PHYC/ECE 463: Advanced Optics I

Prof. F. Elohim Becerra
Office: PAÍS 2514
Phone: 505 277-2673

Teaching Assistant
Ahmed Alhassan
Office: PAÍS

Description of the class

This course studies the fundamentals of optics and some applications, and covers diverse topics in geometrical and physical optics. The course addresses the study of electromagnetic theory, fundamental properties of light, waves, Gaussian beams, ray tracing and matrix methods, basic optical elements and devices, image formation, interference, diffraction and topics in modern/advanced optics.

Prerequisites: E&M, Undergraduate Physics, Knowledge of Differential Equations, Linear & Complex Algebra, Matrix representations, Optics.


Tuesday and Thursday, 2:00-3:15 pm PAÍS 1140


There are many useful texbooks that cover the topics on the class.

The course will use the textbook by Frank L. Pedrotti, Leno M. Pedrotti, and Leno S. Pedrotti. We will cover topics from some chapters within Ch1-23, and other additional topics form other resources.

Introduction to Optics (3rd Edition): Frank L. Pedrotti, Leno M. Pedrotti, and Leno S. Pedrotti.

Additional Resources

Homework Assignments

There will be regular assignments of problem sets including problems from the textbook by E. Pedrotti and other exercises, about one set per week. 

The assignments will be given throughout the semester and will be posted in the Tentative Schedule about one week before they are due. Homeworks must be turned in to the TA's mailbox before 5:00 pm on the due date.

Office hours

Office Tuesday 11 am - 12 pm. You may also arrange a meeting for another time via email.

TA office hours: Monday 1-2 pm in the lobby. You may also arrange a meeting for another time via email.


The final grade will be based on the homework assignments, one midterm exam and a final exam. The contribution to the final grade is as follows:

  1. Homework: 20%
  2. Report and presentation 20%
  3. Midterm exam: 25%
  4. Final: 35%

Exam Dates (subject to change):

  • Midterm, October 19.
  • The Final Exam is comprehensive and is scheduled for Thursday, December 7, 10:00 am- 12:00 pm

Formal Reports: You will write a formal report from one topic suggested related to optics covering fundmanteal concepts and applications. You will write the lab report using LaTeX, which is widely used in the scientific community in different areas including physics and engineering. It should follow the format of a scientific paper. Lab reports should be submitted as a word or PDF document by email with the subject “Lab Report". The file name should be your last name followed by the name of the experiment. Lab reports and presentations are individual.

Presentation: You will give a presentation at the end of the semester about the topic in your report (15 minutes+ 5 for questions). It should discuss fundamentals and theoretical background, development in the field, and applications of the subject studied to science and/or technology. Some tipsmore tips.

Suggested topics for the formal report and repsentations are here. You may choose another topic and you should discuss with the instructor about the suitability for an article and presentation.

Syllabus Topics

Below is a tentative list of topics that will be covered. You can find the calendar for the course in the Tentative Schedule

  1. Introduction to optics
    - Overview; optics and fundamental of light; Fermat principle; reflection and refraction; ray and ekional equations.
  2. Geometrical optics
    Image formation and ray tracing; Paraxial optics and basic optical elements (lens, mirrors, etc.); Matrix methods in paraxial optics; Stops and apertures; Aberration theory
  3. Physical optics
    Maxwell Equations, E&M waves and Gaussian beams; Index of refraction, dispersion, and group and phase velocity; Radiometry and photometry; Fresnel equations of reflection and refraction though dielectric interface
  4. Interference
    Superposition of fields; Interference of multiple fields; Interference in multi-layer thin films (matrix formalism); Interferometers
  5. Diffraction theory
    Fraunhofer (far field) diffraction; Diffraction grating; Fresnel (near-field) diffraction; Fresnel plates
  6. Polarization
    Polarization of light; Jones matrix formalism; Polarizers and waveplates; Stokes vectors
  7. Modern and quantum optics
    If time allows, we will discuss some special topics such as Fundamentals; Field quantization and Dirac notation; Quantum properties of states of light

Additional resources

Class overview: Lecture 1

Lasers: Anthony E. Siegman.
Laser Physics
: P. W. Milonni, J. H. Eberly.
Optics, Light and Lasers: (2nd Edition) Dieter Meschede.
Fundamentals of Photonics , 2nd Edition: E. A. Saleh, Malvin Carl Teich.
Optics, 4th Edition: E. Hecht.
Laser Electronics (3rd Edition) by Joseph T. Verdeyen.

Tentative Schedule

Topic Date Subject Reading Homework HW Due Solutions
Introduction to Optics 08/24 (T) Overview, Fermat's principle; Reflection and refraction        
Geometrical Optics 08/26 (Th) Ray Equations, Image formation and Ray tracing Chapter 2 (.0-3) HW1 (Th) Sep 2 HW1sol
  08/31 (T) Paraxial optics, mirrors and lenses (.5-8)      
  09/02 (Th) Matrix methods in paraxial optics Chapter 18 HW2 (Th) Sep 9 HW2sol
  09/07 (T) Paraxial ray equation; GRIN systems        
  09/09 (Th) Optical resonators Chapter 3 HW3 (Th) Sep 16 HW3sol
  09/14(T) Optical resonators        
  09/16(Th) Apertures Chapter 3 HW4 (Th) Sep 23 HW4sol
  09/21(T) Prisms and optical systems        
  09/23(Th) Prisms and optical systems   HW5 (Th) Sep30 HW5sol
Wave Optics 09/28(T) Wave Optics Chapter 4      
  09/30(Th) Field propagation in a dielectric medium Chapter 25 HW6  (Th) Oct07 HW6sol
  10/05(T) Fresnel Equations Chapter 23,25      
  10/07(Th) "   HW7  (Th) Oct21 HW7sol
Interference 10/12(T) Superpositions of fields Chapter 5      
  10/14(Th) Fall Break        
 Formula Sheet MT1 10/19(T) Midterm Formula Sheet MT1      
  10/21(Th) Interference Chapter 7      
  10/26 (T) Interference and Fabry Perot Chapter 8 HW8 (T) Nov 02 HW8sol
  10/28 (Th) " Chapter 8      
Diffraction 11/02 (T) Difraction Chapter 11 HW9 (T) Nov 09 HW9sol
  11/04 (Th) "        
  11/09 (T) Diffraction gratings Chapter 12 HW10 (T) Nov 16 HW10sol
  11/11 (Th) "        
  11/16 (T) Fresnel Difraction Chapter 13 HW11 (T) Nov 23 HW11sol
  11/18 (Th) "        
Polarization 11/23 (T) Polarization: polarization states and Jones matrices Chapter 14-15      
  11/25 (Th) Thanksgiving        
Polarization 11/30 (T) Polarization: polarization states and Jones matrices Chapter 14-15  HW12 (T) Dec 7 HW12sol
  12/02 (Th) Student Presentations        
Polarization 12/07 (T) Student Presentations        
  12/11 (Th)  "        
  12/14 (T) FINAL 10 am Formula Sheet Final      
  12/16 (Th) Report DUE via email