The Aim of the course is threefold: (i) to introduce the student to the theoretical foundations and main applications of Microoptics and Nanooptics; (ii) to provide the student with a set of advanced tools and methods for the design and quantitative description of optical components and devices at the micro and nanoscale; (iii) to give the student the theoretical basis for the understanding of highly innovative topics in modern Photonics.

- Knowledge and understanding (DD1)
• The student understands the physical basis of the optical phenomena taking place at the micro and nanoscale.
• The student knows the guidelines for the modeling and design of micro and nanooptical devices.

- Apply knowledge and understanding (DD2)
• The student is able to retrieve the analytical solution of standard problems in integrated and telecom optics, guided-wave photonics, dielectric periodic media, metal based (plasmonic) nanostructures and metamaterials.
• The student is able to provide a quantitative description of some prototypal optical devices at the micro and nanoscale, with particular attention to the validity limits of the models under consideration.

- Making Judgements (DD3)
• The student is aware of the key functionalities implemented in micro and integrated optics and of the innovative challenges of nanooptics.
• Given a specific optical functionality readily implemented in the market or under development, the student is able to identify the operating principles and evaluate the potential impact of mcro and nanooptic technologies in the field.

- Lifelong learning skills (DD5)
• The student is capable of understanding new trends in the high-tech market (from IT highways, to lab-on-chip and nanomedicine) dealing with advanced photonic structures.
• The student is capable of autonomously learn the operating principles of novel microoptical and nanooptical devices.

1. Introduction to optical communication systems. Historical evolution. Introductory concepts: analog and digital transmission, multiplexing techniques, modulation formats. Layout of an optical communication system: topology, design criteria, integrated optical devices. Analysis of the bit-error-rate as a function of the main noise system sources. Communication systems limited by attenuation and dispersion.

2. Integrated optical devices. Couplers and power splitters in integrated optics. Coupled mode theory. Transfer matrix of the directional coupler. Functional analysis of the directional coupler as a 3-dB coupler, as a frequency filter and as an optical switch. Other types of couplers and beam splitters: the bifurcation, the multimode interference coupler, the star coupler.

3. Optical filters in integrated optics. FIR (Finite Impulse Response) and IIR (Infinite Impulse Response) filters. General spectral properties of filters. Mach-Zehnder interferometer: spectral response and engineering guidelines. The Arrayed Waveguide Grating (AWG): operation principle, transfer function, engineering guidelines. Functional analysis of the AWG as a de/multiplexer, as a router and as a reconfigurable add-drop filter. Ring resonant filter: transfer function and main features.

4. Electro-optic intensity modulators. The electro-optic effect: basic principles. X-cut and Z-cut lithium niobate modulators. Lumped and travelling electrodes. Bandwidth limitations. Integrated optical intensity modulators: architectures (Mach-Zehnder interferometer, directional coupler, deltabeta-reversed directional coupler) and performance. Comparison with bulk modulators.

5. Recent advances in the field of optical communications. DPSK modulation formats: signal to noise ratio and architecture of transmitters and receivers. Coherent detection and digital signal processing for multi-level transmission formats and dispersion compensation. Concluding seminar on fabrication techniques, packaging issues and new technological perspectives.

6. Theoretical Foundations of Nanooptics. Electromagnetism as an eigenvalue problem: electromagnetic harmonic modes, symmetries and classification of harmonic modes. Scaling properties of Maxwell's equations. Wave propagation in homogeneous and inhomogeneous media: angular spectrum representation, TE-TM decomposition, scalar diffraction theories, optical Schroedinger equation.

7. Photonic Crystals. Generalities on periodic lattices. Bloch electromagnetic theorem. Photonic band structure. One-dimensional PCs: periodic layered media, band states and gap states, surface states and bulk defect states. Applications to Bragg reflectors and filters, omnidirectional dielectric mirrors, photonic Bragg fibers. Two-dimensional PCs: a polarization-indepenendent band-gap, point and line defects and application to PC cavities and waveguides, out-of-plane propagation and PC fibers. PC Interfaces: negative refraction and superprism effect.

8. Near-field Optics. Evanescent waves. The diffraction limit to optical imaging. From the far-field to the near-field. Introduction to near-field optical microscopy and applications.

9. Plasmonics. Optical properties of noble metals. Surface Plasmon Polaritons (SPPs): derivation of the SPPs dispersion equation, optical properties of SPPs, excitation and detection of SPPs, plasmon-polaritons in thin metallic films (SR/LR-SPPs). Introduction to plasmonic waveguides. Localized plasmons (LPs): quasistatic theory of localized plasmonic resonances in noble metal nanospheres, optical properties of metallic nanoparticles (resonant polarizability, absorption and scattering cross-sections, field-enhancement, resonance tuning). Introduction to plasmonic nanosensing (SPR and SERS).

10. Metamaterials. Negative dielectric media. Artificial magnetism and materials with negative magnetic permeability (stack of metal cylinders, split ring resonators). Negative refractive index materials (NRM) and the effects of a reversed wave-vector. Surface electromagnetic modes in NRMs and Pendry's Perfect Lens. Experimental evidence of super-lenses with real materials. Introduction to Transformation Optics for the steering of light and cloacking of objects.

No pre-requisites, but the teaching makes use of the basic concepts of Optics and Electromagnetism.

Written examination, optionally followed by an oral examination. The written exam consists of open questions (typically 3 questions to be solved in 2 hours and 15 minutes), aimed at ascertaining:

• the understanding of the physical basis of the optical phenomena at the micro and nanoscale;
• the knowledge of the definitions, theorems and general concepts dealing with optical waveguides, integrated optics telecom components, photonic crystals, plasmonic nanostructures and metamaterials;
• the capability to discuss, both qualitatively and quantitatively, the performance of prototypal micro and nanooptical devices as a function of their key parameters;