Free & Guided Propagations

In order to use waves, it is essential to understand how they propagate, whether in free space or in guided media such as microwave lines and waveguides, or optical fibers. Studying propagation in free space allows you to accurately size your beams, whether for long-distance communication with satellites, for propagating fast signals in electronic circuits, or for high-speed communication with optical fibers.

• Understand the principles of transverse wave confinement and the associated guiding mechanisms (reflection, coherence, dispersion).
• Know how to 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 the parameters of a waveguide in order to select the guiding performance (attenuation, dispersion).
• Understanding and knowing the mechanisms of resonance and stationarity in a longitudinal cavity: spectral transfer function and beam stability.
• Understanding wave propagation along a line and the impact of its parameters on transmission performance and component design.
• Know how to use Smith charts to characterize propagation or size impedance matching.
• Develop experimental skills in photonics and microwave frequencies, in free space or in guided media (microwave lines, optical fibers), particularly with resonant cavities.

Knowledge of waves, knowledge of diffraction and interference, basic knowledge of propagation in an electrical transmission line (telegraph 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
   • Transformation of 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 two insulators
   • Presentation of waveguide types
2. Microwave waveguide
   • Approach to plane wave guidance, principle of autocohérence
   • Properties of modes (angle of incidence, cutoff frequencies, phase velocity, group velocity, dispersion, polarization, etc.)
   • Power and attenuation
   • Determination of modes by separation of variables
3. Optical fibers
   • Determination of modes
   • Mode properties (transverse field distribution, polarization, effective index)
   • Dispersion in optical fibers (material, modal, guiding)
   • Guided, radiated, and leakage modes
   • Other types of optical guides (planar guides, structured fibers)

III. Propagation along a line

1. Reminders
   • Line modeling, propagation equation, and its solutions
   • Reflection coefficient, characteristic impedance, standing wave ratio
2. Smith's abacus
   • Description of the abacus
   • Using the abacus
3. Lines with losses
   • Skin effect, propagation parameter, characteristic impedance
   • Voltage, current, impedance, reflection coefficient, power 
4. Coaxial lines
   • Primary and secondary parameters of a coaxial line
   • Dimensioning and optimal power of a coaxial line
5. Strip lines
   • Main types of lines
   • Microstrip line (effective permittivity, characteristic impedance, dimensioning, attenuation)

Practical work

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

CM: 33 hours

Practical work: 6 p.m.