Electromagnetic Metamaterials and Its Applications

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.