Empirical Model of Dual Loss of Spiral Bend Optical Fiber

Page 1

Communications in Control Science and Engineering (CCSE) Volume 3, 2015

www.as-se.org/ccse

Empirical Model of Dual Loss of Spiral Bend Optical Fiber Feng Ni*1, Ruodan Ni2, Ben Buryar3 School of Materials Science and Engineering, Henan University of Science and Technology

1

Sannen Laboratory of Mechanics and Dynamics,

2, 3

Luoyang 471003, China nifeng@haust.edu.cn; 2niruodan@163.com; 3Buryar@163.com

*1

Abstract By a theoretical analysis, it was indicated that multiple losses of optical fiber transmission were suitable to superposition principle, i.e. the total loss of optical fiber transmission equaled the linear superposition of losses caused by various factors. On the basis of the superposition principle and the regression analysis of experimental data, a bend-torsion dual loss model of spiral bend optical fiber was proposed that the spiral bend loss of optical fiber was the superposition of pure bend loss and torsion loss. The pure bend loss was related to the real curvature radius and the number of spirals and the torsion loss was only related to the torsion rate of the spiral. Keywords Optical Fiber Transmission; Multiple Loss Superposition; Spiral Bend Loss Model

Introduction The bend loss of optical fiber is one of the most important modulation methods of fiber optic sensor (FOS) technology. Compared to reflection and irradiation modulations, the bend loss modulation has better anti-noise ability with a closed light path and is applied widely in FOS technology[1]. Experimental researches along with theoretical models on the bend loss of optical fiber are the technological basic for developing the bending fiber sensor and have been investigated widely so far. The causes of optical fiber bend loss are complicated and manifold, so an exact theoretical model is often difficult to be built or too complicated in form to be used. Therefore, it is more significant practically to build a statistical model based on experimental data. The earlier and the most fundamental works were finished by D. Marcuse[2] and K. Petermann[3] in 1976. They respectively gave out two different theoretical formulas to calculate the bend loss of optical fiber. And the formulas were all simpler than most of other results based on model coupling theories[4-7]. D. Marcuse simplified the structure of optical fiber as a dielectric core surrounded by an infinite cladding, assumed the refractive index distribution of the medium inside and outside of the core as a two value step function, used weak guidance approximation and acquired a bend loss formula as following[2]. 2α =

C1 exp(−C 2 r ) r1 2

(1)

Where, α is the loss coefficient; C1 and C2 are constants related to characteristics of optical wave and fiber; r is curvature radius of optical fiber axis. K. Petermann assumed the bend loss of optical fiber transmission to the result of power loss induced by converting of guided modes into radiation modes. A constant gradient of refractive index profile and random bends of fiber axis were considered. From a coupled-mode theory, using a quasi-guided mode instead of the radiation modes, the bend loss is calculated by taking account of the coupling between the guided and the quasi-guided modes. And the bend loss coefficient was expressed as following[3]. 2α = C (1 r )

2

(2)

Where, C is a constant related to the characteristics of optical wave and fiber; (1 r )2 indicates the square mean of the

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