Topics requested for admission to the doctoral study PE-LPP

Physical engineering - department of laser physics and photonics (laser physics and photonics specialization)

Filed: ELECTRODYNAMICS

  1. The electromagnetic field in a homogeneous environment. Macroscopic Maxwell's equations, vector and scalar potential, Hertz vectors. Charge density and current continuity equation.
  2. Gauss and Stokes theorem. Physical meaning of divergence and rotation operators. Orthogonal curvilinear coordinates, cylindrical and spherical coordinates.
  3. Laplace and Helmholtz equation. Emission of electromagnetic fields from time harmonically variable system sources. The general time dependence - retarded potentials.
  4. Radiation of elemental time harmonic electric and magnetic dipole.
  5. Far field characteristics of radiation from time harmonic generally distributed sources.
  6. Plane electromagnetic waves in homogeneous isotropic medium. Plane waves
  7. complex wave vector - uniform and non-uniform wave. The flow of energy and energy conservation law.
  8. Spherical wave.Solution of homogeneous scalar Helmholtz equation in spherical coordinates.
  9. Legendre polynomials and Legendre functions, spherical harmonics. Spherical Bessel functions.
  10. Electromagnetic waves in spherical coordinates.
  11. Cavity resonator. Eigen modes, eigen frequencies. Energy field in the resonator. Resonator quality factor, complex resonance frequency.
  12. The electromagnetic radiation propagation in waveguides. Perfectly conductive walls. Concept of waveguide mode. TE and TM modes in a metal waveguide.
  13. Propagation of optical radiation in the multimode optical fibers. Types of optical fibers.
  14. Numerical aperture, V-parameter, led and flowing modes.

Field: QUANTUM ELECTRONICS AND LASERS

  1. Description of quantum systems using the Dirac formalism, the wave function and abstract state vectors, basic axioms of quantum theory, probabilistic interpretation, Hermitian linear operators, basic operator algebra eigenvalue problem and eigenvalues, discrete and continuous spectrum, Heisenberg uncertainty principle.
  2. Statistical operator and its properties, examples: statistical operator of two level system,
  3. Bloch vector, the statistical operator of system in a state in thermodynamic equilibrium, coherent
  4. state, ideal laser. Quantum Liouville equation. Measurements on pure and mixed states.
  5. Reduced statistical operator.
  6. The dynamic development of quantum systems. Evolution operator, Schrödinger, Heisenberg and Dirac (interaction) formalism describing the development. Heisenberg equation, Schrödinger equation in the interaction picture.
  7. The quantum linear harmonic oscillator. Creation and annihilation operators, quantum number operator, arrangement of boson operators.
  8. Quantization of the electromagnetic field. The operator of the number of photons of quantum electrodynamics, the Casimir effect, Fock and coherent states of electromagnetic fields and their properties. Single mode and multimodal description.
  9. Hamiltonian atom and charged particles in the electromagnetic field, relativistic approach.
  10. Interaction Hamiltonians.
  11. Matter as a set of quantum systems. Energy levels. Quantum transitions. Population energy levels. The interaction of radiation with matter. Spontaneous and stimulated emission. Einstein coefficients. Stimulation of active environment. Gain. Gain factor, the threshold condition for generation. The dynamics of operation of the laser - rate equations.
  12. Open resonators. Elements of open resonators. Basic characteristics and use. Losses in the open resonator. Fresnel number and quality factor of the resonator. Electromagnetic distribution. field in the optical resonator. Resonator optical modes. Stability. Stable and unstable resonators. Longitudinal and transverse modes, transverse and longitudinal modes selection methods. Gauss beam as an application of the basic transverse mode. ABCD method. M2 factor to describe laser beam, description and propagation of general beams. The radius and divergence general beams.
  13. Types of lasers. Solid state lasers - the matrix and the activator, the group of transition elements and lanthanides, and the second matrix of their characteristics, lasers using stimulated Raman scattering, harmonic generation of the second, up-conversion lasers, the principle of optical parametric amplification and generation. dye lasers. Excitation methods, active medium excitation, linear and coaxial configuration. Semiconductor lasers. Spectral and spatial properties of the semiconductor laser light, the configuration of high-performance semiconductor lasers, VECSEL lasers. Gas, plasma and X-ray lasers. Amplified spontaneous emission. Laser without mirrors. Metal vapor lasers. Ion lasers. X-ray (XUV) lasers. Free electron laser (FEL). Excimer lasers. Chemical excitation of lasers. Gas dynamics lasers.
  14. Methods for generating laser pulses. Modes of generation. Free-running mode. Q-switching, mode locking.
  15. Ultrashort pulses (UKP) UKP characteristics, Gaussian chirped pulse, femtosecond pulses.
  16. Measurement UKP. Autocorrelation, FROG and SPIDER.
  17. Use of dispersion and its compensation. Shaping the laser pulses, methods of UKP amplification.

