Automatic fringe analysis of the induced anisotropy of bent optical fibres

A new theoretical model considering the refraction of the incident light beam by the fibre is suggested to determine the refractive index profile of bent optical fibres. This new model (slabs model) considering the cross section of the bent optical fibre consists of large number of slabs. The slabs model bases on the refraction of the incident beam by the fibre. The refractive index profile of the optical fibre cladding before bending obtained using the automated Fizeau interferometer with the aid of suggested model is compared with other models such as, the homogenous model and the multilayer model to verify the ability of this slab model. The refractive index profile of the bent optical fibre cladding is investigated using this suggested model. In addition, the new model is used to obtain the induced birefringence and the guiding parameters. The bending radius is recommended to be greater than 7.1 mm for the used optical fibre. The consideration of the refraction increases the accuracy of the results.     

Loss calculations in bent multimode optical waveguides

We present a straightforward geometric optics method to calculate the power attenuation induced by a circular bend in the axis of a multimode optical waveguide. The method involves tracing of rays and use of generalized power transmission coefficients. Both slab and fibre waveguides (with either step-index or parabolic core profiles) have been considered; the source has been assumed to be Lambertian.     

Optical characteristics of bent dielectric rectangular waveguides

Bent rectangular waveguide characteristics are analysed using conformal transformation and four-layered waveguide approximation. Using this method the physical model is clear, the optical characteristic expressions given are uncomplicated and the computed result is in good agreement with the results of Marcatili and Marcuse.     

Metal-clad graded-index planar optical waveguides: accurate perturbation analysis

We present a perturbation analysis of propagation constants and attenuation coefficients of TE and TM modes in a metal-clad linear index planar optical waveguide. The imaginary part N″ of the complex modal index N=N′ + iN″ is given by N″ = (∂N′ / ∂′), where =′ + i″ is the complex dielectric constant of the metal cladding and ∂N′ / ∂′ is obtained by numerical differentiation of the solution of the real eigenvalue equation. The cumbersome solution of a complex transcendental equation is thus completely eliminated. The results are in good agreement with those obtained by solving the eigenvalue equation in the complex plane. By taking the metal-clad linear planar waveguide as a preselected waveguide, we can use our RWKB method to solve metal-clad planar waveguides with parabolic, exponential, gaussian and complementary error function index profiles.     

Transmission characteristics of various bent periodic dielectric waveguides

The transmission characteristics of various bent periodical dielectric waveguides (PDWGs) are analyzed by the finite-difference time-domain (FDTD) method in this work. The bending structures include a conventional 90° abrupt bend, a 90° transitional bend, and 90° circular arcs with different quantized radii of curvatures. The simulation results can make us to design a suitable bent PDWG in the photonic circuits.     

Stimulated four-photon mixing in bent few-mode optical fibres

A divided-pump four-photon mixing process is used to investigate the behaviour of modes on a bent few-mode optical fibre. The second-order mode set becomes non-degenerate, even for slight bending; the two modes propagate along the fibre with different group delays and preferred axes of symmetry. Our experimental results are compared with a theoretical analysis.     

A perturbation analysis for modes in diffused waveguides with a gaussian profile

We have developed a first order perturbation approach to obtain the propagation constants for a gaussian index profile by considering it as a perturbation on an appropriately matched secant hyperbolic profile. The secant hyperbolic profile itself well approximates the gaussian profile and hence the perturbation approach yields very accurate results. We have also compared our results with those obtained by the WKB or ray technique and earlier perturbation approaches.     

A perturbation analysis of modes in diffused optical waveguides with Gaussian index profile

Inclusion of a quartic term with adjustable coefficient in the Taylor expansion approximation to gaussian index profiles of diffused optical waveguides is shown to provide an improved approximation to the true gaussian curve to beyond the e-folding depth. A first-order perturbation to the square-law “harmonic oscillator” solutions is applied to improve the calculations of mode indexes and to illustrate the manner in which the corrected wave functions are extended deeper into the substrate.     

Ray theory of the impulse response of randomly bent multimode fibres

A ray theory based on the time-independent Fokker-Planck equation and the integration of time along ray trajectories provides analytical expressions for the average arrival time and spread of optical pulses propagating in randomly distorted, multimode, optical fibres. A clear physical picture emerges from the theory. The analytical expressions obtained for t and t ² coincide with the ones obtained by Olshansky from coupled-mode theory. The t ³ and t ⁴ moments of the impulse response are also calculated. Simple closed-form formulae are given for the step-index slab. The coupling between all modes is effectively taken into account in our ray theory.On leave of absence at the Laboratoire des Signaux et Systèmes.     

