Fundamentals of plane wave propagation, reflection, and transmission; basic theorems, equivalent currents, and Green's theory; radiation fields generated by current sources.

The topics covered in this course are fundamental for graduate students in the area of electromagnetics. This course builds upon undergraduate electromagnetic courses and enables the students to gain an in-depth understanding of fundamental electromagnetic concepts, theorems, and analytical techniques. The course also provides an introduction to numerical techniques that are becoming increasingly important in solving electromagnetic wave problems in complex geometries. Many topics covered in this course are essential for graduate courses in areas such as radio frequency and microwave engineering, antennas, photonics, and space sciences.

Graduate Standing

- Use Maxwell's equations to determine basic properties of plane waves, including direction of propagation, polarization, phase velocity, group velocity, and energy transport.
- Compute the reflection and transmission of a plane wave at a planar interface.
- Apply the basic theorems of electromagnetics to analyze problems of electromagnetic waves interacting with inhomogeneous materials or structures.
- Apply the concepts of equivalent current and Green's theory to analyze electromagnetic problems.
- Evaluate electromagnetic fields generated by ideal current distributions and demonstrate the ability to determine near field zone, Fresnel zone, and far field zone.

## Topic |
## Percentage of Course |

1. Maxwell's Equations and Plane Wave Solutions: a) Differential and integral forms, boundary conditions; b) Constitutive relations and material properties; c) General form of the uniform and non-uniform plane wave solutions; d) Polarization, Poynting vector, direction of propagation, and energy considerations; e) Phase velocity and group velocity | 20% |

2. Reflection and transmission of plane waves by planar boundaries: a) Decomposition into TE and TM polarization; b) Applying the boundary conditions, Snell's laws; c) Total internal reflection and evanescent waves; d) Fresnel reflection and transmission coefficients, energy considerations; e) Applications | 20% |

3. Basic electromagnetics theorems: a) Duality; b) Reciprocity; c) Uniqueness & image theory; d) Equivalence theory | 20% |

4. Application of EM theorems: a) Construction of equivalent sources and applications; b) Green's theory; c) Dyadic Green's functions | 20% |

5. Radiation by sources: a) Current to potential to fields; b) Deriving the free space Green function; c) Solution for radiation by an elemental dipole; d) Zones of radiation and behavior of the fields; e) Behavior of the far and Fresnel zone fields | 20% |

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