1. Introduction

Owing to the progress of dense wavelength-division multiplexing (DWDM) technology using an optical-fiber amplifier, we can exchange large amounts of data at a rate of over 100 Tbit/s over several hundred kilometers [1]. However, it is widely recognized that the maximum transmission capacity of a single strand of fiber is rapidly approaching its limit of 100 Tbit/s owing to the optical power limitations imposed by the fiber fuse phenomenon and the finite transmission bandwidth determined by optical-fiber amplifiers [2]. To overcome these limitations, space-division multiplexing (SDM) technology using a multicore fiber (MCF) was proposed [3, 4], and 1 Pbit/s transmission was demonstrated using a lowcrosstalk 12-core fiber [5].

The fiber fuse phenomenon was first observed in 1987 by British scientists [6–9]. Several review articles [10–14] have been recently published that cover many aspects of the current understanding of fiber fuses.

A fiber fuse can be generated by bringing the end of a fiber into contact with an absorbent material or melting a small region of a fiber using an arc discharge of a fusion splice machine [6, 15–17]. 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. The temperature and pressure in the region where this flash occurs have been estimated to be about 10<sup>4</sup> K and 10<sup>4</sup> atm, respectively [18]. Fuses are terminated by gradually reducing the laser power to a termination threshold at which the energy balance in the fuse is broken.

length of the void-free segment or the occurrence of an irregular void pattern was

Cavity Generation Modeling of Fiber Fuse in Single-Mode Optical Fibers

From these observation results, the cavity patterns occurring in single-mode fibers can be classified into the four patterns shown in Figure 2, where l is the length of the cavity and Λ is the (periodic) cavity interval. The observed periodic cavity patterns belong to patterns (a)–(c) with the pattern depending on the value of l=Λ. The long non-periodic cavity pattern (filaments) can be considered as a

These cavities have been considered to be the result of either the classic Rayleigh instability caused by the capillary effect in the molten silica surrounding a vaporized fiber core [32] or the electrostatic repulsion between negatively charged layers induced at the plasma–molten silica interface [33, 34]. Although the capillary effect convincingly explains the formation mechanism of water droplets from a tap and/or bubbles through a water flow, this effect does not appear to apply to the cavity formation mechanism of a fiber fuse owing to the anomalously high viscosity of the silica glass [23, 33]. Yakovlenko proposed a novel cavity formation mechanism based on the formation of an electric charge layer on the interface between the liquid glass and plasma [33]. This charge layer, where the electrons adhere to the liquid glass surface, gives rise to a "negative" surface tension coefficient for the liquid layer. In the case of a negative surface tension coefficient, the deformation of the liquid surface proceeds, giving rise to a long bubble that is pressed into the liquid [33]. Furthermore, an increase in the charged surface due to the repulsion of similar charges results in the development of instability [33]. The instability emerges because the countercurrent flowing in the liquid causes the liquid to enter the region filled with plasma, and the extruded liquid forms a bridge. Inside the region separated from the front part of the fuse by this bridge, gas condensation and cooling of the molten silica glass occur [34]. A row of cavities is formed by the repetition of this process. Although Yakovlenko's explanation of the formation of a long cavity and rows of cavities is very interesting, the concept of "negative" surface tension appears to be unfeasible in the field of surface science and/or plasma

Low-frequency plasma instabilities are triggered by moving the hightemperature front of a fiber fuse toward the light source. It is well known that such a low-frequency plasma instability behaves as a Van der Pol oscillator with instability frequency ω<sup>0</sup> [35–55]. Therefore, the oscillatory motion of the ionized gas

observed, respectively [26].

physics (see Appendix A).

Figure 2.

43

Cavity patterns observed in optical fiber.

sequence of two or more of pattern (d).

DOI: http://dx.doi.org/10.5772/intechopen.81154

The critical diameter dmelted, which is usually larger than the core diameter 2rc, is a characteristic dimensional parameter of the fiber fuse effect. In the inner area with diameter d≤ dmelted, a fiber fuse (high-temperature ionized gas plasma) propagates and silica glass is melted [18]. dmelted, defined as the diameter of the melting area, is considered as the radial size of the plasma generated in the fiber fuse [19]. Dianov et al. reported that the refractive index of the inner area with d≤dmelted in Ge-doped and/or pure silica core fibers is increased by silica-glass densification and/ or the redistribution of the dopant (Ge) [20].

