Download EE 5336-7336agendaHW1to3_Spring2017Feb16-1

EE 5336/7336 Integrated Photonics
Class Roster
Group A
Rami Abdelqader
HW#1, HW#11
Mary Dezfuli
HW#2, HW#12
Alex Holland
HW#3, HW#13
Group B
Yang Hu
HW#4, HW#14
Regan Klein
HW#5, Midterm part 1
Robert Lartigue
HW#6, Midterm, part 2
Group C
Muralidhar Madabhushi Balaji
HW#7
Nahid Mirzaie
HW#8, ??
Yasaman Sahba
HW#9, ??
Unaiza Tariq
HW#10, ??
Agenda
First Day, Tuesday, January 24, 2017
0. To view videos of class lectures, try this:
https://lyle.smu.edu/academic/downloads/
You will be prompted for a username and password.
Use your 8 digit SMUID for the username.
For security and privacy purposes the password will be your My.SMU.edu password.
Select the “1152-2017-Spring” folder.
Select your Course Number folder.
RIGHT click on the file link and select SAVE TARGET AS to save the file to your computer.
0. Help Session in room 338 starting about 5:05 or 5:15 on Mondays
1. Syllabus, course over view
2. Discussion and review of Maxwell’s Equations (only made it to about page 6)
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Agenda
Thursday, January 26, 2016
0. Videotape of next Tuesday’s lecture at 5 PM, Junkins 205 today. Please attend if
possible…
1. Discussion and review of Maxwell’s Equations, continued from about page 6
(discussed Snell’s Law and relationship to waveguides)
2. Boundary Conditions (derived BCs on tangential E and H; discussed permittivity:
tensors, nonlinearities, …)
3. Derivation of the Electromagnetic Wave Equation from Maxwell’s Equations
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Agenda
Tuesday, January 31, 2017
To download your online lecture, please visit:
https://lyle.smu.edu/academic/downloads/
You will be prompted for a username and password.
Use your 8 digit SMUID for the username.
For security and privacy purposes the password will be your My.SMU.edu password.
Select the “1172-2017-Spring” folder.
Select your Course Number folder.
RIGHT click on the file link and select SAVE TARGET AS to save the file to your computer.
(NOTE: This videotaped lecture stopped just before page 30 of the hand
written notes. Discussed derivation of the wave equation and the concept of a
waveguide using Snell’s Law)
0. HW#1 reviewed by Rami Abdelqader on Thursday, January 28th
1. Review “Wave Concepts” (includes group and phase velocity which is also reviewed
in Fiber Optics Tutorial)
2. Classification of Modes in waveguides
3. Solution of the wave equation for plane waves (see EE 3330 text)
4. 3-layer dielectric waveguide for electromagnetic waves (ray tracing)
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Agenda
Thursday, February 2, 2017
HW#1 reviewed by Rami Abdelqader
0. Instructions on downloading WAVEGUIDE, initial setup (Ruo-Hua He)
1. Review E&M material covered to date (start about slide 32)
--discuss why only TE and TM modes exist in 1D cross section slab waveguides
--discuss why hybrid modes exist in waveguides with 2D cross sections
2.
Discuss nature of the solution of the wave equation in a 3 layer dielectric
waveguide; can generalize to n-layer dielectric waveguides. Use ray “theory” and
total internal refraction (TIR) to discuss difference between k (propagation
constant in bulk material), (propagation constant in the direction of propagation
or the longitudinal axis of the wavegide) and s and  which are the transverse
propagation constants. The propagation constants can also be written as
propagation vectors.
3. 3-layer symmetric dielectric waveguide (wave equation solution)
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Agenda
Tuesday, January 7, 2017
HW#2 reviewed by Mary Dezfuli on Thursday
1. Review E&M material covered to date (start about slide 32)
--discuss why only TE and TM modes exist in 1D cross section slab waveguides
--discuss why hybrid modes exist in waveguides with 2D cross sections
2.
Discuss nature of the solution of the wave equation in a 3 layer dielectric
waveguide; can generalize to n-layer dielectric waveguides. Use ray “theory” and
total internal refraction (TIR) to discuss difference between k (propagation
constant in bulk material), (propagation constant in the direction of propagation
or the longitudinal axis of the wavegide) and s and  which are the transverse
propagation constants. The propagation constants can also be written as
propagation vectors.
3. 3-layer symmetric dielectric waveguide (wave equation solution)
Agenda
Thursday, February 9, 2017
1. HW#2 will be reviewed by Mary Dezfuli
2. Extra Credit Assignment
Due on or before Tuesday, March 2nd, 2017
Problem 1 (40 points) See the movie Hidden Figures—or read the book. Write a
summary of the movie or the book. If seeing the movie or buying the book
causes a financial hardship, you can submit your receipt to me for the cost of the
movie (which could include the cost of a guest that accompanies you) or the cost
of the book.
This assignment is motivated in part by a recent dinner conversation with friends, one
who works at Apple and another that is now an independent photonics consultant and
business partner—and in part by an anonymous reviewer’s comment of a recent paper
submitted (and now accepted) to the IEEE and OSA Journal of Lightwave Technology.
An important part of the paper dealt with deriving analytic formulas related to gratings in
optical waveguides. This was the reviewer’s comment: “Today it is better to let
computers do the work.”
Write a summary of the movie/book and include your thoughts. You can also comment
on why I wanted to send movie tickets or a copy of the book to the anonymous reviewer.
NOTE: The JLT paper and the response to the reviewers’ comments on the paper
are (will be) posted with the Extra Credit Homework assignment on Canvas.
3. Intel Museum and Moment of Silence? Photos of the Intel Museum and where
Shockley Labs use to can be found here:
https://www.dropbox.com/sh/6j3n9sok9066yh4/AABy47jarUwkLxX0nawyblUDa?dl
=0
4. Explain HW#3—give the formulas
x1. Review E&M material covered to date
--discuss why only TE and TM modes exist in 1D cross section slab waveguides
--discuss why hybrid modes exist in waveguides with 2D cross sections
5.
