Bragg gratings have been written in many types of optical fibers using various methods, however, the mechanism of index change is not fully understood. Several models have been proposed for the photoinduced refractive-index change. The
only common elements in these theories is that the germanium-oxygen vacancy defects, Ge-Si or Ge-Ge (the so-called “wrong bonds”) are responsible for the photo-induced index changes.
In 1989, Meltz et al. [42] showed that a strong index of refraction change occurred when a germanium-doped fiber as exposed to UV light close to the absorption peak of a Germania-related defect at a wavelength range of 240 - 250 nm. The fact that the change of the index of refraction in a germanosilicate optical fiber is triggered by a single photon at ~ 240 nm, which is well below the band gap at 146 nm, implies that the point defects in the ideal glass tetrahedral network are responsible for this process. Defects in optical fibers first attracted attention because of the unwanted absorption band associated with them, which caused transmission losses. Normally the defects are caused by the fiber drawing process, and ionizing radiation as described in the previous paragraphs.
The radiation induced defect centers were identified and characterized by electron spin resonance spectroscopy. The creation of defect bands are centered at 195, 213, and 281 nm. The photosensitivity phenomenon, which is a basis for the fabrication of fiber gratings, is commonly ascribed to two essential physical mechanisms: creation of color centers and structural transformations. Both effects are well established. However, there is no general agreement about which mechanism dominates in the case of Ge-doped silica fibers.
The analysis of the color-center contribution assumes a rather straightforward application of the Kramers–Kronig relations. The model, known as “color center
model”, proposed the breaking of the GeO defect resulting in a GeE’ center with the
release of an electron, which is free to move within the glass matrix until it is retrapped.
The Kramers-kronig relationship is given as:
𝜖𝑟(𝜆) = 1 + ∫
𝜖𝑖(𝜆)
𝜆′− 𝜆 𝑑𝜆
′ (2.13)
Relates the real and imaginary parts of the dielectric constant 𝜖 = 𝜖𝑝+ 𝑖𝜖1 = (𝑛 + 𝑖𝑘)2 where 𝑛 is the refractive index and 𝑘 is the absorption
index.
The relationship arises from the causality condition for the dielectric response and demonstrates that the index change produced in the infrared/visible region of
the spectrum by the photoinduced processing results from a change in the absorption spectrum of the glass in the UV/far-UV spectral region.
The Eq. (2.13) can be explicated as follow:
Δ𝑛(𝜆) = 1 2𝜋2+ ∫ ∆𝛼 (𝜆) 1 − (𝜆 𝜆′⁄ )2 ∞ 0 𝑑𝜆 (2.14)
∆𝛼 is an increase of attenuation, Δ𝑛 is the change of the refractive index, 𝜆 is the wavelength for which the refractive index is calculated and 𝜆′ is the centre wavelength of an absorption band.
Since the radiation-induced attenuation strongly depends on the wavelength of the transmitted light, with a minimum at about 1100 nm, a moderate increase towards the far infrared and a strong increase towards shorter wavelengths [93], the choice of the FBG with a specific sensitivity is recommended according to the application. In this model, UV exposure changes the material properties of the glass and introduces new electronic transitions of defects (color centers). The underlying premise of the color center model is that the photosensitive effect arises from localized electronic excitations of defects. The wrong-bond defects, which initially absorb the light, are transformed to defects that are more polarized by virtue of the fact that their electronic transitions occur at longer wavelengths or have stronger transitions. According to the color center model, the refractive index at a point is related only to the number density and orientation of defects in that region and is determined by their electronic absorption spectra.
A structural rearrangement of the atoms of the silica matrix is the base of the predicting model known as “compaction effects” [91, 94, 95]. It is well known that radiation exposure of vitreous silica can cause changes in the physical properties such as density [93]. The detailed origin of this density change has never been quite clear, but the compaction effect has been so universally observed in vitreous silica that it appears to be an inherent property of the material.
The theoretical basis of the relationship between reflective index and mass density is embedded in the Lorentz–Lorenz, which relates macroscopic optical/electrical properties (dielectric constant and refractive index) to the corresponding microscopic molecular properties (e.g., molecular polarizability).
(𝑛
2− 1)
(𝑛2+ 2) =
𝛼𝜌
3 (2.15)
where 𝜌 is the number density of the material molecules, 𝛼 is the mean molecular polarizability.
In terms of the mass density 𝜌𝑚, which is related to the number density by
𝜌𝑚= (𝑀 𝑁⁄ 𝐴) 𝜌, the Lorentz–Lorenz relation becomes
(𝑛 2− 1) (𝑛2+ 2) 𝜌 𝑚 = 𝑁𝐴 𝛼 3 𝑀 (2.16)
where 𝑁𝐴 is the universal Avogadro’s number and 𝑀 is the molecular weight of the chemical element of the material.
In general, the dose dependence of compaction in vitreous silica obeys a power law [94]:
Δ𝜌𝑚 𝜌𝑚
= 𝐴′𝐷𝑐 (2.17)
where 𝐷 is the absorbed radiation dose, 𝐴′ and 𝑐 are constants. The dose exponent 𝑐 is found to be dependent on the nature of the radiation source and the effect of radiation on silica. For example, 𝑐 is close to 1 for knock-on (atomic displacement) radiation (neutron, He+, or D+, etc.) [97] and is about 272 for ionizing radiation (𝛾-ray [97-99]), e-beam [97, 100] and ultraviolet (UV) radiation [101-103].
The phenomenon of compaction of silica after irradiation suggest a bond rearrangement leading to a decrease in the volume of the system and a refractive index variation accordingly, results both from trivial organizational events and from bond rupture followed by re-formation of bonds. To explain the photoinduced changes in glass network structure further interesting theories have been proposed, but none of them provide a structural interpretation that is consistent across glass families and explains the wide range of photoinduced property variations because of the complex dynamic of the phenomenon. The models are discussed in depth in the review article [72].