Part IV Damage Phenomena in Optical Connector End Faces · Damage Phenomena in Optical Connector...

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Part V Damage Phenomena in Optical Connector End Faces 1 High-Power Performance of Fiber-Optic Con- nectors When optical signals are transmitted over a long distance using single-mode optical fibers (SMFs), it is necessary to connect long optical fibers along the transmission path. Optical connectors for SMFs were developed for this pur- pose. In addition to single-core connectors such as SC-type connectors [1], MU- type connectors [2], LC-type connectors [3], and so forth, MT-type connectors [4] capable of collectively connecting a large number of optical fibers are widely used. Several research institutes have studied the high power performance of single- mode fiber-optic connectors [5]–[8]. One of the most common types of degra- dation observed in the connectors is related to end-face contamination, often induced by plug/unplug operations. The contamination in optical connectors comprises dust or other organic particles, which are mainly produced during network installation as a result of handling by human operators. When the plug/unplug procedure is performed with contaminated connectors, the impuri- ties can enter the fiber core region. These adherent impurities act as absorbing centers, and the surrounding material is heated to sufficiently high temperatures to induce permanent damage. The temperature rise in the connector may also trigger the fiber fuse effect. The high-power damage phenomena in fiber-optic connectors were previously investigated from the viewpoint of the adhesion of absorbing organic materials, such as carbon-black-doped resin [5], [8] and a thin layer of carbon black [7], on the core end faces in the connectors. The carbon black was used to represent organic contaminants in these studies. De Rosa et al. prepared mated connector pair sets that consisted of end faces with carbon black uniformly covering the fiber cores [5]. These contaminated samples were prepared using a carbon-black-doped UV-curable acrylate resin. A thin, even layer of solution was applied to the end face of one connector of the mated pair and was cured using UV light to provide a known end-face condition. Samples contaminated with 5 wt% carbon-black-doped acrylate resin exhibited end-face damage at an initial laser power P 0 of 49 mW when they were exposed to CW laser light with a wavelength λ 0 of 1.55 μm [5]. Seo et al. reported that optical connectors with light-absorbing contami- nants such as carbon-black-doped epoxy resin and/or oil-based black ink showed end-face damage at P 0 = 2 W when exposed to laser light with λ 0 = 1.48 μm [8]. 1

Transcript of Part IV Damage Phenomena in Optical Connector End Faces · Damage Phenomena in Optical Connector...

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Part V

Damage Phenomena in OpticalConnector End Faces

1 High-Power Performance of Fiber-Optic Con-nectors

When optical signals are transmitted over a long distance using single-modeoptical fibers (SMFs), it is necessary to connect long optical fibers along thetransmission path. Optical connectors for SMFs were developed for this pur-pose. In addition to single-core connectors such as SC-type connectors [1], MU-type connectors [2], LC-type connectors [3], and so forth, MT-type connectors[4] capable of collectively connecting a large number of optical fibers are widelyused.

Several research institutes have studied the high power performance of single-mode fiber-optic connectors [5]–[8]. One of the most common types of degra-dation observed in the connectors is related to end-face contamination, ofteninduced by plug/unplug operations. The contamination in optical connectorscomprises dust or other organic particles, which are mainly produced duringnetwork installation as a result of handling by human operators. When theplug/unplug procedure is performed with contaminated connectors, the impuri-ties can enter the fiber core region. These adherent impurities act as absorbingcenters, and the surrounding material is heated to sufficiently high temperaturesto induce permanent damage. The temperature rise in the connector may alsotrigger the fiber fuse effect.

The high-power damage phenomena in fiber-optic connectors were previouslyinvestigated from the viewpoint of the adhesion of absorbing organic materials,such as carbon-black-doped resin [5], [8] and a thin layer of carbon black [7], onthe core end faces in the connectors. The carbon black was used to representorganic contaminants in these studies.

De Rosa et al. prepared mated connector pair sets that consisted of end faceswith carbon black uniformly covering the fiber cores [5]. These contaminatedsamples were prepared using a carbon-black-doped UV-curable acrylate resin.A thin, even layer of solution was applied to the end face of one connector of themated pair and was cured using UV light to provide a known end-face condition.Samples contaminated with 5 wt% carbon-black-doped acrylate resin exhibitedend-face damage at an initial laser power P0 of 49 mW when they were exposedto CW laser light with a wavelength λ0 of 1.55 μm [5].

