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 guides, optical fibers. The study of propagation in free space allows you to dimension your beams precisely, whether to communicate over long distances with satellites, to propagate fast signals in electronic circuits, to communicate at high speed with optical fibers.

• To know the principles of transverse confinement of a wave 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 by a lens and control its propagation (divergence, curvature of the phase plane).
• Know how to dimension the parameters of a waveguide to choose the guiding performances (attenuation, dispersion).
• Understand and know the mechanisms of resonance and stationarity in a longitudinal cavity: spectral transfer function and beam stability.
• Understand the propagation of a wave along a line and the impact of its parameters on transmission performance, component design.
• Know how to use the Smith chart to characterize a propagation or to dimension an impedance adaptation.
• To develop experimental skills in photonics and microwave, in free space or in a guided environment (microwave lines, optical fibers), including resonant cavities.

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
   • Transformation of a Gaussian beam
   • Higher order transverse modes
3. Cavities
   • Gaussian beam in cavity
   • Longitudinal modes
   • Transversal modes
   • Active cavities

1. Guided propagation

1. Introduction
   • Reflection on a metal surface
   • Total reflection between 2 insulators
   • Presentation of waveguide types
2. Microwave waveguide
   • Approach to plane wave guidance, principle of autocoherence
   • Properties of the modes (angle of incidence, cut-off frequencies, phase velocity, group velocity, dispersion, polarization, etc.)
   • Power and attenuation
   • Determination of modes by separation of variables
3. Optical fibers
   • Determination of modes
   • Properties of the modes (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
   • Modeling of a line, propagation equation and its solutions
   • Reflection coefficient, characteristic impedance, standing wave ratio
2. Smith's Abacus
   • Description of the chart
   • Use of 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
   • Dimensioning and optimal power of a coaxial line
5. Strip lines
   • Main types of lines
   • 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 by coupled lines

CM : 33h

TP : 18h