Symmetric Fiber Research Articles

Index mapping for fibers with symmetric and asymmetric refractive index profiles

The application of phase imaging to refractive index profiling of an optical fiber slice is described. It is shown that the refractive index profile of axially symmetric and asymmetric optical fibers can be obtained from quantitative phase image of thin transverse optical fiber slices. Although this method requires careful and time consuming sample preparation, one advantage of this technique is that it can be applied to a wide range of optical fibers. In this paper results for both symmetric and non-symmetric fibers are presented and good agreement with the industry-standard refracted near-field technique demonstrated.

DORSAL LUMBAR INTERBODY FUSION FOR CHRONIC AXIAL, MECHANICAL LOW BACK PAIN

AbstractLUMBAR SPINAL FUSION is a popular method for treating degenerative disc disease leading to chronic low back pain. Some of the techniques most commonly undertaken are posterior lumbar interbody fusion and transforaminal lumbar interbody fusion. These techniques have their own advantages and disadvantages. In this article, we briefly describe a modified technique, dorsal lumbar interbody fusion, which retains the advantages and avoids the disadvantages of the others. The goal of this procedure is to combine the aggressive decompression of both the thecal sac and bilateral nerve roots and symmetrical bilateral graft placement obtained via the posterior lumbar interbody fusion with the transforaminal placement of interbody grafts obtained via the transforaminal lumbar interbody fusion procedure. This modification has several advantages: it permits more aggressive removal of the disc bilaterally, larger and more symmetrical lordotic-shaped carbon fiber cages and structural allograft can be placed bilaterally, and the nerve roots can be aggressively decompressed bilaterally.

Dorsal lumbar interbody fusion for chronic axial, mechanical low back pain: a modification of two established techniques.

Lumbar spinal fusion is a popular method for treating degenerative disc disease leading to chronic low back pain. Some of the techniques most commonly undertaken are posterior lumbar interbody fusion and transforaminal lumbar interbody fusion. These techniques have their own advantages and disadvantages. In this article, we briefly describe a modified technique, dorsal lumbar interbody fusion, which retains the advantages and avoids the disadvantages of the others. The goal of this procedure is to combine the aggressive decompression of both the thecal sac and bilateral nerve roots and symmetrical bilateral graft placement obtained via the posterior lumbar interbody fusion with the transforaminal placement of interbody grafts obtained via the transforaminal lumbar interbody fusion procedure. This modification has several advantages: it permits more aggressive removal of the disc bilaterally, larger and more symmetrical lordotic-shaped carbon fiber cages and structural allograft can be placed bilaterally, and the nerve roots can be aggressively decompressed bilaterally.

Defocused transfer function for measurement of refractive index profiles of axially symmetric optical fibers

A defocused transfer function of experimental microscopic bright-field images, closely connected with the evaluation of the relative refractive index profile of axially symmetric optical fibers, is presented. It is shown that with this function it is possible to obtain, with high precision, the defocused bright-field images of investigated fibers from their focus images and then to easily evaluate the relative refractive index profiles of the fibers.

All fiber on-axis coupling scheme between single mode fiber and GRIN fiber

In this paper we present a simple and novel method to maximize on-axis coupling efficiency to radially symmetric fibers without the need for extra free space optical elements. The method is based on inserting a segment of step-index multimode fiber (MMF), cleaved to a particular length, between the input fiber and the output fiber (OF). The MMF segment modifies the input field to match the guided modes in the OF. Using this technique we show that, by inserting an appropriate length MMF segment, it is theoretically possible to obtain a coupling coefficient as high as −0.8 dB between a single mode fiber and a graded index ring-shaped fiber and −0.32 dB for a multi-shell fiber. Our experimental measurements showed good agreement with theoretical predictions for the ring fiber.

Analysis of leaky-mode losses for optical fibers

We present a direct, rigorous, and fast numerical method for obtaining leaky-mode losses in optical fibers by solely solving complex propagation constants of the characteristic equation of leaky modes. Both the modified Bessel function and the Hankel function of the second kind are individually used to express the field component of leaky modes in the outermost cladding. The characteristic equation of cylindrically symmetric fiber structures, which consist of uniform and graded layers, is derived by combining the Runge-Kutta method and the exact solution of a homogeneous layer. Since complex root searching is the key technique in this method, we also present a numerical algorithm for solving the characteristic equation of optical fibers. Moreover, because for both guided and leaky modes the field distributions in the outermost cladding region have the same expression, the leaky mode can be easily obtained by choosing an improper solution, and therefore the calculation of leaky modes demonstrates the simplicity of this method. An approximation rule of branch choices for lossy material is also derived. The approach we present is consistent with the results of previously published papers.