Discuss nature of the solution of the wave equation in a 3 layer dielectric
waveguide (page 48, handwritten notes); can generalize to n-layer dielectric
waveguides. Use ray “theory” and total internal refraction (TIR) to discuss
difference between k (propagation constant in bulk material), (propagation
constant in the direction of propagation or the longitudinal axis of the wavegide)
and s and  which are the transverse propagation constants. The propagation
constants (sometimes called wavenumbers, especially k = nko, n being the index
of refraction, ko = 2o) can also be written as propagation vectors.
6. 3-layer symmetric dielectric waveguide (wave equation solution)
Agenda
Tuesday, February 14, 2017
HW#3 to be reviewed by Alex Holland on Thursday
x1. Review E&M material covered to date (start about slide 32)
--discuss why only TE and TM modes exist in 1D cross section slab waveguides
--discuss why hybrid modes exist in waveguides with 2D cross sections
2.
Discuss nature of the solution of the wave equation in a 3 layer dielectric
waveguide (page 48, handwritten notes); can generalize to n-layer dielectric
waveguides. Use ray “theory” and total internal refraction (TIR) to discuss
difference between k (propagation constant in bulk material), (propagation
constant in the direction of propagation or the longitudinal axis of the wavegide)
and s and  which are the transverse propagation constants. The propagation
constants (sometimes called wavenumbers, especially k = nko, n being the index
of refraction, ko = 2o) can also be written as propagation vectors.
3. 3-layer symmetric dielectric waveguide (wave equation solution) (stopped at about
page 62)
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Agenda
Thursday, February 16, 2017
HW#3 will be reviewed by Alex Holland (delayed one week)
1. Continue/complete 3-layer symmetric dielectric waveguide (wave equation
solution)
2. Discuss general 3-layer symmetric dielectric waveguide (wave equation solution)
3. Start 2D waveguide derivation
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**below this point, the Agendas reflect what
was covered during the Spring 2016 classes**
Agenda
Thursday, February 11, 2016
1. HW#3 review by Sai Jiang
2. Continue 3-layer symmetric dielectric waveguide (wave equation solution)
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Agenda
Tuesday, Thursday, February 26 and 18, 2016
1. HW#3 reviewed by Sai Jiang
2. Jin Huang: In today's (Tuesday’s) Photonics class, I went over the definition and
meaning of the parameters in WGIII's (Waveguide III) input file and output table. I
showed them how to search for all bound modes, how to plot the near field and
index profile of a three-layer symmetric waveguide (Problem 1 of HMWK 5), and how to
loop the thickness of waveguide. I also explained the difference between bound modes
and leaky modes.
I'll show them how to find the transverse wave vector in the .ot file in the next class and
how to use the WGIII output data to plot the neff vs kW relation of a three-layer
waveguide.
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Agenda
Tuesday, February 23, 2016
1. HW#5 review by Nicole Hartman
2. Start 2D waveguide derivation
3. written midterm handout Friday (or so), due March 18; oral exam week following
spring break
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Agenda
Thursday, February 25, 2016
1. HW#5 review by Nicole Hartman
2. Start 2D waveguide derivation
3. written midterm handout Friday (or so), due March 18; oral exam week following
spring break
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Agenda
Tuesday, March 1, 2016
1. HW#6 will be reviewed by Sakpal, Sahil
2. Why we don’t like ghosts! (Grating Fabrication)
3. Continue 2D waveguide derivation
4. written midterm handout Friday (or so), due March 18; oral exam week following
spring break
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Agenda
Thursday, March 3, 2016
0. Written Midterm emailed and due March 25 (first two problems) and April 1
(second problem).
0.1 Course Project emailed and due on the last day of class, May 2nd.
0.2 HW assignments 7 through 10 have been added to the agenda document
0.3 oral exam week following spring break (March 14 -18). Will email link to Doodle for
group sign ups for oral exam “soon.”
1. HW#6 review by Sakpal, Sahil
2. Continue/complete 2D waveguide derivation
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Agenda
Tuesday, March 15, 2016
0. Written Midterm emailed and due March 25 (first problem)
1. Course Project emailed and due on the last day of class, May 2nd.
2. HW assignments 7 through 10 have been added to the agenda document
3. Schedule Group Oral Midterm exams during period of March 22 to 25 at
https://doodle.com/poll/g2s3q7wawgvxbbem
4. HW#7 review on Thursday by Charles Stevens
5. Complete 2D waveguide derivation
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Agenda
Thursday, March 17, 2016
0. Questions?
1. Schedule Group Oral Midterm exams during period of March 22 to 25 at
https://doodle.com/poll/g2s3q7wawgvxbbem
2. HW#7 review on Thursday by Nicole Hartman (replacing Charles Stevens)
2. Continue “effective” gain and loss calculations (start on slide 226)
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Tuesday, March 22, 2016
0. Questions?
1. Schedule Group Oral Midterm exams during period of March 22 to 25 at
https://doodle.com/poll/g2s3q7wawgvxbbem
2. HW#8 review on Wednesday by Wang , Zhan
2. Complete “effective” gain and loss calculations (which started on slide 226)
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0. Questions?
Agenda
Thursday, March 24, 2016
1. Group Oral Midterm exams in room 338 tonight and tomorrow.
https://doodle.com/poll/g2s3q7wawgvxbbem
2. HW#8 review by Wang , Zhan
3. Questions related to Midterm? Or class project? Or?
4. Complete “effective” gain and loss calculations (start on slide 226)
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Tuesday, March 29, 2016
1. Questions?
2. HW#9 review on Thursday by Samantha Williams
3. gain outside the center layer has applications to Silicon Photonics
4. Pulse spreading in a dispersive media
5. Directional coupler
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Agenda
Thursday, March 31, 2016
1. Questions?
2. HW#9 review by Samantha Williams
3. Questions class project? Or?
4. Pulse spreading in a dispersive media
5. Directional coupler
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Agenda
Tuesday April 5, 2016
1. Questions?
2. HW#10 review Thursday by Meinecke,James (Parker)
3. Questions about class (laser design) project? Class Exam (mention Poynting
Vector)? Or?
4. (More on Directional couplers later!)
