A technique for the study of mode cut-offs in multimode optical fibres

We describe a technique of using a variable wavelength source to study mode cut-offs up to aV value of 20 for the optical fibre by means of the radiated (scattered) power leaving the fibre. This allows the identification of individual modes in a fibre carrying up to 80 or 100 modes in all and provides a non-destructive method for the study of the length and bend dependence of the energy carried by the highest order modes.     

Local fields in single-mode helical fibres

The scalar local-field wave equations in helical fibres are derived and, with the aid of a special mathematical treatment, solved approximately in a local coordinate system—the Serret-Frenet frame from the Maxwell's equations. Two basic results are obtained: (1) The local modes in a single-mode helical fibre are circularly polarized. (2) The difference of the propagation constants between the two fundamental modes is 2, where is the torsion. They agree well with the known experimental measurements.     

Resonance modes in optical fibres

The weakly nonlinear boundary value problem of wave propagation in an optical fibere(for the transverse electric mode,for example)is formulated and a modified linear solution is obained.It is shown that a self-consistent theory of fibre optics should be weakly nonlinear,The mode of critical refraction that does not exist in the linear theory is obtained,showing that it is a mode consisting of resonance modes,It is shown that the signal carriers in a long fibre are of resonance modes,not normal modes,Some experimental data are given for comparison with the theoretical predictions and the agreement seems satisfactory.     

Variational approximations for higher-order modes of weakly-guiding fibres

Simple approximations for the fields and propagation constants of low-order modes on circular weakly guiding fibres are derived using variational techniques. The high accuracy of these approximations for quasi-parabolic profiles is demonstrated in the case of the Gaussian profile, for which there are no analytical solutions of the scalar wave equation.     

Curvature effects on leaky modes in weakly guiding optical fibres

The effect of curvature on leaky modes with low losses in weakly guiding optical fibres is investigated, within a theoretical model where the cladding (outer cladding in case of multiclad fibres) is extended to infinity. Such modes already radiate rays in the cladding when the fibre is straight and two cases can be considered according to whether this ray pattern is modified near the core area in the bent fibre (strong curvature) or is not modified (weak curvature). A general loss formula is given for the case of weak curvature. The rays which are emitted in the curvature plane, towards the inner side of the bend are captured later on by the core and induce an oscillating modulation of the leakage loss, with an amplitude varying asR ^–1/2 but limited to a few per cent in practical cases (for weak curvatures). The case of strong curvatures is analysed in the special case of the LP 01 mode in fibres with a large depressed inner cladding, through a 2-D ray method. It is found that the loss oscillations are rapidly damped while the average loss is considerably increased.     

Structure and scaling of helical modes of light

Modes of light that contain topological defects such as screw dislocations can be focused into optical traps with interesting and useful properties. The way in which the intensity distribution within helical modes of light varies with topological charge is discussed, and new scaling predictions for their radial profiles that are consistent with experimental observations are introduced.     

Evidence for helical edge modes in inverted InAs/GaSb quantum wells

We present an experimental study of low temperature electronic transport in the hybridization gap of inverted InAs/GaSb composite quantum wells. An electrostatic gate is used to push the Fermi level into the gap regime, where the conductance as a function of sample length and width is measured. Our analysis shows strong evidence for the existence of helical edge modes proposed by Liu et al [Phys. Rev. Lett. 100, 236601 (2008)]. Edge modes persist in spite of sizable bulk conduction and show only a weak magnetic field dependence-a direct consequence of a gap opening away from the zone center.     

Length-dependent effects due to leaky modes on multimode graded-index optical fibres

The radiation losses of tunnelling leaky modes in graded-index optical fibres are calculated theoretically, and it is shown that the near-field intensity profile has a length dependence. Consequently measurements of the near-field intensity distribution do not give the refractive index profile directly, and a correction factor must be applied. We have investigated this factor and find that it depends only on a single normalisation parameter involving fibre length, core radius and normalised frequency. A further use of the correction factor is to determine the total power attenuation due to the loss of leaky modes.     

Investigation of elastic modes propagating in multi-wire helical waveguides

Elastic guided waves have some potential for non-destructive inspection of civil engineering multi-wire steel cables. However, wave propagation inside such structures is not yet fully understood. This paper investigates multi-wire helical waveguides with special attention to the common seven-wire strand configuration (one straight core surrounded by one layer of six helical wires). A helical coordinate system is first proposed. Though non-orthogonal, this system preserves translational invariance along the helix centreline to explicitly perform a spatial Fourier transform. Then, it is shown that for the analysis of multi-wire helical strands a twisting system—which is a special case of helical systems—is translationally invariant. A semi-analytical finite element method is developed reducing the problem on the cross-section only. A straightforward computation of energy velocity is proposed. Dispersion curves for a single straight wire and a helical wire are first computed to verify the adequacy of the twisting system. Finally the seven-wire strand is analysed using simplified contact conditions. Theoretical dispersion curves are compared to low-frequency magnetostrictive measurements. Good agreement is found for the first compressional-like mode and its associated veering central frequency (‘notch frequency’).     

