ECE 452

• Electromagnetics, Optics and Remote Sensing

https://courses.grainger.illinois.edu/ece452/fa2020/

Electromagnetic waves, polarizations, and applications to photonic and electrooptical devices, metallic and optical waveguides.

To introduce electromagnetic phenomena in different isotropic and anisotropic media and waveguides. Introduce electrooptical phenomena.

• Electromagnetic fields: Maxwell's equations, Poynting's theorem, propagation of a laser pulse, group velocity dispersion
• Reflection and refraction of uniform plane waves, boundary conditions, polarizations, oblique incidence, Brewster angle, critical angle
• Wave propagation in anisotropic media: index ellipsoid, ordinary and extraordinary waves, characteristic polarizations, polaroid and quarter-wave plate
• Waveguide theory: optical dielectric waveguides, optical fibers, coupled mode theory
• Waveguide devices: waveguide couplers, inteferometers, ring resonators
• Electro-optics: Linear and quadratic electro-optical effects, wave propagation in electro-optic crystals
• Electro-optical devices: Electro-optical light modulators, bistable electro-optical devices

Course Outline: Hours (approx.)

1. Electromagnetic fields: Maxwell's equations, Boundary conditions,

Time-harmonic fields and duality principle, Poynting's theorem,

Plane wave solutions, Propagation in isotropic media 5

2. Reflection and refraction of uniform plane waves, boundary conditions,

polarizations, oblique incidence, Brewster angle, critical angle, multilayered

media, matrix optics 8

3. Wave propagation in anisotropic media: index ellipsoid, ordinary and

extraordinary waves, characteristic polarizations, polaroid and quarter-wave

plate, applications 5

4. Waveguide theory: metallic waveguides, optical dielectric waveguides, surface

plasmonic waveguides, optical fibers, numerical aperture, signal attenuation

and dispersion 9

5. Waveguide couplers, coupled-mode theory, coupled waveguides,

directional couplers, optical ring resonators and add-drop filters 6

6. Electro-optics: linear electro-optical effects, wave propagation

in electro-optic crystals, amplitude modulators, phase modulators,

photonic or electro-optical waveguide modulator devices 7

7. Midterm exams 3

TOTAL = 43 hours

Students are encouraged to solve some of the homework problems using computers.

Electromagnetic wave propagation at an intermediate level

Main text: S.L.Chuang, Physics of Photonic Devices, second edition, Wiley, New York, 2009.

Recommended: B. Saleh and M.C. Teich, Fundamentals of Photonics, 2nd ed., Wiley, 2007.

Engineering Science: 2 credits or 67%
Engineering Design: 1 credit or 33%

The goals of this course are to teach advanced concepts in electromagnetics including electromagnetic waves, polarizations, applications to electro-optical devices, and optical waveguides, as well as integrated waveguide-based optoelectronic devices.

A. By the time of Exam I (after 10 lectures, 80 minutes per lecture), the students should be able to do the following:

1. Obtain general solutions to Maxwell's equations given charge and current densities. (1)

2. Obtain general plane wave solutions to Maxwell’s equations in source-free homogenous isotropic and anisotropic media. (1)

3. Derive Poynting's theorem for power conservation in electromagnetic systems. (1)

4. Formulate and calculate plane wave reflection coefficients from a planar boundary between two dielectric media for TE and TM polarizations. Check power conservation for the reflected and transmitted powers. (1)

5. Calculate the Brewster angle and the critical angle for plane wave reflection from a dielectric surface. (1)

6. Derive the propagation-matrix for a multi-layered media. Find the reflection and transmission coefficients for a multi-layered medium. (1)

7. Obtain general solutions for the electromagnetic field including its polarization in uniaxial media. Obtain the index ellipsoid of a uniaxial medium. (1)

8. Derive the dispersion relations (k-surfaces) and polarizations for ordinary and extraordinary waves in uniaxial media. (1)

9. Apply items 7 and 8 to optical components including polaroids and quarter-wave plates. (1)

B. By the time of Exam II (after 20 lectures, 80 minutes per lecture), the students should be able to do all of the items listed under A, plus the following:

10. Find the electromagnetic modes and guidance conditions in metallic waveguides. (1)

11. Find the analytical expressions for the electromagnetic fields and guidance conditions in symmetric dielectric waveguides for TE modes. (1)

12. Calculate the propagation constant and effective index, optical confinement factor for a given guided optical mode in a dielectric waveguide. (1)

13. Do the same as items 11 and 12 above for the TM modes. (1)

14. Find the cutoff conditions, cutoff frequency and general solutions for TE and TM modes in asymmetric dielectric waveguides. (1)

15. Use the ray optics approach to find the guidance conditions in a uniform two-dimensional metallic, dielectric and hybrid (metallic/dielectric) waveguides. (1)

16. Find the guidance condition and general solutions for the modes in surface Plasmon waveguides. (1)

17. Apply coupled-mode theory to calculate power exchange in coupled optical waveguides. (1)

C. By the time of Final Exam (after 27 lectures, 80 minutes per lecture), the students should be able to do all of the items listed under A and B, plus the following:

18. Design and analyze optical ring resonators, optical couplers, and add-drop filters. (1)

19. Calculate the numerical aperture and understand various optical fiber structures including single-mode, multiple-mode, and graded-index fibers. (1)

20. Understand mode classification in step-index optical fibers, the development of the pertinent characteristic equations, and their application for the calculation of number of propagating modes and associated propagation constants. (1)

21. Understand LP modes in step-index optical fibers, the development of the pertinent characteristic equations, and their application for the calculation of number of propagating modes and associated propagation constants. (1)

22. Understand the concepts of group velocity and dispersion (material, modal, waveguide) in waveguides. (1)

23. Calculate dispersion and attenuation in optical waveguides. (1)

24. Understand the source-to-fiber and source-to-waveguide power launching. (1)

25. Be versed on the major scientific discoveries and technical advances that led to today’s state of the art in fiber technology and integrated optics, and their impact on every-day life. (1,3,4)

26. Be interested in and comfortable with applying the concepts and mathematical tools they learned in this course to advance their learning and understanding of optoelectronic devices and systems. (3,4)