Solution of mode coupling in step-index optical fibers by the Fokker-Planck equation and the Langevin equation

The power-flow equation is approximated by the Fokker-Planck equation that is further transformed into a stochastic differential (Langevin) equation, resulting in an efficient method for the estimation of the state of mode coupling along step-index optical fibers caused by their intrinsic perturbation effects. The inherently stochastic nature of these effects is thus fully recognized mathematically. The numerical integration is based on the computer-simulated Langevin force. The solution matches the solution of the power-flow equation reported previously. Conceptually important steps of this work include (i) the expression of the power-flow equation in a form of the diffusion equation that is known to represent the solution of the stochastic differential equation describing processes with random perturbations and (ii) the recognition that mode coupling in multimode optical fibers is caused by random perturbations.     

A transmission length limit for space division multiplexing in step-index silica optical fibres

ABSTRACT

By solving the power flow equation, we investigate the influence of mode coupling on space division multiplexing capability of three multimode step-index silica optical fibres with a different strengths of mode coupling. Results show that mode coupling significantly limits the length of these fibres at which the space division multiplexing can be realized with a minimal crosstalk between the neighbour optical channels. This is most pronounced in silica optical fibres with the strongest mode coupling. The two and three spatially multiplexed channels in the investigated step-index silica optical fibres can be employed with a minimal crosstalk up to the fibre lengths of few hundred of meters and few tens of meters, respectively. These lengths are much shorter than kilometer lengths at which these fibres are usually employed without space division multiplexing. Such characterization of optical fibres should be considered in designing an optical fibre transmission system for space division multiplexing.     

Mode coupling in strained and unstrained step-index plastic optical fibers

Using the power-flow equation, we have examined the state of mode coupling in strained and unstrained step-index plastic optical fibers. The strained fibers show much stronger mode coupling than unstrained fibers of the same types. As a result, the coupling lengths where equilibrium mode distribution is achieved and the lengths of fiber required for achieving a steady-state mode distribution for strained fibers are much shorter than the corresponding lengths for unstrained fibers.     

Calculation of the coupling coefficient in strained step index plastic optical fibers

The coupling coefficient in a strained step index plastic optical fiber is determined using our recent simplified method. This enabled the calculation of the length z(s) at which the steady-state distribution (SSD) is achieved. Results are in good agreement with measurements reported earlier. The strained fiber shows a much stronger mode coupling than the unstrained one of the same type. Consequently, the fiber length for achieving the SSD is much shorter for strained than unstrained fibers.     

Optical power flow in plastic-clad silica fibers

Using the time-independent power-flow equation, we have examined the mode coupling caused by intrinsic perturbation effects of step-index plastic clad silica fiber carrying more than 10(5) modes. Result show that the equilibrium mode distribution for this fiber is achieved at a length of approximate 550 m, which is longer than reported previously. While this coupling length is much longer than that of plastic optical fibers, it is sorter than that of all-glass fibers.     

Influence of numerical aperture on mode coupling in step-index plastic optical fibers

Using the power-flow equation, we have examined the state of mode coupling in step-index plastic optical fibers with different numerical apertures. Our results confirm that the coupling rates vary with the coupling coefficient of the fibers as the dominant parameter, especially in the early stage of coupling near the input fiber end. However, we show that the fiber's numerical aperture has a significant influence on later stages of this process. Consequently, equilibrium mode distribution and steady-state distribution are achieved at overall fiber lengths that depend on both of these factors. As one of our examples demonstrates, it is possible for the coupling length of a high-aperture fiber to be similar to that of a low-aperture fiber despite the three-times-larger coupling coefficient of the former.     

Photo‐Thermo‐Mechanical Behaviour Under Quasi‐Static Tensile Conditions of a PMMA‐Core Optical Fibre

As the optical power transmitted by an optical fibre under tensile stress varies with strain, it can be used as a sensor for strain monitoring in structural elements. In the present work, quasi‐static tensile tests of step index polymer optical fibres (POF) with simultaneous measurement of surface temperature and optical power are described. Young's modulus, yield stress and tensile strength are derived from experimental tests. Morphological characterization of the POF fibres using scanning electron microscope images and differential calorimetry technique is performed. The contributions of both elastic and plastic strain components to the variation of temperature and optical power loss are also estimated. The evolution of the POF mechanical properties as well as that of temperature and optical power loss is explained in terms of the progressive relative movement and alignment of the molecular chains in the direction of the applied load. Strain, temperature and optical power loss are then correlated.     

