Elliptical Optical Fiber Research Articles

Elliptical fibre dielectric waveguides: a transverse transmission line analysis

The authors present a new method for determining the optical properties of arbitrary refractive index elliptical core fibres. The method applies the elliptic cylindrical coordinate system to Maxwell's equations and appropriately, using Fourier Transforms, operated on an elliptical core optical fibre waveguide, derives a flexible algorithm, which can be used to determine the optical properties of elliptical fibre waveguides. By dividing the fibre into a series of uniform consecutive thin dielectric layers transversely across the elliptical cross section with suitable transforming functions representing voltage and current themselves based on the electromagnetic field components, leads to transverse transmission line equations. The resonance frequencies of the cascaded matrices determine the mode propagation constants. The analysis leads to a numerical algorithm for calculating the exact modes of propagation constants. The method is analytically exact and computationally accurate, leading to algorithmic implementation, without making use of Mathieu functions which are solutions for step index waveguide. The advantage of this work is also the fact that it can be applied to arbitrary refractive index profiles. They present results of modal b ¯ − V diagrams for various fibre ellipticities and also apply this method to determine the birefringence of graded index profile fibres and mode cut-off frequencies.

3D refractive index measurements of special optical fibers

Abstract A digital holographic microscopic chromatography-based approach with considerably improved accuracy, simplified configuration and performance stability is proposed to measure three dimensional refractive index of special optical fibers. Based on the approach, a measurement system is established incorporating a modified Mach–Zehnder interferometer and lab-developed supporting software for data processing. In the system, a phase projection distribution of an optical fiber is utilized to obtain an optimal digital hologram recorded by a CCD, and then an angular spectrum theory-based algorithm is adopted to extract the phase distribution information of an object wave. The rotation of the optic fiber enables the experimental measurements of multi-angle phase information. Based on the filtered back projection algorithm, a 3D refraction index of the optical fiber is thus obtained at high accuracy. To evaluate the proposed approach, both PANDA fibers and special elliptical optical fiber are considered in the system. The results measured in PANDA fibers agree well with those measured using S14 Refractive Index Profiler, which is, however, not suitable for measuring the property of a special elliptical fiber.

Optical vortices in twisted elliptical optical fibers with torsional stress

In the present paper we have derived the analytical expressions for the modes of twisted elliptical fibers with torsional mechanical stress at various relationships of the fiber parameters. It was shown that circularly polarized optical vortices with the topological charges ±1 can propagate in elliptical fibers as generic modes if ellipticity and the twist-induced circular birefringence suppress the spin-orbit interaction. A comparison of the obtained results with the corresponding results for spun elliptical fibers is made.

Measured and simulated cutoff wavelengths as a function of core ellipticity for higher order modes in elliptical optical fibers

Mode splitting of higher order modes in elliptical dielectric waveguides has been addressed theoretically in great detail since the 1960s. This work presents for the first time detailed experimental measurements of mode splitting in elliptical core optical silica fibers, with a semiminor to semimajor ratio ranging from 1.0 to 0.1. The experimental data are compared with numerical simulations obtained from finite element calculations performed on fiber 2-D refractive index profiles from each of the studied fiber pieces.

Characterization of a novel dual-core elliptical hollow optical fiber with wavelength decreasing differential group delay

The modal distribution of a novel elliptical hollow optical fiber is experimentally and numerically characterized. The fiber has a central elliptical air hole surrounded by a germanosilicate lanceolate ring core. Experiments reveal that the fiber behaves like a dual core waveguide and it is found that the differential group delay of each core decreases with wavelength with a PMD coefficient slope of ~10(-2) ps/m/THz. Experimental results are also compared with numerical modeling based on scanning electron microscopy images.