5. Coupled Mode Theory for Periodic Structures (Kogelnik and Shank’s historic May
1972 paper: Coupled Wave Theory of Distributed Feedback Lasers
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Agenda
Thursday April 7, 2016
1. Questions?
2. HW#10 review by Meinecke,James (Parker)
3. Questions about class (laser design) project? Class Exam (mention Poynting
Vector)? Or?
4. (More on Directional couplers later!)
5. Coupled Mode Theory for Periodic Structures (Kogelnik and Shank’s historic May
1972 paper: Coupled Wave Theory of Distributed Feedback Lasers
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Agenda
Tuesday April 12, 2016
1. Questions?
2.
3.
4.
5.
HW#11 review on Thursday by Dhurgude, Vishal
Questions about class (laser design) project? Or Class Exam?
(More on Directional couplers later!)
Continue Coupled Mode Theory for Periodic Structures (Kogelnik and Shank’s
historic May 1972 paper: Coupled Wave Theory of Distributed Feedback Lasers
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Agenda
Thursday April 14, 2016
1. Questions?
2. HW#11 review by Dhurgude, Vishal
3. Questions about class (laser design) project? Or Class Exam?
4. (More on Directional couplers later!)
5. Continue Coupled Mode Theory for Periodic Structures (Kogelnik and Shank’s
historic May 1972 paper: Coupled Wave Theory of Distributed Feedback Lasers
************************************************************************************
Agenda
Tuesday April 19, 2016
1. Schedule Oral Final Exams next week on Doodle.
2. HW#12 review on Thursday by Meinecke,James (Parker)
3. Questions about class (laser design) project? Or Class Exam?
4. (More on Directional couplers later!)
5. Solve Coupled Mode Equations to obtain laser thresholds, amplifier parameters,
reflection and transmission properties of Periodic Structures.
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Agenda
Thursday April 21, 2016
1. Questions?
2. HW#12 review by Meinecke,James (Parker) will happen April 28
2.5 Sign up for Oral Final Exam (next week!!) slots on Doodle (see email)
3. Questions about class (laser design) project? Or Class Exam?
4. (More on Directional couplers later!)
5. Solved Coupled Mode Equations to obtain laser thresholds, amplifier parameters,
reflection and transmission properties of Periodic Structures. Now discuss DFB
lasers (index and gain coupling) and DBR lasers.
6. Derivation of Fabry Perot threshold condition.
6. Extension of Coupled Mode Theory to “real” lasers.
7. Coupling coefficients in “real” semiconductor lasers.
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Agenda
Tuesday April 26, 2016
1. Questions?
2. HW#12 review by Meinecke,James (Parker) will happen April 28
3 Sign up for Oral Final Exam (next week!!) slots on Doodle (see email)
4. Homework #13/Final Written Exam must be uploaded to Blackboard no later
than 11 AM on Tuesday May 10, 2016.
3. Questions about class (laser design) project? Or Class Exam?
4. (More on Directional couplers later!)
5. Solved Coupled Mode Equations to obtain laser thresholds, amplifier parameters,
reflection and transmission properties of Periodic Structures. Now discuss DFB
lasers (index and gain coupling) and DBR lasers.
6. Derivation of Fabry Perot threshold condition.
6. Extension of Coupled Mode Theory to “real” lasers.
7. Coupling coefficients in “real” semiconductor lasers.
A Newport Corp Application Notes on semiconductor lasers
B Outline of the Far Field derivation
C Some Overview slides
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Agenda
Thursday April 28, 2016
1. Questions? (Newport Corp Application Notes on semiconductor lasers uploaded)
2. HW#12 review by Meinecke,James (Parker)
3. Homework #13/Final Written Exam must be uploaded to Blackboard no later
than 11 AM on Tuesday May 10, 2016.
4. Questions about class (laser design) project? HW#13 questions next Monday
evening?
5. Coupling coefficients in “real” semiconductor lasers. Ended on page 400.
Questions?
6. Outline of the Far Field derivation
7. SMU projects in Photonics
8. Photodigm DBR slides
9. VCSEL talk about IGA (Franklin Institute)
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EE5336/7336 Homework Assignment #1
Due Wednesday, February 1, 2017
Reminder: At the end of each of the following problems, complete one (or both) of these
sentences: “I think my solution is correct because…” Or “I am not sure my solution is
correct because…”
Problem 4: (20 points) Read the article “The conceptual origins of Maxwell’s
equations and gauge theory,” by Chen Ning Yang, Physics Today 67 (11), 45 (2014);
doi: 10.1063/PT.3.2585. This document is available on Blackboard and can also be
viewed online at http://dx.doi.org/10.1063/PT.3.2585. Write a summary of the
article that focuses on the contributions of people who contributed to what we now
call Maxwell’s equations.
5. In your own words, state the format requirements for homework assignments.
What happens if homework is turned in that does not satisfy the format
requirements?
6.
What percentage of all assignments must be completed and turned in
to pass this course? What percentage of problems must be completed on each
assignment?
EE5336/7336 Homework Assignment #2
Due Wednesday, February 8, 2017
Reminder: At the end of each of the following problems, complete one (or both) of these
sentences: “I think my solution is correct because…” Or “I am not sure my solution is
correct because…”
1.
Derive a wave equation for H using the same assumptions that we used for
deriving a wave equation for E.
2.
Derive equations 22, 23, 24 and 25 on pages 35 and 36 of the course notes.

In class (and in the Fiber Optics Tutorial discussed later) we considered the
sum of the electric field of two plane waves, u1(z,t) and u2(z,t), both traveling in the
positive z direction with slightly different frequencies and propagation constants
and with equal amplitudes. The electric fields of both plane waves are oriented in
the y direction, which means that they have the same “polarization”. The time and
space variation of the two electric fields are given by:
u1(z,t) = cos(t - kz)
u2(z,t) = cos ([ + ]t - [k + k]z)
We will show that the sum of these two waves produce an intensity envelope in time
and space. The velocity of the envelope is called the group velocity.

