# Fiber Bragg Gratings – Propagation phenomena

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# Fiber Bragg Gratings – Propagation phenomena

Periodic perturbations of the optical fiber core refractive index along the fiber length can be obtained using different techniques, such as the exposure to an intense laser irradiation, arc discharge or mechanical deformations as it was also mentioned in one of our previous post about long period fiber gratings (LPFGs). This post will not be focused on the fabrication methods used to obtain this type of structures but on the light propagation phenomena originated by these structures and the differences between them.

Fiber Bragg gratings, first demonstrated by Hill et al. in 1978 at the Canadian Communications Research Centre (CRC), Ottawa, Ont., Canada, [12] enable the generation of resonances in the optical transmission and reflection spectrum by coupling of light from the core mode to another co-propagating or counter-propagating mode that may be guided in the core or in the cladding of the optical fiber. On this basis, fiber Bragg gratings can be subdivided into two different groups according to the grating period length: short-period fiber Bragg gratings, usually called fiber Bragg gratings (FBGs), and long-period fiber gratings (LPFGs) [3].

Previous classification attends to the way light is coupled between the core mode and the other mode that is responsible for the generation of the resonance. In FBGs there is a coupling between the core mode and counter-propagating modes, whereas in LPFGs there is a coupling between the core mode and a co-propagating cladding mode.

Concerning FBGs, a further classification can be made between those devices where light is coupled between the core mode and the counter-propagating core mode and those devices where a coupling between the core mode and the counter-propagating cladding modes is enhanced by using a tilted fiber Bragg grating (TFBG) [4]. Figure 1 shows a schematic representation of the three previously mentioned configurations accompanied with a sample transmission spectra: FBGs [2], TFBGs [4] and LPFGs [5].

The first commercial FBGs were available in 1995, and since that moment many companies have commercialized their own FBGs and explored their application in many different fields for temperature and strain monitoring (associated to refractive index changes induced in the optical fiber core).

FBGs are the most commercially used type of fiber Bragg grating because they permit to easily fabricate many different gratings in the same optical fiber cord in order to constitute what is called a multi-point distributed sensing network. These sensing networks exploit the easy wavelength multiplexing capabilities of optical fiber in order to monitor the resonance wavelength of a multiplicity of FBGs, which should be excited adequately using a broadband light source that covers the entire range of the whole FGB network such as a SLED light source (see our previous post). The utilization of these sensing networks has been largely exploited in aircrafts, tunnels, bridges, etc., in what is typically addressed as structural health monitoring.

On the other hand, if we focus not only on the modifications of the refractive index of the core but on the monitoring of changes of the surrounding refractive index (SRI), things are different. Here, FBG response is independent of SRI. The main band observed in Figure 1a is due to coupling between two core modes (the propagating core mode couples to the counter-propagating core modes, and therefore it is possible to track a resonance band in reflection configuration). Since the medium that surrounds the optical fiber is separated by the cladding, there is no sensitivity to the surrounding medium refractive index (SRI) unless we reduce the cladding diameter in order to get access to the core propagating modes of course.

In contrast, the additional resonance bands observed in TFBGs, those observed in Figure 1b, are due to coupling from the core mode to counter-propagating cladding modes, which are in direct contact with the SRI and experience a variation in their effective index as a function of the SRI. A similar idea is obtained with LPFGs in Figure 1c, where there is a coupling with co-propagating cladding modes. Again these cladding modes are in direct contact with the SRI and experience variations in their effective index as a function of the SRI, which has been widely exploited for sensing applications [45].

This idea behind the differences between the three structures commented before can be better understood in a simpler way with the coupling equations for an FBG, a TFBG and a LPFG, represented in equations 1, 2 and 3 respectively:

$\dpi{100}&space;FBG:&space;\lambda&space;=2\,&space;\cdot&space;n_{core}(\lambda)\,&space;\cdot\Lambda$                                   (1)

$\dpi{100}&space;TFBG:&space;\lambda&space;=[n_{core}(\lambda)+n^{i}_{clad}(\lambda)]\cdot\Lambda/cos\theta$           (2)

$\dpi{100}&space;LPFG:&space;\lambda&space;=[n_{core}(\lambda)-n^{i}_{clad}(\lambda)]\cdot\Lambda$                    (3)

where ncore(λ) is the effective refractive index of the core mode at wavelength λ, niclad(λ) is the refractive index of the ith cladding mode, Λ is the period of the grating, and θ is the tilt angle (only applicable to TFBGs). In Eq. (1), the core mode couples to the counter-propagating core mode. In Eq. (2) there is a counter-propagating coupling whereas in Eq. (3), the minus sign indicates that the cladding mode is co-propagating with the core mode.

[1] K. O. Hill, G. Meltz, “Fiber Bragg Grating Technology Fundamentals and Overview,” J. Lightwave Technol., 15(8), 1263-1276 (1997).

[2] K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett., 32, 647–649 (1978).

[3] A. Urrutia, I. del Villar, P. Zubiate, C. R. Zamarreño, “A comprehensive review of optical fiber refractometers: Toward a standard comparative criterion,” Laser Photonics Rev., 1900094, (2019).

[4] J. Albert  L‐Y Shao,  C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photonics Rev. 7(1), 83-108 (2013).

[5] S.W. James, R.P. Tatam, “Optical fibre long-period grating sensors: characteristics and  application,” Meas. Sci. Technol. 14, R49–R61 (2003).

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