Seo et al. reported that optical connectors with light-absorbing contami-nants such as carbon-black-doped epoxy resin and/or oil-based black ink showedend-face damage at P0 = 2 W when exposed to laser light with λ0 = 1.48 μm[8].

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Domingues et al. examined the high-power damage of fiber-core end facescovered with carbon black [7]. Contaminated samples were prepared using acarbon-black aqueous solution to obtain an initial attenuation IA in the rangeof 2–10 dB. Samples with IA ≥ 4 dB exhibited end-face damage at P0 = 1 Wwhen exposed to CW laser light with λ0 = 1.48 μm, and the fiber fuse effectoccurred in the samples with the passage of time at 1.5 W [7]. An IA of 4 dBcorresponds to an optical absorption coefficient α of 9.2 ×105 m−1 when thethickness of the contaminant is about 1 μm. The value of α for the contaminantis closely related to the generation of end-face damage and/or the fiber fuseeffect.

Many researchers have used carbon black as a light-absorbing material be-cause it can be used to model dust mixed into the fiber end face during theconnection of optical fibers to each other and organic contaminants derivedfrom workers.

In this part, we begin by estimating the α value for carbon black. Then, usingthis value, the non-steady-state thermal conduction process in the contaminatedend face of an optical connector is theoretically studied using the explicit finite-difference technique and the thermochemical SiOx production model for SMFs[9].

2 Absorption Coefficient of Carbon Black

The optical properties (or constants) of materials are usually characterized bytwo parameters, the index of refraction n and extinction coefficient k. Theoptical absorption coefficient α is related to k and λ0 by [10]

α =4πk

λ0. (1)

Graphite, which is the raw material of carbon black, has a stratified molec-ular structure. In each layer, many carbon atoms are tightly packed into atwo-dimensional honeycomb lattice [11]. The optical constants of graphite havebeen estimated in the visible and ultraviolet regions [12], [13]. Values of n =2.73 and k = 1.40 at λ0 = 0.63 μm have been reported [13].

Using Eq. (1) and the optical constants, the absorption coefficient of graphiteis estimated to be α = 2.79 ×107 m−1. This value is about three orders ofmagnitude larger than the α values (104 m−1 order) [14], [15] required for fiberfuse generation.

The melting temperature of graphite is 4,800 ± 100 K [16], and liquid carbonexists at high temperatures of > 4,800 K [17]. Carbon vapor containing C1 toC7 species was measured at temperatures (T ) of 5,000–10,000 K [18]. As theoptical constants of liquid carbon and carbon vapor are unknown, α = 2.79×107 m−1 was used throughout the calculation process.

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3 Deformation Temperature of Silica Glass

To generate end-face damage, the temperature of the core layer must reacha critical value, at which silica glass can be readily deformed. This criticaltemperature is known as the working point, which is related to the viscosity ofthe glass.

The working point (Tw) of a glass is defined as the temperature at which ithas a viscosity of 104 P (P: Poise) [19]. On the other hand, the softening point(Ts) is the temperature at which it has a viscosity of 107.6 P [19].

The relationship between the viscosity η (P) and temperature T (K) of silicaglass (fused silica) is [20], [21]

log η = −6.24 + 26, 950/T. (2)

log η for silica glass is shown in Fig. 1 as a function of T .

0

2

4

6

8

10

12

log

η

1600 2000 2400 2800 3200 3600

Temperature (K)

Ts Tw

Silica Glass

Figure 1: Viscosity of silica glass as a function of temperature.

η decreases with increasing T . Using the η data shown in Fig. 1, the Tw andTs values were estimated to be Tw = 2,632 K and Ts = 1,947 K.

Ts is slightly lower than the melting point (Tm = 1,996 K) of silica glass.Moreover, Tw is about 640 K higher than Tm.

In the next section, the thermal conduction behavior within contaminatedend faces of fiber-optic connectors is investigated by numerical computationusing the α values estimated above.

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4 Heat Conduction Behavior in ContaminatedOptical-Fiber Connector

An SMF-28 optical fiber is assumed to be set in the center of a ferrule. Thisfiber has an outer radius of rf (= 62.5 μm), a core radius of a (= 4.1 μm), anda refractive index difference of Δ = 0.36%.