For this problem, consider the sum of two slightly different waves with similar
electric fields:
v1(z,t) = sin(t - kz)
v2(z,t) = sin([ + ]t - [k + k]z)
Derive analytically (using a procedure similar to that used in class if you want) an
expression for the group and phase velocity for the sum of the two fields.
HINT: sin() + sin() = 2 sin[()/2]cos[()/2]



Problem 4. Choose appropriate values of , , k and k and plot the sum of
v1(z,t) = sin(t - kz) and v2(z,t) = sin([ + ]t - [k + k]z) for a) a fixed value of
time as a function of z; and b) for a fixed value of z as a function of time. You can use
any software that is convenient for you. The plots shown in the previous problem
were done using Excel.
Problem 5. Is the velocity at which information in an electromagnetic wave travels
given by the phase velocity or by the group velocity or by some other velocity? Why?
Does it matter if the information is digital or analogue?
Problem 6. What direction is a wave of the form cos (t + kz) traveling? What is the
phase and group velocity of this wave?
Problem 7. What direction is a wave of the form cos (t - kz) traveling? What is
the phase and group velocity of this wave?
Problem 8. In what situations are the group and phase velocities equal for an
electromagnetic wave?
Extra Credit Assignment #1
Due on or before Tuesday, March 2nd, 2017
Problem 1 (40 points) See the movie Hidden Figures—or read the book. Write a
summary of the movie or the book. If seeing the movie or buying the book
causes a financial hardship, you can submit your receipt to me for the cost of the
movie (which could include the cost of a guest that accompanies you) or the cost
of the book.
This assignment is motivated in part by a recent dinner conversation with friends, one
who works at Apple and another that is now an independent photonics consultant and
business partner—and in part by an anonymous reviewer’s comment of a recent paper
submitted (and now accepted) to the IEEE and OSA Journal of Lightwave Technology.
An important part of the paper dealt with deriving analytic formulas related to gratings in
optical waveguides. This was the reviewer’s comment: “Today it is better to let
computers do the work.”
Write a summary of the movie/book and include your thoughts. You can also comment
on why I wanted to send movie tickets or a copy of the book to the anonymous reviewer.
NOTE: The JLT paper and the response to the reviewers’ comments on the paper
are (will be) posted with the Extra Credit Homework assignment on Canvas.
EE5336/7336 Homework Assignment #3
Due Wednesday, February 15, 2017
1. For a symmetric 3-layer waveguide waveguide with n1 = 3.2, n2 = 3.5 and n3 = 3.2,
what is the maximum thickness W of the waveguide that will insure that only one TE
mode will propagate? Assume wavelengths of a) 0.6 microns, b) 1.0 micron and c)
1.55 microns.
2. For a symmetric 3-layer waveguide waveguide with n1 = 3.45, n2 = 3.6 and n3 =
3.45, what is the minimum thickness W of the waveguide that will allow 10 TE
modes to propagate? Assume the wavelength is a) 0.6 microns, b) 1.0 micron and c)
1.55 microns.
3. Consider an AlGaAs/GaAs/AlGaAs symmetric waveguide. The index of refraction of
the AlGaAs outer layers is 3.4 and the index of the GaAs center layer is 3.6. The half
width W/2 of the middle layer is 3 microns, so the total width of the middle layer is 6
microns. Light with a wavelength of 1.5 microns is coupled into this waveguide. a)
What is the V parameter (Yariv and Yeh’s notation) or “r” value (class note’s notation) of
this waveguide? b) How many TE modes will this waveguide support? How many TM
modes will this waveguide support?
4. (20) Using a program such as Excel or Matlab, plot the graphical solution (see page
114 of Yariv and Yeh) for the normalized transverse wavevectors (δW/2 and sW/2) for
the TE modes of the waveguide in Problem 3 above.
x5. Download WAVEGUIDE III onto your laptop and bring your laptop to both classes
on February 16th and 18th.
EE5336/7336 Homework Assignment #4
Due Wednesday, February 22, 2017
1. (20) From the plot in problem 4 of HW#3, obtain the values of s, δ (delta) and β (beta)
for each allowed TE mode. Plot the transverse Ey field for each allowed mode (see Fig.
3.3, page 115 in Yariv and Yeh) using these values in the appropriate formula (see the
notes or text) for Ey. (Or at least do the plot for the TE0 and TE1 modes)
2. (30) On page 65 of the class notes, equations 9 and 10 can be graphically solved
for the TE modes of a symmetric 3-layer waveguide. Derive the equivalent
equations for the TM modes a symmetric 3-layer waveguide.
3. We require that the tangential components of the field at the boundaries be
continuous. Using the tangential fields calculated for the TE modes in the 3 layer
symmetric waveguide case, show that the boundary conditions on the normal
components of the field are satisfied.
4. Write a summary of the article “On Physics Education in Brazil,” from the
book Surely You're Joking, Mr. Feynman! (Adventures of a Curious Character), by Ralph
Leighton and Edward Hutchings, 1985. This article can be found on Blackboard under
Course Documents or on numerous sites online.
**below this point, the Homework Assignments
reflect what was assigned during the Spring
2016 classes**
EE5336/7336 Homework Assignment #5
Due Wednesday, February 24th, 2016
1. (30) In Problem 3 of Homework Assignment #3, we considered this problem:
Consider an AlGaAs/GaAs/AlGaAs symmetric waveguide. The index of refraction of the
AlGaAs outer layers is 3.4 and the index of the GaAs center layer is 3.6. The half width
W/2 of the middle layer is 3 microns, so the total width of the middle layer is 6 microns.
Light with a wavelength of 1.5 microns is coupled into this waveguide. a) What is the V
parameter (Yariv and Yeh’s notation) or “r” value (class note’s notation) of this
waveguide? b) How many TE modes will this waveguide support? How many TM
modes will this waveguide support? Use Waveguide III to plot Ey for all (up to 10 modes)
bound modes of this structure. Compare the plots obtained using Waveguide III to your
plots obtained in Problem 5 of Homework #3.
2. Plot the effective index neff (neff = β/ko) for each TE and TM mode as a function of the
normalized frequency V (equivalent to “r” in the notes) for the waveguide described in
problem 1 of this assignment. See Fig. 3.4 on page 116 of Yariv and Yeh for an example
of such a plot.
