Equivalent Step Index Research Articles

Bend-induced losses in a single-mode microstructured fiber with a large core

A study of bend-induced losses in a silica-based single-mode microstructured fiber with a core diameter ranging from 20 to 35 microns and increased relative air content in the holey cladding has been conducted. With the use of the equivalent step-index profile method in approximation of waveguide parameters of microstructured fiber (normalized frequency and normalized transverse attenuation constant) the effect of bending on the spectral position of the fundamentalmode short-wavelength leakage boundary has been analyzed. Upon measurement of spectral characteristics of attenuation in the considered fibers good accordance of numerical and experimental data has been found out. It is shown that increase of the air content in the holey cladding leads to expansion of the mentioned boundary to lower wavelengths for the value from 150 to 800 nm depending on the core size and bending conditions. A single-transverse-mode propagation is achieved on fiber length of 5-10 meters due to a substantial difference in losses of fundamental and higher-order guided modes attained by bending. Optical losses in all studied samples are less than 10 dB/km at the wavelength λ = 1550 nm. The results of the study can be applied in the design of high-power laser systems having such basic requirements as a relatively large mode spot and high beam quality.

Determination of modal effective indices and dispersion of microstructured fibers with different configurations: a variational approach

A simple semi-analytical model based on the variational method is developed for determining the effective indices of the fundamental modes and consecutively the dispersion properties of microstructured optical fibers (MOFs) with different lattice geometries without resorting to any numerical tool. We consider an equivalent step-index (ESI) profile of the MOF and the fundamental mode shape is approximated as a simple Gaussian function in the core. Effective index data and dispersion obtained from the proposed variational method offer reasonable agreement with numerically derived data using the Finite Element Method (FEM). The proposed model offers an alternative and swift way for reasonably precise determination of the effective index of the fundamental mode and dispersion properties of MOF designs with different lattice geometries. Finally, as a major application, the dispersion property of a fabricated MOF, derived through the proposed variational method, is directly used in order to model experimental supercontinuum (SC) spectra with satisfactory agreement.

Bending Loss Evaluations of Holey Fibers Having a Core Consisting of an Elliptical-Hole Lattice by Various Approaches

In general, an accurate evaluation of the bending loss of an optical fiber with an arbitrary refractive index profile is a cumbersome task, especially for holey fibers (HFs). In this paper, various approaches are applied and compared for the bending loss evaluations of single-polarization elliptical-hole core circular-hole HFs (EC-CHFs), which are circular-hole HFs having a core with an elliptical-hole lattice structure. Our simulation results show that when bending loss formulas for weakly guiding circular fibers are applied to a HF by regarding it as an approximate circular fiber having an equivalent step-index (SI) profile, the definition of the core region is the most crucial issue. Moreover, we also show that the results obtained by the approximate approach based on the bending loss formulas for the equivalent SI circular fiber are in good agreement with direct approaches with numerical simulations for the real EC-CHF structure, if the equivalent core radius is suitably defined for the real cross section.

Analysis of the multifilament core fiber using the effective index theory

Multifilament core (MFC) fibers are a new type of microstructured fiber recently introduced. We investigate their properties using finite element modeling and show that the equivalent step index fiber based on moments theory does not provide similar properties. We propose an effective index theory based on the fundamental space filling mode which allows to predict the MFC properties using a semi-analytical modeling. Good resistance to bending is thus attributed to increased core effective index due to the high index filaments.

A new analytical model for the field of microstructured optical fibers

We present an analytical model for the mode of index-guided microstructured fibers. This model exhibits essential symmetry features of the field unlike the commonly used equivalent step-index (ESI) model. The model is shown to be more accurate than the equivalent step-index (ESI) model in predicting the effective-indices of the mode. Results for the modal effective index, near and far fields and dispersion have been included.

Approximation of photonic crystal fibres with large air holes by the step index fibre model

An equivalent step index fibre with a silica core and air cladding is used to model photonic crystal fibres with large air holes. We model this fibre for linear polarisation (we focus on the lowest few transverse modes of the electromagnetic field). The equivalent step index radius is obtained by equating the lowest two eigenvalues of the model to those calculated numerically for the photonic crystal fibres. The step index parameters thus obtained can then be used to calculate nonlinear parameters like the nonlinear effective area of a photonic crystal fibre or to model nonlinear few-mode interactions using an existing model.

