* Discipline "Matrix laser optics" refers to a series of mathematical and natural sciences for masters and based on the knowledge that students have learned in obtaining educational qualification of Bachelor, namely, descriptive geometry, engineering and computer graphics, mathematics , physics, strenght of materials, theory of mechanisms and machines, machine parts, electrical engineering and electronics, fundamentals of scientific research and technical creativity, hydraulic and pneumatic drives, interchangeability and standardization and measurement technology, basic of heat theory, electrophysical and electrochemical methods of materials processing, laser physics, simulation and optimization of objects and systems, laser process equipment and optical systems of laser technological equipment.** Discipline "Matrix Laser Optics" completes theoretical and practical training of future specialists in the field of optical systems in general and laser systems in particular.*

**Contents of the discipline**

Theme 1. The purpose and objectives of the course. Key points and theories. Concepts about matrices and determinants, mathematical actions on them.

1. The concept of the matrix. Zero, single, diagonal and transposed matrices.

2. Actions on matrices: adding, subtracting, multiplying, multiplying, dividing, and rotating matrices.

3. Definition of matrices. Bringing matrices to a diagonal look.

Theme 2. Matrix methods in paraxial optics.

1. The matrix of ray transformation by Kogelnik. Moving and refracting matrices. Fine lens.

2. The transformation matrix for the optical system. Tasks illustrating the matrix approach.

3. Location of the cardinal points of the optical system. Examples of tasks.

4. Transformation of rays in reflective optical systems.

Theme 3. Matrix description of the electromagnetic waves propagation process.

1. Summarize the results for the systems that generate the image.

2. Description of the propagation of waves. ABCD rule. Examples of the ABCD rule.

3. Resolution, the ethanum and the principle of uncertainty.

Theme 4. Matrix description of the optical resonator.

1. Matrix description of optical laser resonator.

2. Differences between stable and unstable resonators.

Topic 5. Laws of the propagation of laser beams.

1. Flat and spherical waves. Gaussian beams.

2. Description of the distribution of Gaussian beams through an optical system. Complex beam parameter.

3. Calculation of parameters of a laser beam.

4. Use the ABCD rule to match the mod.

Theme 6. Matrix description of radiation polarization.

1. Methods of reception and analysis of radiation polarization.

2. Using the Stokes and Müller matrices.

Theme 7. Description of light propagation in crystals.

1. Transactions over vectors in a matrix form. Dielectric properties of anisotropic medium.

2. The propagation of waves in a homogeneous anisotropic crystal.

Theme 8. Results of the use of matrix description of geometrical optics in calculations of laser optical systems.