Simulation of Fiber Fuse Phenomenon in Single-Mode Optical Fibers

Transcription

1 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 11, NOVEMBER Simulation of Fiber Fuse Phenomenon in Single-Mode Optical Fibers Yoshito Shuto, Member, IEEE, Member, OSA, Shuichi Yanagi, Shuichiro Asakawa, Member, IEEE, Masaru Kobayashi, Member, IEEE, and Ryo Nagase, Member, IEEE Abstract The unsteady-state thermal conduction process in single-mode (SM) optical fiber was studied theoretically with the explicit finite-difference method (FDM). In the numerical calculation it was assumed that the electrical conductivity of the core layer increased rapidly above 1323 K. The core-center temperature changed suddenly and reached over K when an optical power of 1 W was input into the core layer heated at 1373 K. This rapid heating of the core initiated the fiber fuse phenomenon. The high-temperature core areas, whose radiation spectrum extended over a wide range from the infrared to the ultraviolet regions, were enlarged and propagated toward the light source at a rate of about 0.7 ms 1. This rate was in fair agreement with the experimentally determined value. Index Terms Fiber fuse phenomenon, single-mode optical fiber, thermal conduction. I. INTRODUCTION THE development of Raman amplifier-based optical network systems is at an advanced stage, and there is a possibility that high-power optical signals will be transmitted through single-mode (SM) optical fibers. As the optical power level rises, nonlinear phenomena start to become important, and these include the effects of the fiber fuse phenomenon. This effect, named because of its similarity in appearance to a burning fuse, can lead to the destruction of an optical fiber waveguide. The fiber fuse phenomenon was first observed in 1987 by Kashyap and Blow [1]. Most experimental results focused on the intensity level of. This is many orders of magnitude below the intrinsic damage limit for silica of [1]. In experiments, the fiber fuse phenomenon can be initiated by bringing the fiber output end into contact with absorbent materials [1] and/or heating the fiber with a flame [2] [4]. The fiber fuse typically involves a zone of absorption that melts and then vaporizes the core at several thousand Kelvin, creating a void. The creation of this bubble is followed by the initiation of another void further down the core in the direction of the optical power source. This process repeats very quickly, moving an intense blue-white flash down the fiber at speeds of several meters per second [1]. Fuses are terminated by gradual laser power reduction to give a termination threshold at which the speed of the fuse is reduced to zero. Manuscript received December 2, The authors are with the Photonics Laboratories, Nippon Telegraph and Telephone (NTT) Corporation, Atsugi, Japan ( shuto@aecl.ntt.co.jp) Digital Object Identifier /JLT Several hypotheses have been put forward to explain the fiber fuse phenomenon. These include a chemical reaction involving the exothermal formation of germanium defects [5], self-propelled self-focusing [1], and thermal lensing of the light in the fiber via a solitary thermal shock wave [2]. Driscoll et al. [5] attributed the high temperature in the fuse to exothermic reactions involving germanium defects, but not to absorption. However, experimental results obtained by Davis et al. [3] indicate that germanium is not required for fuse propagation. Fibers doped with other materials and even pure silica core fibers were found to fuse at power levels similar to those of germanium-doped fibers. Therefore, the exothermic chemical reaction model is not a comprehensive model explaining the fiber fuse phonomenon. Kashyap and Blow [1] suggested that a thermally generated third-order nonlinearity causes the self-focusing of the beam at a few wavelengths, resulting in a new high temperature region and the propagation of the fuse as determined by the heat flow. Although the value of silica is too small to induce the self-focusing effect, they suggest that the cause is avalanche ionization following Yablonovitch and Bloembergen [6]. However, the optical beams in the SM optical fibers are confined as an mode, and most of the incident optical power is concentrated from the start in the narrow core layer. Therefore, the self-focusing effect does not occur in SM optical fibers. Hand and Russell [2] have suggested that a solitary thermal shock wave is responsible for the fuse. In their model, the fuse propagates toward the laser light source at a velocity determined by thermal diffusion and the absorption of the laser light. They stated that elevated absorption in the fiber is due to the creation of germanium defects, and the thermal lensing effect occurring at high temperatures accounts for the observed periodic damage tracks. However, as described above, germanium is not required for fuse propagation, and therefore, as mentioned with regard to the self-focusing effect, the thermal lensing effect does not occur in SM optical fiber. As described above, no report has yet presented reasonable models describing the occurrence of the fiber fuse phenomenon in SM optical fibers. In this paper we attempt to model the heat flow in SM optical fibers, which leads to the fiber fuse phenomenon, using a numerical finite-difference technique. II. HOT ZONE MODEL IN SM OPTICAL FIBERS A. Thermally Induced Optical-Power Absorption In our model, we assume that the electrical conductivity of a fiber core changes abruptly from essentially zero at tempera /03$ IEEE