An analysis of coupling between a whispering gallery mode laser in an elliptical microring and the dominant mode in the coaxially oriented elliptical optical fiber

The problem of coupling a whispering gallery mode laser into an optical fiber is considered. The whispering gallery mode laser is generated in a polymer microring formed coaxially on the optical fiber. The focus of this paper is to determine factors that influence the coupling between the laser and the fiber around which it is formed. The coupling mechanism is analyzed and it is found that when the microring and the fiber are of elliptical cross section, there exists controllable coupling between the laser and propagation mode in the fiber. The coupling between laser mode and fiber mode is due to characteristics of Mathieu functions that describe the fields in elliptical waveguides. It is shown that the coupling between the laser and the dominant mode in the fiber can be optimized by the designing the dimension of microring, the eccentricity of the elliptical cross section, and the material contrast between fiber and microring.

Intensity distributions and cutoff frequencies of linearly polarized modes for a step-index elliptical optical fiber

Intensity distributions of linearly polarized (LP) propagation modes of several orders are plotted for a step-index elliptical-core dielectric waveguide. A simplified characteristic equation is obtained through the weakly guiding approximation, which can be used to find the propagation constants and the cutoff frequencies of each LP mode. These constants are then applied to the solution of the scalar wave equation, which is expanded in series of ordinary and modified Mathieu functions, to obtain the intensity patterns of the LP modes. Results are compared with previous work, and it is found that when the elliptical core tends to a circle (ratio of semimajor to semiminor axis equal to 1.0001) our cutoff frequencies are closer to the LP-mode cutoffs of the circular fiber than are the cutoffs obtained in other papers on elliptical fibers.

Some aspects of theoretical analysis of the light propagation in an elliptical optical fiber

The paper presents the results of theoretical analysis of the propagation of the electromagnetic field in optical fiber with an elliptic core. Due to the elliptic symmetry of the core the analysis had to be carried out in an elliptic coordinate system. This analysis has shown that the functions describing the z-component of the electric field satisfy the Mathieu equations. The presented results of the theoretical analysis are original and have not published so for.

Optical vortices and the higher order modes of twisted strongly elliptical optical fibres

We investigate the structure of the higher order modes in uniformly twisted weakly guiding strongly elliptical optical fibres. An analytical solution of the vector wave equation for this problem is presented based on the effective reduction of a twisted fibre equation to a straight fibre one. On the basis of the perturbation theory the structure of the higher order elliptical screw modes and polarization corrections to the scalar propagation constant are found as functions of the pitch value and the fibre parameters. It is demonstrated that at a certain rate of twisting the l = 1 modes of such fibres are presented by two pairs of almost pure arbitrary polarized optical vortices. The orbital angular momentum of the l = 1 modes is studied as a function of pitch.

Modulational instability in a fibre and a fibre Bragg grating

In this review article, we study the influence of cross-phase modulation, higher order nonlinear effects such as self-steepening, self-induced Raman scattering and higher order dispersion effects such as third and fourth order dispersion on cross-phase modulational instability for a highly elliptical birefringent optical fibre, and obtain the conditions for the occurrence of cross-phase modulational instability in the normal dispersion regime. In addition, we also consider the pulse propagation through a fibre Bragg grating structure where we investigate the occurrence of modulational instability at the two edges of the photonic bandgap as well as on the upper and lower branches of the dispersion curves.

Theoretical analysis of highly elliptical-core optical fibers with arbitrary refractive-index profiles

We present a theoretical analysis of highly elliptical optical fibers by expanding the vector fields as a series of orthogonal functions. Higher-order cutoff values of the normalized frequencies (V numbers) are evaluated for step-index fibers of varying ellipticities. The effect of different refractive-index profiles on the birefringence of the fiber is presented. For fibers operated in the two-mode regime, we discuss the effect of ellipticity and refractive-index profile on the differential propagation constant (Deltab) related to the scalar equivalent of LP(0l) and LP(11)(even)modes.

Determination of the index profile of a graded-index elliptical optical fiber using multiple-beam microinterferometry

Mathematical formulae are derived to calculate both α and Δ n for a graded-index elliptical optical fiber. These formulae are used with the multiple-beam microinterferograms of the Fizeau fringes crossing the fiber perpendicular to its axis. These formulae can be used for the calculation of the refractive index profile of this type of optical fiber.

