**1. Introduction**

By utilizing dense wavelength-division-multiplexed (DWDM) transmission systems using an optical-fiber amplifier, large amount of data can be exchanged at a rate of over 60 Tbit/s [1]. In connection with this achievement, the danger of the "fiber fuse phenomenon" occurring has been pointed out. This occurs when high-power (W order) optical signals are transmitted in an optical-fiber cable [2].

The fiber fuse phenomenon was first observed in 1987 by British investigators [3]–[6]. A fiber fuse can be generated by bringing the end of a fiber into contact with an absorbing material, or melting a small region of a fiber by using an arc discharge of a fusion splice machine [3]. If a fiber fuse is generated, an intense blue-white flash occurs in the fiber core, and this flash propagates along the core in the direction of the optical power source at a velocity on the order of 1 m/s (see Figure 1). Fuses are terminated by gradually reducing the laser power to provide a termination threshold at which the energy balance at a fuse is broken.

When a fiber fuse is generated, the core layer in which the fuse propagates is seriously damaged, and the damaged fiber cannot be used in an optical communication system. The damage is made manifest by periodic or nonperiodic bullet-shaped cavities left in the core [7]–[13]. It was found that molecular oxygen was released and remained in the cavities while maintaining high pressure (about 4 atmospheres) at room temperature [4].

Several review articles [14], [15], [16] and a book [17] have been recently published, which cover many aspects of the current understanding of the fiber fuse.

Most experimental results of fiber fuse generation have focused on an intensity of 0.35–25 MW/cm2 [3]–[13], [18]–[39]. This is many orders of magnitude below the intrinsic damage limit for silica, which exceeds 10 GW/cm<sup>2</sup> [3]. The threshold power for an SMF required to generate and/or terminate a fiber fuse was estimated at about 1.0 [7], 1.19 [37], 1.33 [37], and 1.4 W [30] at *λ*<sup>0</sup> = 1.064, 1.31, 1.48, and 1.56 *µ*m, respectively.

©2012 Author(s), licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

**Figure 1.** Fiber fuse phenomenon.

On the other hand, the fiber fuse effect in a microstructured optical fiber, in which thirty air holes are arranged around the fiber center, was reported by Dianov *et al.* [40]. No propagation of the fiber fuse was observed at the power of ≤ 3 W and *λ*<sup>0</sup> = 0.5 *µ*m. This threshold power (3 W) was an order of magnitude higher than that of a conventional fiber. They also reported that the propagation of the fiber fuse was not observed when the laser light of up to 9 W and *λ*<sup>0</sup> = 1.064 *µ*m entered in the microstructured optical fiber.

It has recently been reported that a hole-assisted fiber (HAF) [41], in which several air holes are arranged near the core of the optical fiber, exhibits high tolerance to fiber fuses [42]–[51]. The fiber fuse propagation in a HAF is affected by both the diameter of an inscribed circle linking the air holes (*Dhole*) and the diameter of the air hole (*dh*) (see Figure 2).

**Figure 2.** Schematic view of SMF and HAF.

No propagation of fiber fuse was observed in HAFs with *dh* = *rc* = 4.5 *µ*m and a ratio *Rh* of the *Dhole* to the core diameter (2 *rc*) of 2 or less when the laser power *P*<sup>0</sup> of 13.5 and/or 15.6 W at *λ*<sup>0</sup> = 1.48 + 1.55 *µ*m was incident to HAFs [43], [45], [46].

Takenaga *et al.* investigated the power dependence of penetration length at a splice point of SMF and the HAF with *dh* of about 16.3–16.9 *µ*m and *Rh* of about 2.3, called "HAF2+" [42], [47]. The fiber fuse propagation immediately stopped in HAF2<sup>+</sup> for *P*<sup>0</sup> of 2.0–8.1 W at *λ*<sup>0</sup> = 1.55 *µ*m, where the penetration length was maintained constant (about 120 *µ*m). But the penetration length in HAF2<sup>+</sup> increased by nearly 600 *µ*m when *P*<sup>0</sup> decreased from 2.0 W to 1.5 W.

They supposed that an inner ring area, which was observed around the cavities after fiber fuse propagation, was the trail of glass being melted. *Dmelted* defined as the diameter of melting area (see Fugure 3) was considered as the radial size of plasma generated in the fiber fuse.

