Waves In Optical Fibers Research Articles

Multiple-pole soliton interactions in optical fibres with higher-order effects

Abstract We consider the Hirota equation which governs the propagation of nonlinear waves in optical fibres with higher-order effects like third-order dispersion, self-steepening and delayed nonlinear response. By using the Hirota bilinear method a special two-soliton solution is derived. We also undertake a special limit corresponding to the multiple-pole case. Physically, this special pair of solitons separates very slowly.

Multiple-Pole soliton interactions in optical fibres with higher-order effects

We consider the Hirota equation which governs the propagation of nonlinear waves in optical fibres with higher-order effects like third-order dispersion, self-steepening and delayed nonlinear response. By using the Hirota bilinear method a special two-soliton solution is derived. We also undertake a special limit corresponding to the multiple-pole case. Physically, this special pair of solitons separates very slowly.

Normal modes of magnetic flux tubes and dissipation

Wave propagation in a zero- magnetic flux tube with a discontinuous Alfven speed at its surface is considered. The problem is reduced to solving a wave equation for the projection of the magnetic perturbation along the axis of the cylinder. The mathematical formalism is identical with that for the propagation of electromagnetic waves in optical fibers with a varying index of refraction in the cross section of the fiber. The dispersion relation is solved in its full generality and three wave numbers are assigned to the normal modes of the cylinder. There is a lower cuto for the longitudinal wave number along the cylinder axis and an upper cuto for the radial wave number. Eigenfrequencies and eigenfields (i.e. the magnetic and velocity fields of modes) are calculated. Resistive and viscous dissipation rates have mathematically identical forms, diering only in their being inversely proportional to the Lundquist and Reynolds numbers, respectively. These rates as well as the energy densities are obtained for each mode and are commented on.

Guidance and leakage properties of chiral optical fibers

The field theory of guided waves in optical fibers with step-index profiles and in which both core and cladding are chiral isotropic media is developed. We show that both surface and semileaky modes can propagate in optically active fibers. To shed light on the guidance and leakage properties of chiral isotropic fibers we present a physical interpretation and several numerical results. The new leakage effect associated with semileaky modes is an important property that cannot be neglected in the analysis of chiral optical fibers but that, nevertheless, has been systematically disregarded in the literature.

Whispering-gallery waves in optical fibres

The process of excitation of whispering-gallery waves (WGWs) in optical fibres (microcavities) with the help of a bitapered fibre is analysed. It is shown that useful information on the WGW modes can be obtained from the spectrograms recorded by scanning the exciting-radiation frequency. Based on the geometrical-optic approximation, the longitudinal sizes of the WGW modes are estimated and it is shown that the ultimate diameter of the fibre exists for optical fibres (microcavities) where a mode can be still excited with the help of a bitapered fibre.

Measurement of speed and attenuation of longitudinal elastic waves in optical fibers

A longitudinal elastic pulse is generated in a segment of op- tical fiber. A laser Doppler vibrometer is used to make noncontact mea- surements of the axial surface velocity at several locations along the optical fiber segment. The measured temporal phase shift and amplitude attenuation of the elastic pulse as it propagates between measurement locations are used to deduce the elastic wave speed and mechanical loss factor for the optical fiber. The knowledge of these properties is important to the design of optical sensors for dynamic phenomena such as vibrations and acoustic pressure. One potential application of the method is nondestructive testing for delamination between an optical fiber's glass cladding and plastic jacket. © 2001 Society of Photo-Optical Instru- mentation Engineers. (DOI: 10.1117/1.1403449)

Raman-assisted three-wave mixing of non-phase-matched waves in optical fibres: application to wide-range frequency conversion

We analyse theoretically and experimentally the Raman-assisted parametric coupling between non-phase-matched waves propagating in normally dispersive single-mode fibres. We perform a careful analysis of the wave-coupling behaviour, which shows that scalar and vector three-wave mixing (TWM) interactions induce a relatively small periodic power flow between a central-frequency pump at frequency ω 0 and a pair of up-shifted (anti-Stokes) and down-shifted (Stokes) sidebands at frequencies ω 0+Ω and ω 0−Ω , respectively. For sufficiently high pump powers, the stimulated Raman scattering enters into play, causing a unilateral transfer of energy from higher to lower frequency waves. This energy transfer destroys the spatial periodicity of the parametric energy-exchange process. As a result, parametric seeding and subsequent Raman amplification of a Stokes idler wave is achieved by mixing a strong pump with a weak anti-Stokes signal. This Raman-induced Stokes power-gain enhancement leads to efficient anti-Stokes → Stokes frequency conversion, with frequency detunings which can be relatively large (typically, from 7 to 30 THz), even for very short parametric coherence. Raman-assisted TWM thus overcomes the strict spectral limitation usually imposed by the phase-matching condition, leading to broadband frequency conversion processes that are inaccessible with a pure parametric interaction.