Transmission characteristics of polarization‐maintaining optical fiber with three‐layer elliptical cross section

AbstractTo realize a single‐polarization, single‐mode optical fiber for high‐speed, long‐distance transmission, a three‐layer elliptical optical fiber is investigated and found to possess the characteristics of absolute single‐polarization and birefringence. Analysis of numerical computations is conducted by the eigenmatrix method using the Mathieu function for a three‐layer fiber with elliptical cross section and with common confocal point for the layers. The difference between propagation constants of the eHE11 and oHE11 modes is examined by using u ‐ w curves. The three‐layer structure permits a W‐type refractive index distribution, with the result that the HE11 modes have a cutoff region. The difference of cutoff frequencies between the eHE11 and oHE11 modes is produced due to the elliptical cross section. It is shown that this fiber can be used as an absolute single‐polarization fiber. Considering a nonaxially symmetric fiber with three‐layer elliptical cross section and flat cladding it is possible to obtain a large value of AB, the difference of propagation constants. This shows the theoretical possibility of achieving long‐distance transmission characteristics with a polarization‐maintaining optical fiber with three‐layer elliptical cross section.

On the higher order modes of elliptical optical fibers

The point-matching numerical method is here employed for the modal analysis of the elliptical optical fiber of any eccentricity. Good agreement with other analytical and numerical methods is obtained. Previous disagreement in the literature is resolved.

Polarization characteristic calculation of three-layer elliptical single-mode fibres

A vector solution is obtained for fields of fundamental modes of an elliptical three-layer optical fibre, which is valid for small ellipticity of boundaries between the layers and for arbitrary differences of core and cladding indices. The modal birefringence is investigated as a function of fibre parameters on the basis of this solution. It is shown that the two-step fibre birefringence is larger than the W-fibre birefringence for equal differences of the core and inner cladding indices. The relationship is inverse for equal differences of the core and outer cladding indices. The correlation between the birefringence value and the effective diameter of the single-mode fibre is discussed.

Effects of joints on mode power distribution and losses in multimode optical fibres

The transformation of mode power distribution at a joint between two different (even elliptical) optical fibres is studied. Simple analytical expressions are obtained also in the most general coupling and mismatch configuration, provided that coupling errors and mismatch parameters are small. Detailed calculations of joint losses are performed in each case, including propagation effects in both fibres. Original results are obtained particularly in the cases of misalignment, end separation between the fibres, mismatches in index profiles and coupling between two elliptical fibres. A strong dependence on the launching conditions and the amount of mode coupling is evidenced in all cases.

Mode cutoff frequencies in elliptical and large numerical aperture optical fibres

It is shown that by perturbation of the weakly-guiding, circular fibre, it is possible to obtain, in a straightforward way, accurate information about the cutoff characteristics of the higher-order modes in optical fibres having either an elliptical cross-section (with aspect ratios as large as 2∶1) or a relatively large numerical aperture.

Measurement of stresses in elliptical optical fibre or preform

It is shown that the measurement method used for determining the stress profile in circular optical fibre or preform is directly applicable to the elliptical counterparts with minor modifications in the Abel inversion procedure.

Orthogonality and transmission characteristics of fundamental modes in elliptically cross‐sectioned optical fiber and representation on Poincaré sphere

The field distribution in the elliptical optical fiber is theoretically analyzed and its polarization stability to the bending and the twist is discussed by using Poincaré sphere representation.

Thermal-stress-induced birefringence in single-mode elliptical optical fibre

The thermal stress distributions in both the core and cladding of a single-mode elliptical optical fibre are analysed. It is found that the stresses in the core do not vary with position but the stresses in the cladding are complicated functions of position. A simple formula is given for the calculation of bire-fringence caused by the thermal stresses.