- Email: [email protected]
Spectral attenuation of fluoride glass fibers
Journal of Non-Crystalline Solids 213 & 214 Ž1997. 189–192
Spectral attenuation of fluoride glass fibers G.F. West
),1
, W. Hofle ¨
Institut fur ¨ Hochfrequenztechnik, Technical UniÕersity of Braunschweig, Braunschweig, Germany
Abstract Intrinsic crystallisation is invoked at each process stage during the manufacture of fluoride glass fibers. Thermal history and crystallisation distributions were calculated by numerical simulation of the entire fibre manufacturing process, from the preform to fibre drawing. Assuming a gaussian field distribution for single-mode fibre, the attenuation due to crystallisation was calculated using classical scattering theory. Results show strong dependence on the temperature of the core melt and fibre drawing conditions. The former can be reduced to acceptable levels under normal manufacturing conditions. During fibre manufacture it is necessary to maximise both fibre tension and speed in order to reduce additional attenuation to a level below that of Rayleigh scattering.
1. Introduction The fluoride glass composition based on the fluorides of zirconium, barium, lanthanum, aluminum and sodium ŽZBLAN. has proved to be one of the most stable and has been widely studied. Much work has been invested in attempts to produce a fluoride glass fibre exhibiting the theoretical optical loss limit, presently lying at 0.044 dBrkm at 2.55 mm w1x. The best value to date is 0.45 dBrkm at 2.35 mm w2x, with progress in reducing the losses generally being very slow. No thorough explanation for the excess loss has been proposed, although it is known to be due to scattering w1x. Previous attempts to calculate the excess scattering due to intrinsic crystallisation have shown that losses can be significant w3–6x.
) Corresponding author. Tel.: q49-631 205 4148; fax: q49-631 205 4147. 1 Present address: AG Optoelektronik, Fachbereich Physik, Universitat ¨ Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany.
Since in these models not all aspects of thermal history and the scattering process were considered, it has not been possible to calculate a definitive contribution to total loss. The model here extends analysis of fibre drawing to include preform collimation and adds a new model for the wavelength dependent relative refractive index of the scattering centre and the field distribution in the fibre. Thus, all relevant theoretical physiochemical and optical aspects necessary for calculation of the attenuation are addressed.
2. Theory The preform manufacturing model corresponds essentially to that used by Carter w5x for a rotationally-cast clad and poured core; the cooling steps having been increased from 60 s to 150 s. Since we are aiming for a prediction of the minimum attenuation possible, experimental values used for nucleation and growth rates in ZBLAN were the smallest found in the literature w7x.
0022-3093r97r$17.00 Copyright q 1997 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 7 . 0 0 0 0 9 - 4
G.F. West, W. Hofle ¨ r Journal of Non-Crystalline Solids 213 & 214 (1997) 189–192
190
The thermal history during collimation and fibre drawing were derived from the local viscosity in the neck-down region using a semi-empirical model. Experience over several years has shown the neckdown shape to be more or less constant under all conditions for the furnace configuration used. The local volume flow rate was derived from an empirical expression for the neck shape. Local viscosity could then be calculated from the fibre tension and drawing speed by local application of the normal expression for viscous flow w8x, assuming a constant radial temperature. Strictly speaking, calculations are thus limited to the preform dimensions and neckdown geometries used here Žpreform diameters 13 mm, neck-down lengths 1 cm..
a r Ž r , l. s
i
2
H0 N Ž a, r . p a Q Ž a, l. d a.
Ž 1.
Attenuation was calculated using classical scattering theory w9x as used by previous authors w5,6x. The local fibre attenuation, a Ž l, r ., is given by the sum of the crystal attenuations, Eq. Ž1.. Here, QŽ a, l. is the scattering efficiency and N Ž a, r . is the differential w.r.t. crystal radius of the number density of crystals of radius a per unit volume of glass at the radial coordinate, r. Unlike the simple number density, the distribution of N Ž a, r . over a should be independent of the time-step used in numerical calculations and can be used to establish a sufficiently small increment.
a Ž l. s
rs qa 2 Hrs ya a Ž r , l . C Ž r , l . r d r
H0‘ C 2 Ž r , l . r d r
.