Algorithm performance in the determination of the refractive-index profile of optical fibers

Three algorithms for computing the refractive-index profile of azimuthally symmetric optical fibers via the inverse Abel transform are compared to determine their relative accuracies. Appropriate values of algorithm parameters are also determined. The direct differentiation algorithm, the iterative algorithm, and the Fourier algorithm are used to calculate the refractive-index profile from simulated measurements of the phase shift of light transmitted transversely through the fiber. The rms error in the calculated index profile is used to quantify the accuracy of each algorithm. The Fourier algorithm is typically the most accurate of the three.

Determination of the refractive index profile of a symmetric fiber preform by the transport of intensity equation

The refractive index profile of an axially symmetric fiber preform is determined by using the transport of intensity equation. In this method the preform is immersed in an index-matching liquid, and a collimated light beam impinges on it laterally. The intensity distributions of the transmitted light are measured on two close parallel planes inside the preform core. From the recorded intensity distributions, the deflection function is calculated by the transport of intensity equation. The refractive index profile is obtained by means of Abel inversion. Also, for comparison, the refractive index profile of the preform is measured by the focusing method and the results are in agreement with less than 3% error.

Discrete wavelength generation using modal interference in a diode-laser-pumped Tm 3+-doped few-mode fibre

By employing a few-mode core fibre in a symmetric cladding-pumped fibre laser arrangement, intermodal interference occurs between the first two symmetric modes that are excited simultaneously. In free-running mode, without the placement of dielectric mirrors, the Tm 3+-doped silica fibre laser oscillates on a number of fringes simultaneously. In a grating-tuned arrangement, the tuning curves comprise of a number of discrete fringes consistent with the theory associated with interference between the two excited symmetric modes propagating the length of the fibre.

Highly Symmetric Optical Fiber Tapers Fabricated With a CO$_{2}$ Laser

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This letter presents a simple technique that improves the symmetry of tapered fibers fabricated with a continuous-wave CO<emphasis><formula formulatype="inline"> <tex>$_{2}$</tex></formula></emphasis> laser. The uniform heat distribution inside an optical fiber is achieved by using a nonscanning dual-spot laser beam which applies heat on two sides of the optical fiber simultaneously. In so doing, highly symmetric tapers are obtained with an ellipticity close to unity. These tapers can be used as low-loss and polarization- dependent loss optical fiber filters or other optical devices such as symmetric fibers lenses. </para>

Fiber Sagnac Loop Filter with a Symmetrical Piecewise Uniform FBG

We propose a novel comb filter by using a symmetrical piecewise uniform fiber Bragg grating (S-PUFBG) in a Sagnac interferometer. The filter has wide bandwidth, equal passband spacing, and low insertion loss. The total transmission bandwidth is determined by the number and the parameters of the grating segments, while the transmission spectrum can be cosine modulated to realize comb-like filtering, and the modulating frequency can be controlled by adjusting the fiber length difference in the Sagnac loop.

Optical switches and all-fiber logical devices based on triangular and planar three-core nonlinear optical fiber couplers

In this paper, we investigate the switching process in a triangular (T) and planar (P1 and P2) symmetric three-core nonlinear fiber coupler (TNLDC) operating in the CW regime. We have numerically shown, via the coupled nonlinear Schrödinger equations (NLSEs), that AND, NAND, OR, NOR, XOR, NXOR and NOT logic gates can be constructed. The first configuration, a triangular (TNLDC-T) symmetrical structure, is composed with three cores in an equilateral-triangle arrangement and using a control signal (CS) applied to the first core. The P1 and P2 configurations presents a planar symmetrical structure with three cores in a parallel equidistant arrangement, with different input positions of the control signal (CS). In the P1 configuration the CS is applied to the input of the first fiber (core 1) while for the P2 configuration the CS is applied to the input of the central fiber (core 2). Looking at the transmission characteristics of the device, through the direct and cross channel, we did a study of the extinction ratio (XRatio(dB) of these devices. In comparing the performance of all switches operating as logic gates we will use the figure-of-merit of the logic gates (FOMELG(dB)) defined as a function of the extinction ratio of the gate outputs.

Measurement of refractive index profiles of axially symmetric optical fibers

A simple experimental technique for the measurement of refractive index profiles of axially symmetric optical fibers is presented. This method is based on image phase gradients introduced into a transmitted optical field by a fiber sample. An image of the phase gradients is obtained using a technique based on bright field microscopy. Then a relative refractive index profile of optical fibers is reconstructed by means of the inverse Abel transform.