**Figure 3.** Schematic view of damaged SMF.

2 Optical Fiber

**Figure 1.** Fiber fuse phenomenon.

**Figure 2.** Schematic view of SMF and HAF.

On the other hand, the fiber fuse effect in a microstructured optical fiber, in which thirty air holes are arranged around the fiber center, was reported by Dianov *et al.* [40]. No propagation of the fiber fuse was observed at the power of ≤ 3 W and *λ*<sup>0</sup> = 0.5 *µ*m. This threshold power (3 W) was an order of magnitude higher than that of a conventional fiber. They also reported that the propagation of the fiber fuse was not observed when the laser light of up to 9 W and

It has recently been reported that a hole-assisted fiber (HAF) [41], in which several air holes are arranged near the core of the optical fiber, exhibits high tolerance to fiber fuses [42]–[51]. The fiber fuse propagation in a HAF is affected by both the diameter of an inscribed circle

SMF HAF

dh

No propagation of fiber fuse was observed in HAFs with *dh* = *rc* = 4.5 *µ*m and a ratio *Rh* of the *Dhole* to the core diameter (2 *rc*) of 2 or less when the laser power *P*<sup>0</sup> of 13.5 and/or 15.6

Takenaga *et al.* investigated the power dependence of penetration length at a splice point of SMF and the HAF with *dh* of about 16.3–16.9 *µ*m and *Rh* of about 2.3, called "HAF2+" [42],

Dhole

2rc

Core

Air hole

Cladding

linking the air holes (*Dhole*) and the diameter of the air hole (*dh*) (see Figure 2).

Core

*λ*<sup>0</sup> = 1.064 *µ*m entered in the microstructured optical fiber.

2rc

Cladding

W at *λ*<sup>0</sup> = 1.48 + 1.55 *µ*m was incident to HAFs [43], [45], [46].

*Dmelted* of HAF2<sup>+</sup> was maintained constant (about 20–22 *µ*m) in the *P*<sup>0</sup> range of 2.0–8.1 W, and decreased with decreasing *P*<sup>0</sup> in the *P*<sup>0</sup> range of 1.33–2.0 W [42], [47]. The constant *Dmelted* value (about 20–22 *µ*m) was almost equal to the *Dhole* value (21.2 *µ*m) of HAF2<sup>+</sup> in the *P*<sup>0</sup> range of 2.0–8.1 W. Therefore, an increase in penetration length observed in HAF2<sup>+</sup> for *P*<sup>0</sup> ≤ 2 W was considered to be induced by the reduction of plasma size. On the other hand, *Dmelted* of an SMF increased monotonously with increasing *P*<sup>0</sup> in the *P*<sup>0</sup> range of 4–14 W [46].

Several hypotheses have been put forward to explain the fiber fuse phenomenon. These include a chemical reaction involving the exothermal formation of germanium (Ge) defects [18], self-propelled self-focusing [3], thermal lensing of the light in the fiber via a solitary thermal shock wave [5], and the radiative collision of SiO and O complexes [52]–[55].

The similarities between the fiber fuse propagation and the combustion flame propagation were pointed out by Facão *et al.* [56], Todoroki [15], and Ankiewicz [57]. A fast detonation-like mode of fiber fuse propagation with a velocity of 3.2 km/s was observed under intense laser radiation intensity of 4,000 MW/cm<sup>2</sup> [58]. Combustion processes, including thermal self-ignition, can be mathematically expressed by the reaction-diffusion equations for temperature and fuel concentration [59], [60], [61]. If the reaction term for fuel concentration in these equations is replaced by the heat source term resulting from light absorption, the fiber fuse propagation can be described by solving the equations [56], [57], [62].

The optical absorption coefficient *α* of a fiber core at high temperatures is closely related to the generation of the fiber fuse. Kashyap reported a remarkable increase in the *α* value of a Ge-doped silica core above the critical temperature *T*<sup>0</sup> (∼ 1,323 K), while the *α* value of about 0 dB/km at room temperature remained unchanged until the temperature (*T*) approached *<sup>T</sup>*<sup>0</sup> [4]. The *<sup>α</sup>* value increased by nearly 1,900 dB/km (∼ 0.44 m<sup>−</sup>1) at *<sup>λ</sup>*<sup>0</sup> = 1.064 *<sup>µ</sup>*m when *<sup>T</sup>*

changed from *T*<sup>0</sup> to *T*<sup>0</sup> + 50 K. Furthermore, Kashyap *et al.* reported that the best fit between the experimental and theoretical fiber fuse velocities was obtained when the *α* value of the Ge-doped silica core at high temperatures of above *<sup>T</sup>*<sup>0</sup> was fixed to be 4.0 ×10<sup>4</sup> <sup>m</sup>−<sup>1</sup> at 1.064 *µ*m [19].