3. Experimental In previous calculations, various relative refractive indices, m s n crystalrn glass , were taken w6x, or the refractive index of the crystal, n x Ž l., was taken to be constant w4,5x. Neither of these assumptions permits the calculation of real spectral attenuations. Measurement of the refractive index of both glass and crystal were therefore instigated. ZBLAN samples containing various amounts of PbF2 Ž0, 2.5 and 9 mol%. where heat treated to promote a small degree of Žin this case surface. crystallisation. X-ray diffraction showed the crystals in all glasses to be exactly the same and most likely to be b-ZrBaF6 . Refractive indices of the glasses were measured with an Abbe refractometer and by phase contrast of ground samples. Measurement of the crystal phase proved impossible with the phase contrast method and the Becke-line method was used to provide an estimate.
4. Results The results of refractive index measurement of the crystal and glass phases Ž n D . are shown in Fig. 1. For the glasses, refractive indices measured by phase contrast corresponded well to those measured with an Abbe refractometer. Although the value for the sample containing 9% PbF2 could not be confirmed by more than one measurement, the refractive index of the crystal-phase was definitely not constant, and lay in each case ; 0.01–0.02 below that of the
Ž 2.
A Gaussian field intensity distribution, C 2 Ž r, l., was calculated w10x from the core size and typical optical parameters Žnumerical aperture, cut-off wavelength and fibre parameter, V .. The total fibre attenuation is given by integration over the fibre radius of the local loss, Eq. Ž2.. Since this distribution is only valid for singlemode fibers and since only the thermal history of the initial preform was considered, the model is only accurate within the spectral region in which significant power is contained within a physical region of the fibre corresponding to the initial preform.
Fig. 1. Refractive indices of glass and crystal phase. Lines are drawn as guides for the eye.
G.F. West, W. Hofle ¨ r Journal of Non-Crystalline Solids 213 & 214 (1997) 189–192
glass. Calculation of the composition and refractive index change w11x in the diffusion zone surrounding the crystals produced values very similar to those measured for the 0 and 2.5% PbF2 samples, Fig. 1. The refractive index for the glass surrounding the crystal in the 9% PbF2 sample was calculated to be both higher than that of the glass matrix and beyond the range of the experimental technique used. The scattering centre is clearly not optically homogeneous. It is therefore assumed that scattering occurs at the boundary between a vitreous diffusion zone and the glass matrix of refractive indices n d Ž l. and n g Ž l. respectively. It can therefore be assumed that the shape of the dispersion curves is the same, their absolute refractive index being displaced. This leads to a more or less composition-independent relative refractive index of the scattering centre, m, of approximately 1.01. Assumption of a constant value for n x Ž l. would inevitably lead to attenuations far larger than those calculated below. Casting temperatures of 4508C and 4008C were taken for cladding and core respectively and a core diameter of 6 mm was chosen as representative for reproducible casting, though further reduction in temperature and core size produced a slight decrease in attenuation. Were it possible to draw such a preform to the appropriate fibre core diameter, the scattering loss would lie well below present theoretical fibre attenuations w1x. The collimation process has not as yet been studied intensively but would appear to play only a minor role, due to the large mass flow rates involved. The preform was collimated twice to 4.15 mm at 0.2 mrmin under a tension of 0.5 N.
Fig. 2. Crystal distributions in the centre of the preform or fibre Žclad cast at 4508C, core cast at 4008C, collimated twice and then drawn at 50 mrmin and 50 cN..
191
Fig. 3. Spectral attenuations for fibers drawn at 50 mrmin under various tensions.
Fibers were pulled at various tensions and drawing rates to give a core diameter of 9.4 mm, suitable for single-mode operation at 2.5 mm. Such a fibre is not typical but allows reliable prediction of the scattering loss in the region of the attenuation minimum. Fig. 2 shows the crystal distributions in the centre after preform manufacture and after fibre pulling. The preform was collimated twice to give a singlemode fibre. Directly after preform fabrication, the distributions are defined by the natural cooling curve at that radial position, with those in the cladding showing further peaks arising from reheating during core casting. Growth of the crystals during collimation and fibre drawing tends to lead to the crystals all reaching a similar size. In most cases, the size of the crystals is given solely by the drawing conditions. In contrast, since the largest crystals are always those nucleated first, their number is defined solely by the casting schedule. Fig. 3 shows the spectral attenuations due to
Fig. 4. Attenuation at 2.5 mm in single-mode fibers for 2.5 mm operation. Lines are drawn as guides for the eye.