Modulational instability induced by randomly varying coefficients for the nonlinear Schrödinger equation

We introduce the theory of modulational instability (MI) of electromagnetic waves in optical fibers. The model at hand is the one-dimensional nonlinear Schrödinger equation with random group velocity dispersion and random nonlinear coefficient. We compute the MI gain which reads as the Lyapunov exponent of a random linear system. We show that the distribution of the MI gain can be expressed in terms of the log-normal statistics. The heavy tail of this probability distribution function involves very different behaviors for the sample and moment MI gains. In the anomalous dispersion regime, random fluctuations of the nonlinear coefficient reduces the sample MI gain peak, although the moment MI peak is enhanced, and the unstable bandwidth is widened. Still in the anomalous dispersion regime, random fluctuations of the group velocity dispersion reduces both the sample MI gain peak and the moment MI peak. Finally, in the normal dispersion regime, randomness extends the MI domain to the whole spectrum of modulations, and increases the MI gain peak. The linear stability analysis is confirmed by numerical simulations of the full stochastic nonlinear Schrödinger equation.

Optical vortices in low-mode fibers: III. Dislocation reactions, phase transitions, and topological birefringence

Topological birefringence of waves in optical fibers resulting from the spin-orbit interaction in the field of optical vortices is manifested, as a rule, in the form of Rytov-Magnus unified optical effect. At the same time, the field transformations caused by this effect are not explicitly related to the evolution of phase dislocations of longitudinal and transverse components of the electric and the magnetic fields. This relation can be provided by the dislocation reactions proposed by Berry. As opposed to the Berry’s approach, where dislocation reactions at the wavefront surface are considered, it is suggested in this work that topological reactions at the specific characteristic surface of the wave field formed by the coordinate representation of the transverse components of the Poynting vector be considered. Using the action of topological birefringence in a low-mode optical fiber as an example, it is shown that the course of a topological reaction in a vector optical field is accompanied by rigorous conservation of the total topological index of the characteristic surface and does not depend on the presence of an interface (where topological charges can originate and annihilate). The total topological index of a dislocation reaction is found to be equal to the absolute value of the sum of the topological charge and the spirality of the vector wave field.

The influence of boundary layer on sound propagation in optical fibers

Physical models of two-layered and three-layered fiber were built. These models were used to calculate acoustic properties of optical fibers. Acoustic properties of fibers with boundary layer and without boundary layer calculated from these model were compared. The propagation of acoustic cylindrical symmetric waves in optical fibers was considered. This problem was treated analytically and numerically in continual approximation. The possibility of simultaneous propagation of two cylindrical symmetric waves in optical fibers with a boundary layer was shown (in a three-layered model). The physical phenomenon of the presence of two waves in the fiber with boundary layer is proposed for study of the boundary layer. Formulas for the calculation of the properties of the boundary layer from the acoustic experiment, verified by numerical calculations, are represented.

On the formation of solitary and periodic waves in optical fibres near the zero-dispersion point

A spectral method is used to investigate nonlinear wave propagation in optical fibres near the zero-dispersion point. The conditions for solitary (bright and dark) or periodic wave generation and propagation without any distortion, as well as the form of the waves, are obtained. It is demonstrated that bright solitary pulses may propagate near the second zero-dispersion point in quadruple-clad fibres, while neither periodic nor solitary wave propagation is practically possible near the sole zero-dispersion point in graded-index fibres, or near the first one in quadruple-clad fibres.

Stable coupled conjugate solitary waves in optical fibers

Four-wave mixing of an intense continuous-wave pump beam with an ultrashort soliton signal in an optical fiber is theoretically analyzed. A novel class of stable two-color coupled solitary waves is found. These vector parametric solitons represent the optimal frequency conversion of an ultrashort pulse.

Measurement of the frequency response induced by electrostriction in optical fibers

Accurate measurements of the frequency response of the nonlinear refractive index induced by the combined effects of Kerr nonlinearity with electrostrictional excitation of acoustic waves in optical fibers are presented. A detailed experimental investigation of both standard (zero-dispersion wavelength,lambda(0) approximately 1.31microm) and dispersion-shifted (lambda(0)=1.55microm) single-mode fibers showed the presence of several resonant peaks induced by the electrostrictive nonlinearity in the fiber structure. This investigation has provided better insight into the frequency behavior of the electrostriction-induced acoustic waves in optical fibers.

Use of a charged coupled device (CCD) camera for evanescent wave optical fiber cure monitoring of liquid composite molding resins

AbstractAn optical fiber evanescent wave fluorescence cure sensor described in a previous paper (1) has been interfaced with a fast detector and computer software to provide real‐time monitoring of fast‐reacting systems. Advantages to the new system include a reduction in data acquisition time (to 200 ms from 3 min), improved time resolution (to 5 sec from 10 min), and improved signal quality. Isothermal cure monitoring measurements were conducted in both distal and evanescent wave sampling modes for an epoxy‐amine system. Following a second order background correction, the results for the two sampling modes were identical. Thus the evanescent wave measurement was unable to detect differences between the chemistry in the bulk and at the fiber‐resin interface (if there were any differences to observe). The sensor system was also demonstrated for a fast curing (<3 min gel time) polyurethane‐isocyanurate system designed for high volume (short cycle time) automotive applications. The system is currently being modified for implementation in a “real world” manufacturing environment.