2 2512 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 11, NOVEMBER 2003 tures below 1323 K ( ) to some large value above it. There are a small number of free electrons in the fiber core. These electrons are present as a result of the thermal ionization of shallow traps [7] in the fiber core layer. The heating process will increase the number of electrons through collisions and, hence, increase the value in the core layer. Therefore, it is assumed that the temperature dependence of can be described as follows: (1) where is Boltzmann s constant, and ( ) is the transition temperature. Parameters and are the empirical parameters for silica, and the decrease in the activation energy at is assumed to be 1 ev. According to (1) the fiber core exhibits a large value at the melting point ( ) of silica. This is consistent with the experimentally observed behavior reported by Hand and Russell [2]. The propagation of light through SM optical fiber is influenced by the electrical conduction in the core layer, and the magnitude of the guided light intensity decreases as the value of the fiber core increases. The absorption coefficient is related to by the following equation [8] Fig. 1. Temperature dependence of the absorption coefficient. where,, and are the wavenumber, the permeability and the velocity of light in a vacuum, respectively. is the refractive index of the core layer. When we compare the three terms on the right-hand side (RHS) of (2), we find that the second term is much smaller than the first one ( ). Therefore, (2) can be approximated as follows: According to (3), is proportional to the value. The relationship between and is shown in Fig. 1. The value at room temperature remains unchanged until the temperature approaches. Thereafter, there is a rapid increase in the value. These results are consistent with the experimental results obtained by Kashyap et al. [9]. Once the core has been raised to a high temperature, it becomes highly absorbent due to the large value (see Fig. 1). As the light is absorbed by the heated core layer, the temperature increases and the produced heat flows from the hot core center to the unheated core and cladding layers. If the value of the heated core layer is large enough to produce the Joule heat, this is added to the heat caused by the light absorption. In Section II-B, we describe some assumptions in relation to the thermal conduction process in SM optical fiber. (2) (3) Fig. 2. Schematic view of hot zone in the core layer. B. Hot Zone in Core Layer We assume the SM optical fiber to have a radius of, and to be in an atmosphere of. We assume that part of the core layer is heated, and that this part (hot zone) has a length of and a temperature of ( (see Fig. 2). In the hot zone, both the and values are larger than those of the other parts in the core layer. Thus, as the light propagates along the normal direction (the direction away from the light source) in this zone, two types of heat, namely the heat due to light absorption and the Joule heat, are produced and become great. Therefore, in the core layer in front of the hot zone we must assume that the heat produced in the zone flows across the boundary surface. In contrast, it should be assumed that the heat in the core layer flows back from the hot zone when the light direction is reversed by the reflection. In Section II-C, we undertake a theoretical study of the thermal conduction process in SM optical fiber along the normal direction of the light using a numerical calculation technique. C. Heat Conduction in Optical Fiber The heat conduction equation for the temperature field in SM optical fiber is given by [10] (4)

3 SHUTO et al.: FIBER FUSE PHENOMENON IN SM OPTICAL FIBERS 2513 where,, and are the density, the specific heat, and the thermal conductivity of the fiber, respectively. Silicate glass has a melting point of at which it changes from the amorphous solid phase to the viscous liquid phase with the absorption of the melting heat ( ) [11]. Furthermore, it has a vaporization (or thermal decomposition) point of about, where it changes from the liquid phase to the vapor phase with the absorption of the vaporization heat ( ) [11]. During this vaporization the silicate glass is thermally decomposed in accordance with the following equation, and the hollow cavity produced in the vaporization process contains high-density gas [1]: Therefore, it is assumed that the properties in the vapor phase are the same as those of the high-density gas. The thermal properties (,, and values) of the silicate glass are summarized in Table I. In order to deal with the thermal behavior near the phase transition (melting and vaporization) points in the calculation, we assumed that the specific heat in the transition range from to equals the specific value given by (6)[12], as follows: where is the transition heat such as the melting heat and/or the vaporization heat. We solved (4) by using the explicit finite-difference method (FDM) [13] under the boundary and initial conditions described later. The area for the numerical calculation had a length ( ) in the axial ( ) direction and a width ( ) in the radial ( ) direction. There were 24 and 2000 divisions in and, respectively, and we set the calculation time interval at 0.1. We assumed that the hot zone was located at the center of the fiber length and that the length of the hot zone was equal to the calculation step ( ) in the direction. The boundary conditions are as follows: 1) There is an axisymmetrical distribution of the optical fiber, whose center axis is located at. (5) (6) (7) TABLE I THERMAL PROPERTIES OF SILICATE GLASS IN VARIOUS PHASES ( ) surface, and no flux across the cladding ( ) surface. if (9) if where and are the optical power intensity and the amplitude of the electric field of the core layer. When, the first and second terms on the RHS of (9) represent the heat produced by light absorption and the Joule heat, respectively. 