Spectra of fiber Bragg grating and long period fiber grating undergoing linear and quadratic strain

Abstract

The effects of linear and quadratic strain on the reflective spectrum of FBG and the transmission spectrum of LPFG have been numerically investigated based on the coupled -mode equations. The results show that for the FBG or LPFG undergoing only linear strain, the reflection or transmission spectrum is symmetrical about its central wavelength, the dependence relationships of the central wavelength shift, full-width-at-half-maximum, peak intensity upon the strain gradient have been obtained.Using a FBG or LPFG as a single-point sensor, the strain distribution on the sensor is assumed to be uniform, such assumption only considers the 0-order term of Taylor expansion of strain profile, and the space resolution is limited to the grating length. But the nonuniform strain distributions on the FBG or LPFG with certain length exist widely in practical applications and affect the measuring resolution. In order to use the FBG or LPFG sensor in the field of strain sensing with high resolution, it is necessary to investigate the effects of strain profile on the FBG or LPFG [1] .To obtain the strain distribution along the FBG or LPFG sensor from its reflection or transmission spectrum, some reconstruction methods have been proposed [2][3][4] . But these methods are not suitable to the real-time measurement for strain gradient due to their long cost time. In this paper, based on the numerical simulations for the coupled-mode equations of the FBG or LPFG undergoing linear and quadratic strain, the effects of linear and quadratic strain on their reflection and transmission spectra have been investigated, the dependence relationships of the wavelength shift, full-width-at-halfmaximum, and peak intensity upon the strain parameters are also obtained.For a FBG or a LPFG written in a single-mode fiber, the total index perturbation can be expressed as [5] 2 0 1 2 ( )where z L , L is the grating length, 0 is the uniform strain, k 1 =[d /dz] z=0 is the strain gradient at z=0, and k 2 =[d 2 / dz 2 ] z=0 is the 2-order expansion coefficient of Taylor expansion of the strain profile.As the FBG undergoes a strain, the additional phase can be written as [6]