Learning objectives This is an intermediate level course in electromagnetic fields and assumes background in electrostatics, magnetostatics and introductory knowledge in electrodynamics. The main objective is to introduce electromagnetic fields with emphasis on analytical rigour and physical reasoning required for solving problems having direct application. The course will also provide sufficient background to motivate students to take up advanced levels courses such as, electromagnetic scattering, computational electrodynamics, etc. Learning outcomes Upon successful completion, the students will have learned i) the importance of constitutive properties of materials and their use in applications, ii) the effect of boundaries and be able to develop and analyze optical coatings, iii) time dependent formulation of potentials and fields, and fields dues to moving charges, iv) the fundamental ideas in electromagnetic scattering with relevance to applications and v) the concept of waveguides and propagation of guided electromagnetic waves.

**CourseContent:**Maxwell’s equations and wave propagation Maxwell’s equations in general form – wave equation – electromagnetic wave propagation in different media: metals, dielectrics and lossy media – models for complex permittivity: Drude, dipolar relaxation and oscillator models – Hagen-Reuben equation – Kramer-Kronig relations. Electromagnetic waves at boundaries EM waves and interfaces – reflection and refraction of S- and P-polarized waves at interface between free space and different (dispersive, absorbing and conducting) media for normal and oblique incidences – reflectance and transmittance at multiple interfaces – Transfer matrix method – applications to multilayer structures: antireflection coatings, dielectric mirrors and Fabry-Perot etalon. Time dependent potentials and fields Time dependent potential formulation – Gauge transformation – continuous source distribution and retarded potentials – time dependent formulation of Coulomb’s and Biot-Savart Law, Jefimenko’s equations –moving point charge – Lienard-Wiechert potential – field due to a moving point charge. Electromagnetic radiation and scattering Electromagnetic radiation – radiation from oscillating electric and magnetic dipoles – time averaged energy density, pointing vector and radiated power – half wave antenna - classical theory of scattering by an electron - Thomson scattering – scattering due to atoms and molecules – Rayleigh scattering – scattering by collection of charges – X-ray diffraction - Interaction of electromagnetic fields with sub-wavelengths structures and introduction to plasmonics. Guided electromagnetic waves Propagation between parallel conducting plates – guided waves – propagation of TE and TM waves in hollow rectangular waveguides – TEM waves and coaxial transmission lines – standing waves and resonant cavities – spherical cavities and Schumann resonances.

Introduction to electromagnetism, 3rd edition, David J Griffiths, Phi learning pvt ltd, 1999.

2. Electromagnetic Fields, 2nd edition. Roald K. Wangsness, Wiley, 1986.

3. Optical properties of thin solid films, O.S. Heavens, Dover Publications, 1991.

**Reference Books:**1. Principles of optics, 4th edition (reprint), M. Born and E. Wolf, Pergamon, Oxford, 1986.

2. Classical electrodynamics, J.D. Jackson, John_Wiley, New York, 1974. 3. Handbook of optical properties: Thin films for optical coatings, Volume I, Rolf E. Hummel and Karl H. Guenther, CRC Press 1995.

4. Classical electrodynamics, J. Schwinger, Lester L. DeRaad, Jr, Kimball A. Milton and Wu-yang Tsai, West view press, 1998.