University of Illinois at Urbana-Champaign
Department of Electrical and Computer Engineering

ECE 570 – NONLINEAR OPTICS (4 credits)


Course Syllabus

Course Description:

Nonlinear optics allows us to change the color of a light beam, to change its shape in space and time, and to create the shortest events ever made by humans.  Nonlinear optical phenomena are the basis of many components of optical communications systems, optical sensing, biomedical imaging, and materials research.  This course introduces the fundamentals and applications of the nonlinear interaction of radiation with matter.  The goal is to provide a working knowledge of nonlinear effects, nonlinear materials, and the applications of nonlinear optics in various technologies.


Prerequisites:             ECE 520 or consent of the instructor.


Requirements:           ECE major, graduate-level course.



Prof. Yang Zhao

Office Location:

Holonyak Micro and Nanotechnology Lab, Rm 1106

208 N. Wright Street

Urbana, IL 61801

Office Hours: TBD



Lecture:                        This class will meet every Tue & Thu 1:00pm-2:20pm.


Course website:

Zoom Link:

Meeting ID: 829 0405 7587

Password: Send by email


Course Objectives:

This class aims to provide a rigorous introduction to material-light interactions through nonlinear processes mainly using classical optics approaches. We will also study quantum mechanical foundations of nonlinearities. With this fundamental knowledge, I will introduce applications of nonlinear optics for example, in spectroscopy and imaging.


List of Topics:

Several main topics of nonlinear optics will be covered in this course.



I: Second Order Phenomena

  • Second order susceptibility, χ(2)
  • Coupled Wave Equations
  • Phase-matching
  • Susceptibility Tensor
  • Second-harmonic Generation (SHG)
  • Three Wave Mixing
  • Optical Parametric Amplifiers and Oscillators
  • χ(2) Nonlinear Materials


II: Nonlinear Susceptibilities

  • Perturbation Theory of Susceptibilities


III: Third Order Phenomena

  • Third Order Susceptibilities
  • Nonlinear Refraction and Absorption
  • χ(3) Nonlinear Materials
  • Solitons
  • Four-Wave Mixing
  • Mechanisms for NLR & NLA
  • Nonlinear Spectroscopy
  • Stimulated Scattering



There are no required textbooks for this course. Any required readings for a lecture will be posted on the course website as a pdf file. Students who desire supplementary reading for further detail can use the following textbook:


  • “Nonlinear Optics, phenomena, materials and devices”, George & Robert Stegeman, Wiley Series in Pure and Applied Optics, Glenn Boreman, Series editor, 2012.
  • “Nonlinear Optics”, Robert Boyd, Academic Press.
  • “Principles Of Nonlinear Optics”, Yuen-Ron Shen, Wiley-Interscience.



There will be two mid-term exams (open-book, open-notes). The exams will account for 30% of the final grade. There will be no final exam. No use of cell phones, PDAs, digital music players or other personal electronics is allowed in the during exams. Use of electronic devices during an exam may be construed as a violation of the student code of conduct.


Final Presentation/Report:

There will be a final presentation due on the last day of class. The presentation account for 30% of the final grade (the equivalent of one normal final exam). The report will involve writing a review paper on a subject. Several potential subjects will be provided by the instructor. The final few lecture periods of the course will be reserved for in-class student presentation. A one-page topic proposal (worth 5% grade included in the final presentation grade) will be due by 4/15 to ensure that all students will have an individual topic for the project.



There will be 8 homework assignments. You can drop the lowest grade homework, the total homework account for 35% of the final grade.


Contesting Grades:

If you feel that your assignment or exam has been graded inappropriately, you are welcome to contest grades via a written statement within one week of receiving the graded assignment. To contest a grade, you must submit a written statement (preferably via email) of what you believe was graded incorrectly and why the grade should be altered. No oral contesting of grades will be considered, nor will we consider any contest of grades submitted after one week. Note, that contesting a grade means the item in question will be completely regraded, which may result in a lower grade overall.