Field: OPTICS

  1. Wave and Helmholtz equation. The optical medium having a dielectric constant and conductivity. Helmoltz paraxial wave equation - spherical parabolic wave, Gaussian beams.
  2. Energy in the optical wave, both planar progressive and standing. Real and complex Poynting
  3. vector, light intensity.
  4. Concepts of successive planar optical wave: Wave vector, the complex refractive index, the TEM field and polarization, characteristic admittance of medium, phase and group velocity.
  5. Elementary electric dipole and Rayleigh scattering. Emission distribution of elemental
  6. dipole in light field. Application to Rayleigh scattering.
  7. Boundary condition for light transition between two homogenous environments. Snell's law and Fresnel formula, applications of total internal reflection of light. Stokes relations of reciprocity.
  8. Statistics in light optics. Spatial and temporal coherence, the observed intensity structure, coherence parameters (length, width). Impact on coherent and incoherent tracking of the physical parameters of a device (e.g. interferometers, etc.).
  9. Dual-light interference.The interference structure, interference vector, the period of interference fringes, interferometers.
  10. Multiple wavelength interference. Fabry-Perot interferometer, a general dielectric layer, multiple layers and their applications.
  11. Scalar diffraction theory. Basic scalar diffraction theory, the transition to scalar theory, Huygens principle, Fresnel, Kirchhoff and Sommerfeld approach to derive the diffraction integral.
  12. Fresnel and Fraunhofer diffraction, Fresnel and Fraunhofer approach to scalar
  13. diffraction integrals, approximation limits, basic examples, analytical and numerical calculations of diffraction and graphic interpretation.
  14. Thin diffraction grating. Classification of diffraction gratings, approaches to describe thin diffraction grating, the grating equation and its interpretation, the diffraction efficiency of thin grids, spatial restrictions thin grid, examples of thin grids.
  15. Holography. Fundamentals of holography, recording and reconstruction of holograms, transmission and reflectance holograms, copy holograms.
  16. Nonlinear optics. Nonlinear susceptibility concept, Helmoltz coupled-wave equations,
  17. conservation laws.
  18. Nonlinear phenomena. (E.g. generation of higher harmonics, parametric oscillator, phase conjugation, soliton).
  19. Approximation of physical optics geometrical optics, what beam is, eikonal equation postulates and historical form of geometrical optics. Basic points and planes of imaging system in the ideal view, focal and afocal system.

Field: COMPUTATIONAL PHYSICS METHODS

  1. Programming languages ​​used in physics. Compilers, debugging, operation systems.
  2. Numerical Library. Library programs for physics.
  3. Programs for scientific visualization. Virtual reality.
  4. Numerical methods for solving physical models. Finite differences, finite volumes and finite elements.
  5. Fluid models. Hydrodynamics of fluids, Eulerian, Lagrangian and ALE methods.
  6. Kinetic models. Vlasov equation.
  7. Methods for solving Maxwell's equations. Finite difference in time domain.
  8. Parallel computing. MPI, PVM, Cuda, resources for intensive computing.
  9. Integrated Computer Systems. Computer algebra.
  10. Monte Carlo method in statistical physics. Metropolis algorithm.
  11. Neural networks and genetic algorithms. Physical applications.
  12. Expert systems. Possible applications in physics.
  13. Techniques for presentation and publication of scientific documents. Creating Web documents with mathematical text.
  14. Scientific databases. Search and evaluation of scientific information, impact factor, h-index, citation analysis.

Field: NUMERICAL METHODS

  1. Correctness and compliance tasks. Numerical stability, rounding errors representation of real numbers in the computer, the rounding error in arithmetic operations, error and order accuracy numerical methods.
  2. Iterative and gradient methods for solving linear equations. Gauss-Seidel and superrelaxation method, convergence conditions, sparse matrices and methods for solving a sparse matrix, the system with triagonal matrix.
  3. Solving nonlinear equations in one or more dimensions. Method, and without the use of derivatives, Newton-Raphson method.
  4. Numerical solution of ordinary differential equations with initial condition, Runge-Kutta methods, stability of the solution of ordinary differential equations.
  5. Numerical solution of ordinary differential equations with boundary condition, method shooting method, moving boundary conditions, finite difference method.
  6. The basic difference schemes for solving advection equation. Their properties.
  7. Convergence, consistency, stability, conditionality PDR, Lax-Richtmyer sentence.
  8. Explicit and implicit difference scheme, Courant-Friedrichs-Lewy condition.
  9. The difference scheme stability, Fourier method, von Neumann stability condition, PDR for stability with variable coefficients, multistep scheme, PDR system.
  10. Draft difference scheme, Order accuracy, derive the Lax-Wendroffova scheme.
  11. Parabolic equation, Conditionality differential scheme for solving the heat conduction equation.
  12. Numerical solution of boundary value problems for parabolic PDR. Method of lines.
  13. Elliptic equations. Laplace equation, Poisson equation, integrability condition, boundary conditions, maximum principle.
  14. Numerical solution of boundary value problems for elliptic PDR, Convergence, estimation errors.
  15. Conservation laws. Types of waves, weak solutions, integral and differential form.
  16. Difference schemes for conservation laws. Conservatibility, Riemann problem.
  17. Rankine-Hugoniot condition for conservation laws. Shallow water equations, Euler equation.
  18. Lagrangian methods for Euler equations. ALE methods.