G.F. West, W. Hofle ¨ r Journal of Non-Crystalline Solids 213 & 214 (1997) 189–192
192
Fig. 5. Theoretical spectral attenuations in ZBLAN fibers.
intrinsic crystallisation for several drawing conditions, together with the normalised power within the initial preform. Loss of guided power to the cladding towards longer wavelengths causes an apparent decrease in attenuation. Not shown in this figure is the appearance of higher guided modes at shorter wavelengths, which would lead to a redistribution of the field intensities. The results in Fig. 3 are summarised in Fig. 4 as the loss at 2.5 mm. An equivalent curve is included for a fibre geometrically optimised — with respect to both collimation and ultimate core size — for an operating wavelength of 1.3 mm. The loss at 2.5 mm is probably slightly underestimated in this case due to degradation of the guiding properties of this fibre at 2.5 mm. In order to calculate the ultimate spectral attenuation of a real fibre it is necessary to combine all relevant absorption and scattering loss mechanisms. Taking typical values for Rayleigh scattering and the multiphonon edge w1x together with the curves above, it is possible to define a new theoretical spectral attenuation for ZBLAN fibers, Fig. 5, which — in contrast to silica fibers — is now strongly process dependent. Using present preform casting technology, the current theoretical limit can only be reached under the most stringent of drawing conditions, if at all.
5. Discussion The attenuations calculated here are in general lower than those from previous Žincomplete. models. This is partly due to the lower nucleation and growth rates used and no doubt also to the assumption of a
field distribution. Assumptions in this work regarding the refractive index of the scattering centre would tend to underestimate the loss, since more scattering boundaries are present than are implicit in the scattering equations. These assumptions are nevertheless more appropriate for spectral calculations than that of a constant refractive index for the scattering centre. Sakaguchi also considered the effect of fibre drawing conditions w6x and trends in the effect of these conditions were confirmed here. Where similar parameters were used, the attenuations calculated by Sakaguchi and those here were similar. It should however be stressed that the crystallisation process is statistical and results would probably overestimate the loss in shorter fibre lengths.
6. Conclusions Intrinsic crystallisation in ZBLAN fluoride fibers during manufactured by pouring techniques leads to significant densities of scattering centres. The number and size of these scattering centres is strongly dependent on preform casting and fibre drawing conditions respectively. The spectral attenuation of fibers is thus process dependent for all but the most extreme drawing conditions.
References w1x P.W. France, M.G. Drexhage, J.M. Parker, M.W. Moore, S.F. Carter and J.V. Wright, Fluoride Glass Optical Fibres ŽBlackie, Glasgow, 1990.. w2x D. Szebesta, S.T. Davey, J.R. Williams and M.W. Moore, J. Non-Cryst. Solids 161 Ž1993. 18. w3x H.W. Schneider, A. Schoberth, A. Staudt and C. Gerndt, Siemens Forsch. Entwicklungsber. 17 Ž1988. 147. w4x A.A. Hopgood and G. Rosman, J. Non-Cryst. Solids 140 Ž1992. 301. w5x S.F. Carter and J.M. Parker, Glass Technol. 31 Ž1990. 245. w6x S. Sakaguchi, J. Lightwave Technol. 11 Ž1993. 187. w7x P. Hart, G. Lu and I. Aggarwal, Mater. Sci. Forum 32&33 Ž1988. 179. w8x H. Rawson, Properties and Applications of Glass ŽElsevier, Amsterdam, 1980.. w9x M. Kerker, The Scattering of Light ŽAcademic Press, New York, 1969.. w10x H.-G. Unger, Optische Nachrichtentechnik ŽBand 1. ŽHuthig, ¨ 1993.. w11x L. Zhang and F. Gan, Glass Technol. 33 Ž1992. 23.