When a fiber fuse is generated, the core layer in which the fuse propagates is seriously damaged, and the damage has the form of periodic bullet-shaped cavities or non-periodic filaments remaining in the core [6–9, 16–32] (see Figure 1). Needless to say, the density in a cavity or filament is lower than that of the neighboring silica glass. It has been found that molecular oxygen is released and remains in the cavities while maintaining a high pressure (about 4 atm [7] or 5–10 atm [20]) at room temperature. Recently, several types of sensors based on periodic cavities have been proposed as a cost-effective approach to sensor production [27–29].

The dynamics of cavity formation have been investigated since the discovery of the fiber fuse phenomenon. Dianov and coworkers observed the formation of periodic bullet-shaped cavities 20–70 μs after the passage of a plasma leading edge [30, 31].

Kashyap reported that the cavity shape was dependent on the nature of the input laser light (CW or pulses) operated at a wavelength λ<sup>0</sup> of 1.064 μm when the average input power was maintained at 2 W [7, 15]. When CW light was input, the cavities appeared to be elliptical and cylindrically symmetric. On the other hand, short asymmetric cavities were formed by injecting (mode-locked) pulses with 100 ps FWHM (full width at half maximum), while long bullet-shaped cavities were observed by injecting pulses with 190 ps FWHM [7, 15]. Hand and Russell reported the appearance of highly regular periodic damage tracks in germanosilicate fibers at λ<sup>0</sup> ¼ 488 and 514 nm [9]. Davis et al. reported that long non-periodic filaments occurred in germanium-doped depressed clad fibers, and a periodic damage pattern was observed in fibers doped with phosphorus and germanium at λ<sup>0</sup> ¼ 1:064μm [21, 22]. Atkins et al. observed both periodic and long non-periodic damage tracks created in a germanosilicate-core single-mode fiber transmitting about 2 W of power at 488 nm [32]. Dianov and coworkers reported the formation of periodic damage in a silica-core fiber at 1.064 and 1.21 μm [18, 30, 31] and long non-periodic damage in a germanosilicate silica core fiber at 488 and 514 nm [20].

Todoroki classified fiber fuse propagation into three modes (unstable, unimodal, and cylindrical) according to the plasma volume relative to the pump beam size [26]. When the pump power was increased or decreased rapidly, an increase in the

Figure 1. Schematic view of damaged optical fiber.

Cavity Generation Modeling of Fiber Fuse in Single-Mode Optical Fibers DOI: http://dx.doi.org/10.5772/intechopen.81154

length of the void-free segment or the occurrence of an irregular void pattern was observed, respectively [26].

From these observation results, the cavity patterns occurring in single-mode fibers can be classified into the four patterns shown in Figure 2, where l is the length of the cavity and Λ is the (periodic) cavity interval. The observed periodic cavity patterns belong to patterns (a)–(c) with the pattern depending on the value of l=Λ. The long non-periodic cavity pattern (filaments) can be considered as a sequence of two or more of pattern (d).

These cavities have been considered to be the result of either the classic Rayleigh instability caused by the capillary effect in the molten silica surrounding a vaporized fiber core [32] or the electrostatic repulsion between negatively charged layers induced at the plasma–molten silica interface [33, 34]. Although the capillary effect convincingly explains the formation mechanism of water droplets from a tap and/or bubbles through a water flow, this effect does not appear to apply to the cavity formation mechanism of a fiber fuse owing to the anomalously high viscosity of the silica glass [23, 33]. Yakovlenko proposed a novel cavity formation mechanism based on the formation of an electric charge layer on the interface between the liquid glass and plasma [33]. This charge layer, where the electrons adhere to the liquid glass surface, gives rise to a "negative" surface tension coefficient for the liquid layer. In the case of a negative surface tension coefficient, the deformation of the liquid surface proceeds, giving rise to a long bubble that is pressed into the liquid [33]. Furthermore, an increase in the charged surface due to the repulsion of similar charges results in the development of instability [33]. The instability emerges because the countercurrent flowing in the liquid causes the liquid to enter the region filled with plasma, and the extruded liquid forms a bridge. Inside the region separated from the front part of the fuse by this bridge, gas condensation and cooling of the molten silica glass occur [34]. A row of cavities is formed by the repetition of this process. Although Yakovlenko's explanation of the formation of a long cavity and rows of cavities is very interesting, the concept of "negative" surface tension appears to be unfeasible in the field of surface science and/or plasma physics (see Appendix A).