3. Consider a 3 layer waveguide consisting of a layer of SiO2 (n = 1.5), a layer of silicon
(n = 3.5) and a layer of air (n = 1.0). Plot neff as a function of V for the TE and TM
modes of this structure.
4. For the structure in Problem 3, what is the minimum thickness of the center layer for
the structure to guide light at a wavelength of 1.55 microns?
5. Using the sketch shown in Fig. P2, show that the numerical aperture (defined as
(nosino ) is given by
nosino = SQRT(n12 – n32)
assuming that n3 > n2. Hint: apply Snell’s law at the n0-n2 interface and require total
internal reflection at the n2-n3 interface.
Figure P2. Illustration used for calculating the numerical aperture of a waveguide.
EE5336/7336 Homework Assignment #6
Due Wednesday, March 2nd, 2016
1. Consider a 3 layer asymmetric dielectric waveguide (n1 < n3 < n2) that has a cutoff
width T at the operating wavelength of o. Assume that such a long waveguide has a
width of 1.25T and that a short section of the same waveguide, but with a width of
3T/4, is inserted in the middle of the waveguide of width 1.25T. If the radiation is
propagating from left to right, will any radiation make it through the “cutoff”
waveguide section and into waveguide of width 1.25T on the right hand side of the
narrow waveguide section? Explain your answer.
Fig. P1. Waveguide of varying width described in Problem 1.
2. Derive Snell’s law using the principle of least time.
3. Derive Snell’s law by requiring that the tangential electric field be continuous at
the boundary between an interface between two materials that have different
indices of refraction.
4. Read the paper “Wedged plate beam splitter without ghost reflections” and design a
50-50 beam splitter without ghosts in fused quartz that will work at a wavelength of 266
nm. Note: you can assume that on one surface a coating can be used that will reflect
50% of the incoming light and transmit 50% of the incoming light into the fused quartz.
An almost perfect anti-reflect (AR) coating can be used on the output facet. However, no
AR coating is perfect, which is why we have to worry about ghosts. You should be able
to find the (complex) index of refraction of fused quartz on several websites.
EE5336/7336 Homework Assignment #7
(due Wednesday, March 16th, 2016)
1. (50 points) Design a rectangular dielectric waveguide that is single mode in both the x
and y directions (see, for example, page 185 in the course notes). The index of the
rectangular center region n1 is 3.4. The horizontal index steps in the y direction are
limited to a range between 0.005 and 0.03. The vertical index steps in the x direction are
limited to a range of 0.15 to 0.4. You can assume that n2 = n3 and that n4 = n5. Such a
structure is typical of structures fabricated in AlGaAs/GaAs and InGaAsP/InP material
systems to provide an optical waveguide for a laser structure or other optical component.
We want large values of b (the width in the y direction) and d (the width in the x
direction) for several reasons. Note that the wavelengths emitted from AlGaAs/GaAs
lasers are in the 0.7 to 0.9 micron range.
If we are making a laser, the output power is proportional to the volume of the laser, so
making b and d large (for a fixed length L of the laser) allows higher output power. In
addition, for a fixed output power, a larger optical spot size has a lower power density.
The maximum optical output power of a semiconductor laser is limited by
catastrophic optical damage (COD) which occurs at a power density in the 15 to 20
MW/cm2 range. Another reason for large values of b and d is that a large near-field spot
size results in a narrow far-field beam divergence.
If we are making a passive waveguide, it is easier to couple into a waveguide with a
large cross section than a waveguide with a small cross section.
2. Why does a large near-field intensity in a dielectric waveguide result in a narrow farfield?
EE5336/7336 Homework Assignment #8
(due Wednesday, March 23rd, 2016)
1. (25 points) Plot the near-field intensity profiles in the x and y directions for the
waveguide you designed in Problem 1 of HW #7.
2. For the structure you designed in Problem 1 of HW #7, what is the maximum optical
power that your waveguide can handle, considering the COD limits?
3. (25 points) Plot the far-field intensity profiles in the vertical and horizontal directions
for the waveguide you designed in HW#7.
4. (20 pts extra credit) Show the near-fields and far-fields in a 3D plot.
EE5336/7336 Homework Assignment #9
(due Wednesday, March 30th, 2016)
1. (30 points) Reproduce Fig. 3.2, which is shown below:
In the 3 layer symmetric waveguide plot of the effective gain shown in Fig. 3.2,
the center layer has an index of refraction of 3.6 and the outer layers have an
index of 3.5. (See equation (17) on page 236 and equation (20) on page 240 of
the handwritten notes for equations of the effective gain.)
2. Plot a figure similar to that shown in problem 1, but with the center index n1 = 1.5 and
the outer index n2 = 1.0.
3. Plot a figure similar to that shown in problem 1, but with the center index n1 = 3.5 and
the outer index n2 = 1.0.
EE5336/7336 Homework Assignment #10
(due Wednesday, April 6th, 2016)
The 1978 paper “Material Dispersion in Lightguide Glasses” by J. W. Fleming is a
fundamental paper because it showed that “…there is no evidence that a suitable
dopant exists which, when added to a silicate glass, can shift the point of zero
material dispersion to wavelengths in the 0.8 to 1.1 µm range where sources are
currently available.” As a result of the findings of this and other papers, researchers
had to develop semiconductor lasers that emitted at wavelengths in the 1.3 to 1.6
µm range. This paper is available at the Blackboard site for this course. Use Eq. 1 of
the paper to plot n() over the wavelength range of 0.5 to 2.5 µm for glass samples
A, C and D. See the power point slides “Glass Dispersion” for an example of such a
plot. Use any software you want. The plots in the powerpoint slides were made
using Excel.
2. Using Eq. 1 of the same paper, plot dn/d over the wavelength range of 0.5 to 2.5
µm for the glass samples shown in the paper.
3. Using Eq. 1 of the same paper, plot d2n/d2 over the wavelength range of 0.5 to
2.5 µm for the glass samples shown in the paper.
4. Using results from the above problems, plot the group index Ng = n() –  dn/d
over the wavelength range of 0.5 to 2.5 µm for the glass samples shown in the paper.
