Laboratory of the Theory of Nonlinear Processes

Laboratory Staff

Selected Publications

Research Focus

• Bound states in the continuum
• Propagation of light in photonic crystal waveguides coupled with nonlinear microcavities
• Transport of ultra-cold atoms in optical lattices
• Guiding electromagnetic waves in directional dielectric arrays above the light cone

Advanced Results

• Trapping of light above the light cone
• Trapping of sound and electrons in cavitites with a variable shape
• Symmetry breaking in nonlinear photonics
• Optical diode
• No-go theorem for spin polarization in two-terminal microstructures
• Vortical ground state in spinor Bose−Einstein condensates
• Universal statistics of currents in chaotic billiards

Research Techniques

In our theoretical studies on transport phenomena, we employ combinations of analytical methods and numerical techniques, which both provide an insight into physical phenomena and allow their quantitative (numerical) description. The analytical and semi-analytical approaches include the coupled-mode theory, effective non-Hermitian Hamiltonian formalism, random matrix theory, and Bogolubov-Mitropolsky method for solving nonlinear equations. In numerical modeling, the most up-to-date techniques are utilized, such as the finite-difference and finite-element methods in both time and frequency domains in combination with the absorbing boundary conditions.