When two connector plugs with ferrules are joined in an adaptor, compres-sive contact forces (about 6 N (N: Newton) for an SC-type connector [22]) aregenerated on the ferrule end faces. These compressive forces result from thedifference between the spring compressive force of the plug and the gauge reten-tion force of the adaptor [23], [24]. The compressive forces deform the ferruletip and compress the optical fiber held in the ferrule. When the optical fiberwith rf = 62.5 μm is compressed by the compressive force (about 6 N), a highpressure of about 0.5 GPa (5,000 atm) acts on the fiber end faces.

It is considered that the contaminant (carbon black) enters the gap betweenthe ferrule end faces as shown in Fig. 2.

Optical Fiber

FerruleContaminant

Air Gap

Contact Force

Figure 2: Schematic view of ferrule end faces with adhering contaminant.

The adhering contaminant is compressed by the compressive contact forceto form a thin absorbent layer between the end faces of the optical fibers facingeach other. A schematic view of the absorbent layer between the optical-fiberend faces is shown in Fig. 3, where αa and ΔLa are the absorption coefficientand the thickness of the absorbent, respectively.

The αa value of the contaminant is very large as described above. Thus, itcan be expected that when laser light enters the core layer shown in Fig. 3, it isefficiently absorbed near the incident interface with the core, and the generationof heat takes place near this interface.

To verify this prediction, we theoretically studied the non-steady-state ther-mal conduction process in the region near the core end faces in Fig. 3 using anexplicit finite-difference technique. In the calculation, it was assumed that theinitial temperature of the absorbent layer was equal to room temperature (298K).

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����������������

2 rf

ΔLa

Absorbent

Core

Cladding

2 a

αa

Figure 3: Schematic view of absorbent layer between optical-fiber end faces.

4.1 End-Face Damage Caused by Carbon-Black Adhesion

First, we investigated the temperature distribution of the core end face in theexperiments carried out by De Rosa et al. [5]. In their experiments, the coreend face was in contact with an absorbent layer consisting of 5 wt% carbon-black-doped UV-curable acrylate. It was assumed that laser light of wavelengthλ0 = 1.55 μm and initial laser power P0 = 49 mW was incident to the opticalfiber held in the ferrule (see Fig. 2). The value of αa for the absorbent layerwas estimated to be about 1.40 ×106 m−1 by multiplying α (2.79 ×107 m−1)for graphite by 5%.

The area in the numerical calculation had a length of 2L (= 2 mm) in theaxial (z) direction and a width of 2rf (= 125 μm) in the radial (r) direction.There were 24 and 4,000 divisions in the r and z directions, respectively, andthe calculation time interval was set to 1 ns. It was assumed that the absorbentlayer was located at the center of the fiber (length 2L) and that the length ΔLa

of the layer was 1 μm.It is well known that UV-curable acrylate resin is pyrolyzed at 350–450 K

[25] and charred at high temperatures.Therefore, in the heat conduction calculation, we used the following values

of λ (W m−1 K−1), ρ (kg m−3), and Cp (J kg−1 K−1) in each temperaturerange.

(1) Parameters of acrylate resin in the temperature range from room tem-perature (298 K) to 450 K [26]:

Cp = 1, 400λ = 0.21ρ = 1, 190.

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(2) Parameters of coal for T > 450 K [26]:

Cp = 1, 260λ = 0.28ρ = 1, 350.

The temperature field of the core center along the z direction was calculatedat a time of 100 μs after the incidence of the 49 mW laser light. The calculatedresult is shown in Fig. 4.

Distance L (μm)

Tem

pera

ture

T (

103

K)

Tw = 2,632 K

Tp

P0 = 49mW

0

2

4

6

8

-30 -20 -10 0 10 20 30

Figure 4: Temperature field around carbon-black-doped UV-curable acrylatelayer placed between optical fibers after 100 μs when P0 = 49 mW and λ0 =1.55 μm.

The heat generated in the absorbent layer is transferred to the neighboringcore layers of the optical fibers. At a time of 100 μs after laser light incidence,a peak temperature (Tp) of 4,800 K or above occurs in the immediate neighbor-hood of the absorbent layer (see Fig. 4). As a result, the temperatures of theregions of about 4 and 3 μm depth in the left and right core layers, respectively,become higher than the working point (Tw = 2,632 K) of silica glass. In theseheated core regions, it can be expected that the melting and flow of silica glasswill occur locally and that the surfaces of the core layers will be damaged asobserved by De Rosa et al. [5].

