1. Introduction

FBGs are typically used as a selective wave-length reflector. Fiber Bragg grating nuts are spectral filters based on the Bragg reflection principle. The light usually reflects the narrow wavelength and sends all other wavelengths. When light is spread by periodic rotation of regions of the upper and lower refractive index, it is partially reflected in each interface between those regions [1]. The power of coupling, and hence the reflection and transmission spectra at an angle of inclination, fiber geometry, and the refractive index (RI) of the surrounding medium are affected [2]. There are a number of parameters in which FBG spectra have been shown, such as change in refractive index, bending of fibers, period of grating, excitation conditions, temperature, and length of tree fibers [3]. The fiber Bragg grating separator (FBG) is an optical device that periodically changes the refractive index along the direction of propagation at the heart of the fiber. The basic property of FBGs is that they reflect the light in a narrow band centered around Bragg wave length. There is a different structure of FBG such as uniform, wet, peep, slanted and long period. When light diffuses through FBG in a narrow band of wavelength, the total reflection occurs at the Bragg wavelength and the other wavelength is not affected by the Bragg derivation except for some side lobes present in the reflection spectrum. These side lobes can be suppressed using the coding technique. The reflection range depends on the length and force of the refractive index formation. Wave reflection also depends on temperature and voltage [4]. In order to achieve

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[1] Ren F, Zhang W, Li Y, Lan Y, Xie Y, Dai W. The temperature compensation of FBG sensor for monitoring the stress on hole-edge. IEEE Photonics Journal. 2018;**10**(4). DOI: 10.1109/

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high-efficiency long-range fiber connections, WDM is introduced. Scattering is a key factor limiting the design of long-distance optical links. Several techniques have achieved effective dispersion compensation (DC). The widely used technologies are DCF and broken glass panels (CFBG). Although DCF is a large-scale unit, CFBG is superior to many faces [5]. Due to its excellent multicast capabilities, the fiber Bragg grating (FBG) sensors are particularly attractive for applications where a large number of sensors are desirable such as industrial process control, fire detection systems, and temperature conversion of power, since sensor FBG occupies a narrowband bandwidth that is very narrow and can easily create a distributed sensor matrix by writing several FBG sensors on a single fiber at different locations [6]. The refractive index of the nucleus is permanently changed. Germanium doped silica fiber is used in the manufacture of FBG because it is sensitive which means that the refractive index of the nucleus changes through exposure to light. The amount of change depends on the intensity and duration of exposure. It also depends on optical fiber sensitivity, so the level of fission with germanium should be high for high reflectivity [7]. Fiber Bragg grating nuts are spectral filters based on the Bragg reflection principle. The light usually reflects the narrow wavelength and sends all other wavelengths. When light is spread by periodic rotation of regions of the upper and lower refractive index, it is partially reflected in each interface between those regions [8]. This chapter is organized as follows. After the introduction in Section 1, Section 2 presents a basic model and analysis. In Section 3, we present the proposed system. The simulation results are displayed and discussed in Section 4. Finally we devoted to the main conclusions.

2.1.2 Theory and principle of operation

Theoretic Study of Cascaded Fiber Bragg Grating DOI: http://dx.doi.org/10.5772/intechopen.83020

Basic structure of fiber Bragg grating.

For maximum reflectivity [12]:

the effective refractive index.

refractive profile can be expressed as [6, 14]:

the grating is:

9

Figure 1.

The study of the spectral characteristics of the uniform fiber Bragg grating is carried out by solving the dual mode equations. Dual mode theory is an important tool for understanding the design of fiber dividers from fiber Bragg grating [7]. FBG can be considered as a weak wave structure so that the pair mode theory can be used to analyze light propagation in a weak waveguide structure such as FBG. Dual-mode equations that describe the propagation of light can be obtained in FBG using the couple mode theory. The theory of marital status was first introduced in the early 1950s to microwave devices and later applied to optical devices in early 1970 [11].

Rpeak <sup>¼</sup> tanh<sup>2</sup>

Δλ ¼ λB s

Reflective bandwidth, Δλ of uniform FBG is defined as wavelength bandwidth between the first zero reflective wavelength of both sides of peak reflection wavelength. It can be calculated by a general expression of the approximate bandwidth of

> Δnac 2neff !<sup>2</sup>

Where λ<sup>B</sup> is the Bragg (center) wavelength, s is a parameter indicting the strength of the gratings (�1 for strong gratings and �0.5 for weak gratings), N is the number of grating planes, Δnac is the change in the refractive index and neff is

Where λ<sup>B</sup> is the Bragg wavelength (wavelength of the reflection peak amplitude), n is the effective refractive index of optical mode propagating along the fiber and Ʌ is the period of FBG structure. For a uniform Bragg grating formed within the

The forward propagated light is reflected at Bragg wavelength [13]:

core of an optical fiber with an average refractive index no. The index of the

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

þ

1 N � �<sup>2</sup>

vuut (2)

λ<sup>B</sup> ¼ 2nΛ (3)

ð Þ kL (1)
