M. A. Bisyarin

Fundamentals of Optical Fiber Sensing Schemes Based on Coherent Optical Time Domain Reflectometry: Signal Model Under Static Fiber Conditions

The paper develops a statistical model for the signals received in phase-sensitive optical time domain reflectometry (OTDR) probed by highly coherent sources. The backscattering process is modelled by a set of discrete scatterers with properly chosen parameters. Explicit equations for calculating the amplitude and the phase of the backscattered signal are obtained. The developed model predicts spectral and autocorrelation characteristics of the amplitude signals that are validated by experimental results. Characteristics of the phase signals, practicable for studying the sensing applications of the OTDR system, are presented and studied as well, demonstrating good correspondence with experiment. A more detailed modelling of distributed vibration sensing systems and their response to disturbances along an optical fiber will be possible as an extension of the developed formalism.

Rayleigh backscattering from the fundamental mode in multimode optical fibers

Rayleigh backscattering produced by an incident fundamental mode in a multimode optical fiber is analyzed using a diffraction technique, with a full set of backward-propagating modes being taken into consideration. Explicit formulas are derived for mode excitation efficiency via radial distributions of the mode fields, and it is proved that only half-azimuthal modes are backscattered by the incident wave of a fixed polarization. Advanced analytical expressions are developed for fibers with a quadratic refractive-index profile, and mode groups of even numbers, composed of modes with equal propagation constants, are stated to be excited with equal efficiencies.

Minimizing the optical losses in anisotropic single-mode lightguides with elliptical boron germanosilicate cladding

This paper discusses how the damping at wavelength 1.55 µm depends on various factors for anisotropic single-mode lightguides with boron germanosilicate elliptical cladding. It is shown that the refractive index of this cladding in the preform has a substantial effect on the optical losses of the lightguides. The thickness of the cladding that isolates the core from the boron-containing glass of the elliptical cladding is optimized. The optical losses to Rayleigh scattering are reduced by doping the core with small additives of moisture. For a lightguide with a glass-fiber diameter of 125 µm in a two-layer polymeric coating, an optical loss level equal to 0.5 dB/km is achieved, with a polarization maintenance of 5×10 -6 m -1 .

Subpicosecond pulse propagation in optical fibres with transverse and longitudinal inhomogeneities

Abstract Short optical pulse propagation is investigated in the light guide characterized with a strong dependence of the fibre material refractive index on the radial coordinate and a weak dependence on the longitudinal coordinate, with a weak spatial bending of the light guide axis being allowed as well. A three-dimensional nonlinear wave equation used in modeling the process is solved asymptotically with respect to a small parameter setting the order of magnitude of the pulse amplitude. A relationship between the propagating modes and the eigenvalues and eigenfunctions of a singular Sturm–Liouville problem is elucidated. The pulse propagation is shown to be three-scale: the high-frequency carrier is modulated with the envelope which evolves in a two-scale manner and is described with a nonlinear Schrodinger equation with coefficients depending on the longitudinal coordinate. For several types of the transverse and longitudinal inhomogeneities, expressions through elementary functions are obtained for the transverse distribution of the wave field and the envelope soliton. The possibility is stated for managing pulse parameters by means of varying the transverse and longitudinal inhomogeneities of the light guide.

Finite-amplitude pulses in light guides with the quadratic profile of the refractive index

Weak nonlinear process of propagation of short optical pulses in graded-index light guides with the quadratic dependence of the refractive index on the transverse coordinate and a slight dependence on the longitudinal coordinate is modelled with the nonlinear wave equation. Transverse distribution of the wave field is shown to be characterized with the parabolic cylinder functions, and the nonlinear Schroedinger equation with variable coefficients is obtained for the pulse envelope. A solution of this equation describing a soliton pulse is found for a class of longitudinal inhomogeneities and formulae are presented for variations of amplitude, shape and velocity of the pulse during its propagation.

Self-action of short pulses in nonhomogeneous graded-index light guides

The weak nonlinear process of propagation of short pulses in graded-index light guides that are weakly inhomogeneous in the longitudinal direction and slightly bent is investigated by means of a consistent asymptotic method. The process as a whole is proved to be three-scale in respect to a small parameter related to the magnitude of nonlinearity. The phase of the most rapid process and transverse distribution of the wave field are expressed explicitly in terms of a certain Sturm-Liouville problem. For a pulse envelope the nonlinear Schrödinger equation is derived, its coefficients depending on the longitudinal coordinate. The existence of a guaranteed interval of conservation of concentration of the pulse envelope is ascertained. For a class of very smooth inhomogeneities formulae are obtained describing the variation of the amplitude and width of the pulse during propagation.

Anisotropic single-mode lightguide with an elliptical germanium silicate core and depressed cladding

The properties of anisotropic single-mode fiber lightguides with an elliptical highly doped germanium core and elliptical fluorine-doped cladding have been investigated. When the difference of the refractive indices of the core and the cladding equals 0.033 and the ratio of the axes of the core is about 2, the birefringence is about 0.00037. The fabricated lightguides, despite the differential optical losses of the orthogonal modes to radiation leakage, are distinguished by a low level of polarization stability. The degree to which the radiation remains polarized in them (≈0.003  m−1) is two orders of magnitude worse than in commercially produced lightguides. This is probably caused by local microstrain of the low-viscosity glass of the core.

Weak‐Nonlinear Acoustic Pulse Dynamics In A Waveguide Channel With Longitudinal Inhomogeneity

Weak‐nonlinear acoustic pulse propagation in a waveguide channel with longitudinal inhomogeneity is investigated. Euler equations are reduced to a nonlinear wave equation with quadratic nonlinearity, and it is stated that the medium is self‐focusing if the adiabatic exponent is greater than 3/2 and defocusing otherwise. The propagation is shown to be characterized with three scales. Nonlinear Schrodinger equation with variable coefficients is obtained for the pulse envelope and a “dark” soliton is presented for a special type of longitudinal inhomogeneity.

Vortex mode soliton propagation in graded-index optical fiber with longitudinal inhomogeneity vortex vs azimuthal modes comparative analysis

Propagation of a vortex mode of a short pulse in the graded-index optical fiber is studied with an analytical technique taking into account either nonlinearity of the propagation process and longitudinal inhomogeneity of the fiber. Quantitative estimates are obtained for differences in the soliton envelope dynamics of vortex and azimuthal modes.

The effect of an inhomogeneous cladding of a gradient optical waveguide on the mode and envelope characteristics of a soliton pulse

The nonlinear dynamics of a short pulse in a gradient waveguide layer is studied analytically taking into account the occurrence of a cladding layer and the longitudinal inhomogeneity of the two layers. The class of functions is presented in terms of which the transverse profiles of the refractive indices of both the gradient and the cladding layers can be represented, and, at the same time, the mode structure of the pulse can be explicitly described in terms of a hypergeometric equation. Expressions are presented that describe the variations of the propagation constant and transverse distribution of the wave field under the action of the longitudinal inhomogeneities of the gradient and cladding layers. It is shown that the envelope of the pulse satisfies the generalized nonlinear Schrödinger equation the coefficients of which are functions of the longitudinal coordinate and are expressed via the refractive indices of the waveguide layer and cladding.