Prediction of First Higher Order Modal Field for Graded Index Fiber in Presence of Kerr Nonlinearity

AbstractWe report evaluation of first higher order modal field for dual mode optical fiber having step and parabolic index profiles. The study is carried out both in absence as well as in presence of Kerr nonlinearity. The analysis is based on a simple iterative method involving Chebyshev formalism. Taking some typical step- and parabolic-index fibers as examples, we show that our results agree excellently with the exact results which can be obtained by applying rigorous methods. Thus, our simple formalism stands the merit of being considered as an accurate alternative to the existing cumbersome methods. The prescribed formalism provides scope for accurate estimation of different propagation parameters associated with first higher order mode in such kinds of fibers in presence of Kerr nonlinearity. The execution of formalism being user friendly, it will be beneficial to the system engineers working in the field of optical technology.

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A Novel and Simple Formalism for Study of Effect of Kerr Nonlinearity on Petermann I and II Spot Sizes of Single-Mode-Graded Index Fiber

Journal of Optical Communications ◽

10.1515/joc-2019-0167 ◽

2019 ◽

Vol 0 (0) ◽

Cited By ~ 4

Author(s):

Jayanta Aich ◽

Anup Kumar Maiti ◽

Angshuman Majumdar ◽

Sankar Gangopadhyay

Keyword(s):

Power Series ◽

Single Mode ◽

Kerr Nonlinearity ◽

Linear Optics ◽

Graded Index ◽

Non Linear Optics ◽

Simple Formalism ◽

Element Technique ◽

Modal Field ◽

Analytical Expressions

AbstractWe present investigation of Petermann I and II spot sizes in the presence of Kerr nonlinearity. Our study is based on the simple power series formulation for fundamental modal field of single-mode-graded index fiber developed by Chebyshev formalism. Based on the said power series expression in the absence of nonlinearity, analytical expressions of the said spot sizes can be prescribed. Using the analytical expressions of the said spot sizes in the absence of nonlinearity, we apply iterative technique in order to predict the said propagation characteristics in presence of Kerr nonlinearity. In this context, we choose some typical single-mode step and parabolic index fibers. We show that the our results agree excellently with the exact results which can be obtained by using rigorous finite-element technique. This leads to verification of accuracy of our simple technique. Moreover, evaluation of the concerned parameters by our formalism involves little computation. Thus, our method provides an accurate but simple alternative to the existing rigorous methods in this context. Accordingly, this novel and simple formalism will prove user friendly to the system engineers in the field non linear optics.

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Influence of Kerr nonlinearity on group delay and modal dispersion parameters of single-mode graded index fibers: evaluation by a simple but accurate method

Journal of Optical Communications ◽

10.1515/joc-2020-0192 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Tilak Mukherjee ◽

Angshuman Majumdar ◽

Sankar Gangopadhyay

Keyword(s):

Group Delay ◽

Single Mode ◽

Kerr Nonlinearity ◽

Accurate Method ◽

Dispersion Parameters ◽

Modal Dispersion ◽

Graded Index ◽

Wide Range ◽

Propagation Parameters ◽

Modal Field

AbstractThis paper reports simple but accurate analytical expressions of group delay and modal dispersion parameters for single-mode graded index fibers over a wide range of V numbers. The formulation employs power series expression for the fundamental modal field of graded index fiber derived by Chebyshev formalism. Choosing some typical step, parabolic and triangular index fibers as examples in our present study, we use the prescribed formulations to estimate group delay and modal dispersion parameters of those fibers both in presence and absence of Kerr nonlinearity. Iterative technique is applied for prediction of concerned propagation parameters in presence of Kerr nonlinearity. Our results show excellent agreement with the numerical exact ones both in absence and presence of Kerr nonlinearity. The exact results in case of Kerr nonlinearity are obtained using cumbersome finite element method. The execution of our accurate formalism involves little computation and is thus user friendly for technologists and researchers working in the field of nonlinear optical engineering.