Spectral attenuation of fluoride glass fibers G.F. West
),1
, W. Hofle ¨
Institut fur ¨ Hochfrequenztechnik, Technical UniÕersity of Braunschweig, Braunschweig, Germany
Abstract Intrinsic crystallisation is invoked at each process stage during the manufacture of fluoride glass fibers. Thermal history and crystallisation distributions were calculated by numerical simulation of the entire fibre manufacturing process, from the preform to fibre drawing. Assuming a gaussian field distribution for single-mode fibre, the attenuation due to crystallisation was calculated using classical scattering theory. Results show strong dependence on the temperature of the core melt and fibre drawing conditions. The former can be reduced to acceptable levels under normal manufacturing conditions. During fibre manufacture it is necessary to maximise both fibre tension and speed in order to reduce additional attenuation to a level below that of Rayleigh scattering.
1. Introduction The fluoride glass composition based on the fluorides of zirconium, barium, lanthanum, aluminum and sodium ŽZBLAN. has proved to be one of the most stable and has been widely studied. Much work has been invested in attempts to produce a fluoride glass fibre exhibiting the theoretical optical loss limit, presently lying at 0.044 dBrkm at 2.55 mm w1x. The best value to date is 0.45 dBrkm at 2.35 mm w2x, with progress in reducing the losses generally being very slow. No thorough explanation for the excess loss has been proposed, although it is known to be due to scattering w1x. Previous attempts to calculate the excess scattering due to intrinsic crystallisation have shown that losses can be significant w3–6x.
) Corresponding author. Tel.: q49-631 205 4148; fax: q49-631 205 4147. 1 Present address: AG Optoelektronik, Fachbereich Physik, Universitat ¨ Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany.
Since in these models not all aspects of thermal history and the scattering process were considered, it has not been possible to calculate a definitive contribution to total loss. The model here extends analysis of fibre drawing to include preform collimation and adds a new model for the wavelength dependent relative refractive index of the scattering centre and the field distribution in the fibre. Thus, all relevant theoretical physiochemical and optical aspects necessary for calculation of the attenuation are addressed.
2. Theory The preform manufacturing model corresponds essentially to that used by Carter w5x for a rotationally-cast clad and poured core; the cooling steps having been increased from 60 s to 150 s. Since we are aiming for a prediction of the minimum attenuation possible, experimental values used for nucleation and growth rates in ZBLAN were the smallest found in the literature w7x.
0022-3093r97r$17.00 Copyright q 1997 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 7 . 0 0 0 0 9 - 4
G.F. West, W. Hofle ¨ r Journal of Non-Crystalline Solids 213 & 214 (1997) 189–192
190
The thermal history during collimation and fibre drawing were derived from the local viscosity in the neck-down region using a semi-empirical model. Experience over several years has shown the neckdown shape to be more or less constant under all conditions for the furnace configuration used. The local volume flow rate was derived from an empirical expression for the neck shape. Local viscosity could then be calculated from the fibre tension and drawing speed by local application of the normal expression for viscous flow w8x, assuming a constant radial temperature. Strictly speaking, calculations are thus limited to the preform dimensions and neckdown geometries used here Žpreform diameters 13 mm, neck-down lengths 1 cm..
a r Ž r , l. s
i
2
H0 N Ž a, r . p a Q Ž a, l. d a.
Ž 1.
Attenuation was calculated using classical scattering theory w9x as used by previous authors w5,6x. The local fibre attenuation, a Ž l, r ., is given by the sum of the crystal attenuations, Eq. Ž1.. Here, QŽ a, l. is the scattering efficiency and N Ž a, r . is the differential w.r.t. crystal radius of the number density of crystals of radius a per unit volume of glass at the radial coordinate, r. Unlike the simple number density, the distribution of N Ž a, r . over a should be independent of the time-step used in numerical calculations and can be used to establish a sufficiently small increment.
a Ž l. s
rs qa 2 Hrs ya a Ž r , l . C Ž r , l . r d r
H0‘ C 2 Ž r , l . r d r
.