Low-frequency plasma instabilities are triggered by moving the hightemperature front of a fiber fuse toward the light source. It is well known that such a low-frequency plasma instability behaves as a Van der Pol oscillator with instability frequency ω<sup>0</sup> [35–55]. Therefore, the oscillatory motion of the ionized gas

Figure 2. Cavity patterns observed in optical fiber.

reducing the laser power to a termination threshold at which the energy balance in

The critical diameter dmelted, which is usually larger than the core diameter 2rc, is a characteristic dimensional parameter of the fiber fuse effect. In the inner area with diameter d≤ dmelted, a fiber fuse (high-temperature ionized gas plasma) propagates and silica glass is melted [18]. dmelted, defined as the diameter of the melting area, is considered as the radial size of the plasma generated in the fiber fuse [19]. Dianov et al. reported that the refractive index of the inner area with d≤dmelted in Ge-doped and/or pure silica core fibers is increased by silica-glass densification and/

When a fiber fuse is generated, the core layer in which the fuse propagates is seriously damaged, and the damage has the form of periodic bullet-shaped cavities or non-periodic filaments remaining in the core [6–9, 16–32] (see Figure 1). Needless to say, the density in a cavity or filament is lower than that of the neighboring silica glass. It has been found that molecular oxygen is released and remains in the cavities while maintaining a high pressure (about 4 atm [7] or 5–10 atm [20]) at room temperature. Recently, several types of sensors based on periodic cavities have been proposed as a cost-effective approach to sensor production [27–29].

The dynamics of cavity formation have been investigated since the discovery of

Kashyap reported that the cavity shape was dependent on the nature of the input

the fiber fuse phenomenon. Dianov and coworkers observed the formation of periodic bullet-shaped cavities 20–70 μs after the passage of a plasma leading edge

laser light (CW or pulses) operated at a wavelength λ<sup>0</sup> of 1.064 μm when the average input power was maintained at 2 W [7, 15]. When CW light was input, the cavities appeared to be elliptical and cylindrically symmetric. On the other hand, short asymmetric cavities were formed by injecting (mode-locked) pulses with 100 ps FWHM (full width at half maximum), while long bullet-shaped cavities were observed by injecting pulses with 190 ps FWHM [7, 15]. Hand and Russell reported the appearance of highly regular periodic damage tracks in germanosilicate fibers at λ<sup>0</sup> ¼ 488 and 514 nm [9]. Davis et al. reported that long non-periodic filaments occurred in germanium-doped depressed clad fibers, and a periodic damage pattern was observed in fibers doped with phosphorus and germanium at λ<sup>0</sup> ¼ 1:064μm [21, 22]. Atkins et al. observed both periodic and long non-periodic damage tracks created in a germanosilicate-core single-mode fiber transmitting about 2 W of power at 488 nm [32]. Dianov and coworkers reported the formation of periodic damage in a silica-core fiber at 1.064 and 1.21 μm [18, 30, 31] and long non-periodic damage in a germanosilicate silica core fiber at 488 and 514 nm [20]. Todoroki classified fiber fuse propagation into three modes (unstable, unimodal, and cylindrical) according to the plasma volume relative to the pump beam size [26]. When the pump power was increased or decreased rapidly, an increase in the

the fuse is broken.

[30, 31].

Figure 1.

42

Schematic view of damaged optical fiber.

or the redistribution of the dopant (Ge) [20].

Fiber Optics - From Fundamentals to Industrial Applications

plasma during fiber fuse propagation can be studied phenomenologically using the Van der Pol equation [56].

In this paper the author describes a novel nonlinear oscillation model using the Van der Pol equation and qualitatively explains both the silica-glass densification and cavity formation observed in fiber fuse propagation. Furthermore, an investigation of the relationship between several cavity patterns and the nonlinearity parameters in the nonlinear oscillation model is reported.