采用基本空间充填模式的掺铒多孔光纤分析

Erbium-doped holey fiber with hexagonal lattice was modeled by using effective index method. In order to calculate the equivalent step index of the periodic structure of the cladding holey optical fiber, all-vectorial fundamental space filling mode approach was utilized. By using EH11 mode, we have numerically solved the rate equations of a three-level pumping scheme for a fiber laser. The obtained results have shown a good agreement with the other experimental results, recently. The results have predicted amplifiers with gain efficiencies as high as 10 dB/mW. OCIS codes: 060.2310, 060.2410, 060.2320, 140.3500, 140.4480. doi: 10.3788/COL20080609.0644. In erbium doped fiber amplifiers (EDFAs), to obtain high gain efficiency one needs to use fibers with high numerical aperture (NA) to achieve the maximum population inversion of the erbium ions. It is useful to confine the erbium ions to the central part of the core to enforce the pumping light propagating with the fundamental HE11 mode [1,2] . Germanium-doping, which is used in the core of high NA fiber, reduces the emission bandwidth of the Er 3+ ions and limits its concentrations. This results in narrower gain bandwidths and increases the device

Comparison of different methods for rigorous modeling of photonic crystal fibers

We present a summary of the simulation exercise carried out within the EC Cost Action P11 on the rigorous modeling of photonic crystal fiber (PCF) with an elliptically deformed core and noncircular air holes with a high fill factor. The aim of the exercise is to calculate using different numerical methods and to compare several fiber characteristics, such as the spectral dependence of the phase and the group effective indices, the birefringence, the group velocity dispersion and the confinement losses. The simulations are performed using four rigorous approaches: the finite element method (FEM), the source model technique (SMT), the plane wave method (PWM), and the localized function method (LFM). Furthermore, we consider a simplified equivalent fiber method (EFM), in which the real structure of the holey fiber is replaced by an equivalent step index waveguide composed of an elliptical glass core surrounded by air cladding. All these methods are shown to converge well and to provide highly consistent estimations of the PCF characteristics. Qualitative arguments based on the general properties of the wave equation are applied to explain the physical mechanisms one can utilize to tailor the propagation characteristics of nonlinear PCFs.

Complete Analysis of the Characteristics of Propagation into Photonic Crystal Fibers, by the Finite Element Method

Using the finite element method, we propose an accurate vector analysis of the lowest electromagnetic modes of photonic crystal fibers. The likeness of their propagation characteristics to those of step index fibers is emphasized. Within the determined limits of a domain of validity, an equivalent step index fiber is defined. In addition, the single-mode broadband behavior of photonic crystal fibers is analyzed. The chromatic dispersion at any wavelength is reliably predicted from the geometric parameters of these fibers. With suitable geometrical parameters, the zero dispersion wavelength can be shifted, for example, toward values close to 1 μm.

Bend loss in single-mode fibers

In this paper, we present the results of extensive single-radius bend loss measurements for two different fibers over wide ranges of wavelength (800-1600 nm) and curvature radius (13.5-27.5 mm). A new bend loss formula is also derived, allowing a good fit of experimental data over the whole range of both parameters. Using an equivalent step-index (ESI) approach we obtain a good agreement between estimated and real parameters: e.g., cutoff wavelengths are within 1%.

New equivalent step index methods for designing nonlinear fibres

The equivalent step index (ESI) framework is shown to provide a convenient approximation for evaluating the performance of different optical fibre designs for potential use in nonlinear signal processing elements. New ESI methods are presented which combine reasonable accuracy with simple expressions for the ESI parameters, allowing fast and reliable solution of fibre design problems, and straightforward comparison between theory and measurements on experimental nonlinear fibres.

