**2. The basic theory of POF grating devices**

Grating devices in optical fibers normally belong to two main types, which depending on the mode-coupling mechanism, counter-directional coupling is the responsible mechanism in fiber Bragg gratings (FBGs) and co-directional coupling as main mechanism for long-period gratings (LPG).

FBG is a device due to periodic modulation of the refractive index along the optical fiber, normally obtained through the exposure of the optical fiber core with an intense optical interference pattern [29]. The periodic structure in an FBGs as a selective mirror, and the wavelength satisfies the Bragg condition expressed as:

$$
\lambda\_{\text{Braqq}} = \mathbf{2} n\_{\text{eff}} \,\,\Lambda \tag{1}
$$

where neff is the average effective refractive index along the fiber and Ʌ is the grating period. Then, **Figure 2** shown a component reflects one wavelength and transmits all others with a wavelength-specific dielectric mirror response.

The ability of the FBGs shown optical communication applications such as band stop filters in Raman amplifiers [30] dispersion compensators [31], and wavelength division multiplexers [32]. Also, FBG can be used for sensing purposes, such as humidity, strain and temperature measurements.

As **Figure 3** shown, LPG is based on a periodic modulation of the refractive index of the fiber core along of the direction of propagation of the light, and the core mode couples to co-propagating cladding modes, different attenuation bands are obtained when the resonance condition is satisfied the equation below:

$$
\lambda\_{\text{res}} = \Lambda \ast \Delta \mathbf{n} \tag{2}
$$

**Figure 2.**

*The transmission and reflection spectrum of a broad light go through one fiber with FBG inside.*

**Figure 3.** *LPG transmission graph.*

Where Δ*n* =- shown the difference between the effective refractive indices of the fundamental mode in core and the *i* th mode in cladding. As can be seen from the relation of the resonance wavelength, which is determined by the effective refractive indices of the core and cladding modes, so that any photo-induced, thermal-induced, geometrical, or mechanically induced periodic change will modify the position of the resonance wavelength. Which makes LPFGs are useful for the applications in fields as biological, chemical and optical sensing.