Trapped Rays in Cylindrically Symmetric Media and Poles of the Analytically Continued Resolvent

The acoustic (stratified) propagator is defined as the positive self-adjoint operatorK≡−c2(y)ρ(y)∇zρ−1(y)∇zon L2(Rn,(c2ρ)−1dnz), wherez=(x,y)x∈Rk,y∈Rm. Bounds on the weighted resolvent ofK, defined as〈z〉−α(K−ζ)−1〈z〉−αfor α>1/2 and 〈z〉=(1+|z|2)1/2, are obtained at high energies (i.e., in the semi-classical limit Re(ζ)⪢0) using the Virial conditionc−y·∇c≥εc>0. This implies energy decay estimates for trapped waves in fiber optics. With further smoothness assumptions oncand ρ the resolvent can be analytically extended onto the second Riemann sheet. The failure of the Virial condition on some radial interval, form≥2, implies the existence ofresonant-traveling modesfor the wave equation (∂t2+K)ψ=0. In particular it is shown that ifn>m≥2 thenKhas resonance states at high energies. No such states exist ifm=1. This is explained using a shape resonance picture.

Hybrid Organic/Inorganic Copolymers with Strongly Hydrogen-Bond Acidic Properties for Acoustic Wave and Optical Sensors

Hybrid organic/inorganic polymers have been prepared incorporating fluoroalkyl-substituted bisphenol groups linked using oligosiloxane spacers. These hydrogen-bond acidic materials have glass-to-rubber transition temperatures below room temperature and are excellent sorbents for basic vapors. The physical properties such as viscosity and refractive index can be tuned by varying the length of the oligosiloxane spacers and the molecular weight. In addition, the materials are easily cross-linked to yield solid elastomers. The potential use of these materials for chemical sensing has been demonstrated by applying them to surface acoustic wave devices as thin films and detecting the hydrogen-bond basic vapor dimethyl methylphosphonate with high sensitivity. It has also been demonstrated that one of these materials with suitable viscosity and refractive index can be used to clad silica optical fibers; the cladding was applied to freshly drawn fiber using a fiber drawing tower. These fibers have potential as evanescent wave optical fiber sensors.

Measurement of the refractive-index modulation generated by electrostriction-induced acoustic waves in optical fibers

The refractive-index modulation generated in optical fibers by electrostriction-induced acoustic waves is investigated directly by a pump-probe measurement technique in a 1-km-long fiber Sagnac-loop interferometer. Pump pulses propagating unidirectionally around the loop generate transverse acoustic waves that produce a time-dependent relative phase shift for the probe pulses. The consequent interferometer transmission changes are used as a measure of the acoustic interaction. The acoustic impulse response function of the fiber is measured by use of short optical pulses with a 1-MHz repetition rate. The response consists of a series of peaks separated by ~21 ns with a maximum value of refractive-index modulation of -1.1 x 10(-11) generated by the 230-pJ pump pulses. At a higher pulse repetition rate of 100 MHz additional temporal structure is generated in the 0-5-ns period after the pump pulse, leading to a response similar to that observed in longrange soliton interaction.

Analysis of polarization-mode coupling by acoustic torsional waves in optical fibers

Coupling of polarization modes of the LP01 spatial mode by acoustic torsional waves in an optical fiber is considered in detail. Analytic expressions of the coupling coefficients based on the combined effects of birefringence and photoelastic contributions are found. The results show that for regular fibers the birefringence component is the larger of the two. By the use of higher radial orders of the acoustic torsional modes, the coupling efficiency can be increased.

Integrability and singularity structure of coupled nonlinear Schrödinger equations

Multimode propagation of electromagnetic waves in optical fibre is often described by coupled nonlinear Schrödinger (NLS) equations. To understand the integrability properties of such coupled NLS systems, we extend the Painlevé singularity structure analysis of two coupled systems to three coupled systems and identify four integrable sets of parameters. We bilinearize these cases to obtain soliton solutions. The results are extended to N-coupled systems, completing the earlier analysis of Sahadevan, Tamizhmani and Lakshmanan.

Evanescent wave immunoprobe with high bivalent antibody activity

We have determined the kinetic response of an evanescent wave optical fibre immunosensor and its absolute sensitivity. Using both kinetic methods and optical determinations of bound antigen, we infer that there are 2·4 × 10 11 active antibodies per cm 2 probe area. We estimate that 75% of the active antibodies are in the bivalent form, with both binding site capable of binding antigen. Using the kinetic data and optical measurements of the number of antigens bound to the fibre, we estimate that the unstirred dead layer thickness next to the fibre surface in the stirred solution, across which the antigens must diffuse, is 55 μm. Approximately 10 9 FITC labelled antigens are necessary to achieve a threshold signal, defined as 1% of the signal obtained when the fibre is saturated with antigen.