4) Heat loss is assumed to be through radiation from the surface of the fiber end ( ). (10) In contrast, the initial condition is at except for the ( ). if if and/or (11) We assume that the value for the fundamental mode of SM optical fiber can be given by dividing the transmission power in the care layer by the area of the spot size. That is, is given by (12) where is the spot size radius, and is approximately equal to the radius of the core layer if uninfluenced by heat. is the optical power carried by the mode, is the propagation constant in the direction, and is the normalized frequency. and are the normalized transverse wavenumbers in the direction in the core and cladding, respectively. is the th-order Bessel function. In contrast, the value is assumed to equal the amplitude coefficient of the electromagnetic field of the mode. This is given by [14] 2) Heat loss is assumed to occur through radiation from the surface of the cladding of the fiber. where is the Stefan-Boltzmann constant, and ( ) is the emissivity of the surface. In what follows, is assumed to be 298 K ( ). 3) The core-center temperature at the hot-zone end ( ) equals. There is heat transfer only across the core (8) By using (3), (12), and (13), the heat transfer terms ( ) in (9) can be rewritten as follows: where That is, the terms are proportional to both and. (13) (14) (15)

4 2514 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 11, NOVEMBER 2003 The light propagates through the fiber core for a length, and then reaches the hot zone. Because of the light absorption the value decreases as the light propagates along the forward direction in the hot zone. As, the value after passing through the hot zone is given by (16) where is the initial optical power. The term represents the light absorption in a fiber core of length. On the other hand, when the core layer is heated above the vaporization point of silica ( ), an enclosed hollow cavity will be produced in the core center. This cavity contains oxygen as described earlier. We assume that the cavity has a refractive index and a length. The heat conductivity of the oxygen (0.03 ) is two orders smaller than that of the silicate glass. Therefore, the heat transferred in the silica core will be stopped at the cavity. Futhermore, the light propagating in the normal direction (the direction away from the light source) in the core layer will be reflected at the cavity wall, and the light direction will be reversed by the reflection. In this case, the direction of the heat flow in the core layer will be back from the hot zone. In this case, the boundary and the initial conditions described above can be employed for the calculation of the temperature field except for the expression of given by (16). In this case the light propagates through the fiber core of length, and then back and forth in the hot zone, whose length is. The multiple reflection in the cavity walls must be considered when the light direction is reversed at the cavity. By considering these points, the value is given by (17) where is the reflectance of the optical power at the cavity. The values under multiple reflection are given by [15] (18) where is the wavelength of the guided light in the SM fiber, and is the reflectivity at the boundary of the silica core and the cavity. is given by (19) As shown in (18), the value under multiple reflection depends on the cavity length. The relationship between and is shown in Fig. 3. exhibits a maximum value of about when is an odd-numbered multiple of one-fourth of the wavelength ( ). Conversely, it exhibits a minimum value of about zero when is an even-numbered multiple of (see Fig. 3). This is the cause of the interference with the multiple reflected beams. Fig. 3. Reflectance of optical power versus cavity length. In Section III, we describe the calculated time ( ) dependence of in SM optical fibers. III. SIMULATION OF FIBER FUSE PHENOMENON A. Propagation of Fiber Fuse in SM Optical Fiber We calculated the values at, 100, 200, 300, 400, and 500 when and. In the calculation, we used the refractive index data of and at, where is the refractive index of the cladding. The calculated results are shown in Figs As shown in Fig. 4, the core-center temperature near the hot-zone end ( ) changes abruptly to the large value of after 10. This rapid heating phenomenon initiates the fiber fuse phenomenon as shown in Figs After 100, 200, 300, 400, and 500, the high-temperature front in the core layer reached,,,, and, respectively. The average propagation rate can be estimated to be 0.71 by using these data. This value is in fair agreement with the experimental values (about ) [4], [9] obtained for the fiber fuse phenomenon. In contrast, as shown in Figs. 5 and 6, there is a periodical temperature difference in the direction in the hot-temperature core areas. The values at the areas are in the 7 to 5 range. The temperature difference is considered to reflect the cavity length ( ) dependence of the reflectance of the optical power at the cavity. That is, when is an odd-numbered multiple of, the reflected optical power reaches its maximum value (see Fig. 3), and the value in the high-temperature core area becomes large. Conversely, the value exhibits its minimum value when is an even-numbered multiple of. After 300, there is a sharp temperature peak at the hightemperature front, as shown in Fig. 7. The value of about 3.5 at the peak is seven times larger than the maximum value (about 5 ) of the periodical temperature difference described earlier. The origin of the sharp peak is unknown. However, the periodical temperature difference in the hot-temperature core areas may be responsible for the peak formation.

