Issue 5, 2026
Stochastic Differential Equations In Nonlinear and Quantum Optics
Stochastic Differential Equations In Nonlinear and Quantum Optics
A. M. Basharov$^{1,2}$
Based on Ito's differentials, the paper considers basic and classical and quantum stochastic differential equations (SDEs) describing the interaction of electromagnetic fields with qubit systems. In the classical case, everything has been derived from the concept of a counting (Poisson) process, including classical white noise. In the quantum case, the notion of quantum white noise is meant to be the basic process that defines all other quantum random processes, including the quantum counting process. As has been shown Stark interaction serves as an important tool for introducing both a classical and quantum counting process into the problem of qubit-radiation interaction. In the quantum case, the counting process is represented by elementary processes of virtual photon emission and absorption, which are described by quantum white noise. Eight examples are provided to illustrate typical cases of constructing, modeling, and presenting effective Hamiltonians and deriving the corresponding SDEs and kinetic equations.
Show AbstractEffects of multiphoton scattering by terahertz polaritons in Mg:LiNbO3 crystals in the high parametric gain regime
Effects of multiphoton scattering by terahertz polaritons in Mg:LiNbO3 crystals in the high parametric gain regime
M. A. Seleznev, K. A. Kuznetsov, G. K. Kitaeva
Our study of terahertz wave generation in Mg:LiNbO3 crystals, carried out under high-power picosecond laser pumping at a wavelength of 1064 nm with pulse energies up to 1 mJ, revealed unusual emission in the visible wavelength range from 510 to 570 nm with a complex angular structure dependent on the pump power. The frequency-angular intensity distributions of the accompanying visible radiation were measured at various IR pump powers. Analysis of the data obtained in the terahertz and visible spectral ranges indicates the multiphoton nature of the processes occurring, involving phonon polaritons from the lower branch of the dispersion law of Mg:LiNbO3 crystal. The Stokes and anti-Stokes cascades of polariton scattering of the non-phase-matched second harmonic of pump radiation lead to the appearance of repeating branches in the frequency-angular spectra of visible radiation. In addition, the bright narrow polariton-scattering lines are also observed at frequencies that are multiples of the frequency of the optical E-phonon with orthogonal polarization. Studying the nature of the discovered polariton-scattering effects is important for further exploration of ways to increase the efficiency of laser-induced terahertz radiation sources and to elucidate the structural features of the crystal lattice dynamics of lithium niobate crystals, which are widely used in modern nonlinear-optical technologies.
Show AbstractKhokhlov and nonlinear acoustics
Khokhlov and nonlinear acoustics
O. V. Rudenko
Rem Viktorovich Khokhlov began studying the propagation of powerful acoustic disturbances in 1960. He developed a modern mathematical framework based on a family of nonlinear evolutionary equations. This framework was used by R. V. Khokhlov himself, his students, and followers to describe new nonlinear phenomena and to calculate new technical devices.
Show AbstractFrom the light beam self-focusing to the light bullets in transparent dielectrics under femtosecond laser pulse filamentation
From the light beam self-focusing to the light bullets in transparent dielectrics under femtosecond laser pulse filamentation
S. V. Chekalin, V. O. Kompanets
This work presents a retrospective analysis of the development of notions in nonlinear optics: from beam self-focusing and pulse filamentation to light bullets – wave packets extremely compressed in space and time during laser light propagation in the bulk of a transparent medium. The state of the art in studies of mid-IR light bullets in condensed media performed in joint ISAN and MSU Physical Department investigations is described. It is shown that the light bullet - extremely compressed wave packet in transparent dielectric in contrast to solitons in guiding structures is a short-lived formation which path length is not more than a few hundred micrometers. The spectrum superbroadening of supercontinuum generated by the light bullet and the rise of isolated anti-Stokes wing in its takes place under bullet compression up to near single cycle that confirmed experimentally by observing the periodic modulation of the induced color centers density in LiF under single femtosecond pulse filamentation.