Final Grade Breakdown:

Exam 1 15 %
Exam 2 15 %
Final presentation/report 30 %
In class/zoom participation 5 %
Homework 1 5 %
Homework 2 5 %
Homework 3 5 %
Homework 4 5 %
Homework 5 5 %
Homework 6 5 %
Homework 7 5 %
Homework 8 5 %
Total 100 %


Course Grading Philosophy:

I. I use the following grade system. Depending on the distribution of points at the end of the semester I may drop the cut-off points slightly (e.g., 85% might become the A cut-off) but I will not raise the cut-offs; I will not “curve” the exams or assignments.

A+             >= 95%

A               90% to <95%

A-             85% to <90%

B+            80% to <85%

B               75% to <80%

B-             70% to <75%

C+            67% to <70%

C              63% to <67%

C-             60% to <63%

D+           57% to <60%

D              53% to <57%

D-             50% to <53%

F               <50%

II. To get the 5% participation*, the student will need to attend for at least 90% of the lectures**.

*Participation of class will account for 5% of the final grade. {Note: if you are located in a different time zone and cannot log in for the lecture at the designated time, please watch the recording within 24 hours, which will count for the ‘in-class’ participation.}

**Students are encouraged to contact the instructor directly to discuss their absence due to illness/medical conditions.


Course Calendar (Spring 2021):

Lecture Date Topic Unit Comments
1 1/26 Introduction
2 1/28 Second Order Susceptibility
3 2/2 Coupled Wave Equations for Generating New Frequencies
4 2/4 Phase Matching
5 2/9 Susceptibility Tensor HW 1 due
6 2/11 High SHG Conversion Efficiency and Nonlinear Modes
7 2/16 Complexities in SHG HW 2 due
8 2/18 QPM SHG Engineering
9 2/23 Three Wave Mixing Processes HW 3 due
10 2/25 Optical Parametric Generators and Oscillators
11 3/2 Exam 1
12 3/4 Nonlinear Materials
13 3/9 Quantum Mechanical Formulation of Susceptibilities HW 4 due
14 3/11 Third Order Susceptibilities and Effects
15 3/16 Nonlinear Absorption (NLA) and Refraction (NLR) HW 5 due
16 3/18 Material Third Order Nonlinearities
17 3/23 Measuring Third Order Nonlinearities HW 6 due
18 3/25 Applications of Nonlinear Refraction I
19 3/30 Applications of Nonlinear Refraction II HW 7 due
20 4/1 Exam 2
21 4/6 Degenerate Three and Four Wave Mixing HW 8 due
22 4/8 Nonlinear Raman Spectroscopy I
4/13 No Class - university day off
23 4/15 Nonlinear Raman Spectroscopy II Proposal due
24 4/20 Stimulated Scattering
25 4/22 Final Project Presentation
26 4/27 Final Project Presentation
27 4/29 Final Project Presentation
28 5/4 Final Project Presentation



Course Policies:

All students are assumed to have read and understood the “Code of Policies and Regulations Applying to All Students,” University of Illinois, and will be expected to act accordingly. The Code is available online at:


Academic Integrity:

According to the Student Code, `It is the responsibility of each student to refrain from infractions of academic integrity, from conduct that may lead to suspicion of such infractions, and from conduct that aids others in such infractions.’ Please know that it is my responsibility as an instructor to uphold the academic integrity policy of the University, which can be found here:


Disabilities and Religious Observances:

Please contact your instructors or TAs during the first week of classes to make requests for disability accommodations or observation of religious holidays.


To obtain disability-related academic adjustments and/or auxiliary aids, students with disabilities must contact the course instructor and the Disability Resources and Educational Services (DRES) as soon as possible. To contact DRES you may visit 1207 S. Oak St., Champaign, call 333-4603 (V/TTY), or e-mail a message to


To obtain waivers for student athlete (cheerleader, marching band, etc.) activities, submit your documentation in person during the first week of class.


Emergency Response Recommendations:

The Department of Homeland Security and the University of Illinois at Urbana-Champaign Office of Campus Emergency Planning recommend the following three responses to any emergency on campus: RUN> HIDE > FIGHT. Please refer to the following websites for more detail: