Weak Guidance Approximation Research Articles

Efficient multimode vectorial nonlinear propagation solver beyond the weak guidance approximation

In this paper, we present an efficient numerical model able to solve the vectorial nonlinear pulse propagation equation in circularly symmetric multimode waveguides. The algorithm takes advantage of the conservation of total angular momentum of light upon propagation and takes into account the vectorial nature of the propagating modes, making it particularly relevant for studies in ring-core fibers. While conventional propagation solvers exhibit a computational complexity scaling as Nmode4, where Nmode is the number of considered modes, the present solver scales as Nmode3/2. As a first example, it is shown that orbital angular momentum modulation instability processes take place in ring-core fibers in realistic conditions. Finally, it is predicted that the modulation instability process is followed by the appearance of breather-like angular structures.

Theoretical analysis of mode evolution in a tapered double clad fiber based on the coupled local mode theory

Mode characteristics of a tapered double clad fiber should be analyzed based on three-layer waveguide model, so it is more complicated than that of a single clad fiber. In this paper, a method based on coupled local mode theory is introduced to calculate the mode evolution process in a tapered double clad fiber. Mode field characteristics of double clad fiber are calculated analytically with weak guidance approximation, and the expression of mode coupling coefficient is derived. Based on this, the local mode characteristics and mode coupling characteristics in a tapered double clad fiber are analyzed. The mode evolution characteristics of tapered double clad fibers with different parameters are simulated. As an example, the structure optimization process of a tapered double clad fiber is introduced. High efficiency coupling with a six-mode single clad fiber is realized, and the theoretical transmission loss is less than 0.3 dB.

MODAL DISPERSION CURVES OF A METAL COATED OPTICAL WAVEGUIDE WITH TREFOIL CROSS-SECTION UNDER WEAK GUIDANCE APPROXIMATION

In this paper the author investigated a special type of core cross-section bounded by metallic boundary. In this structure three cores embedded in a common metallic boundary. Characteristic equation in derived for the guided modes under weak guidance approximation by choosing an appropriate coordinate system. This study in done by using analytical method. From the characteristic equation, dispersion curves are obtained and interpreted.

Weak Guidance, Multi-index and Exact Mode Eigenvalue Calculation for Mode Intensity Profiles in Tapers

The fundamental mode intensity profile is calculated for different points along the transition of an optical fibre taper from standard size (125 μm external cladding diameter and 8 μm core diameter) down to micro (1 μm external fibre diameter) and submicro size (down to 440 nm fibre diameter) at 1550 nm operational wavelength. The first section of the taper was evaluated using weak guidance approximation, the second section was treated as a three-index layer structure (double-clad) and evaluated with eigenvalue equations for three refractive indices. An external medium being a liquid with a refractive index close to silica is being considered. The third and thinnest section of the taper was evaluated with the exact mode eigenvalue equation. The results show that the fundamental mode intensity for the third section show a discontinuity just at the fibre edge with a peak amplitude larger than the optical field at the centre of the fibre. The taper shape that complies with the adiabaticity criterion and how the mode intensity profile and the spot size (Petermann 1 definition) of the fundamental mode change along their position on the taper were determined.

Fundamental mode intensity evolution in tapered optical fibres

The mode field intensity, spot size, central peak intensity evolution and adiabaticity are calculated for different points along the transition of an optical fibre taper that adiabatically tapers from the standard 125 nm down to 1 µm and then to 440 nm diameter for low loss operation at 1550 nm wavelength. The first section of the taper is evaluated using a weak guidance approximation. The second section is treated as a three-index layer structure (double-clad) and evaluated with eigenvalue equations for three refractive indices. The third and thinnest section of the taper is studied using an exact mode eigenvalue equation. The results show that the fundamental mode for the third section has a discontinuity at the fibre edge with a peak intensity larger than the intensity at the centre of the fibre. Since the guiding by the core disappears in the first section of the taper, the mode field does not simply reduce monotonously along the taper with the outer diameter of the fibre. By this novel approach, and for the first time, to the best of our knowledge, the taper shape that complies with the adiabaticity criterion, the mode intensity profile and the spot size (first Petermann definition) of the fundamental mode evolution, along their position on the taper are determined.

Modal cut off properties of a metal coated optical waveguide with trefoil cross-section under weak guidance approximation

In the present paper the author investigated the propagation of electromagnetic wave through the special cross-sectional waveguide whose guiding region consist three cores embedded in common metallic boundary. By choosing an appropriate coordinate system, the scalar wave equation is solved, and thereby characteristic equation for the guided modes under the weak guidance approximation is derived using analytical method. To understand the basic modal properties in a simple manner, the cutoff equation is derived, and the modal cutoff properties of some lower order modes are determined numerically. The author also gave a comparative study of metallic boundary instead of dielectric cladding boundary on the modal cutoff behavior of waveguide.

Toward modal dispersion characteristics of a new unconventional optical waveguide with a core cross-section of plano-concave lens shape

By using point-matching approach under the weak guidance approximation, the dispersion curves of a dielectric light guide, with a new unconventional cross-section of plano-concave lens shape, are investigated. The suggested structure may be conceived as a distortion of the square with transverse compression at its one side. A comparison is made between the dispersion curves of the proposed and square waveguides. It is noticed that the lowest cutoff value (Vc) for the proposed waveguide is increased as compared to a square waveguide, and it supports more modes than the square waveguide at a particular value of normalized frequency V. Subsequently, the cutoff V-values are crowded within small range V=2.9–5.4, which is considered as an important feature of such plano-concave light guide. The obtained results are compared and interpreted with those already reported for biconcave lens shaped waveguides. Hence, this paper also reports the tolerance behavior of a square waveguide into concave lens shapes.

Modal dispersion curves of an optical waveguide with a core cross-section partially bounded by one turn of an equiangular spiral under weak guidance approximation

In this paper, we present a theoretical analysis of propagation of electromagnetic waves through a fiber with a spiral shape core cross-section with two cases. In one case the remaining unbounded part closed by a straight line and in other case remaining part not bounded by well defined line. Using Goell's point matching method under weak guidance condition modal characteristic equations for the lowest order modes are derived. The comparison of dispersion curves for two cases is also shown and interpreted.

A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: Stimulated Raman Scattering

The significance of full vectorial pulse propagation through emerging waveguides has not been investigated. Here we report the development of a generalised vectorial model of nonlinear pulse propagation due to the effects of Stimulated Raman Scattering (SRS) in optical waveguides. Unlike standard models, this model does not use the weak guidance approximation, and thus accurately models the modal Raman gain of optical waveguides in the strong guidance regime. Here we develop a vectorial-based nonlinear Schrödinger Eq. (VNSE) to demonstrate how the standard model fails in certain regimes, with up to factors of 2.5 enhancement in Raman gain between the VNSE and the standard model. Using the VNSE we are able to explore opportunities for tailoring of the modal Raman gain spectrum to achieve effects such as gain flattening through design of the optical fiber.

Modal Analysis of a Doubly Clad Optical Waveguide Having a Cross-section of the Shape of a Lemniscate

In this paper, we choose a simple analytical method based on scalar wave approximation to study the modal behaviour of an unconventional doubly clad optical waveguide having a cross section of the shape of a lemniscate. We take the appropriate orthogonal coordinates for the proposed structure and impose the boundary conditions under the weak guidance approximation to get the modal eigen value equation. Using this equation we obtain numerical results in the form of dispersion curves and cutoff frequencies. An attempt has been made to estimate how the modal behaviour changes when a single cladded waveguide having a lemniscates of Bernoulli type core cross-section is changed to a waveguide having double cladded shape of a lemniscate. It is noted that the double cladded waveguide provides an additional degree of freedom to control the cutoff frequencies on our choice.

Supermodes Analysis for Linear-Core-Array Microstructured Fiber

Linear-core-array microstructured fibers are fabricated using the modified chemical-vapor deposition (MCVD) for preparing each core performs, and two D-shape large-scale silica rods are also used in the linear-core-array fiber perform stacking. The supermodes in optical fibers with linearly distributed 23 cores are presented by using coupled-mode theory. The coupling coefficients between two adjacent cores are estimated based on the weak guidance approximation. The near- and far-field distributions of supermodes supported by the multicore fiber (MCF) are presented. A Talbot cavity is exploited to select wanted supermodes. The calculated results show that the in-phase supermode can dominate the output. The coupling field propagation characteristics of the optical fibers are also analyzed.

Effect of curvature of the boundary on the modal dispersion of a single-mode dielectric waveguide of core cross-section bounded by involuted spirals

In this paper, we are presenting an analytical study of the effect of curvature of the spiral shape on the modal dispersion characteristics of the waveguide whose core cross-section is bounded by two involuted spirals of the form 1/ r= ξθ, where ξ is a constant and represents the curvature of the spiral taken to design the waveguide into consideration. This study has been done under the weak guidance approximation. Analyzing the dispersion curves for different curvature we found that this waveguide supports only the single mode, and their cutoff value decreases as the the curvature of the spiral increases.

Effective index method for all-solid photonic bandgap fibres

An effective index method is proposed for all-solid photonic bandgap fibres, where the effective cladding index is taken to be that of the lower edge of the bandgaps. The weak-guidance approximation allows the effective indices of both the fibre cladding and the defect modes to be calculated analytically. Comparison with a vectorial plane wave method shows that good accuracy is obtained.

Modal analysis and dispersion curves of a curvilinear triangular cored light guide using Goell's point matching method

This paper gives, in brief the theoretical and computational investigation of a new light guide having a curvilinear triangular core cross-section. This structure is here introduced for the first time and may be conceived as a distortion of a rectangular core cross-section. Using Goell's point matching method under weak guidance approximation, the modal characteristics equations for the lowest order mode have been derived in two cases. In one case, all the sides of the proposed light guide are bounded by dielectric material. In other case we will consider all the sides bounded by conducting materials. From these equations the modal dispersion curves are obtained and compared. It is seen that the dielectric light guide supports more modes than the metallic light guide. Thus, metallic light guide may be used as a mode filter.