An equivalent step-index model for single-mode fibers based on matching of bend loss and spot size at one wavelength: a simulation study

A method for the determination of equivalent step index (ESI) parameters for a given single-mode fiber is presented. The method is based on the matching of bend loss characteristics and (Petermann II) spot size at one wavelength. Numerical simulation studies have been carried out for fibers with parabolic and triangular index profiles having zero total dispersion at 1300 or 1550 nm. The results show that the method gives a model that is both stable with respect to the matched wavelength in the 1500-1600-nm range and accurate for predicting fiber characteristics such as spot size, waveguide dispersion, bend loss, and the cutoff wavelength (of the next higher mode) over this range of wavelength.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Variational approach to nonlinear waveguides—Gaussian approximations

Gaussian and equivalent step index approximations have been very useful for characterising linear waveguides. A variational approach can be used to derive similar, very accurate approximations for nonlinear propagation in both planar and circular waveguides.

Circularly symmetric modal interferometers: Equalization wavelength and equivalent step determination for matched-cladding fibers

Abstract An LP01-LP02 modal interferometer fabricated from a standard matched-cladding telecommunication fiber is studied in the visible wavelength range. Its spectral response in the vicinity of the LP01/LP02 equalization wavelength is used to characterize the fiber by the determination of an equivalent step index profile.

Equivalent step index (ESI) model for elliptic core fibers

We present empirical relations describing the spectral dependence of the spot sizes of the fundamental mode (along the major and minor axes) in a homogeneous elliptic core fiber. These relations are obtained by modeling the fundamental mode by a Gaussian distribution. Using these relations, we present a method for the determination of the equivalent step index (ESI) parameters of a monomode elliptic Core fiber. The applicability of the proposed method is shown through a) calculation of the cutoff wavelengths of a parabolic index elliptic core fiber and b) calculations of various fiber parameters like the core radii and index difference of an elliptic core fiber from recently reported experimental data.

Comparison of different methods for the determination of the parameters of the equivalent step profile of the refractive index of single-mode fiber waveguides

An experimental comparison was made of the parameters of an equivalent step-index profile of single-mode fiber waveguides obtained by the following methods: from the spectral dependence of the mode spot size, from the deexcitation wavelength, from the near- and far-field patterns, and by integration of the real profile. It was found that the best results in the determination of the parameters of the equivalent step-index profile of the refractive index were obtained from the spectral dependence of the mode spot size.

Usage-based comparison of ESI techniques

A comparative study of equivalent-step-index (ESI) techniques is performed on the basis of the ESI fiber's ability to predict the bend, transition, microbending and splice loss, waveguide dispersion, launching efficiency, and second-mode cutoff wavelength. Theoretical and experimental investigations were performed to determine the accuracy of the predictions. It was found that none of the present ESI techniques can be used to characterize all features of interest for a single-mode fiber with great accuracy. However, for the purpose of producing specifications on the behavior of single-mode fiber systems, it may be adequate to specify bounds on parameters such as bend loss within a factor of two.

Constant-curvature loss in monomode fibers: an experimental investigation

A new technique for the measurement of constant-curvature (bend) loss as a function of bend radius is described, and it is shown that the influence of transition (microbend) losses can be essentially eliminated. Based on this technique and via the application of curve-fitting procedures and the Newton-Raphson method for two variables, a sensible equivalent step index can be obtained if stress-induced changes in the bent fiber are taken into account. However, the prediction of bend losses at other wavelengths is coarse, and it is shown that, for our fiber, agreement between theory and experiment can be considerably improved via an empirically deduced stress-induced dependence that is far stronger than predicted by published theory.

Slab waveguides characterized by moments of the index profile

The fundamental mode of a symmetric slab waveguide is described to a high degree of accuracy using only two moments of the refractive index profile rather than its exact form. The two moments can be used to define an equivalent step index slab waveguide, and the fundamental mode propagation constant of an arbitrary profile guide is given by the step index value multiplied by a simple correction factor. The limit to single-mode operation, the second-mode cutoff point, is also given by a simple formula requiring only profile moments. Numerical confirmation of the method is given.

Characterization of single-mode fibers from wavelength dependence of modal field and far field

We present direct methods for determination of equivalent-step-index (ESI) parameters and file modal field by measurement of the wavelength dependence of the far-field intensity in single-mode fibers. A comparison is made with the spot-size method commonly used for characterization of such fibers. A new technique for measuring the LP <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> mode cutoff wavelength is also presented.