5. Plot the group velocity (= c/Ng) and the phase velocity (= c/ n()) over the
wavelength range of 0.5 to 2.5 µm for the glass samples shown in the paper.
6. Plot the material dispersion M = - (/c) d2n/d2 over the wavelength range of 0.5
to 2.5 µm for the glass samples shown in the paper.
7. From the definition of M, determine the units.
************************************************************************************
EE5336/7336 Homework Assignment #11
(due Wednesday, April 13th, 2016)
1. (20 pts) Calculate the lateral effective index step of a ridge guide laser. You can use
the index profile of the laser you are designing for your course project. Assume the p and
n clad thicknesses are 1.5 microns thick with a GaAs cap layer that is 0.1 microns thick
with air above. (We won’t bother putting metal on the GaAs cap layer.) The SCH layers
can be 0.15 microns thick. Assume that outside the ridge we etch away the cap layer and
most of the p-clad layer, leaving about 0.1 microns of p-clad above the SCH layer. The
lateral effective index step of a ridge guide laser is the difference between the effective
index calculated for the index profile under the ridge and the effective index calculated in
the region outside the ridge.
2. Give a physical explanation of why the effective index is lower outside the ridge than
under the ridge.
3. (20 points) Calculate lateral effective index step of a CSP laser (see Fig. 4.1 of
CSPbookChapter). You can use the index profiles and layer thicknesses of the channel
and the region outside the channel that are shown in Fig. 4.2 (of CSPbookChapter)
assuming layer 4 is GaAs. MAKE SURE Y = 0.07 (NOT 0.7 as erroneously shown in
Fig. 4.2). Use the thicknesses for layers d2 and d3 shown in Table 4.1 and also in Fig. 4.14
of the CSPbookChapter document.
4. Explain why the effective index of a CSP is lower outside the channel than inside the
channel.
Excerpt from CSPbookChapter:
“4.3. Lateral Optical Confinement
Waveguiding in CSP lasers appears paradoxical at first glance: Based on
intuition for bound modes in dielectric waveguides, we expect that the CSP
geometry has a larger effective index (real part) in the region outside the
channel since a significant portion of the perpendicular field distribution there
"averages in" the high index of the GaAs substrate. In addition, we expect that
the large imaginary component of the effective index outside the channel
region is due to high absorption (because  = 5000-10,000 /cm, at a lasing
wavelength of 0.83 µm [26]) in the GaAs substrate. However, analysis of the
CSP structure shows that
(1) the effective index (real part) is higher inside the channel than outside
(producing a positive index step and corresponding bound lateral modes);
and
(2) the mode loss outside the channel region increases as the substrate absorption
is decreased.”
EE5336/7336 Homework Assignment #12
(due Wednesday, April 27th, 2016)
1. Consider problem 1 of HW#11: 1. (20 pts) Calculate the lateral effective index step
of a ridge guide laser. You can use the index profile of the laser you are designing for
your course project. Assume the p and n clad thicknesses are 1.5 microns thick with a
GaAs cap layer that is 0.1 microns thick with air above. (We won’t bother putting metal
on the GaAs cap layer.) The SCH layers can be 0.15 microns thick. Assume that outside
the ridge we etch away the cap layer and most of the p-clad layer, leaving about 0.1
microns of p-clad above the SCH layer. The lateral effective index step of a ridge guide
laser is the difference between the effective index calculated for the index profile under
the ridge and the effective index calculated in the region outside the ridge.
For the index profile under the ridge in Problem 1 of HW#11, plot Ey, I() and Pz
and find the value of the confinement factor for the quantum well. (Note that this is
closely related to the structure for your Course Project.)
2. For the same ridge structure profile as in Problem 1 above, assume an internal loss i
of 2/cm, a laser length (L) of 500 microns and a mirror reflectivity R1 = 0.1 and R2 =
0.9. Using Eq. 1, what is the required modal gain to obtain threshold?
gth =i + 1/(2L) [ln(1/(R1 * R2)]
(1)
Note: Eq. (1) provides the laser threshold modal gain gth = Ceff*G (which is
approximately QWG), where G is the material gain of the quantum well. (The
definition of threshold is the gain (which is related to current) required for the
onset of lasing.)
3. Using the result of problem 2, what is the required material gain (G) of the
quantum well to obtain threshold?
4. Using the result of Problem 3 and Figure 4.30, what is the current density
required to achieve threshold?
Figure 4.30 is from Diode
Lasers and Photonic
Integrated Circuits, by L.A.
Coldren, S. W. Corzine and
M. L. Masanovic, Wiley,
2012.
5. Using the result of Problem 4, what is the approximate threshold current of the
laser if the width of the ridge is 5 microns? (You can assume that the current
flowing through the quantum well is confined to the same dimension as the ridge
width—however due to current spreading, the width of the current flowing through
the quantum well is likely in the 7 to 10 µm range.)
************************************************************************************
EE5336/7336 Homework Assignment #13/Final Written Exam
(due on or before 11 AM on Tuesday May 10, 2016)
1. (50 pts) Read the articles “The Origin of the Refractive Index,” and “Refractive
Index of Dense Materials,” chapters from Volume I and Volume III of Lectures on
Physics, by Feynman, Sands and Mathews (sent by email and posted on Blackboard).
Summarize the key points of these articles.
2. (50 pts)
a) Derive the following two equations (see class powerpoint slides):
gth = a +
1 æ 1 ö
ln ç
÷
2L è R1R2 ø
and
2 b L = 2p q
b) For a semiconductor laser with a cavity length of 500 microns and an emission
wavelength (free space) of 980 nm and an effective index of the laser designed in
your class project, what is the value of q in the second equation?
c) Derive an equation for the spacing  between adjacent longitudinal modes.
