Physics, Electromagnetic fields.

The goal of these lectures is to introduce the topic of electromagnetic wave interaction with artificial electromagnetic structures (composites, metamaterials and photonic crystals) to engineering students. After explaining the physical foundations the commonly used electromagnetic structures are described and the devices, which utilizes artificial structures are presented. The classes cover the topics required from electromagnetism to develop the theory and presents engineering design methodologies of devices based on artificial structures.

1. The Microscopic Maxwell Equations. The wave equation and gauge theory. Retarded potentials. The sources of the electromagnetic waves.

2. Radiation of electric and magnetic dipoles. The ratio of the radiated powers from electric and magnetic dipoles. The matter modelled as a superposition of radiating dipoles. Magnetic precession in homogeneous magnetic field. The characteristic time of the magnetic precession and why there are no magnetic materials at optical frequencies.

3. The frequency dependence of the electromagnetic material parameters. The electric permittivity of dielectric materials. The electric permittivity of metals. The variation of material parameters at nanometer scale. The properties of anisotropic materials.

4. The transmission and reflection of electromagnetic waves through thin films.

5. The basics of plasmonics. Phenomena at the interface of metal-dielectric structures. Layered structures:  dielectric-metallic-dielectric and metallic-dielectric-metallic structures. Plasmonic waveguides and sensors.

6. Artificial structures in computational electromagnetism. The concept of the perfectly matched layers and utilization as absorbing boundary condition in the Finite Difference Time Domain method.

7. The scattering of the electromagnetic waves from nanoparticles with arbitrary shape. Scattering from spherical particles. Nanoantennas.

8. Composite materials. The Maxwell Garnett and the Brugemann mixing rules.

9. Periodic structures for radio frequencies and microwaves. Frequency selective surfaces. Perfect electric Conducting and Perfect Magnetic Conducting surfaces.

10. Metamaterials. The concept of negative refraction and negative index. Interaction of electromagnetic waves with a negative index media. The homogenization of metamaterials. Design of the electric permittivity with periodic metallic nanowires. The electric permittivity of nanostructures. Magnetism at optical frequencies. The permeability of resonant metallic structures. The split ring resonator and fishnet metamaterials. The application of metamaterials for sub-diffraction imaging, electromagnetic cloaking anmd unconventional lithography.

11. Photonic crystals. The Bragg diffraction. Analytic computation of band structures of one dimensional photonic crystals. Forbidden bands. Two and three dimensional photonic crystals. Dispersion equations. Numerical methods to calculate band structure. Application of the photonic crystals: cavities and waveguides.

12. Outlook: integration of optical, plasmonic and electronic devices.

Lessons with computer demonstrations and exercises.

a. During the semester each student will receive a customized problem, which is required to be solved for the final exam. To qualify for the final exam signature at the end of classes must be obtained. The signature is obtained based on the presentation of a scientific paper related to composites, metamaterials or photonic crystals.

b. Final exam: solution of the problem and oral presentation.

There is no pre-examination.

The presentation can be completed during the last week of the semester.

Consultation during formal office hours, after lectures and anytime you can catch me.

1. D. J. Griffiths, Introduction to Electrodynamics, Third Edition, Pearson, Addison Wesly, 1999.

2. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley-VCH Verlag GmbH & Co. KGaA, 2004.

3. A. Sihvola, Electromagnetic Mixing Formulae and Applications, The Institution of Engineering and Technology, 2000.

4. B. Munk, Frequency Selective Surfaces: Theory and Design, John Willey & Sons, 2000.

5. L. Solymár and E. Shamonina, Waves in Metamaterials. Oxford, University Press, 2009.

6. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals, Molding the Flow of Light, Second Edition, Princeton University Press, 2008.