Step discontinuities in dielectric waveguides (fibres)

The scattering of surface modes by step discontinuities in dielectric waveguides (lightguides) is investigated by the Wiener-Hopf technique and the variational method. The simple analytical expressions for the scattering characteristics are derived both near and far from cut-off. The results are compared with those obtained by other methods.     

Characteristics analysis of metal-clad and absorptive dielectric waveguides by a simple and accurate perturbation method

We present a simple and accurate method for characteristic analysis of metal-clad dielectric waveguides and absorptive waveguides. The real partN of the complex modal indexN=N + iN is obtained by solving the corresponding real eigenvalue equation, and the imaginary partN is given by (n/), where= + i is the complex dielectric constant of the absorptive layer, and N/ is obtained by numerical differentiation. The method is straightforward, and the cumbersome solution of complex transcendental equations is completely eliminated. Results for simple structures are in good agreement with those obtained by exact analysis.     

Characteristics of vertical bent coupling between straight and curved rectangular optical waveguides

In terms of the coupled mode theory (CMT) and the transfer matrix method, we present a technique and relative formulas including the bent coupling coefficient, amplitude coupling ratio, amplitude transmission ratio and propagation power for analyzing the vertical bent coupling between a curved rectangular waveguide and a straight one. Investigations show that the bent coupling appears in an effective coupling region by both sides of the central coupling point. Beyond this effective coupling region, however, the bent coupling is very weak, and the propagation power in the waveguide is closer to a constant. As the bent radius increases, or the thickness of the coupling layer between these two waveguides decreases, this effective coupling region becomes wider, in which the coupling behavior becomes stronger.     

Application of small-roughness perturbation theory to reverberation in range-dependent waveguides

A rough-interface reverberation model is developed for range-dependent environments. First-order perturbation theory is employed, and the unperturbed background medium can be layered and heterogeneous with arbitrary range dependence. To calculate the reverberation field, two-way forward scatter due to the slowly changing unperturbed environment is handled by fast numerical methods. Backscatter due to small roughness superimposed on any of the slowly varying interfaces is handled efficiently using a Monte Carlo approach. Numerical examples are presented to demonstrate the application of the model. The primary purpose of the model is to incorporate relevant physics while improving computational speed.     

Eigenmodes expansions in lossy open waveguides (fibres)

The properties of the radiation eigenmodes propagating in lossy open waveguides (fibres) are examined by the-operator method. The radiation eigenmode fields are demonstrated to be transversely unbounded at infinity. For these modes the orthogonal relationships are derived by regularization of divergent integrals.     

Difference between TE and TM modal gain in amplifying waveguides: analysis and assessment of two perturbation approaches

The commonly used confinement factor-based formula for modal gain in amplifying waveguides – gmod=Γgmat, with Γ a confinement factor – is well established and accurate for TE modes. The TM case is rarely, and sometimes erroneously, described in the literature. Using a variational formulation the fundamental difference between TE and TM modal gain is illustrated. An accurate expression, correct up to first order, for the TM modal gain is then derived from a known general perturbation formula. However, as this does not lead to a true confinement factor formulation, some approximations are introduced, leading to a unified formulation of both TE and TM modal gain. A second method to calculate the modal gain, based on the analyticity of the dispersion equation, is also discussed. Simulation and comparison with modal gain values from a complex mode solver will finally illustrate the validity of the different approaches. This revised version was published online in November 2006 with corrections to the Cover Date.     

An examination of the effect of polarization on the radiation losses of bent optical fibres

It has long been recognized that the bending losses in weakly guiding optical fibres are independent of the polarization for large bend radius. Here, we show this fact using the volume equivalent current method. The procedure is then applied to a helically bent fibre and it is shown that the radiation from the helical fibre is also independent of the polarization as long as the fibre is weakly guiding.     

Mode coupling in graded-index optical fibres due to perturbation of the index profile

Applied Physics A - Core diameter fluctuations in graded-index optical fibres entail a perturbation of the whole index profile whose effects on mode coupling are investigated. The model here...     

组合型TM01-TE11弯形圆波导模式转换器研究

 研究了组合型TM₀₁-TE₁₁弯形圆波导模式转换器（两弯曲段中间加一段直圆波导），在保持其输出与输入端口轴线平行的前提下，分别从理论推导、数值计算、软件模拟三个方面对此结构进行了分析，模拟结果与数值计算结果吻合得很好。结果表明：计及功率损耗，频率为3.75 GHz，铜波导内径为9.0 cm，轴向间距为10.57 m时，模式转换器总的功率转换效率为93.8%。