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Analysis of optical Kerr effect on effective core area and index of refraction in single-mode dispersion shifted and dispersion flattened fibers

Journal of Optical Communications ◽

10.1515/joc-2021-0211 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Jayanta Aich ◽

Angshuman Majumdar ◽

Sankar Gangopadhyay

Keyword(s):

Single Mode ◽

Kerr Nonlinearity ◽

Index Of Refraction ◽

Core Area ◽

Simple Method ◽

Mode Dispersion ◽

Propagation Parameters ◽

Simple Formalism ◽

A New Technique ◽

Effective Index Of Refraction

Abstract A new technique is presented for computing very useful propagation parameters like effective core area and effective index of refraction of mono-mode dispersion shifted and dispersion flattened fibers both in the presence and in the absence of Kerr nonlinearity. The technique involves application of accurate but simple expressions for modal fields developed by Chebyshev formalism. The study of the influence of Kerr nonlinearity on the aforementioned parameters, however, requires the application of the method of iteration. For the purpose of such investigation, in linear as well as nonlinear region, we take some typically used dispersion shifted and dispersion flattened fibers and we show that the results found by our simple formalism are in excellent agreement with those obtained by using complex finite element method. Further, the necessary evaluation by our simple method needs very less computations. Thus, our formalism generates ample opportunity for applications in many areas in the field of nonlinear optics.

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Prediction of Fundamental Modal Field for Graded Index Fiber in the Presence of Kerr Nonlinearity

Journal of Optical Communications ◽

10.1515/joc-2017-0126 ◽

2019 ◽

Vol 41 (1) ◽

pp. 67-72 ◽

Cited By ~ 3

Author(s):

Subhalaxmi Chakraborty ◽

Chintan Kumar Mandal ◽

Sankar Gangopadhyay

Keyword(s):

Power Series ◽

Iterative Method ◽

Single Mode ◽

Kerr Nonlinearity ◽

Exact Results ◽

Propagation Characteristics ◽

Graded Index ◽

Modal Noise ◽

Modal Field ◽

Simple Fashion

Abstract The power series formulation for modal field of single-mode graded index fibers by Chebyshev technique has worked excellently in predicting accurately different propagation characteristics in simple fashion. Here we develop a simple iterative method involving Chebyshev formalism to predict the modal field of single-mode graded index fiber in the presence of Kerr-type nonlinearity. Taking step and parabolic index fibers as typical examples, we show that our results match excellently with the available exact results obtained vigorously. Thus, the reported technique can be considered as an accurate alternative to the existing cumbersome techniques. Accordingly, this formalism will be beneficial to the technologies for evaluation of modal noise in single-mode Kerr-type nonlinear graded index fibers.

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A Simple Method for Prediction of Effective Core Area and Index of Refraction of Single-mode Graded Index Fiber in the Low V Region

Journal of Optical Communications ◽

10.1515/joc-2014-0020 ◽

2014 ◽

Vol 35 (4) ◽

Author(s):

Angshuman Majumdar ◽

Satabdi Das ◽

Sankar Gangopadhyay

Keyword(s):

Refractive Index ◽

Single Mode ◽

Index Of Refraction ◽

Core Area ◽

Exact Results ◽

Simple Method ◽

Graded Index ◽

Core Areas ◽

V Region ◽

User Friendly

AbstractBased on the simple power series formulation of fundamental mode developed by Chebyshev formalism in the low V region, we prescribe analytical expression for effective core area of graded index fiber. Taking step and parabolic index fibers as examples, we estimate the effective core areas as well as effective refractive index for different normalized frequencies (V number) having low values. We also show that our estimations match excellently with the available exact results. The concerned predictions by our method require little computation. Thus, this simple but accurate formalism will be user friendly for the system engineers.

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Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part I

PNRPU Mechanics Bulletin ◽

10.15593/perm.mech/2020.4.20 ◽

2020 ◽

pp. 237-249

Author(s):

L. V Stepanova

Keyword(s):

Series Expansion ◽

Digital Image ◽

Power Series Expansion ◽

Crack Tip ◽

Higher Order ◽

Accurate Estimation ◽

Principal Stresses ◽

Isochromatic Fringe ◽

Higher Order Terms ◽

Fringe Patterns

This study aims at obtaining coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending by the use of the digital photoelasticity method. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give a more accurate estimation of the near-crack-tip stress, strain and displacement fields and extend the domain of validity for the Williams power series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. By means of the developed tool, the fringe patterns that contain the whole field stress information in terms of the difference in principal stresses (isochromatics) are captured as a digital image, which is processed for quantitative evaluations. The developed tool allows us to find points that belong to isochromatic fringes with the minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of the stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The iterative procedure of the over-deterministic method is utilized to find the higher order terms of the Williams series expansion. The procedure is based on the consistent correction of the coefficients of the Williams series expansion. The first fifteen coefficients are obtained. The experimentally obtained coefficients are used for the reconstruction of the isochromatic fringe pattern in the vicinity of the crack tip. The comparison of the theoretically reconstructed and experimental isochromatic fringe patterns shows that the coefficients of the Williams series expansion have a good match.

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