(Hint: solve the second equation above for the genral case of q and q+1.) What is
for the laser in problem b)?
d) Derive an equation for the spacing between the wavelengths  of adjacent
longitudinal modes. (Hint use the result of problem c.) What is for the laser in
problem b)?
e) Derive an equation for the spacing between the frequencies  of adjacent
longitudinal modes. (Hint use the result of problem c.) What is for the laser in
problem b)?
f) The gain of a semiconductor laser is broad by comparison with gas and other
types of lasers. Assume that there is gain from 970 nm to 990 nm for the laser
described in part b) of this problem. Approximate the number of longitudinal
modes of such a laser. (Hint: just divide 20 nm by ) The document
GainSpectrum.pdf has some background on the gain spectrum of diode lasers.
ELECTRICAL ENGINEERING DEPARTMENT
SOUTHERN METHODIST UNIVERSITY
SMU EE 5336/7336
Name:
Integrated Photonics
Midterm
Available: Thursday March 3, 2016
Due: March 25 and April 1, 2016
Student ID:
CERTIFICATION OF TESTING ENVIRONMENT: I certify that I have completed this
test in the time period allotted. The work I am presenting represents my knowledge
of the subject. The time I spent working on this exam was ____ hours. I have
attached ____ pages to this exam.
Signed__________________________ date: ______________________________
TIME: there is no time limit on this exam, except that it must be uploaded to
Blackboard before midnight ON A DATE TO BE DETERMINED. Indicate how long
you took to complete the exam (see above).
CONSTRAINTS: This exam is an open book(s) and open notes exam. Read and sign
the CERTIFICATION OF TESTING ENVIRONMENT
In formulating your response to the questions, clearly explain your approach using
words in complete sentences. All steps should be clearly shown in sequence. There
is no time limit except the due date, so write clearly. If you use WAVEGUIDE II or
other software, include the input files you use with your solutions. Print your name
on each page and number each attached page and state the number of attached
pages on all pages. All parts of the exam must be uploaded as either a single pdf
file or a single WORD file.
QUESTIONS ABOUT THE EXAM: You can email any questions to me at
([email protected]). I can also be reached on my cell phone at 214 207 9427.
1. (45 pts) a) Design either one 3 layer waveguide that supports a) at least one
bound mode, b) at least one “substrate” mode, and c) at least one superstrate
“radiation” mode; OR design three different waveguides, one that supports at least
one bound mode; one that supports at least one “substrate” mode; and one that
supports at least one “radiation” mode.
d) Plot the electric field and near field intensity for at least one of each type of
mode. e) plot the far-field for each mode plotted in d). f) State the values of the
transverse wavevectors in the core and in the layers, the longitudinal wavevectors,
and the free space wavevector for all modes plotted in d). g) What is the effective
index of each mode? h) What angle does the ray corresponding to each mode make
with respect to the normal to the boundary of core-cladding interface? i) calculate
the angles corresponding to total internal reflection at each waveguide boundary
and compare with the angles calculated in h). j) what is the V number for this
waveguide? Note: you can choose the indices of refraction for each layer and you
can choose the wavelength of the light propagating in the waveguide. (March 25,
2016)
2. (10 pts) Consider a three layer symmetric waveguide. In the following cases,
explain if the number of modes increases or decreases as:
a) the width of the waveguide increases
b) the wavelength of the light propagating in the waveguide increases
c) the index difference between the “core” and the “cladding” regions decreases
Does the effective index of the fundamental mode increase or decrease in each of the
three cases above?
I (Gary Evans) think that the best way to answer this question is to look at how the
graphical solutions change in each case. (March 25, 2016)
3. (45 pts) Design a directional coupler that will couple approximately 100% of the
light from one waveguide to another waveguide in a distance Lc of 2 mm or less. The
only constraint is that the minimum value of the electric field for the TE0 mode
between the two waveguides should be 20% or less than the peak value of the
electric field. Plot a) the electric field and b) the near field intensity distribution in
both waveguides at distances of z = 0, Lc/8, L /4, 3Lc/8, Lc /2, 5Lc /8, 3Lc/4, 7Lc/8,
and Lc.
(April 18, 2016)
EE5336/7336 Course Project
(due date: May 2nd, 2016)
Project Title: “Design of a Single Quantum Well Separate Confinement
Heterostructure Semiconductor Laser”
Project: provide an epitaxial design of a ridge-guide Single Quantum Well (SQW)
Separate Confinement Heterostructure (SCH) semiconductor laser emitting at a
wavelength of 0.98 microns. The laser should operate in a single mode in the
vertical direction and in the lateral direction.
A. Determining the epitaxial structure (the x direction)
Assumptions and considerations:
a) An 80 Angstrom InGaAs quantum well surrounded by Al0.15Ga0.85As will result in a
lasing wavelength of 980 nm. The composition of the SCH layers will be
Al0.15Ga0.85As. Assume the index of the InGaAs QW is 3.66.
b) To avoid electrons populating the L and X bands instead of the  band, we will
keep the composition of the p- and n-cladding layers at Al0.3Ga0.7As.
c) Typical p- and n- cladding thicknesses are on the order of 1 micron thick, but
need to be thick enough to not contribute to optical losses (because of radiation
losses into the outer high index GaAs layers) but making the cladding layers thicker
than necessary increases the series resistance of the laser and increases the cost of
materials; note: to make a good electrical contact to the p-side, we need a heavily pdoped GaAs layer above the p-doped AlGaAs p-clad layer. (Why?) In addition, the
epitaxial layers are grown on an n-type GaAs substrate that will also serve as the ncontact material. So we need to have the cladding layers thick enough that the
radiation losses are less than 0.1/cm. (note: optical losses due to inhomogeneities
and interface irregularities along with p- and n- doping losses can add up to about
1/cm.)
d) we would like the vertical far-field beam divergence to be narrow—perhaps in
the 30 to 35 degree range; (note: the far-field beam divergence is proportional to
the Fourier Transform of the near field.)
Items a) through d) provide the information needed to determine the dimensions
and the compositions of the layers of the epitaxial structure of the semiconductor
laser. Note: because the reflectivity of the TE modes are slightly higher than the TM
modes, the threshold for lasing is lower for TE modes. So the modes in the vertical
(x) direction are TE polarized if there is no tensile strain (due to lattice mismatch) in
the quantum well. Since we are using an InGaAs quantum well, there is compressive
strain which also favors TE mode operation.