Next, we studied the temperature distribution of the core end face in theexperiments carried out by Domingues et al. [7]. In their experiments, the coreend face was in contact with an absorbent layer produced by spreading carbonblack. It was assumed that laser light of wavelength λ0 = 1.48 μm and initialpower P0 = 1 W was incident to the optical fiber held in the ferrule (see Fig. 2).The length ΔLa of the absorbent layer and the calculation time interval wereassumed to be 1 μm and 1 ns, respectively.

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The relationship between αa (unit: m−1) and the initial attenuation IA(unit: dB) of the absorbent layer is given by

αa = 0.23026IA

ΔLa. (3)

In the calculation, the following thermal conduction parameters of carbonblack were used: λ = 98 W m−1 K−1, ρ = 1,900 kg m−3, and Cp = 710 J kg−1

K−1, which are the parameters of black lead [27].The Tp values around absorbent layers with IA = 0.5–8 dB were calculated

as a function of the irradiation time after the incidence of the 1 W laser light.The calculated results are shown in Fig. 5.

0

1

2

3

4

1010-6 1

Time (s)

10-5 10-4 10-3 10-2 10-1

Tp

(10

3 K

)

8 dB6 dB

4 dB

IA = 3 dB

2 dB

1 dB

0.5dB

Tpb

Figure 5: Peak temperatures around carbon-black layers with IA = 0.5–8 dB(ΔLa = 1 μm) spread between optical fibers versus irradiation time when P0 =1 W and λ0 = 1.48 μm.

As shown in Fig. 5, Tp increased with increasing time and approached acertain temperature T b

p with the passage of time, where T bp is the temperature

at which the balance of heat is achieved in the absorbent layer.In the case of a heat source in part of the core layer, the non-steady heat

conduction equation for the temperature field T (r, z, t) in an SMF is given by

ρCp∂T

∂t= λ

(∂2T

∂r2+

1r

∂T

∂r+

∂2T

∂z2

)+ Q, (4)

where the first term on the right of Eq. (4) expresses the diffusion or dissipationof the heat in the optical fiber and the absorbent layer. The last term Q in Eq.(4) represents the heat source resulting from light absorption, which is mainly

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required for the absorbent layer between the optical fibers. Q can be expressedby

Q = αI, (5)

where I is the optical power intensity in the core layer, which can be estimatedby dividing the incident optical power P0 by the effective area Aeff of the fiber.

When laser light enters the absorbent layer, heat is produced in the layerby optical absorption of the incident light. The heat generated by optical ab-sorption in the layer is effectively dissipated by heat conduction because thethermal conductivity λ of the absorbent (carbon black) is large. As a result,the quantity of heat required to raise the temperature from T b

p is canceled bythe effective dissipation of the heat.

As shown in Fig. 5, samples with IA = 6 and 8 dB exhibit steep temperaturegradients at an irradiation time of about 10 ms. This behavior is considered tobe related to the fiber fuse generation described below. In this case, the heatsupplied from the heat source to the core layer is smaller than the heat requiredfor fiber fuse initiation. As a result, the fiber fuse generation is hindered inthese samples.

The relationship between T bp and IA for the absorbent layer was examined.

The result is shown in Fig. 6.

0

1

2

3

4

0 2 4 6 8 10

IA (dB)

ΔLa = 1 μm

Tpb

(10

3 K

)

Tw =2632 K

Ts = 1947 K

Figure 6: T bp versus IA for spread carbon black layers when P0 = 1 W and λ0

= 1.48 μm.

The T bp values for the absorbent layers with IA ≥ 3 dB are higher than Tw

for silica glass (see Fig. 6). Therefore, it can be expected that the surfaces of

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the core layers will be damaged when IA > 3 dB, as reported by Domingues etal. [7].

On the other hand, T bp (2,680 K) in the case of IA = 2 dB is almost equal to

Tw (2,632 K). Thus, when IA < 2 dB, it can be expected that the melting andflow of silica glass will not be observed in the core layers, which are adjacent tothe absorbent layer.