Calculating Dispersion Derivatives in Fiber-Optic Design

Maxwell's equation for modeling the guided waves in a circularly symmetric fiber leads to a family of partial differential-equation-eigenvalue systems. In fiber design, one would like to determine the index profile, which is involved in Maxwell's equation so that certain optical properties, which sometimes involve derivatives of the eigenvalues, are satisfied. In this paper, we will discuss how to determine derivatives of the eigenvalue problem and the gradients of the dispersion with respect to design parameters in the model

Novel optical properties of six-fold symmetric photonic quasicrystal fibers

We have investigated optical properties of an optical fiber having a six-fold symmetric quasiperiodic array of air holes in cladding, a six-fold symmetric photonic quasicrystal fiber. The photonic quasicrystal fiber exhibits larger cutoff ratio for endlessly single mode operation than that of a triangular photonic crystal fiber having six-fold symmetry and almost zero ultra-flattened chromatic dispersion, 0+/-0.05 ps/km/nm, in the range of wavelength from 1490 to 1680 nm. The dispersion value is much less than those of the proposed dispersion flattened PCFs.

Melt electrospinning of poly‐(ethylene glycol‐block‐ϵ‐caprolactone)

Various block copolymers of poly(ethylene glycol) and poly(epsilon-caprolactone) (PEG-b-PCL) with molecular weights between 7000 and 26,900 g/mol were synthesized, and melt electrospun at temperatures between 60 degrees C and 90 degrees C. Two types of fibers were collected, including excellent quality fibers - highly coiled and continuous, with a constant diameter and relatively defect free. Such fibers, termed "solid fibers", were sufficiently cooled during their path between the spinneret and the collector that the symmetric fiber shape is maintained after landing on the collector. The second type of melt electrospun fiber were poor quality, large diameter fibers, flattened on the collector - termed "molten fibers". The solid and molten fibers were morphologically distinct from each other as determined from scanning electron microscopy (SEM). Using an SEM imaging method to assess the regional variations of collected electrospun material, we found the spinneret pump rate largely influenced the fiber quality. The polymer flow rate to the spinneret and the molecular weight of PEG-b-PCL had the greatest effect on the electrospun fibers collected, with an optimum rate of 0.05-0.1 mL/h for the highest molecular weight copolymers. The lowest molecular weight PEG-b-PCL tended to electrospray, while the material collected from higher molecular weight copolymers were conducive to fiber formation. The highest quality fibers were PEG-b-PCL block copolymers (22,000 and 26,900 g/mol) melt electrospun at temperatures of 85 degrees C and 90 degrees C, corresponding to shear viscosities of the polymer of between 28.1 and 39.4 Pa.S.

Full vectorial modal analysis of specialty fibers and their Bragg grating characterization

Optical fibers and specialty waveguides are the bases of the majority of today's telecommunication, biomedical, sensing, and light-delivery applications. Modal analysis plays an important role in optimizing the optical performance of these fibers when they are integrated with optical systems. We present a full vectorial modal theoretical analysis of specialty cylindrical symmetric fibers with arbitrary index profiles, using a staircase approximation and scattering matrix approach with no constraints on the refractive index profile. We demonstrate the generality of this method by investigating the modal characteristics of two specialty fibers: graded-index fiber and concentric-shell multicore fiber. The calculated modal effective indices for the graded-index fiber are compared with those calculated by the WKB method, stressing the main differences between the scalar and vectorial approaches. Using the same approach, we calculate the Bragg grating response of a holographic grating written in the guiding regions of a concentric-shell fiber and compared them with experimental measurements.

Phase-sensitive imaging techniques applied to optical fibre characterisation

Phase-sensitive imaging measurements of optical fibres using quantitative phase microscopy (QPM) are described. In the case of axially symmetric fibres, these measurements can be used to non-destructively determine the refractive-index profiles of single- and multi-mode optical fibres. QPM presents a sensitive, robust, rapid and high spatial resolution technique for reconstructing the refractive-index profile of various fibres and fusion splices. In addition, when used with polarised light, the method is applicable to the investigation of stresses, residual or applied, in single- and multi-mode optical fibres.

Optimization technique for simple reconstruction of the index modulation profile of symmetric fiber Bragg gratings from their reflective spectrum

We propose a new and simple method to reconstruct the refractive-index modulation of a symmetric fiber Bragg grating (FBG) from its magnitude reflection spectrum (i.e., phase information is not required). The reconstruction method uses an FBG model based on some known parameters of the fabricated FBG (grating length, number of subgratings, and grating period) and an optimization technique, namely, the Quasi-Newton method, to find the local parameter values of the FBG. To our knowledge, this is the first time that the reconstruction of FBG is experimentally realized by an optimization technique. Compared with other reconstruction methods, the proposed method is so simple that it requires only the reflection spectrum of the fabricated FBG.

Eigenvalue Problems in Fiber Optic Design

Maxwell's equation for modeling the guided waves in a circularly symmetric fiber leads to a family of partial differential equation-eigenvalue systems. Incorporating the boundary condition into a discretized system leads to an eigenvalue problem which is nonlinear in only one element. In fiber design one would like to determine the index profile which is involved in Maxwell's equation so that certain optical properties, which sometimes involve derivatives of the eigenvalues, are satisfied. This contribution discusses how to handle the nonlinear eigenvalue problem and how to determine derivatives of the eigenvalue problem.