3. Experimental In previous calculations, various relative refractive indices, m s n crystalrn glass , were taken w6x, or the refractive index of the crystal, n x Ž l., was taken to be constant w4,5x. Neither of these assumptions permits the calculation of real spectral attenuations. Measurement of the refractive index of both glass and crystal were therefore instigated. ZBLAN samples containing various amounts of PbF2 Ž0, 2.5 and 9 mol%. where heat treated to promote a small degree of Žin this case surface. crystallisation. X-ray diffraction showed the crystals in all glasses to be exactly the same and most likely to be b-ZrBaF6 . Refractive indices of the glasses were measured with an Abbe refractometer and by phase contrast of ground samples. Measurement of the crystal phase proved impossible with the phase contrast method and the Becke-line method was used to provide an estimate.
4. Results The results of refractive index measurement of the crystal and glass phases Ž n D . are shown in Fig. 1. For the glasses, refractive indices measured by phase contrast corresponded well to those measured with an Abbe refractometer. Although the value for the sample containing 9% PbF2 could not be confirmed by more than one measurement, the refractive index of the crystal-phase was definitely not constant, and lay in each case ; 0.01–0.02 below that of the
Ž 2.
A Gaussian field intensity distribution, C 2 Ž r, l., was calculated w10x from the core size and typical optical parameters Žnumerical aperture, cut-off wavelength and fibre parameter, V .. The total fibre attenuation is given by integration over the fibre radius of the local loss, Eq. Ž2.. Since this distribution is only valid for singlemode fibers and since only the thermal history of the initial preform was considered, the model is only accurate within the spectral region in which significant power is contained within a physical region of the fibre corresponding to the initial preform.
Fig. 1. Refractive indices of glass and crystal phase. Lines are drawn as guides for the eye.
G.F. West, W. Hofle ¨ r Journal of Non-Crystalline Solids 213 & 214 (1997) 189–192
glass. Calculation of the composition and refractive index change w11x in the diffusion zone surrounding the crystals produced values very similar to those measured for the 0 and 2.5% PbF2 samples, Fig. 1. The refractive index for the glass surrounding the crystal in the 9% PbF2 sample was calculated to be both higher than that of the glass matrix and beyond the range of the experimental technique used. The scattering centre is clearly not optically homogeneous. It is therefore assumed that scattering occurs at the boundary between a vitreous diffusion zone and the glass matrix of refractive indices n d Ž l. and n g Ž l. respectively. It can therefore be assumed that the shape of the dispersion curves is the same, their absolute refractive index being displaced. This leads to a more or less composition-independent relative refractive index of the scattering centre, m, of approximately 1.01. Assumption of a constant value for n x Ž l. would inevitably lead to attenuations far larger than those calculated below. Casting temperatures of 4508C and 4008C were taken for cladding and core respectively and a core diameter of 6 mm was chosen as representative for reproducible casting, though further reduction in temperature and core size produced a slight decrease in attenuation. Were it possible to draw such a preform to the appropriate fibre core diameter, the scattering loss would lie well below present theoretical fibre attenuations w1x. The collimation process has not as yet been studied intensively but would appear to play only a minor role, due to the large mass flow rates involved. The preform was collimated twice to 4.15 mm at 0.2 mrmin under a tension of 0.5 N.
Fig. 2. Crystal distributions in the centre of the preform or fibre Žclad cast at 4508C, core cast at 4008C, collimated twice and then drawn at 50 mrmin and 50 cN..
191
Fig. 3. Spectral attenuations for fibers drawn at 50 mrmin under various tensions.
Fibers were pulled at various tensions and drawing rates to give a core diameter of 9.4 mm, suitable for single-mode operation at 2.5 mm. Such a fibre is not typical but allows reliable prediction of the scattering loss in the region of the attenuation minimum. Fig. 2 shows the crystal distributions in the centre after preform manufacture and after fibre pulling. The preform was collimated twice to give a singlemode fibre. Directly after preform fabrication, the distributions are defined by the natural cooling curve at that radial position, with those in the cladding showing further peaks arising from reheating during core casting. Growth of the crystals during collimation and fibre drawing tends to lead to the crystals all reaching a similar size. In most cases, the size of the crystals is given solely by the drawing conditions. In contrast, since the largest crystals are always those nucleated first, their number is defined solely by the casting schedule. Fig. 3 shows the spectral attenuations due to
Fig. 4. Attenuation at 2.5 mm in single-mode fibers for 2.5 mm operation. Lines are drawn as guides for the eye.