Furthermore, T bp (1,780 K) in the case of IA = 0.5 dB is smaller than Ts

(1,947 K). From the viewpoint of reliability, IA ≤ 0.5 dB is desirable for main-taining the initial insertion loss of single-mode fiber-optic connectors.

4.2 Fiber Fuse Generation Caused by Carbon-Black Ad-hesion

The occurrence of a fiber fuse was reported by Domingues et al. [7]. Sampleswith IA = 4–8 dB exhibited the fiber fuse effect at P0 = 1.5 W when theywere exposed to CW laser light with λ0 = 1.48 μm. The Tp values around theabsorbent layers with IA = 4, 8, and 12 dB were calculated as a function ofthe irradiation time after the incidence of 1.2–2.6 W laser light (λ0 = 1.48 μm).The calculated results are shown in Fig. 7.

As shown in Fig. 7, Tp values of 1.5 ×104 K or above occur 0.75–7.4 ms afterlaser light incidence. This rapid rise in the temperature initiates the fiber fusephenomenon. The minimum initiation power Pinit at λ0 = 1.48 μm required togenerate a fiber fuse was estimated to be 2.25, 1.62, and 1.28 W when IA = 4,8, and 12 dB, respectively. The minimum irradiation times tmin at P0 = Pinit

were 7.4, 4.3, and 3.3 ms in the cases of IA = 4, 8, and 12 dB, respectively.The relationship between Pinit and IA was investigated. The calculated

results are shown in Fig. 8.As shown in Fig. 8, the estimated Pinit values of the samples with IA =

4–8 dB are larger than 1.5 W, and those with IA ≥ 10 dB exhibit Pinit valuesof less than 1.5 W. On the other hand, Domingues et al. reported that sampleswith IA = 4–8 dB exhibited the fiber fuse effect with the passage of time atP0 = 1.5 W [7]. These experimental results are different from the calculatedresults shown in Fig. 8.

This discrepancy may be caused by the difference in the ΔLa values of theabsorbent layers. As shown by Eq. (3), αa for the absorbent layer increaseswith decreasing ΔLa. In the calculation, we assumed ΔLa = 1 μm. If ΔLa isassumed to be 0.4 μm in the fiber fuse generation experiments conducted byDomingues et al., the αa values at IA = 4–8 dB in their experiments correspondto those at IA = 10–20 dB in this calculation. Furthermore, the fiber fuse occurson the boundary between the core and the absorbent layer and is unrelated tothe thickness of the absorbent layer. As a result, the samples with IA = 4–8dB investigated by Domingues et al. will exhibit the fiber fuse phenomenon atP0 = 1.5 W because the Pinit values of the samples with IA = 10–20 dB shownin Fig. 8 are less than 1.5 W.

Next, the temperature field T (r, z) was calculated t = 1.6, 1.8, and 2.0 ms

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IA = 4 dB

2.25W

2.6W2.4W

2.0W

Fiber Fuse

5

10

15

20

25

30

35

Tp

(103

K)

IA = 8 dB

5

10

15

20

25

30

1.62W

2.0W1.8W

1.5W

Fiber Fuse

10-6

Time (s)

10-5 10-4 10-3 10-2 10-1

IA = 12dB

1.28W

1.6W1.4W

1.2W

Fiber Fuse

0

5

10

15

20

25

30

Figure 7: Tp values around absorbent layers with IA = 4, 8, and 12 dB (ΔL =1 μm) versus irradiation time when P0 = 1.2–2.6 W.

after the incidence of the 1.8 W laser light for IA = 8 dB. The calculated resultsare shown in Figs. 9–11, respectively.

As shown in Fig. 9, the core center temperature near the end of the absorbentlayer (L ∼ –29 μm) changes abruptly to a large value of about 2 ×104 K after1.6 ms. This rapid rise in the temperature initiates the fiber fuse propagation asshown in Figs. 10 and 11. After 1.8 and 2.0 ms, the high-temperature front inthe core layer reaches L values of –113 and –196.5 μm, respectively. The average

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Min

imum

Initi

atio

n P

ower

(W

)0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14 16 18 20

Initial Attenuation (dB)

λ0 = 1.48 μm

ΔLa = 1 μm

Figure 8: Minimum initiation power at λ0 = 1.48 μm required to generate fiberfuse versus IA for absorbent layer (ΔLa = 1 μm) between optical fibers.

t = 1.6 ms

-250-200

-150-100

-500

50L (μm) -1

-0.5

0

0.5

1

r / rf

0

5

10

15

20

25

T (×103 K)

Figure 9: Temperature field around absorbent layer with IA = 8 dB after 1.6ms when P0 = 1.8 W and λ0 = 1.48 μm.

propagation velocity Vf was estimated to be about 0.42 m/s using these data.This value is close to the experimentally determined Vf value of 0.35 m/s [28]and 0.36 m/s [29].

