The influence of skew rays on angular losses in air-clad fibres

Detailed experimental transmission properties of high numerical aperture air-clad undoped fibres are presented. Measurements of the angular transmissivity indicate a 15% lower numerical aperture (NA = 0.75) compared to theoretical predictions for the bridge thickness and wavelength ratio of δ/λ = 0.226. The discrepancy is attributed to skew rays that are deliberately launched and which are subject to larger loss rates through diffractive tunnelling in frustrated total internal reflection than meridional rays. Measurements of the angular propagation losses show that light launched at angles less than the critical angle for total internal reflection experiences low initial losses as well as low propagation losses. Light launched at steeper angles experiences a significant initial loss attributed to loss of skew rays within 1.5 m of propagation as well as larger general propagation losses.     

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.     

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.     

Tunnelling rays in graded-index fibres

An analysis of the role of tunnelling rays in pulse propagation in graded-index fibres is presented. Tunnelling ray attenuation is handled by using the generalized parameter technique which allows attenuation coefficients to be dispensed with and relevant families of tunnelling rays to be identified. Results are given for impulse response pulse widths and shapes. Incorporation of tunnelling ray pulse contributions into the formalism for determining optimum refractive-index profiles is presented. For most cases, tunnelling ray effects are small, but significant corrections may be necessary when measurements are made on short lengths of fibre.     

General method for determining the first order gradients of skew rays of optical systems with non-coplanar optical axes

Current commercial software for the analysis and design of optical systems uses finite difference (FD) approximation methodology to estimate the gradient matrix of a ray with respect to system variables. However, FD estimates are intrinsically inaccurate and are subject to gross error when the denominator is excessively small relative to the numerator. This paper avoids these problems and determines the gradient matrix of the exit ray traveling along an optical system with a non-coplanar axis. To achieve this, the gradient matrix of the rays reflected/refracted by flat or spherical boundary surfaces are first determined by directly differentiating the skew-ray tracing equations. By introducing a Jacobian matrix, which represents the partial derivatives specifying the rates of changes between boundary variables and element variables, one can obtain the gradient matrix of the exit ray of an element with respect to its independent variables. This methodology will be useful in the analysis of rays and in design of optical systems with non-coplanar axis. A right-angle prism is used as illustrative example to validate its applications.     

Tunnelling leaky modes on optical waveguides

The lossless dielectric waveguide of circular cross section with an index of refraction greater than its surround supports trapped modes in addition to two subclasses of leaky modes: refracting and tunnelling modes. Refracting modes leak because their fields are formed by waves that undergo refraction at the core-cladding interface. Tunnelling modes leak because their fields are formed by waves that undergo a form of electromagnetic tunnelling at the core-cladding interface due to the curvature of its cross section. Tunnelling modes have a very slow leakage compared to refracting modes and are therefore important for the understanding of propagation in multimode, optical waveguides of circular cross section.     

Asymmetries in optical fibres

Two methods for treating the effects of small asymmetries in the cross sections of roughly cylindrical optical fibres are described. These predict the presence of stable power distributions, ribbons for example, within the fibre core. Experimental results on actual fibres showing these effects are given. To be effectively asymmetric a fibre of elliptical cross section need have major and minor diameters differing by only 0.08 μm.     

Twin-hollow-core optical fibres

Twin-hollow-core microstructured optical fibres have been fabricated and characterised for the first time. The fibre cladding structure results in guidance by the inhibited coupling mechanism, in which there is a low overlap between the core modes and surrounding structure. This results in minimal interaction between the modes of each core in the transmission bands of the fibre and hence minimal coupling between the cores. It is shown that light is able to couple between the cores via coupling to cladding struts in the high loss wavelength bands.     

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.     

Use of skew rays in multimode fibers to generate speckle field with nonzero vorticity

Beams at the output of an axially symmetric multimode fiber were produced with mostly positive or negative values of angular index m through skew illumination of the input end of the fiber. In this way rays with predominantly positive or negative helicity were excited inside the fiber. The output cw speckle field at the wavelength lambda = 632.8 nm contained large densities N(+) and N(-) of wave-front dislocations, or optical vortices, of both positive and negative sign. Vorticity was defined as V = N(+) - N(-) , was expressed analytically through the Wigner function of the field, and was found experimentally to be in good agreement with theory.     

Dual-core leaky optical waveguide as an integrated-optic polarizer

We present a design of a dual-core leaky waveguide that can be used as an integrated-optic polarizer. The proposed polarizer works on the principle of mode filtering. The structure is characterized by two cores, namely core-1 and core-2 and a high index layer in the upper-most region, such a structure supports leaky modes. The leakage losses of the modes have been calculated by using the transfer matrix method (TMM). Single polarization operation is ensured by high differential leakage loss between fundamental TE and TM modes. We show TE-pass operation with 0.5 dB/mm loss in TE₀ mode and 13 dB/mm loss in TM₀ mode, and TM-pass operation with 0.36 dB/mm loss in TM₀ mode and 7.45 dB/mm loss in TE₀ mode. Besides single-polarization operation, single-mode operation of the structure is ensured by high leakage loss of all the other higher-order modes.     

Bend radiation of optical fibres

Theoretical and experimental investigations of the radiation far field from a curved optical fibre have been carried out for the lowest order LP-modes. The investigations concern the characteristics of pure bend loss radiation in a direction orthogonal to the plane of the bend. Possible applications involving the bend radiation are briefly discussed.     

Anomalous group delay in optical fibres

It is shown, by means of computation on a specific model, how pulse broadening in multimode gradedindex optical waveguides is significantly affected by the levels of excitation of the high-order modes. Pulse widths are computed as functions of the profile parameter, under conditions of equal excitation, high-order mode suppression and GaAs laser excitation.     

Use of optical fibres in Raman spectroscopy

A detailed study of the parameters governing the design of an optical fibre system for use in Raman spectroscopy is described. The results have led to the design and construction of a flexible fibre optic remote sampling system which is easily adaptable for use on most commercial instruments. A variety of samples were used to evaluate the performance of the system and have been classified in terms of the efficiency of the new technique relative to more conventional methods of excitation and collection.     

Theory of scattering in multimode optical fibres

The problem of scattering in multimode optical fibres is treated in a rigorous way by means of both a ray and a statistical approach. These two methods are interlaced and harmonized. Applications to microbending, ellipticity, core radius and maximum numerical aperture variations, and fluctuations of index profile shape are performed. Useful results about power distribution and fibre attenuation are derived in each case.     

Fluoride fibres for optical transmission

Optical fibres made from heavy metal fluorides have been under development for much of the past decade. There have been significant advances in understanding the fundamental characteristics of these materials. Progress towards achieving low optical losses and in optimizing the design of fluoride fibres for use in long transmission systems is reviewed.