**1. Introduction**

The development of optical fiber gratings (OFGs) had made significant advances both in terms of research and development of optical communications and sensors. OFGs are intrinsic devices that allow modulate the properties of light propagation within the fiber. Grating structures are comparatively simple and in its most basic form, consist on a periodic modula‐ tion of the properties of an optical fiber (usually the refraction index of the core). Its application as a sensing element is advantageous because of the intrinsic characteristics of the fiber sensors, such as remote sensing, electromagnetic immunity, weight and compactness, and capability for real time sensing and low cost [1].

Among OFGs, long period fiber gratings (LPFGs) are one of the most important fiber-based sensors. They were first presented by Vengsarkar and co-workers in 1996 [1] as band-rejection filters. Since then, LPFG technology has been receiving continuously growing attention from scientific community. Due to their spectral characteristics, LPFGs have found many applica‐ tions in both optical communications and sensing systems. In the optical communications field, they have been demonstrated as gain equalizers [1], dispersion compensators [2], optical switches [3], components in wavelength division multiplexing (WDM) systems [4], band rejection filters and mode converters [5]. For optical sensing applications, LPFGs have been implemented as a temperature [6], strain [7] and refractive index sensor [8-10]. As element sensor a LPFG exhibits high sensitivity to the refractive index (RI) of the material surrounding the cladding surface. Other strengths are their low insertion losses, low back-reflection, polarization independence, relatively simple fabrication, and remote sensing easily multi‐ plexed.

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These gratings devices operate in transmission mode and are manufactured with periods typically in the range from 100 μm to 1000 μm [6]. Their large modulation period promotes the coupling of the light from the fundamental core mode to co-propagating cladding modes in a single-mode fiber [1]. The light coupled to the cladding decays quickly due to the absorp‐ tion and scattering by the coating over the cladding.

A commonly-used optical fiber typically consists of a core and a cladding. In Figure 1 it is schematized the coupling mode that occurs in a LPFGs inscribed in single-mode fiber (SMF). As a result, the transmission spectrum of a LPFG has a series of resonant loss peaks (attenuation bands) centered at discrete wavelengths. A typical (theoretical) example is shown in Figure 2.

**Figure 1.** Schematic diagram of a mode coupling in a long period grating [11].

**Figure 2.** Theoretical example of the spectrum of a 500 μm-LPFG inscribed in a Corning SMF-28 fiber.

The resonant wavelength at which coupling takes place satisfies the phase matching condition

$$\mathcal{N}\_{\rm res}^{\rm un} = \left(\mathfrak{m}\_{\rm eff,co} - \mathfrak{m}\_{\rm eff,cl}^{\rm un}\right)\Lambda \tag{1}$$

in which *neff,co* and *neff,cl* are the effective refractive indices of the fundamental core mode and the mth cladding mode, respectively; *λres* is the center wavelength of the transmission resonance; and *Λ* is the period of refractive index modulation [12].

These gratings devices operate in transmission mode and are manufactured with periods typically in the range from 100 μm to 1000 μm [6]. Their large modulation period promotes the coupling of the light from the fundamental core mode to co-propagating cladding modes in a single-mode fiber [1]. The light coupled to the cladding decays quickly due to the absorp‐

A commonly-used optical fiber typically consists of a core and a cladding. In Figure 1 it is schematized the coupling mode that occurs in a LPFGs inscribed in single-mode fiber (SMF). As a result, the transmission spectrum of a LPFG has a series of resonant loss peaks (attenuation bands) centered at discrete wavelengths. A typical (theoretical) example is shown in Figure 2.

tion and scattering by the coating over the cladding.

288 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

**Figure 1.** Schematic diagram of a mode coupling in a long period grating [11].

**Figure 2.** Theoretical example of the spectrum of a 500 μm-LPFG inscribed in a Corning SMF-28 fiber.

l

The resonant wavelength at which coupling takes place satisfies the phase matching condition

*res eff co eff cl n n* (1)

= -L ( , , ) *m m*

Both resonant wavelength and attenuation amplitude of LPFGs are sensitive to a several physical parameters: temperature, strain, external refractive index, fiber dimensions, grating pitch, etc. These physical parameters affect the coupling between the core and cladding modes, which could lead to both amplitude and wavelength shift of the attenuation bands in the transmission spectrum [13]. The measurement of these spectral parameters in response to the environment surrounding the grating region is the basis of sensing with these devices.

In particular, LPFGs exhibits high sensitivity to changes in the RI of the medium surrounding the fiber due to the dependence of the phase matching condition upon the effective refractive index of the cladding modes. This characteristic makes these structures very attractive for sensing applications and several configurations, as well as applications, of LPFG devices for the measurement of physical and chemical quantities have been studied [6-13].

As mentioned before, LPFGs are created by inducing a periodic refractive index modulation (typically 10-4 [14-19]) in the core of an optical fiber with period lengths of several hundred micrometers. This can be made by permanent modification of the refractive index of the optical fiber's core or by physical deformation of the fiber.

Since the first demonstration of these devices by writing the grating with ultraviolet (UV) laser light through an amplitude mask in 1996 [1], several methods have been developed to create and improve the quality of the LPFGs. The conventional UV writing method is based on the exposure of photosensitive optical fibers to UV light through an amplitude mask, phase mask or by interferometry [8-9]. In germanium-doped (Ge-doped) silica fibers, UV light changes the refractive index of the core fiber, being this effect related with the formation of Ge-associated defects [20]. However, this method has some inherent limitations. It requires complex and time-consuming processes, including annealing and hydrogen loading for making the fibers photosensitive, and different amplitude masks when different dimensions are required. Also, the masks need replacement after prolonged usage and the required laser equipment is expensive.

There are, however, many non-photochemical methods available for gratings inscription. These include ion beam implantation [21], applying mechanical pressure [22], electric-arc discharge [23, 24] and irradiation by femtosecond laser pulses [25] or CO2 laser beam [26, 27]. Among these methods, the latter is particularly flexible, as it can be applied to different types of fibers and the writing process can be computer-controlled to fabricate complicated gratings profiles without using amplitude masks. Furthermore, the use of infrared radiation as showed that the resulting interaction mechanisms are more efficient and allow creating devices with particular characteristics.

Taking this in consideration, this chapter addresses the application of CO2 laser radiation in writing LPFGs and the physical principles involved in the process. A special emphasis will be given to the modulation of the refractive index resultant from the interaction between the midinfrared (MIR) radiation (emitted by these lasers) and a conventional Ge-doped SMF.

In section 2 it will be described the fabrication process for applying the MIR radiation, starting with a review on the use CO2 lasers in the creation of LPFGs. Experimental work is presented as well as the physical principles that may be responsible to induce the periodic refractive index modulation in the fiber's core.

Section 3 will address the subject of simulating the thermal mechanical processes involved in the process. Analytical and numerical models will be analysed and compared. In particular, a 3D finite element method (FEM) model will be presented, including the temperature depend‐ ence of the fiber's main parameters.

In section 4, it is presented a practical example of writing LPFGs on a Ge-doped fiber using a CO2 laser. A comparison between calculated data and experimental data is made, and future work towards a full understanding of the physical processes is foreseen.