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t = 1.8 ms

-250-200

-150-100

-500

50L (μm) -1

-0.5

0

0.5

1

r / rf

0

5

10

15

20

25

T (×103 K)

Figure 10: Temperature field around absorbent layer with IA = 8 dB after 1.8ms when P0 = 1.8 W and λ0 = 1.48 μm.

t = 2.0 ms

-250-200

-150-100

-500

50L (μm) -1

-0.5

0

0.5

1

r / rf

0

5

10

15

20

25

T (×103 K)

Figure 11: Temperature field around absorbent layer with IA = 8 dB after 2.0ms when P0 = 1.8 W and λ0 = 1.48 μm.

4.3 Formation Process of Fiber Fuse around AbsorbentLayer

A sudden temperature increase in an extremely short time was observed whena fiber fuse occurred as shown in Fig. 7. To investigate the formation process

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of the fiber fuse, we calculated the change in the temperature at the core centerposition with time after the incidence of 1.8 W laser light for IA = 8 dB. Thecalculated results are shown in Fig. 12.

-80 -60 -40 -20 0 20 40 60 80L (μm) 0

0.20.4

0.60.8

11.2

1.41.6

t (ms)0

5

10

15

20

25

T (×103 K)

Figure 12: Core center temperature distribution in the longitudinal direction ofthe optical fiber around absorbent layer with IA = 8 dB up to 1.6 ms when P0

= 1.8 W and λ0 = 1.48 μm.

As shown in Fig. 12, the temperature rise from 0.1 to 1.4 ms was relativelyslow. As the Tp values of 0.1 and 1.4 ms were 1,960 and 3,290 K, respectively,Tp increased by only 1,330 K in 1.3 ms.

In contrast, Tp reached 5,340 K after 1.5 ms and exceeded 2.0 ×104 K after1.6 ms. This rapid rise in the temperature initiates the fiber fuse phenomenonas shown in Figs. 9–11.

A sudden temperature change was not seen even after 100 ms when P0 was1 W (see Fig. 5). In this case, Tp tended to rise at about 10 ms and thendecreased. This means that P0 of 1 W is insufficient for Tp to increase from3,000 K to over 5,000 K.

Why did a fiber fuse occur above 5,000 K?One reason is the light absorption behavior of the optical fiber at high tem-

peratures. We calculated the temperature dependence of the absorption coeffi-cient (α) at 1.48 μm when heating an SMF-28 optical fiber using the proceduredescribed in the literature [9]. The result is shown in Fig. 13. As shown in thefigure, the α value (11.3 ×104 m−1) at 5,000 K is larger than that (6.5 ×104

m−1) at 3,000 K. A rapid change in α occurs when the temperature changes from2,000 K to 3,000 K. In contrast, there is little change in α when the temperature

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Abs

orpt

ion

α (x

104

m- 1

)Temperature T (K)

0

5

10

15

20

0 1000 2000 3000 4000 5000 6000 7000

λ0 = 1.48μm

Figure 13: Absorption coefficient of SMF-28 at 1.48 μm vs temperature.

changes from 4,000 K to 7,000 K (see Fig. 13).The radiating part of a fiber fuse consists of a low-density ionized gas plasma

whose temperature exceeds 4,000 K [30]. To maintain the ionized gas plasmastate in the fiber fuse, heat must be supplied constantly even if the temperaturechanges. To this end, it is necessary for α to take roughly the same valuewhen the temperature changes while remaining above 4,000 K. The temperaturedependence of α for the SMF-28 fiber satisfies this requirement (see Fig. 13).This indicates that a core temperature of more than 4,000 K is necessary togenerate and maintain a fiber fuse. The temperatures of the fiber fuse estimatedand/or measured experimentally were 5,400 K [14] and 5,800–6,500 K [31]. Thetheoretically estimated temperature of > 4,000 K for fiber fuse generation andmaintenance does not contradict these experimental results.