G.F. West, W. Hofle ¨ r Journal of Non-Crystalline Solids 213 & 214 (1997) 189–192
192
Fig. 5. Theoretical spectral attenuations in ZBLAN fibers.
intrinsic crystallisation for several drawing conditions, together with the normalised power within the initial preform. Loss of guided power to the cladding towards longer wavelengths causes an apparent decrease in attenuation. Not shown in this figure is the appearance of higher guided modes at shorter wavelengths, which would lead to a redistribution of the field intensities. The results in Fig. 3 are summarised in Fig. 4 as the loss at 2.5 mm. An equivalent curve is included for a fibre geometrically optimised — with respect to both collimation and ultimate core size — for an operating wavelength of 1.3 mm. The loss at 2.5 mm is probably slightly underestimated in this case due to degradation of the guiding properties of this fibre at 2.5 mm. In order to calculate the ultimate spectral attenuation of a real fibre it is necessary to combine all relevant absorption and scattering loss mechanisms. Taking typical values for Rayleigh scattering and the multiphonon edge w1x together with the curves above, it is possible to define a new theoretical spectral attenuation for ZBLAN fibers, Fig. 5, which — in contrast to silica fibers — is now strongly process dependent. Using present preform casting technology, the current theoretical limit can only be reached under the most stringent of drawing conditions, if at all.
5. Discussion The attenuations calculated here are in general lower than those from previous Žincomplete. models. This is partly due to the lower nucleation and growth rates used and no doubt also to the assumption of a
field distribution. Assumptions in this work regarding the refractive index of the scattering centre would tend to underestimate the loss, since more scattering boundaries are present than are implicit in the scattering equations. These assumptions are nevertheless more appropriate for spectral calculations than that of a constant refractive index for the scattering centre. Sakaguchi also considered the effect of fibre drawing conditions w6x and trends in the effect of these conditions were confirmed here. Where similar parameters were used, the attenuations calculated by Sakaguchi and those here were similar. It should however be stressed that the crystallisation process is statistical and results would probably overestimate the loss in shorter fibre lengths.
6. Conclusions Intrinsic crystallisation in ZBLAN fluoride fibers during manufactured by pouring techniques leads to significant densities of scattering centres. The number and size of these scattering centres is strongly dependent on preform casting and fibre drawing conditions respectively. The spectral attenuation of fibers is thus process dependent for all but the most extreme drawing conditions.
References w1x P.W. France, M.G. Drexhage, J.M. Parker, M.W. Moore, S.F. Carter and J.V. Wright, Fluoride Glass Optical Fibres ŽBlackie, Glasgow, 1990.. w2x D. Szebesta, S.T. Davey, J.R. Williams and M.W. Moore, J. Non-Cryst. Solids 161 Ž1993. 18. w3x H.W. Schneider, A. Schoberth, A. Staudt and C. Gerndt, Siemens Forsch. Entwicklungsber. 17 Ž1988. 147. w4x A.A. Hopgood and G. Rosman, J. Non-Cryst. Solids 140 Ž1992. 301. w5x S.F. Carter and J.M. Parker, Glass Technol. 31 Ž1990. 245. w6x S. Sakaguchi, J. Lightwave Technol. 11 Ž1993. 187. w7x P. Hart, G. Lu and I. Aggarwal, Mater. Sci. Forum 32&33 Ž1988. 179. w8x H. Rawson, Properties and Applications of Glass ŽElsevier, Amsterdam, 1980.. w9x M. Kerker, The Scattering of Light ŽAcademic Press, New York, 1969.. w10x H.-G. Unger, Optische Nachrichtentechnik ŽBand 1. ŽHuthig, ¨ 1993.. w11x L. Zhang and F. Gan, Glass Technol. 33 Ž1992. 23.