5 SHUTO et al.: FIBER FUSE PHENOMENON IN SM OPTICAL FIBERS 2515 Fig. 4. Temperature field in SM optical fiber after 10 s when P =1Wand T =1373K. Fig. 7. Temperature field in SM optical fiber after 300 s when P =1W Fig. 5. Temperature field in SM optical fiber after 100 s when P =1W Fig. 8. Temperature field in SM optical fiber after 400 s when P =1W Fig. 6. Temperature field in SM optical fiber after 200 s when P =1W That is, the periodical temperature difference along the direction may behave like a thermal wave with a velocity of.if is slightly larger than, the thermal wave can reflect at the frontend of the cavity, and there will be interference with the forward and backward waves near the high-temperature front. The superposition of the peaks of the forward and backward thermal waves may produce the sharp temperature peak seen in Figs B. Radiation Spectrum From High-Temperature Core Area As described earlier, the values in the high-temperature core areas are in the 7 to 3.5 range. The average temperature in these areas was estimated to be about Fig. 9. Temperature field in SM optical fiber after 500 s when P =1W 3. If the high-temperature core area is assumed to be a blackbody, the spectral emissive power of the body is given by (20) where is the wavelength of the radiated light, and is Planck s constant. The relationship between and at can be calculated by using (20). The calculated results are plotted in Fig. 10. In this figure, the data shown by the open circles are the radiation spectrum data measured by Hand and Russell [2]. As shown in Fig. 10, the calculated

6 2516 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 11, NOVEMBER 2003 Fig. 10. Spectral emissive power of blackbody versus wavelength. indicates the data from [2]. values are in fair agreement with the measured values except for the data obtained at a short wavelength of. When, the peak wavelength for the value is shorter than 0.1. The silica glass absorbs light in this region (vacuum ultraviolet (UV) region). Therefore, the observable radiation spectrum from the high-temperature core areas will be in the near UV to near infrared (IR) regions, and have its maximum in the near UV region. This spectrum will be seen as blue-white light with the eyes. In fact, several researchers have reported that this blue-white flash of light is always accompanied by the fiber fuse phenomenon [1], [2]. IV. CONCLUSION The thermal conduction process in SM optical fiber was studied theoretically with the explicit FDM. In the numerical calculation it was assumed that the electrical conductivity of the core layer increased rapidly above 1323 K. The core-center temperature changed suddenly and reached over three hundred thousand Kelvin when an optical power of 1 W was input into the core layer heated at 1373 K. This rapid heating phenomenon initiated the fiber fuse phenomenon. The high-temperature core areas were enlarged and propagated toward the light source at a rate of about 0.7. This rate was in fair agreement with the experimental value obtained for the fiber fuse phenomenon. If the high-temperature core area is assumed to be a blackbody, the calculated spectral emissive powers were in fair agreement with the measured values. The observable radiation spectrum from the high-temperature core areas, which extended over a wide range from the infrared to the ultraviolet regions, was actually observed in the fiber fuse experiments. [2] D. P. Hand and P. S. J. Russell, Solitary thermal shock waves and optical damage in optical fibers: The fiber fuse, Opt. Lett., vol. 13, pp , Sept [3] D. D. Davis, S. C. Mettler, and D. J. DiGiovani, Experimental data on the fiber fuse, in Proc. Soc. Photo-Opt. Instrum. Eng., vol. 2714, Oct. 1995, pp [4], A comparative evaluation of fiber fuse models, in Proc. Soc. Photo-Opt. Instrum. Eng., vol. 2966, Oct. 1996, pp [5] T. J. Driscoll, J. M. Calo, and N. M. Lawandy, Explaining the optical fuse, Opt. Lett., vol. 16, pp , July [6] E. Yablonovitch and N. Bloembergen, Avalanche ionization and the limiting diameter of filaments induced by light pulses in transparent media, Phys. Rev. Lett., vol. 