5 Stability of Gas Plasma in Fiber-Optic Con-

nector

We investigated the stability of a low-density ionized gas plasma in a fiber-opticconnector, where the absorbent (carbon black) enters the gap between the endfaces of SMF-28 optical fibers. The gas plasma exhibits a high temperature andhigh pressure [32] because it is confined in a small space with a width of about20 μm [33] around the core layer. The following relationship is known to holdbetween the temperature T and pressure p of the gas plasma [34]:

p = NgkBT, (6)

where Ng is the number density of a Si + O atomic gas. We assumed Ng

∼ 0.8×1022 cm−3, which is the average number density of Si in the temperaturerange of 3,000–10,000 K [30]. By using this Ng value, the pressure p of thegas plasma is estimated to be about 5,450 atm when the temperature of the

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gas plasma reaches 5,000 K. This high pressure of the plasma is maintainedin the optical fiber because the leakage of the plasma is obstructed by theneighboring rigid silica glass. In the fiber-optic connector, the end face of thefiber is constantly compressed with a high pressure p0 of about 5,000 atm, whichis caused by the compressive force in the connector.

However, when a fiber fuse occurs, the peak temperature of the fuse reaches1×104 K order as shown in Figs. 9–12. If the thermal peal is very near the fiberend face, the temperature and the pressure at the end face will exceed 5,000 Kand 5,000 atm, respectively.

The temperature of the core center at the end face (L = –0.5 μm) abuttingthe absorbent (carbon black) layer with IA = 8 dB (ΔL = 1 μm) was calculatedas a function of the irradiation time after the incidence of 1.62, 2, and 3 W laserlight. The calculated results are shown in Fig. 14. In the temporal axis ofthis figure, the time of 0.1 ms is the start time for the sudden temperature rise.As shown in Fig. 14, for a short time (about 0.4 ms), the temperature at the

Time (10-4 s)

IA = 8 dB

T (

103

K)

T = 5,000 K

0

5

10

15

20

-1 0 1 2 3 4 5 6 7

3W

2W

1.62W

Figure 14: Temperature of the core center at the end face abutting the carbon-black layer with IA = 8 dB (ΔL = 1 μm) versus irradiation time when P0 =1.62, 2, and 3 W and λ0 = 1.48 μm.

end face exceeds 5,000 K after the temperature rise begins. This means that,with increasing temperature, the pressure of the plasma exceeds the acceptablepressure p0 (about 5,000 atm) for maintaining the primary (equilibrium) condi-tions of the plasma at the end face. As a result, leakage (or protrusion) of thegas plasma into the neighboring vaporized (or melted) silica glass of the coreof the mated pair passing through the thin carbon-black layer occurs along thelongitudinal (z) direction for a short time (about 0.4 ms) after the temperaturerise starts.

Next, the temperature fields at the end face (L = –0.5 μm) abutting thecarbon black layer with IA = 8 dB (ΔL = 1 μm) after the incidence of 1.62,

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2, and 3 W laser light were calculated along the radial (r) direction at a timeof 0.1 ms after the temperature rise starts. The calculated results are shown inFig. 15. As shown in the figure, the temperatures at the outer cladding surfaces

0

2

4

6

8

10

12

14

16

18

-1.0 -0.5 0.0 0.5 1.0

3W

2W

1.62W

T (

103

K)

L = -0.5μm

Ts = 1,947 K

r / rf

Figure 15: Temperature fields at the end face abutting the carbon-black layerwith IA = 8 dB (ΔL = 1 μm) at 0.1 ms after the start of the temperature risewhen P0 = 1.62, 2, and 3 W and λ0 = 1.48 μm.

(r/rf = ±1) of the three samples are lower than the softening point (Ts = 1,947K) of the silica glass when t = 0.1 ms after the temperature rise starts. Thismeans that the high pressure of the plasma in the optical fiber is maintainedin the radial direction because the leakage of the plasma through the claddinglayer is obstructed by the neighboring rigid silica glass.