One possible approach to finding a reasonable epitaxial structure would be to:
i) start with a structure that has the p- and n-cladding layers as the infinite outer
layers with SCH layers about 0.5 microns thick.
ii) calculate the modal gain (related to WZI), the quantum well confinement factor
(GAMMA(3)) and the full width at half power of the vertical near-field and vertical
far-field as a function of the SCH layer thicknesses. (note: vary the thickness of the
SCH layers from 0.5 to 0.0 microns.) Plot all of these parameters as a function of
the SCH layer thicknesses.
iii) choose the thickness of the SCH layers: the amount of gain required for
threshold of the laser is given by
gth =i + 1/(2L) [ln(1/(R1 * R2)]
(1)
Use Eq. (1) to calculate the laser threshold gain for an internal loss i of 2/cm, a
laser length (L) of 500 microns and a mirror reflectivity R1 = 0.1 and R2 = 0.9. Note
that the laser modal threshold gain (see paragraph below) gth = Ceff*G (which is
approximately QWG), where G is the material gain of the quantum well. What is
the required material gain (G) of the quantum well for threshold?
The amount of gain in a quantum well layer generally increases logarithmically with
current density and ranges from about 10/cm to 200/cm. We want to minimize the
threshold current, which we can do by optimizing the thickness of the SCH layers to
achieve a maximum value of the quantum well confinement factor. Hopefully the
far-field beam divergence will be within an acceptable range when the quantum
well confinement factor is near a maximum value. Using Equation (1), calculate the
laser threshold gain (sometimes called modal gain) for an internal loss i of 2/cm, a
laser length (L) of 500 microns and a mirror reflectivity R1 = 0.1 and R2 = 0.9.
iv) choose the thickness of the p- and n-clad layers: add the GaAs p-cap layer and
the GaAs n-substrate layers and start with p- and n-cladding layer thicknesses of
about 2 microns. Plot the losses of the fundamental mode as a function of the
thicknesses of the p- and n-cladding layer thicknesses. Choose a thickness for
the p- and n-clad layers that result in a power loss of 0.1/cm or less.
B. Determining the lateral confinement of a ridge structure (the y direction)
We can now use the effective index approach to make the laser single mode in the
lateral direction. We do this by:
e) calculating the effective index of the epitaxial structure as the cap layer and the
p-cladding layer is etched away. (Provide a plot of the effective index as a
function of the thickness of the p-clad layer.) This plot tells us the lateral index
step on either side of the ridge.
f) determing the ridge width: The minimum thickness of a ridge guide is typically
about 2 microns, depending on how the device is processed. The maximum
thickness is limited by how wide the ridge can be and still have single lateral mode
operation. (The laser power increases with ridge width.) For an
InGaAs/AlGaAs/GaAs laser, the minimum lateral index step is about 0.003 (this is
because when current is injected into the quantum well of the laser, the index of the
quantum well decreases). Another consideration is that the ridge width could
possibly support a TM1 mode in addition to a TM0 mode if the TM1 mode has a very
small lateral index step and a large confinement factor. (Note: from Marcatilli’s
analysis of 2D waveguides using the effective index approach, if the Electric field is
TE polarized in the vertical direction, we should consider the lateral waveguide to
be TM polarized.
From this information, determine the maximum width of the ridge.
In summarizing these calculations, plot the near-fields and far-fields in the vertical
(x) and lateral (y) directions.
C. Determining the threshold current density and threshold current for the
laser
g) From the discussion related to equation 1 and Figure 4.30, what is the current
density required to achieve threshold?
Figure 4.30 is from Diode
Lasers and Photonic
Integrated Circuits, by L.A.
Coldren, S. W. Corzine and
M. L. Masanovic, Wiley,
2012.
h) Using the values of the ridge width and the length of the laser, approximate
threshold current of the laser.
i) Assume an internal quantum efficiency i of 90% and plot the optical output
power as a function of current (often called the L-I curve) for this laser diode design.
7336 Final Oral Exam Groups
Spring 2016
Each group schedules an exam time on doodle.com during the period March 22 to
March 25.
Link to schedule your exam: https://doodle.com/poll/g2s3q7wawgvxbbem
Group A
Dhurgude
Vishal
Hartman
Nicole
Jiang
Sai
Group B
Meinecke,James (Parker)
Sakpal
Sahil
Stevens
Charles
Group C
Wang
Zhan
Williams
Samantha
HW#1, 11
HW#2, 5
HW#3, 4
HW10, 12
HW#6, 13
HW#7
HW#8
HW#9
Oral midterm: Each group should come up with three course topics that
they do not understand, or do not fully undertand. In addition, each group
should come up with three course topics that they believe they fully
understand.
2. After the oral exam, each individual must submit a written report about
the discussion and what concepts were discussed and clarified in the exam.
This report is due one week after the group oral exam.
Oral final:
1. Each group should be prepared to explain basic concepts covered in the
course.
2. After the oral exam, each individual must submit a written report about
the discussion and what concepts were discussed and clarified in the exam.
This report is due one week after the group oral exam.
Oral Exam Rubric
(also applies to in-class group homework discussions and reviews)
1. Concepts
Strong understanding of basic
Some understanding of
concepts and ability to apply
concepts and some ability
concepts to devices and processes. to apply concepts to devices
and processes
2. Technical accuracy
Oral discussion contains few
Oral discussion contains some
numerous
technical errors and
technical errors and some
few misconceptions
misconceptions
3. Clarity
Oral discussion is extremely
coherent and clear
4. Level of detail
Level of detail is
always or almost
always appropriate
Oral discussion contains
technical errors and numerous
misconceptions
Oral discussion is generally
coherent and clear
Oral discussion is at least
somewhat incoherent or unclear
Level of detail is
generally appropriate
Key details are
frequently missing
5. Integration of knowledge
Students incorporate knowledge Students incorporate some
and ideas from class related
knowledge and ideas from
and outside discussions and
class related and outside
readings
readings
Weak understanding of
concepts and/or how to apply
concepts to devices or processes
discussions and readings
Students incorporate little
or no knowledge and ideas
from class related and
outside discussions and