Dispersion of tubular modes propagating in multimode optical fibres

We have already used interferometric techniques for measuring, first, the impulse response of optical fibres and further the different times of flight of modes of a multimode fibre. Apart from time of flight, our set-up provides the intramodal dispersion of each mode (d² β/dω ²). To demonstrate, we have measured the modal dispersion difference between two tubular modes that were selectively excited in a multimode graded index fibre. For comparison, a theoretical expression has been derived, based on a ray optics approach.     

The prism-taper coupler for the excitation of single modes in optical transmission fibres

A coupler is described which allows the excitation of pure single guided fibre modes with a single mode laser. The coupler uses a prism and precision taper fibre end to access any of the fibre modes. The conditions for obtaining excitation of single modes are discussed and the technique for producing the tapers is described. In the first tests, an excitation efficiency of approximately ?16 dB has been obtained.     

Numerical investigation of elastic modes of propagation in helical waveguides

Steel multi-wire cables are widely employed in civil engineering. They are usually made of a straight core and one layer of helical wires. In order to detect material degradation, nondestructive evaluation methods based on ultrasonics are one of the most promising techniques. However, their use is complicated by the lack of accurate cable models. As a first step, the goal of this paper is to propose a numerical method for the study of elastic guided waves inside a single helical wire. A finite element (FE) technique is used based on the theory of wave propagation inside periodic structures. This method avoids the tedious writing of equilibrium equations in a curvilinear coordinate system yielding translational invariance along the helix centerline. Besides, no specific programming is needed inside a conventional FE code because it can be implemented as a postprocessing step of stiffness, mass and damping matrices. The convergence and accuracy of the proposed method are assessed by comparing FE results with Pochhammer-Chree solutions for the infinite isotropic cylinder. Dispersion curves for a typical helical waveguide are then obtained. In the low-frequency range, results are validated with a helical Timoshenko beam model. Some significant differences with the cylinder are observed.     

Guided modes in fibres with parabolic-index core and homogeneous cladding

Mode propagation characteristics of parabolic-index fibres with a homogeneous cladding are studied by using vector wave analysis. By investigating the asymptotic behaviour of the eigenvalue equations and the field components at cut-off and far from cut-off, a comprehensive and consistent scheme for the designation of the various modes is established. Strong similarities with step index fibres are found for both the mode designation schemes and the degeneracy properties among the hybrid modes as well as the TE_0m and TM_0m modes. This suggests that the technique employed in this paper can be applied to other types of graded-index fibres. In addition, numerical results obtained by solving the eigenvalue equations for a wide range of parameters are presented, which verify the theoretical predictions. Comparisons with the infinite-core approximation (ICA) and the field decomposition technique (FDT) are given. It is shown that neither the ICA nor FDT are applicable for modes near cut-off.Work supported in part by the Department of Communications, Canada.     

Prediction of giant breathing and rocking modes in double helical RNA

A theoretical calculation of the normal mode spectrum of double helical RNA shows large breathing and rocking modes at low frequencies.     

External helical modes of a solitary current in an unconfined plasma

Siberian Institute of Terrestrial Magnetism, the Ionosphere, and Radio Propagation, Siberian Branch, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 10, pp. 1168–1175, October, 1990.     

Effective baryon-lepton coupling and the proton decay modes

We present a simple model for the phenomenology of baryon-number violating nucleon decays in which the basic process is taken to be a direct conversion of a baryon into a lepton or an antilepton. A large number of branching modes are found to be correlated, independently of any specific grand unification scheme.     

Stabilization of neoclassical tearing modes by an externally applied static helical field

The effect of a static helical magnetic field on the nonlinear growth of the neoclassical tearing mode (NTM) is investigated. The NTM is found to be stabilized by an externally applied helical field of a different helicity if the field magnitude is sufficiently large, suggesting a very simple method for stabilizing the NTM. The mechanism responsible for this stabilization is the decreased fundamental harmonic pressure perturbation of the NTM in the presence of the helical field.     

Quantization of intrinsic localized modes: Effective linear lattice method

A working method is proposed to quantize intrinsic localized modes (ILMs) in lattices with hard quartic anharmonicity in the framework of the rotating-wave approximation. This is done by reducing a nonlinear eigenvalue problem to a linear one by averaging slowly varying reduced effective force constants over frequencies, enabling us to quantize the ILM in a straightforward manner. Such an effective linear lattice (ELL) method is first applied to an analytically tractable d-dimensional cubic lattice to show that the concept of the ELL holds exactly in the strong localization limit. Next, general lattice models are investigated to achieve quantization of the ILM in an approximate manner. The obtained analytical results are tested by solving numerically a model one-dimensional lattice to show that phase-space trajectory of an ILM-bearing atom is of elliptic type with finite but small width. The numerical result confirms the validity of the ELL leading to its semi-classical quantization. On the other hand, orbits of all the remaining atoms exhibits complex non-periodic trajectory to which a direct application of the semi-classical quantization rule appears impossible.