The application of optical fibres as witness devices for the detection of plastic strain and cracking

Low cost optical fibres have recently become readily available for telecommunications purposes. Silica fibres are characterised by high elastic strains to failure. The feasibility of using these fibres for structural integrity monitoring particularly for offshore structures is investigated. The basis of the technique is that a fibre may be bonded to a critical part of a structure and provides an optical path which will be broken if the fibre fails due to plastic strain or crack opening in the critical area.
Groups of fibres which have been given predetermined fracture strains by surface etching were encapsulated in special packs. These packs were bonded to steel and concrete tensile specimens. Strain transfer occurred successfully between the specimens and individual fibres. The distribution of strain to fibre fracture appeared to be uniform along the fibre. The use of several fibres with a range of fracture strains caused fibres to break progressively with increasing strain. For applications to offshore structures it has been found possible to use water-repellent adhesives which can be applied and cured in sea water and suffer no deterioration.
The advantages of this system include versatility, relatively low cost, adaptability to continuous monitoring and the possibility of being fitted retrospectively and refitted after repair operations.     

Spatial Chaotic Power Cross-talk in Nonlinear Multibeam Co-propagation in Optical Fibres

Abstract

We investigate spatial power coupling and chaotic cross-talk when beams co-propagate in multimode optical fibres, specifically among four beams that belong to two weakly degenerate mode families. The nonlinear mechanism responsible for the power and phase coupling is the optical Kerr effect in fibres. The power of each of the modes is theoretically demonstrated to be spatially unstable and chaotically dependent on launch conditions. It is shown that the spatial instabilities and irregular energy exchange occur over broad operating conditions as long as the system deviates from its spatial steady states.     

λ³/1000 plasmonic nanocavities for biosensing fabricated by soft UV nanoimprint lithography

Arrays of plasmonic nanocavities with very low volumes, down to λ(3)/1000, have been fabricated by soft UV nanoimprint lithography. Nearly perfect omnidirectional absorption (3-70°) is demonstrated for the fundamental mode of the cavity (λ ? 1.15 μm). The second-order mode exhibits a sharper resonance with strong angular dependence and total optical absorption when the critical coupling condition is fulfilled (45-50°, λ ? 750 nm). It leads to high refractive index sensitivity (405 nm/RIU) and figure of merit (～21) and offers new perspectives for efficient biosensing experiments in ultralow volumes.     

GeSe4 glass fibres with low optical losses in the mid-IR

This study proposes the realisation of low-loss fibres in the Ge–Se system. Ge–Se chalcogenide fibres are transparent in the near and middle infrared and show a high non linear refractive index. So, such fibres are of high interest for new optical applications like all optical telecommunication provided that optical losses be sufficiently low. To decrease the optical losses of fibres, several GeSe₄ glasses have been prepared with different chemical and physical purification steps and thorough distillation of selenium under dynamic vacuum. The lowest the optical losses of GeSe₄ fibre are lower than 0.5 dB/m between 1.7 and 7.5 μm except at 4.5 μm where losses are equal to 2.8 dB/m because of Se–H absorption.     

Compressive behaviour of Kevlar 49 fibres and composites

The low compressive strength of Kevlar 49^® unidirectional composites cannot be satisfactorily explained in terms of current theories which assume that failure is due to the matrix material. For a given matrix, Kevlar 49 composites are considerably weaker in compression than those based on other comparable high strength, high modulus filaments. Fracture is found to occur before any plastic deformation of the matrix is observed.This behaviour can be explained in terms of the very low compressive yield strength of the Kevlar 49 fibres themselves. Elastica loop tests show that non-Hookean deformation of the fibres occurs at quite low stresses corresponding to values of the order of those at which fracture takes place in the composite. This deformation is plastic in nature.Buckled areas on the compression side of the elastica loop can be seen in the optical and scanning electron microscopes. It is suggested that the buckling follows from the separation of microfibrils under compression.     

Modeling of the loss and mode coupling due to an irregular core-cladding interface in step-index plastic optical fibers

The core-cladding boundary in step-index plastic optical fibers is imperfect. Surface irregularities locked in during the manufacturing process couple the guided modes by reflecting them in directions that deviate unpredictably from the expected directions. This causes an additional loss as the multiple reflections from surface elements with directions randomized around the nominal for the cylinder transfer the power to the radiation modes that are carried away from the core into the cladding. We model such loss and mode coupling by ray tracing. The irregular core-cladding interface is represented by nominally cylindrical surface elements with orientations randomly perturbed around two geometric axes. The results show mode coupling and relative loss per unit fiber length caused by the core-cladding interface irregularities. The loss is high close to the input fiber end where mode coupling is intense. It drops farther along the fiber as mode coupling slows down and stabilizes where the equilibrium mode distribution is reached.     

On a quasiclassical Langevin equation

It is shown that the motion of a quantum mechanical particle coupled to a dissipative environment can be described by a Langevin equation where the stochastic force is generalized such that its power spectrum is in accordance with the fluctuation-dissipation theorem. This generalized Langevin equation has an interesting range of applicability. It includes the quasiclassical regime provided that the damping, that is, the coupling of the particle to its environment, is sufficiently strong.     