Furthermore, the temperature fields of the core center along the z directionwere calculated for the three P0 conditions shown in Figs. 14 and 15 at a time of0.1 ms after the temperature rise starts. The calculated results are shown in Fig.16. In this figure, triangles indicate the locations with the highest temperature.As shown in Fig. 16, the gas plasma in the sample with P0 = 1.62 W, which isPinit when IA = 8 dB (see Fig. 7), exhibits its thermal peak at L = –2.5 μm.This place is very near the fiber end face (L = –0.5 μm). Therefore, if a fiberfuse occurs and propagates towards the light source along the −z direction inthis sample, its propagation will be affected by the leakage (or protrusion) ofthe gas plasma into the neighboring silica core of the mated pair, moving alongthe +z direction.

Here, we consider the motion of a gas particle (Si and/or O atomic gas) ina gaseous medium (gas plasma) in the presence of a fluctuating force owing tothe leakage of the gas plasma into the neighboring silica core. The equation of

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0

10

20

30

40

50

-40 -30 -20 -10 0 10T

(10

3 K

)

3W

2W1.62W

t = 0.1ms

L (μm)

End Face

Figure 16: Temperature fields around the end face abutting the carbon blacklayer with IA = 8 dB (ΔL = 1 μm) at 0.1 ms after the start of the temperaturerise when P0 = 1.62, 2, and 3 W and λ0 = 1.48 μm. Triangles indicate thelocations with the highest temperature.

motion for the particle is of the form

md2z

dt2+ γ

dz

dt= f(t), (7)

where m is the mass of the particle, γ is the friction or damping coefficient, andf(t) is the random fluctuating force exerted by the surrounding medium. In thecalculation, we used m = 4.65 ×10−26 kg of Si atomic gas.

Equation (7) can be written as an energy equation by the substitution

zd2z

dt2=

12

d2z2

dt2−

(dz

dt

)2

,

and then

m

2d2z2

dt2− m

(dz

dt

)2

2dz2

dt= zf (t). (8)

This equation is integrated over time to yield

z2 =2γ

∫ t

0

[m

(dz

dt

)2]

dt +2γ

∫ t

0

zf (t)dt − 2m

γ

[zdz

dt

]t

0. (9)

From statistical mechanics, it is known that the mean kinetic energy of theparticle should, in equilibrium, reach a value of [35]

<12m

(dz

dt

)2

>=12kBT, (10)

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and the averages < zf > and < zdz/dt > can be equal to zero since f and dz/dtare random variables with zero average values and are statistically independentof z at the same instant of time t [36]. With these assumptions, the averagesquared displacement during time interval t of the gas particle is given by

< z2 >=2kBT

γt. (11)

The term γ is the damping constant for the particle. If the particle is sphericaland the particle is in a gas medium, Stokes’ law can be used for the viscous dragforce, and [37]

γ = 6πηa, (12)

where η is the coefficient of viscosity and a (= 1 A) is the radius of the particle.η of a gas medium is given by [38], [39]

η =1

πσ2

√mkBT

π, (13)

where σ (= 1.5 A) is half of the collision diameter. Using Eqs. (11)–(13), weestimated < z2 > at T = 5,000 K as follows:

< z2 >= 48.6 × 10−8 · t m2. (14)

Using Eq. (14), the average displacement at t = 0.1 ms after the start of thetemperature rise when P0 = 1.62 W is obtained as

√< z2 > = 7.0 μm.

This displacement is larger than the distance δL (= 2.0 μm) between the thermalpeak position (L = –2.5 μm) and the fiber end face (L = –0.5 μm). Therefore,the fuse may be terminated by the random fluctuating force owing to the leakageof the gas plasma into the neighboring silica core when P0 = 1.62 W. In contrast,when P0 = 2 and 3 W, the δL values are 14.5 and 33.0 μm, respectively (seeFig. 16). As these δL values are larger than the average displacement (7 μm),the fiber fuse propagation is hardly affected by the leakage of the gas plasmainto the neighboring silica core of the mated pair when P0 = 2 and 3 W.

Simmilar phenomena of fiber fuse termination were reported by Kurokawaand co-workers [40]–[43] in some studies on hole-assisted fibers (HAFs) (see PartVI).

References

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[43] K. Tsujikawa, K. Kurokawa, N. Hanzawa, S. Nozoe, T. Matsui, andK. Nakajima, “Hole-assisted fiber based fiber fuse terminator supporting22 W input,” Optical Fiber Technol., Vol. 42, pp. 24–28, 2018.

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