Free and Guided Propagation

In order to use electromagnetic 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 free-space propagation allows you to accurately design your beams, whether for long-distance communication via satellites, for transmitting high-speed signals in electronic circuits, or for high-speed communication via optical fibers.

• Understand the principles of transverse wave confinement and the associated guidance mechanisms (reflection, coherence, dispersion).
• Be able to determine the transverse profile of a mode in free space or in a guided medium.
• Understand how to transform a Gaussian beam using a lens and control its propagation (divergence, curvature of the phase plane).
• Know how to determine the dimensions of a waveguide to select the desired guidance performance (attenuation, dispersion).
• Understanding and analyzing the mechanisms of resonance and stationarity in a longitudinal cavity: spectral transfer function and beam stability.
• Understand how a wave propagates along a line and the impact of its parameters on transmission performance and component design.
• Know how to use Smith's chart to characterize a transmission line or design an impedance matching network.
• Develop experimental skills in photonics and microwave technology, in free space or guided media (microwave lines, optical fibers), particularly involving resonant cavities.

Understanding of waves, understanding 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 lab exam (30%)

1. Free Propagation & Cavities
2. Free distribution
   • Paraxial propagation equation
   • Gaussian solution
   • Transformation of a Gaussian beam
   • Higher-order transverse modes
3. Cavities
   • Gaussian beam in a cavity
   • Longitudinal modes
   • Cross-functional modes
   • Active cavities

1. Guided propagation

1. Introduction
   • Reflection off a metal surface
   • Total reflection between two insulating materials
   • Overview of Waveguide Types
2. Microwave Waveguide
   • An Approach to Plane-Wave Guidance: The Principle of Autocohérence
   • Mode properties (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, and guiding)
   • Guided, radial, and leakage modes
   • Other types of optical waveguides (planar waveguides, structured fibers)

III. Propagation along a line

1. Reminders
   • Modeling a Line, the 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 Cables
   • Primary and Secondary Parameters of a Coaxial Cable
   • Coaxial Cable Sizing and Optimal Power Rating
5. Striped lines
   • Main Types of Lines
   • Microstrip Line (Effective Permittivity, Characteristic Impedance, Sizing, Attenuation)

Practical Exercises

1. Optical & Microwave Metrology
2. Optical & Microwave Cavities
3. Gaussian Beams
4. OTDR & Optical Fiber
5. Microwave Lines
6. Microwave Filters Using Coupled Lines

CM: 33 hours

Practical Training: 6:00 p.m.