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.

A new method of analytical representation and numerical simulation of multimode fiber interferometer signals is developed. A system of averaged normalized characteristics, called amplitude and spectral characteristics, is introduced for this end. Interferometer signals generated by fiber length variation or laser frequency modulation were investigated at various parameters of the fiber. Joint usage of amplitude and spectral characteristics proved to substantially broaden the dynamical range of measurements of weak and strong external disturbances of the fiber. The method may be used for analysis and design of various optical sensor schemes with multimode fiber interferometers. It is also usable for estimating modal noise characteristics in optical systems with undesirable effects of intermodal interference.

The Rayleigh backscattering produced by an incident fundamental mode in a multimode step-index optical fiber was analyzed using a recently developed diffraction technique. The complete set of backward propagating modes, both radial and azimuthal, was determined and regarded. For this type of fiber, normalized mode functions were constructed in an explicit form, thus providing a unified power scale to characterize the relationships between various excited modes. The dependencies of the mode excitation efficiencies on the technical parameters of the fiber and the frequency of the launched radiation were studied. A comparison of the mode excitation efficiencies was performed with those in the fiber with quadratic refractive index profiles.

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.

The averaged characteristics of the multimode fiber interferometer signals have been investigated, with the average being performed over ensemble, “long realization”, frequency, cross-section, and combination of these methods as well. The signals were produced at two wavelengths in few- and multi-mode regimes in the graded-index fiber. A practical example of the cross-section average is discussed in more details. The results would be useful for the multimode fiber interferometer utilization as a real-time high-accuracy sensor.

The recently developed diffraction technique of analytical investigation of the Rayleigh backscattering produced by an incident fundamental mode in a multimode optical fiber with an arbitrary refractive index profile is generalized to admit an arbitrary incident mode, either radial or azimuthal. The relative powers of all backscattered modes are determined with explicit formulas via the properly normalized transverse distributions of the incident and backscattered mode fields within the fiber cross section. The regularities conditioned by azimuthal indices are expressed via a universal set of coefficients, and dependences on the radial mode indices are estimated numerically. Excitation coefficients are shown to be symmetrical for any pair of incident and backscattered modes.