تجزیه و تحلیل حساسیت ضریب شکست گریتینگ فیبر طولانی مدت با استفاده از روش جدید ماتریس انتقال

The refractive index sensitivity of long period fiber grating is analyzed by new transfer matrix method. Compared to traditional transfer matrix method, The new transfer matrix method can be used to analyze the modes coupling between the core mode and multiple cladding modes through only one time calculation. Compared with the previous method used, such as solving the coupled mode equation by the fourth order adaptive step size Runge-Kutta algorithm, the new transfer matrix method has a faster calculation speed. Theoretical results are excellent agreement with the method of solving the coupled mode equation.

Long period fiber gratings (LPFGs) have been found many applications in optical telecommunications and optical sensor such as mode converters [1], rejection filters [2], gain-flattening filters for erbium-doped fiber amplifiers [3], optical fiber sensors for strain [4], temperature [5], and refractive index measurements [6] because of their capability to couple power between core and cladding modes at resonant wavelengths [7], [8], [9] and [10]. The refractive index sensitivity of LPFG can be obtained by analyzing spectral variation under a certain ambient index changes. The common methods used to analyze the spectral characteristics of LPFG and fiber Bragg gratings include transfer matrix method (TMM) and solving the coupled mode equations (SCME) [11] and [12]. The traditional TMM is able to analyze the uniform and non-uniform LPFG and fiber Bragg gratings when only two modes are considered [11] and [12]. The SCME method can obtain the spectrum of the uniform and non-uniform structure LPFG when multiple modes are considered. In this paper, a new TMM about LPFG with multiple cladding modes coupled is proposed and applied to analyze the refractive index sensitivity of LPFG. Compared to traditional TMM, the advantage of the new TMM is that multiple cladding modes can be considered through only one time calculation for analyzing the transmission characteristic of LPFG. This new TMM can be used to analyze the modes coupled both about the uniform and the non-uniform between the core mode and the multiple cladding modes. And the new TMM is simple to implement, almost always sufficiently accurate, and generally faster than that of SCME.

In this paper a new transfer matrix method about long period fiber grating with multiple cladding modes is proposed. The new method can be used to analyze the refractive index sensitivity of long period fiber grating. Compared to traditional TMM, the advantage of the new TMM is that multiple cladding modes can be considered through only one time calculation for analyzing the transmission characteristic of LPFG. Compared with the usually used method, such as solving the coupled mode equation by the fourth order adaptive step size Runge-Kutta algorithm, the new transfer matrix method is of a faster calculation speed. The theoretical results are exactly agreed with the method of solving the coupled mode equation.