Free & Guided Propagation

In order to be able to use waves, it is essential to understand how they propagate, whether in free space or in guided media such as microwave lines and guides, optical fibers. The study of free-space propagation allows you to precisely size your beams, whether to communicate over long distances with satellites, to propagate fast signals in electronic circuits, or to communicate at high speeds with optical fibers.

• Know the principles of transverse wave confinement and the associated guiding mechanisms (reflection, coherence, dispersion).
• Determine the transverse profile of a mode in free space or in a guided medium.
• Know how to transform a Gaussian beam using a lens and control its propagation (divergence, phase plane curvature).
• Know how to dimension waveguide parameters to select guiding performance (attenuation, dispersion).
• Understand and understand resonance and stationarity mechanisms in a longitudinal cavity: spectral transfer function and beam stability.
• Understand wave propagation along a line and the impact of its parameters on transmission performance and component design.
• Know how to use the Smith chart to characterize propagation or size an impedance match.
• Develop experimental skills in photonics and microwaves, in free space or in guided media (microwave lines, optical fibers), with resonant cavities in particular.

Knowledge of waves, knowledge of diffraction and interference, basic knowledge of propagation in an electrical transmission line (telegrapher's equation).

Recommended prerequisites* :

Basic knowledge of electromagnetism and geometric optics.

Final exam (70%) and practical exam (30%)

1. Free propagation & cavities
2. Free propagation
   • Paraxial propagation equation
   • Gaussian solution
   • Transforming a Gaussian beam
   • Higher-order transverse modes
3. Cavities
   • Gaussian beam in cavity
   • Longitudinal modes
   • Transverse modes
   • Active cavities

1. Guided propagation

1. Introduction
   • Reflection on a metal surface
   • Total reflection between 2 insulators
   • Overview of waveguide types
2. Microwave waveguide
   • Planar wave guidance approach, self-coherence principle
   • Mode properties (angle of incidence, cutoff frequencies, phase velocity, group velocity, dispersion, polarization, etc.)
   • Power and attenuation
   • Determining modes by separating variables
3. Optical fibers
   • Determining modes
   • Mode properties (transverse field distribution, polarization, effective index)
   • Dispersion in optical fibers (material, modal, guiding)
   • Guided, radiated and leaky modes
   • Other types of optical guides (planar guides, structured fibers)

III. Propagation along a line

1. Reminders
   • Line modeling, propagation equation and solutions
   • Reflection coefficient, characteristic impedance, standing wave ratio
2. Smith chart
   • Description of the abacus
   • Using the abacus
3. Lossy lines
   • Skin effect, propagation parameter, characteristic impedance
   • Voltage, current, impedance, reflection coefficient, power 
4. Coaxial lines
   • Primary and secondary parameters of a coaxial line
   • Coaxial line sizing and optimum power ratings
5. Strip lines
   • Main line types
   • Microstrip line (effective permittivity, characteristic impedance, sizing, attenuation)

Practical work

1. Optical & Microwave Metrology
2. Optical & Microwave Cavities
3. Gaussian beams
4. OTDR & Fiber optics
5. Microwave lines
6. Microwave filters using coupled lines

CM: 33h

Practical work: 18h