Asymptotic Characteristics of the Evolution of Polarization of Nonmonochromatic Radiation in Single-Mode Optical Fibers with a Random Twisting of Axes of Linear Birefringence. I. Limiting of Polarization in an Infinitely Long Fiber

We reduce the problem of finding the limiting value of the fiber-ensemble averaged degree of radiation polarization of in an infinitely long optical fiber to the problem of distributions (including joint distributions) of random complex amplitudes E(,z) of the electric field in an optical wave for different wavelengths and the fiber length z tending to infinity. We prove that the random complex vector E(,z) is uniformly distributed on a three-dimensional sphere if z. It is also proved that the random vectors E(₁,z) and E(₂,z) are independent if ₁₂ and z, whence it follows that their joint distribution is entirely determined by the distribution of each of them. The result obtained allows us to find the limiting average values of various quantities describing the radiation upon passing an optical fiber with a random twisting of the anisotropy axes. In particular, on the basis of this result, we show that the average degree of polarization of incoherent radiation upon passing a fiber with such random irregularities tends to zero as the optical-fiber length goes to infinity.     

Increase in the correlation length of nonmonochromatic radiation during propagation in a single-mode optical fiber containing random inhomogeneities and the influence of this increase on the operation of a fiber ring interferometer

An analysis is made of the conditions under which the coupling of orthogonal polarization modes at random inhomogeneities in single-mode optical fibers leads to an increase in the correlation length of a source of nonmonochromatic radiation. It is shown that when long-base fiber ring interferometers with a single-mode fiber ring system possessing weak linear birefringence are used, the correlation length of the nonmonochromatic radiation at the interferometer exit is increased, which means that the interference pattern can have satisfactory visibility even when there is an appreciable difference between the interferometer arms as a result of the Sagnac effect due to the Earth’s rotation. The calculations were made by mathematical modeling of random inhomogeneities in the fiber. Zh. Tekh. Fiz. 69, 140–143 (July 1999)     

Phase transitions and electrical properties of solid solutions of sodium, lithium, and strontium niobates

An additional study of solid solutions in the (Na, Li, Sr_0.5)NbO₃ ternary system was performed. More detailed information concerning its phase diagram and physical parameters in a wide range of component concentrations is obtained. The compositions obtained are of interest for application in highly sensitive and high-frequency transducers.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XVI. Depolarization and repolarization of polychromatic radiation in single-mode optical fibers with random inhomogeneities

The dependences of the degree of polarization of polychromatic radiation on the length of a single-mode optical fiber (SMF) with random inhomogeneities have been obtained by mathematical modeling. The case is considered where radiation having both polarization modes excited with equal weights of linear polarization is first introduced into a depolarizer of polychromatic radiation (a SMF segment with high linear birefringence) and arrives at an SMF with low linear birefringence. It is shown that the degree of polarization of radiation after transmission through the first segment becomes significantly suppressed and remains almost constant upon propagation through the second segment, after which it begins to sharply increase at some length; i.e., repolarization of radiation occurs. It is shown that repolarization of radiation depends weakly on the angle made by the axes of unperturbed linear birefringence of the first and second segments. The conditions for the length of the first segment (depolarizer) under which the degree of polarization remains minimum throughout the second segment are determined.     

Phase diagram and physical properties of the sodium niobate-lithium niobate-cadmium niobate three-component system

The phase diagram of the (Na,Li,Cd_0.5)NbO₃ ternary system is refined. The electrical properties of solid solutions over a broad range of the component concentrations were studied. The compositions promising for high-temperature transducers were obtained.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: X. Verification of the ergodic hypothesis for fiber ring interferometers

The problem of the validity of the ergodic hypothesis as applied to a fiber ring interferometer (FRI) is considered on the basis of a comparison between magnitudes of the zero drift of an FRI calculated upon changing temperature of the fiber and upon random realizations of inhomogeneities in a single-mode optical fiber (SMF). The physical nature and statistical characteristics of random inhomogeneities in an SMF, types of polarization nonreciprocity in an FRI, and thermo-optical parameters of an SMF are analyzed. An algorithm for calculation of the zero drift of an FRI on changing temperature is proposed. The conditions under which the ergodic hypothesis is satisfied in an FRI are formulated. In particular, it is shown that many random inhomogeneities have to be placed on the depolarization length of polychromatic radiation in the SMF loop of an FRI; otherwise, the zero drift of the FRI calculated by the method of averaging over an ensemble of independent realizations may significantly exceed its actual value. Numerical estimations are made. It is shown that thermostabilization of an FRI with a polychromatic radiation source may significantly reduce its zero drift.     

Longitudinal excitations in Mg-Al-O refractory oxide melts studied by inelastic x-ray scattering

The dynamic structure factor S(Q,omega) of the refractory oxide melts MgAl2O4 and MgAl4O7 is studied by inelastic x-ray scattering with aerodynamic levitation and laser heating. This technique allows the authors to measure simultaneously the elastic response and transport properties of melts under extreme temperatures. Over the wave vector Q range of 1-8 nm-1 the data can be fitted with a generalized hydrodynamic model that incorporates a slow component described by a single relaxation time and an effectively instantaneous fast component. Their study provides estimates of high-frequency sound velocities and viscosities of the Mg-Al-O melts. In contrast to liquid metals, the dispersion of the high-frequency sound mode is found to be linear, and the generalized viscosity to be Q independent. Both experiment and simulation show a weak viscosity maximum around the MgAl4O7 composition.     

A spread in electrophysical parameters of ferroelectric piezoelectric solid solutions and its minimization

A spread in electrophysical parameters of solid solutions based on PZT and niobium oxides is considered for a wide range of component concentration. It is shown that composition fluctuations and their associated solution imperfection cause a significant deviation of the parameters from their mean values. The fluctuations are most pronounced when the crystal structure is unstable (e.g., at morphotropic transitions and near the solubility limits of the components). The optimization of methods for solid solution preparation greatly reduces the effect of process variables on parameter reproducibility.     

Ferroelectric elastance of sodium niobate-lithium niobate solid solutions in relation to A-O bond covalence

The ferroelectric elastance of (Na, Li, A _0.5 ^′ )NbO₃ solid solutions was found to vary directly with the total electronegativity of elements A (EN _{∑ A} ), that is, with the A-O bond covalence at B=const. Using EN _{∑ A} values and the position on the phase diagram, one can determine the solid solution parameters optimum for use in high-frequency (A′=Sr, Pb), medium-frequency (A′=Cd), and elevated-temperature (A′=Cd) devices.