Light guidance in new chalcogenide holey fibres from GeGaSbS glass

Holey fibres have a broad range of optical properties thanks to their microstructuration and offer a wide range of applications. The combination of intrinsic properties of compound glass, such as chalcogenide glass, and a microstructured fibre geometry allows to consider exacerbated optical properties such as dispersion and nonlinearity for these fibres. In this study, high-index sulphide glass holey fibres (n = 2.251 at 1.55 μm) have been accomplished using the capillary-stacking technique. Sulphide glasses from the GeGaSbS system are used. The drawing step is crucial for microstructuration and for determination of optical properties. Sulphide holey fibres, which were optically characterised with near-field spectroscopy at 1.55 μm, show a single-mode guidance with an effective mode area of 108 μm².     

Low loss, low refractive index fluorinated self-crosslinking polymer waveguides for optical applications

Synthesis and optical applications of low loss methacrylate-based fluorinated polymers are described. The synthesis of well defined self-crosslinking fluorinated polymers has been carried out in order to tune refractive index in the range of 1.390 < n < 1.450. After thermal crosslinking, one single lithographic step followed by reactive ion etching is necessary to monomode optical waveguide fabrication on silicon substrates. Optical losses lower than 1 dB/cm at 1300 nm and 2 dB/cm at 1550 nm were measured for highly confined modes. Efficient chip coupling to lensed optical fibers was obtained. Using waveguides with an effective index close to that of bulk silica, a significant coupling interaction between the guided modes and the whispering gallery modes of a silica microsphere was evidenced thus opening the way for new device applications.     

Method for calculating the coupling coefficient in step-index optical fibers

A simple method is proposed for determining the mode coupling coefficient D in step-index multimode optical fibers. It only requires observation of the far-field output pattern for one fiber length with the input light launched centrally along the fiber axis (theta(0)=0). For illustration, the coupling coefficient determined by this simple method for a step-index plastic optical fiber was used to calculate the coupling length L(c) at which the equilibrium mode distribution is achieved, and length z(s) at which the steady-state distribution is achieved. Our results are in good agreement with experimental results reported earlier.     

Potential interest of optical fibres as immunosensors: study of different antigen coupling methods

New approaches in the field of fluoroimmunoassays involve the use of optical fibres as solid support of reagents and waveguide. Parameters which influence the response of optical fibre fluoroimmunosensors have been studied. Several methods, involving either a physical or a covalent process, have been investigated for immobilizing on silica surfaces polyclonal rabbit immunoglobulin (IgG) as antigen. Fluorescent anti-rabbit IgG has been used for determining immobilized antigen levels. The fluorescence intensity emitted by the immunosensors has been determined by using the evanescent wave phenomenon. The binding capacity of the different immunosensors tested appears nearly similar, except for the sensor prepared with the 3-glycidoxypropyl trimethoxysilane coupling method which seems to exhibit a lower binding capacity. For all sensors prepared with a covalent coupling method, a simultaneous adsorption phenomenon probably affects the long-term stability of immunosensors. In a further step, the possibility of immunosensor regeneration after a dissociation of antigen/antibody complexes has been tested. It appears that the dissociation methods could affect the sensor response. Finally, the specificity of immunosensors has been investigated. A significant cross reactivity was observed forp-toluenesulphonyl chloride and 3-aminopropyl triethoxysilane (APTES)-derivatized fibres. For the APTES-derivatized sensor, the specificity markedly decreased after a dissociation step. Therefore, although the feasibility of a competitive assay has been established, suitable conditions of immunosensor regeneration still require further investigation.     

Bidirectional optical coupler for plastic optical fibers

We have developed a low-loss bidirectional optical coupler for high-speed optical communication with plastic optical fibers (POFs). The coupler, which is fabricated by an injection molding method that uses poly (methyl methacrylate), has an antisymmetric tapered shape. We show that the coupler has low insertion and branching losses. The tapered shape of the receiving branch reduces beam diameter and increases detection efficiency coupling to a photodetector, whose area is smaller than that of the plastic optical fiber. The possibility of more than 15-m bidirectional transmission with a signaling bit rate up to 500 Mbits/s for simplex step-index POFs is demonstrated.     

Fabrication of silicon based glass fibres for optical communication

Silicon based glass fibres are fabricated by conventional fibre drawing process. First, preform fabrication is carried out by means of conventional MCVD technique by using various dopants such as SiCl₄, GeCl₄, POCl₃, and FeCl₃. The chemicals are used in such a way that step index single mode fibre can be drawn. The fibre drawing process consists of various steps such as heating the preform at elevated temperature, diameter monitor, primary and secondary coating, and ultra violet radiation curing. The fibres are then characterized for their geometrical and optical properties. The drawn fibre has diameter of core and cladding to be 8.3 μm and 124.31 μm, respectively whereas non-circularity is found to be 4.17% for core and 0.26% for cladding as seen from phase plot. Mode field diameter is found to be 8.9 μm and 9.2 μm using Peterman II and Gaussian method, respectively. The fabricated fibres showed the signal attenuation of 0.35 dB/km and 0.20 dB/km for 1310 nm and 1550 nm, respectively as measured by the optical time domain reflectometer (OTDR).