Hand and Russell found that this phenomenon was initiated by the generation of large numbers of Ge-related defects at high temperatures of above about 1,273 K, and the *α* values at *λ*<sup>0</sup> = 0.5 *µ*m obtained at temperatures of below 1873 K were modeled quite accurately using an Arrhenius equation [5], [6]. By contrast, they reported that the best fit between the experimental and theoretical fiber fuse velocities was obtained when the *α* value of the Ge-doped silica core at 2,293 K was assumed to be 5.6 ×104 m−<sup>1</sup> at 0.5 *µ*m [5]. This large *α* value, however, could not be estimated using their Arrhenius equation [6]. As the focal length *F* of thermal lense effect is inversely as the *α* value [63], large *α* value of 5.6 ×10<sup>4</sup> m−<sup>1</sup> is necessary to obtain small *F* value of 10 *µ*m order, which is comparable with observed interval and/or large front size of the cavities (see Appendix).

Furthermore, Hand and Russell reported that the electrical conductivity *σ* of the fiber core increased with the temperature and that the hot spot at the fiber fuse center was plasmalike [5]. Kashyap considered that the large *α* values may be attributable to an increase in the *σ* value of the fiber core at high temperatures of above *T*<sup>0</sup> [4].

It is well known that silica glass is a good insulator at room temperature, and the electrical conductivity in silica glass below 1,073 K is due to positively charged alkali ions moving under the influence of an applied field [64], [65]. The ionic conduction in the glass is not related solely to optical absorption.

We previously investigated the optical absorption mechanism causing the increase in the *σ* value and reported the relationship between *σ* and *α* in silica glass at high temperatures of above 1,273 K [66]–[69]. It was found that the increase in loss observed at 1.064 *µ*m can be well explained by the electronic conductivity induced by the thermal ionization of a Ge-doped silica core, and it is not directly related to the absorption of Ge *E* ′ centers.

However, the calculated *α* values resulting from the electronic conductivity at 1.064 *µ*m were of 102 m−<sup>1</sup> order at 2,873 K, about two orders smaller than the *α* values (1.0–4.0 ×104 m<sup>−</sup>1) reported by Kashyap *et al.* [4], [19]. Therefore, we need another mechanism to explain the increase in loss at high temperatures of above 2,273 K to account for the large (104 m−<sup>1</sup> order) *α* values.

To satisfy this requirement, we proposed a thermochemical SiO*x* production model in 2004 [68], [69]. Using this model, we theoretically estimated large *α* values of 104 m−<sup>1</sup> order as a result of SiO*x* absorption at high temperatures of 2,800 K or above. This model was able to quantitatively explain the relation between the fiber fuse propagation velocity and the incident laser-power intensity previously reported by other research institutions.

On the other hand, since the parameters (particularly the light-absorbing parameter) used for the numerical simulation were not optimized, the shortcoming that the maximum temperature of the core center obtained by calculation became unusually high (10<sup>5</sup> K order) was observed.

We have improved this model by optimizing several parameters required for the numerical computation, and we proposed an improved model in 2014 [70].

In the first half of this chapter we describe the improved model in detail. That is, we explain the mechanism of the increased absorption in optical fibers at high temperatures due to the thermochemical production of SiO*x*, and estimate high-temperature *α* values at *λ*<sup>0</sup> = 1.064 *µ*m. Then, using these values, we theoretically study the non-steady-state thermal conduction process in a single-mode optical fiber using the explicit finite-difference technique.

Next we have analyzed the heat transfer of HAFs with *dh* = *rc* on the basis of the improved model, and simulated the fiber fuse propagation behavior when a high optical power of 1–20 W at *λ*<sup>0</sup> = 1.55 *µ*m is injected into an HAF. In the latter half of this chapter we describe the results of this analysis.