Show AbstractThe influence of heating of the medium on spatio-temporal optical vortices arising during the self-action of an elliptically polarized pulse in the isotropic phase of a nematic liquid crystal near the transition temperature to the mesophase
The influence of heating of the medium on spatio-temporal optical vortices arising during the self-action of an elliptically polarized pulse in the isotropic phase of a nematic liquid crystal near the transition temperature to the mesophase
G. M. Shishkov, K. S. Grigoriev, V. A. Makarov
The self-interaction of an elliptically polarized Gaussian pulse in the isotropic phase of a nematic liquid crystal (NLC) near the mesophase transition temperature is studied numerically. The influence of nonlocality of the orientational mechanism of nonlinear optical response and the change in the nonlinearity relaxation time caused by the absorption of propagating radiation on its propagation is taken into account. The initial system of equations for the analysis contained two equations for the slowly varying complex amplitudes of the circularly polarized components of the electric field, equations for the components of the order parameter tensor, and the heat conduction equation. The statistics of realizations of the parameter values characterizing the propagating pulse, as well as the patterns of the generation and evolution of spatio-temporal optical vortices (STOVs) with opposite signs of topological charges, are analyzed based on numerical solution for more than $10^5$ different sets of parameters characterizing the incident pulse and the initial state of the NLC.
Show AbstractRaman spectroscopy of aqueous ethanol solutions: study of hydrogen bonding and diagnostics of multicomponent systems
Raman spectroscopy of aqueous ethanol solutions: study of hydrogen bonding and diagnostics of multicomponent systems
S. V. Patsaeva$^1$, S. A. Burikov$^1$, I. V. Plastinin$^{1,2}$, I. V. Isaev$^2$, S. A. Dolenko$^{1,2}$, T. A. Dolenko$^{1,2}$
This study investigates the structural features of water-ethanol solutions across an ethanol concentration range from 0 to 96 vol.% (alcohol mole fraction up to 0.85) using Raman spectroscopy. A review of existing literature and original results regarding the Raman spectroscopy of water-ethanol solutions and its application to the characterization of these systems are presented. Particular attention is paid to structural transformations within the hydrogen-bonding network of the solutions and how these changes are manifested in various vibrational bands. For the first time, within a single study the changes in the intensity of the translational band (120–350 cm-1) are compared with changes in the shape of the stretching band (2600–3900 cm-1) in the Raman spectra of water-ethanol solutions. The intensity of the translational band in the 120–350 cm-1 region reflects the number of hydrogen bonds in the solution, while changes in the shape of the OH-group stretching vibration band characterize the number of hydrogen bonds with varying strengths of intermolecular interaction. Based on a combination of Raman spectroscopy data and literature findings, a model of the structural organization of water-ethanol solutions as a function of alcohol concentration has been developed. A detailed description is provided of a developed non-contact method for determining ethanol concentration in solutions based on the intensity of CH- or OH-group stretching vibration bands, normalized to the total intensity of both bands. A formula is presented for calculating ethanol concentration in a solution using the recorded integrated intensities within the stretching vibration region. Results are also presented on the application of Raman spectroscopy combined with neural network methods for the analysis of multicomponent alcohol-containing liquids and alcoholic beverages.
Show AbstractParametric interactions in a nonlinear optical crystal with a structured input surface; generation of multimode quantum states
Parametric interactions in a nonlinear optical crystal with a structured input surface; generation of multimode quantum states
A. S. Chirkin
Quantum theory of the parametric interactions in a nonlinear optical crystal, the input surface of which modulates the radiation entering the crystal, has been developed. A system of coupled equations for the angular distribution of parametrically excited waves, taking into account the diffraction phenomenon, has been derived. These equations describe the excitation of multimode entangled states. A three-mode state, including the photon statistics in individual modes and the pairwise cross-correlation of photons within modes, has been studied in detail.
Show AbstractNonlinear optical effects in organic micristructures
Nonlinear optical effects in organic micristructures
T. V. Murzina, I. A. Kolmychek, A. A. Ezhov, N. D. Lapin, K. A. Smirnov, A. I. Maydykovskiy, V. B. Novikov, A. D. Belyaev
Organic microstructures with unique properties attract a significant scientific interest due to their wide potential for application in various fields of photonics. Many organic microstructures and dye-based crystals exhibit pronounced photoluminescence and resonant properties, as well as a highly efficient nonlinear optical response that can be enhanced by the excitation of resonant light modes. This paper presents the results of studies of nonlinear optical effects in active organic microstructures of various compositions and geometries. The possibility of linear and nonlinear optical excitation of Fabry-Perot modes, whispering gallery modes, and quasi-whispering gallery modes in microstructures with linear dimensions up to 20 μm is demonstrated, and the efficiency of nonlinear optical methods for characterization of their structural and optical properties is demonstrated. The presented results reveal an extensive potential for the development of nonlinear organic microstructures and their application as elements of integrated photonics.
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