem 1. The Thulium fiber amplifier
Tm-doped fibers are used for amplifying radiation at 1.9 um (check out the data at ThorLabs
https:/www.thorlabs.com/newgroupp
(Y) c; 541 MOLM 6km (290-7 " samh'mJ 1 'HQW
® hC Cows? bag
a) L I off, mil/L. P, = [5,), ) (9,0)
Mn 7 @1442 4 M p (
7 'i ()2- 41,0, Or 0)
f" + P? = (V fe/r1)
30 we a. W %¢kv MIA:
V42; FIZ :(?(+?z)z 1 117+; *ZEIMz
L4,: (45: )f c 7,; Guam! we 05L 3
7.
Classical Electrodynamics
Physics 6561 Homework 4. Due: In class on Tuesday, 9/30
1. Angular momentum of EM eld 12.19 from Jackson: Source-free EM elds exist in a localized region of space. Consider the various conservation laws that are contained in the
Classical Electrodynamics
Physics 6561 Homework 3. Due: In class on Tuesday, 9/23
1. Force of charged particle with constant velocity (5 points) Two equal charges q move with equal velocity v . What is the force acting between the two charges? The distanc
ECE 4300
Homework 3
September 17, 2008
Due: Wednesday, September 24, in class I am really going to give you a workout with the ABCD law in this assignment. Once you finish this you will be ready to do a real cavity design. 1. This is an actual des