29, pp , Mar [7] J. J. O Dwyer, The Theory of Electrical Conduction and Breakdown in Solid Dielectrics: Oxford Univ. Press, 1973, ch. 8. [8] A. Shadowitz, The Electromagnetic Field. New York: McGraw-Hill, 1975, ch. 15. [9] R. Kashyap, A. Sayles, and G. F. Cornwell, Heat flow modeling and visualization of catastrophic self-propagating damage in singlemode optical fibers at low powers, in Proc. Soc. Photo-Opt. Instrum. Eng., vol. 2966, Oct. 1996, pp [10] H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. Oxford: Oxford Univ. Press, 1959, ch. 13. [11] G. V. Samsonov, Ed., The Oxide Handbook. New York: Plenum, 1973, ch. 2. [12] M. Shoji, Heat Transfer Textbook, Japan: Univ. Tokyo Press, 1995, ch. 5. [13] G. E. Forsythe and W. R. Wasow, Finite-Difference Methods for Partial Differential Equations. New York: Wiley, 1960, ch. 2. [14] K. Okamoto, Fundamentals of Optical Waveguides. New York: Academic, 2000, ch. 3. [15] M. Born and E. Wolf, Principles of Optics, 7th ed. Cambridge: Cambridge Univ. Press, 1999, ch. 7. Yoshito Shuto (M 03) received the B.S., M.S., and Ph. D. degrees from Kyushu University, Fukuoka, Japan, in 1977, 1979, and 1990, respectively. Japan, in He was engaged in research on oriented crystalline and liquid-crystalline polymer materials for optical-fiber jackets, and diazo-dye-substituted polymer materials for second-order nonlinear optics. He is presently engaged in research on injection molding polymer materials for optical connection technology with NTT Photonics Laboratories. Dr. Shuto is a Member of the Institute of Electronics, Information and Communication Engineers (IEICE), the Japan Society of Applied Physics (JSAP), the Optical Society of Japan, and the Optical Society of America (OSA). Shuichi Yanagi received the B.S., M.S., and Ph.D. degrees from Keio University, Yokohama, Japan, in 1992, 1994, and 1997, respectively. In 1997 he joined the Opto-electronics Laboratories, Nippon Telegraph and Telephone (NTT) Corporation, Ibaraki, Japan. He is presently engaged in research on injection molding polymer materials for optical connection technology with NTT Photonics Laboratories. Dr. Yanagi is a Member of the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan and the Japan Society of Applied Physics (JSAP). ACKNOWLEDGMENT The authors thank Dr. H. Toba for his encouragement. REFERENCES [1] R. Kashyap and K. J. Blow, Observation of catastrophic self-propelled self-focusing in optical fibers, Electron. Lett., vol. 24, pp , Jan Shuichiro Asakawa (M 96) received the B.E., M.E., and D.E. degrees in electrical and computer engineering from Yokohama National University, Yokohama, Japan, in 1990, 1992, and 1995, respectively. Japan, in He has been engaged in research on optical connectors. Dr. Asakawa is a Member of the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan.

7 SHUTO et al.: FIBER FUSE PHENOMENON IN SM OPTICAL FIBERS 2517 Masaru Kobayashi (M 96) received the B.E. and M.E. degrees in mechanical engineering from Nagoya University, Nagoya, Japan, in 1986, and 1988, respectively. Japan, in He has been engaged in research on high-resolution optical reflectometry for characterizing optical waveguide components, and in development of optical fiber connectors. Mr. Kobayashi is a Member of the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan and the Japan Society of Applied Physics (JSAP). Ryo Nagase (M 90) received the B.E., M.E., and Ph.D. degrees in precision engineering from Tohoku University, Miyagi, Japan, in 1983, 1985, and 1998, respectively. Japan, in He has been engaged in the research and development of optical fiber connectors. From 1992 to 1994, his fields of interest were photonic switching systems. Since 1994, he was involved in the research of optical components for fiber-optic communication systems, passive components such as optical fiber cables, and planar lightwave circuits. He is presently a Manager in the research and development of optical fiber connection technology. Dr. Nagase is a Member of the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan and the Japan Society of Mechanical Engineers (JSME).