Applied Optics

At the beginning of this course unit, we will review, on the one hand, the concepts of light rays and the conditions for the approximation of geometric optics and, on the other hand, the concepts in wave physics that are important for physical optics.

Then, starting with the scalar approximation of light waves—a special case of electromagnetic waves—we will describe light sources, interference phenomena involving two waves and N waves, and then diffraction in the Fraunhofer approximation.

We will continue by studying various widely used physical systems, focusing on their resolving power and applications: the microscope, the telescope, the Michelson interferometer, the diffraction grating spectrometer, and the Fabry-Pérot interferometer.

Finally, we will conclude with the concepts of spatial and temporal coherence of light sources and their applications (stellar interferometry, speckle, etc.)

By the end of this course unit, students will have acquired various types of knowledge:

• Understand the theoretical frameworks for studying the most common optical phenomena
• be able to describe a light source and its physical properties
• Calculate and physically describe the interference and diffraction patterns obtained for the most commonly used devices (Young's slits, gratings, rectangular slits, circular slits, etc.)
• Understand the similarities and differences between wave phenomena and wave optics phenomena
• Determine the resolving power of the most commonly used optical systems (imaging, spectrometry, etc.)

This course is intended for students who have already completed their second year of university-level study. Students enrolling in this course must have a solid grasp of the following mathematical concepts: trigonometric functions, complex numbers (real part, imaginary part, modulus, and argument), scalar and vector products, functions of several variables, derivatives, partial derivatives, integrals, first-order series expansions, and differential equations.

These students must have completed a course in geometric optics and wave physics in order to be familiar with the conjugation formulas and concepts related to wave phenomena, particularly the conditions for constructive and destructive interference and phase differences.

Recommended prerequisites*:

This course is intended for students who have already completed their second year of university-level study. Students enrolling in this course must have a solid grasp of the following mathematical concepts: trigonometric functions, complex numbers (real part, imaginary part, modulus, and argument), scalar and vector products, functions of several variables, derivatives, partial derivatives, antiderivatives, first-order series expansions, and differential equations.

These students must also master the concepts and skills related to oscillators, waves, and geometric optics.

25% 2CC 75% CT

- Review of waves (general concepts, standing waves, and the concept of interference)

- Framework for the Study of Wave Optics: The Scalar Approximation

- Two-wave interference: conditions for its occurrence and an initial analysis.

- N-wave interference: the case of a grating (grating formula, N-wave interference pattern, resolving power)

- Interference and diffraction: Huygens' principle, Fraunhofer diffraction

- Interference and diffraction

- Real light sources: temporal coherence and spatial coherence

- The Michelson interferometer: a famous two-wave interferometer.

- The Fabry-Pérot interferometer, another example of N-wave interference in optics

- Optical systems and instruments: applications of diffraction and interference

- Introduction to Fourier Optics

CM: 6:00 p.m.

TD: 6:00 p.m.