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.

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

\n We 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.

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

Abstract We 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.

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

Evaluation of Splice Loss of Single-Mode Graded Index Fiber in Presence of Kerr Nonlinearity

Simple and complete empirical relations are presented here to determine a normalized spot size in terms of normalized frequencies over a long range and aspect ratio of a trapezoidal index single-mode fiber considering Gaussian approximation of the fundamental mode following the Marcuse method for the first time. After verification of their validity for arbitrary values of aspect ratio and normalized frequency, we calculate various propagation characteristics viz. dispersion and splice loss by using our formulations. Upon comparison, we observe an excellent match and the validity of our results with exact values and other results available in the literature. These formulas should attract the attention of experimentalists as a simple alternative to the rigorous methods of estimating the propagation characteristics of such fibers.

Empirical relations to determine the normalized spot size of a single-mode trapezoidal index fiber and computation of its propagation characteristics

The Chebyshev method is very well known for its simplicity as an approximate analytical formalism to study propagation characteristics of single mode fibers with linear optical media. The method is inapplicable in the context of nonlinear fiber for deeply involved multiplication of various power coefficients. In this article, we propose and develop a simple iterative method based on Chebyshev technique to investigate propagation characteristics of single mode nonlinear fibers and show that our results match with available rigorous results reliably. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:787–790, 2014

A simple and effective method to analyze the propagation characteristics of nonlinear single mode fiber using Chebyshev method

A simple and accurate theoretical investigation is presented, based on a novel, effective, and straight- forward ABCD matrix technique, in relation to estimation of optimum coupling efficiency between the laser diode and the photonic crystal fiber (PCF) with a hyperbolic microlens (HML) on its tip. By tailoring different parameters, such as the air-filling factor and lattice constant of the PCF, the criteria for achieving maximum coupling are predicted and reported for two different light wavelengths of practical interest. It is observed that such fiber parameters play a crucial role in predicting the optimum focal length of HML for a particular wavelength. The formulation should find application in the design of HML, for achieving a long working distance between the laser source facet and the fiber tip. © 2015 Society of Photo-Optical Instrumentation Engineers (SPIE) (DOI: 10.1117/1.OE.54.8 .086102)

Investigation of coupling of a laser diode to photonic crystal fiber via hyperbolic microlens on the fiber tip by ABCD matrix formalism

Abstract For a range of fiber parameters and wavelengths, the splice losses between photonic crystal fiber and a single mode fiber are calculated using our simplified and effective model of photonic crystal fiber following a recently developed elaborate method. Again, since the transverse offset and angular mismatch are the serious factors which contribute crucially to splice losses between two optical fibers, these losses between the same couple of fibers are also studied, using our formulation. The concerned results are seen to match fairly excellently with rigorous ones and consistently in comparison with earlier empirical results. Moreover, our formulation can be developed from theoretical framework over entire optogeometrical parameters of photonic crystal fiber within single mode region instead of using deeply involved full vectorial methods. This user-friendly simple approach of computing splice loss should find wide use by experimentalists and system users.

Simplified Loss Estimation of Splice to Photonic Crystal Fiber using New Model

An investigation on the effect of practically possible upper and lower parabolic dips in the refractive index profile of the inner core of the coaxial fiber Raman gain amplifier is reported using matrix method for single pump. It is seen that for lower parabolic dip, the tolerable limits of dip parameters correspond to dip depth of 0.25% and dip width of 25% of the respective parameters for ideal step index profile case and agree with the earlier predicted linear dip. However, for upper parabolic dip, one gets higher gain and better flatness at these limits. Even up to 1% of the dip depth for 25% of dip width or 75% of dip width for 0.25% of the dip depth or 0.5% of dip depth and 50% of dip width, one can expect performance as good as that of the ideal one. However, since system designers will be aimed to produce ideal profile, our recommendation is to keep tolerable limits within 0.25% of dip depth and 25% of dip width of respective parameters. But one can accept profile with upper parabolic dip if there is deviation within the above relaxation limits for such dip.

Anup Karak

Papers

A simple and effective method to analyze the propagation characteristics of nonlinear single mode fiber using Chebyshev method

Investigation of coupling of a laser diode to photonic crystal fiber via hyperbolic microlens on the fiber tip by ABCD matrix formalism

Simplified Loss Estimation of Splice to Photonic Crystal Fiber using New Model

Effect of lower and upper parabolic dips in refractive index profile on performance of coaxial fiber Raman gain amplifier

Prediction of modal dispersion in nonlinear single mode optical fiber using simple Chebyshev technique