Modal Analysis and Waveguide Dispersion of an Optical Waveguide Having a cross-section of the Shape of a Cardioid

In this paper, we choose a simple and practical analytical method based on scalar wave approximation to study the modal behaviour, cutoff condition of an unconventional optical waveguide having a cross section of the shape of a cardioid. We take the appropriate orthogonal coordinates for the proposed structure and impose the boundary conditions under the weak guidance approximation to get the modal eigen value equation. Using this equation we obtain numerical results in the form of dispersion curves and cutoff frequencies. Also the dependence, d(Vb′)/dV on V has been obtained and shown graphically, where V stands for normalized frequency parameter and b′ stands for normalized propagation constant. An attempt has been made to estimate how the modal behaviour and waveguide dispersion change as circular shape is changed to the shape of a cardioid.

Modeling of the polarization behavior of elliptical surface-relief VCSELs

We undertake a theoretical study of the polarization behavior and mode structure of Vertical-Cavity Surface-Emitting Lasers (VCSELS) with an elliptical surface relief. The aim of the relief is twofold, first to enhance the single mode operation by introducing spatially distributed losses, and second, to enhance polarization stability by making these losses anisotropic. First, we use an analytical variational approach, for the two fundamental VCSEL modes within a Gaussian and weak guidance approximation. As a second approach we use a more refined numerical technique based on vectorial plane wave decomposition with periodic boundary conditions, which we formulate to include material anisotropy. Our studies show that whereas the polarization direction is governed by the orientation of the index ellipsoid, the selection of the lasing LP mode is mainly determined by the anisotropy in the mirror losses introduced by the elliptical surface relief.

Effect of Metal Cladding on the Modal Dispersion Characteristic of an Annular Waveguide with the Guiding Region Section Bounded by a Square and a Circle

In this communication we present the modal dispersion curve for four differentannular waveguides and on the basis of these dispersion curves we estimate the effect of metal claddings. The inner boundary of the annular cross-section of each waveguide is taken as a square and outer boundary is a circle. The annular cross-section of the guiding region lies between these claddings. One waveguide is made entirely of dielectric material and in the other three, metal loading are used on one or both boundaries. The dispersion curves for some lower modes are presented and compared. The modal cut off values and number of modes ata particular value of V for these waveguides have also been obtained. For this study we use Goell's point matching method. We use the scalar boundary conditions under weak guidance approximation.

MODAL DISPERSION CHARACTERISTICS AND WAVEGUIDE DISPERSION OF AN OPTICAL WAVEGUIDE HAVING A NEW UNCONVENTIONAL CORE CROSS-SECTION

In this article, we present a simple and practical analytical approach based on scalar wave approximation to estimate the modal dispersion characteristics and cutoff condition of an optical waveguide having an arbitrary and uniform core cross-section. This structure represents the core of a circular waveguide which is compressed at both the ends of a diameter. We choose the new and appropriate orthogonal coordinates for the proposed waveguide structure and impose the boundary conditions under the weak guidance approximation to get the modal eigen value equation. Using this equation, we achieve numerical results in the form of dispersion curves and cutoff frequencies. Further, representing the normalised frequency parameter as V and normalised propagation constant as b′, the dependence of d(Vb′)/dV on V has been obtained and shown graphically. A brief comparison of the proposed waveguide and the circular waveguide has also been made in respect of the number of sustained modes and waveguide dispersion.

Theoretically obtained dispersion characteristics of an annular waveguide with a guiding region cross section bounded by two hypocycloidal loops

AbstractThis article presents a theoretical analysis of the modal dispersion curves of an annular waveguide with a core cross section bounded by two hypocycloids. This cross section can be conceived as having the shape of a distorted annular square and leads to a tolerance study of deformation in an annular square waveguide. We take a new and appropriate coordinate system (ξ, η, z) for the proposed geometry and impose boundary conditions under the weak guidance approximation. The characteristic equation is then derived analytically. Finally, we show some numerical results in the form of modal dispersion curves. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 142–145, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10849

Modal dispersion curves of metal‐clad concave lens shaped waveguides and their comparative study

AbstractThis paper presents a comparative study of dispersion characteristics of metal‐clad waveguides with concave‐lens‐like cross sections. Using the point‐matching method under weak‐guidance approximation, the modal characteristic equation is derived and the modal dispersion curves are obtained. The proposed waveguide may be conceived as a distortion of the square waveguide with a transverse compression at one pair of its parallel sides in order to become concave lens shaped. We find that, the effect of the concave lens shaped distortion is to shift the lowest cutoff value (Vc) towards a larger V value, and increases the number of modes. It is also observed that the lowest cutoff value increases gradually with the increase in the compression depth. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 388–392, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10772