Oleg V. Ivanov

Wavelets and their uses

This review paper is intended to give a useful guide for those who want to apply the discrete wavelet transform in practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to the corresponding literature. The multiresolution analysis and fast wavelet transform have become a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for the achievement of a goal. Analysis of various functions with the help of wavelets allows one to reveal fractal structures, singularities etc. The wavelet transform of operator expressions helps solve some equations. In practical applications one often deals with the discretized functions, and the problem of stability of the wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves to a few examples only. The authors would be grateful for any comments which would move us closer to the goal proclaimed in the first phrase of the abstract.

Fabrication of long-period fiber gratings by twisting a standard single-mode fiber

A new method of fabrication of long-period fiber gratings by twisting of a standard single-mode fiber at high temperature is presented. The method relies on the fact that there always exists some core-cladding eccentricity in the optical fiber. Therefore, when the fiber is twisted, its core follows a helicoidal path inside the cladding. The transmission spectrum of the helicoidal long-period fiber grating that is produced contains several dips that correspond to resonances with the fiber cladding modes.

Origin of coupling to antisymmetric modes in arc-induced long-period fiber gratings

We study the origin of antisymmetric perturbation of the fiber in arc-induced long-period gratings that couple the core mode into the antisymmetric cladding modes. We demonstrate that this perturbation is caused by the temperature gradient in the fiber, which is induced, in turn, by the temperature gradient in the arc discharge. The reproducibility of the process of the grating inscription is higher when the fiber is placed in a region with larger temperature gradient.

Demonstration of coupling to symmetric and antisymmetric cladding modes in arc-induced long-period fiber gratings

The symmetry of cladding modes excited in microbend and arcinduced long-period fiber gratings is investigated. An optimization technique is developed to determine the fiber parameters and to associate grating resonances with cladding modes of a particular symmetry. Using this optimization procedure, we show that the gratings induced in a standard fiber by arc discharges and microbends couple light to the antisymmetric cladding modes. In the case of a boron-germanium codoped fiber, the cladding modes excited by arc-induced gratings are found to be symmetric. Measurements of the near-field intensity distribution of cladding modes confirm the mode symmetry ascertained by the optimization technique.

Characterization of the response of a dual resonance of an arc-induced long-period grating to various physical parameters

We present, for the first time to our knowledge, results on the characterization of response of a dual resonance observed in the spectrum of a single long-period grating arc-induced in a B/Ge co-doped fiber to different physical parameters. The dual resonance is formed by two overlapping resonances corresponding to coupling of the core mode to symmetric and antisymmetric cladding modes. Therefore, these resonances may behave differently when strain, bending, torsion, or temperature is applied to the grating. We show that the bending, strain, and torsion sensitivities of the two resonances are very different, while the temperature sensitivities are almost the same.

Simultaneous temperature and strain measurements performed by a step-changed arc-induced long-period fiber grating

A compact sensor based on step-changed arc-induced long-period fiber gratings was implemented to discriminate between temperature and strain. The proposed sensor consists of a single long-period grating with two sections written consecutively in the SMF-28 fiber using the electric arc discharge technique. The two sections have the same period but different fabrication parameters. The operation of the sensor relies on the existence of a difference between the values of temperature and strain sensitivity of two neighboring resonances observed in the spectrum of the step-changed grating. The temperature and strain resolutions obtained for the sensor are 0.2 degrees C and 35 micro epsilon, respectively.

Wavelength shifts of cladding-mode resonance in corrugated long-period fiber gratings under torsion.

A finite deformation theory of elasticity and a theory of nonlinear photoelasticity are applied to describe the wavelength shifts of cladding-mode resonance in corrugated long-period fiber gratings under torsion. The deformation of fiber is found by use of the Murnaghan model of a solid elastic body. The quadratic photoelastic effect that is proportional to the second-order displacement gradient is investigated and compared with the classical photoelastic effect. The electromagnetic field in the twisted corrugated structure is presented as a superposition of circularly polarized modes of the etched fiber section. The wavelength shift is found to be proportional to the square of the twist angle. As predicted by our theory, a wavelength shift of the same nature has been found in a conventionally photoinduced long-period fiber grating.

Two types of resonances in long-period gratings induced by arc discharges in boron/ germanium co-doped fibers

We demonstrate that under certain conditions it is possible to fabricate in a B/Ge co-doped fiber an arc-induced long-period grating whose spectrum contains a dual set of resonances. These two sets of resonances are formed by distinct mechanisms and are caused by coupling to cladding modes of different symmetries. They behave differently at high temperatures: the set produced by symmetric perturbation disappears during annealing at a temperature of 800 degrees C, while the other set produced by an antisymmetric mechanism can withstand temperatures above 1000 degrees C.

Propagation and coupling of hybrid modes in twisted fibers

The first-order paraxial approximation is used to obtain the distributions of the electric and magnetic fields for the core and cladding hybrid fiber modes. The coupling coefficients of these modes are found for fibers subject to twist. The longitudinal electric field component determines the mode coupling in twisted fibers. It is shown that in the first-order paraxial approximation the cladding hybrid modes propagating in a twisted fiber rotate along the direction of the twist at the same rate as the core mode, independently of the azimuthal and radial mode numbers. Four hybrid modes constituting one linearly polarized mode have different longitudinal components, and the corresponding cladding-mode resonances of a long-period fiber grating undergo different shifts owing to different mode self-coupling coefficients. This results in the removal of mode degeneracy and splitting of resonances of long-period gratings in twisted fibers.

Evaluation of coupling losses in hollow-core photonic crystal fibres

Hollow-core photonic crystal fibres have a high potential for gas sensing applications, since large light-gas interaction lengths can be effectively attained. Nevertheless, in order to enhance effective diffusion of gas into the fibre hollow-core, multi-coupling gaps are needed, which raise coupling loss issues that must be evaluated prior to the development of practical systems. In this communication we present a study on the coupling losses dependence on lateral and axial gap misalignment for single-mode fibre and two different types of hollow-core photonic crystal fibres. In addition, experimental results on the splicing of these fibres are also presented.