inequality (expr. 5) ensures that there is no 'walkoff between the copropagating channel 1 and 2 beams due to fibre dispersion, while the right-hand side provides that there will be many pulses of the modulated light travelling in the fibre. Thus the copropagating channel 1 wave experiences a modulation in its phase of magnitude A(pl synchronous with the channel 2 modulation rate, whereas the counterpropagating channel 1 beam passes many channel 2 pulses and hence has a constant net phase shift A(j)l/2. Therefore, detection of the channel 1 interferometer output with a lock-in amplifier synchronous with the channel 2 modulation rate is a measure of the phase shift A<pl in channel 1 due to crossphase modulation from channel 2. The square-wave modulation rate of 100 kHz that was used satisfies expr. 5. With no light in channel 2 the interferometer output D for channel 1 is Ys cos 4> D = If + lb + (6) where lf and Ib are the channel 1 intensities in the two directions, •/ is a measure of the coherence of the two beams, <p is the relative phase between the two arms of the interferometer. If the interferometer is allowed to drift the detected output will drift between If + Ib- 2j(IfIb)y <D<If + Ib + 2sJ{Iflb)y; i.e. the peak-to-peak drift is 4 N /(/ / / b )y. This is shown in Fig. 2a, obtained by square-wave modulation of channel 1 with a light chopper plus synchronous detection. This drift output serves to calibrate the interferometer phase shift. With light injected into channel 2 as well, the channel 1 interferometer output is 2 N /(/ / / 6 ) 7 cos , X(Qt)) A. R. CHRAPLYVY J. STONE AT&T Bell Laboratories Crawford Hill Laboratory Holmdel, NJ 07733, USA (8) where P is the power per channel, x 1/50 1617/21 Fig. 2 a Drifting output of interferometer with 1-3 /an beam blocked b Output signal; output of interferometer with 1-3 nm and 1-5 /an beams unblocked and phase sensitive detector tuned to modulation frequency of the 1-3 nm laser c Same as b except 1-3 /im beam is blocked d Same as b except 1-5 nm beam is blocked ELECTRONICS LETTERS 22nd November 1984 Vol. 20 22nd October 1984 References 1 CHRAPLYVY, A. R., MARCUSE, D., and HENRY, p. s.: 'Carrier-induced phase noise in angle-modulated optical-fibre systems', J. Lightwave Technol., 1984, LT-2, p. 6110 (7) where Acpl is the added phase change due to crossphase modulation, Q is the modulation frequency of channel 2, and X(Qt) is a square wave of frequency Q. For A({)1 <£ n/2 the output of the lock-in detector tuned to frequency ft will drift between — 2 N /(/ / / fc )y A(f>1 < D < 2^/(7f Ib)y A</>x as the interferometer phase drifts between <p = — n/2 and (p = + n/2- This is shown in Fig. 2b. As expected, blocking either the channel 2 laser (Fig. 2c) or the channel 1 laser (Fig. 2d) causes the crossphase modulation signal to vanish. We also verified that we were not observing stimulated Raman scattering: with either input to the directional coupler blocked only a very small amount of noise was measured. Also, the contribution of silica Raman amplification to the nonlinear phase shift was negligible for the channel 1 and 2 frequency separation used here.1 From eqns. 6 and 7 we see that the ratio of drift amplitude in Fig. 2b to that in Fig. 2a yields A $ , , the crossphase modulation. For 1 mW of injected channel 2 power this phase shift is about 0024 rad (1-4°), which agrees well with the predicted value (eqn. 4) of 0022 rad. The presence of crossphase modulation places certain restrictions on various coherent WDM systems. For an Nchannel ASK system,1 and Le = I/a, from eqn. 2 for a = 0-25 dB/km, A</> = 0-045P(7V - 1) To limit the degradation due to phase crosstalk to an acceptable level (0-5 dB power penalty), A<£< 0-15 rad 3 or P < 3-3/(N — 1) mW. This restriction on P may render coherent detection of ASK unattractive for WDM systems applications. In frequency-modulated systems the amount of residual amplitude modulation is restricted by similar arguments. In phase-modulated systems the only phase noise due to crossphase modulation will arise from residual amplitude noise on the nominally CW laser output. In most instances this will not cause noticeable degradation. 1 In conclusion, we have measured the effects of crossphase modulation in coherent wavelength-division multiplexing using conventional injection lasers. For two-channel multiplexing, 1 mW of power modulation in one channel produces a phase shift of 1-4 in the other channel. The measurement was made using a novel interferometric experimental arrangement that can also be used to measure other weak nonlinear phase-sensitive effects at low laser power. C. A. Burrus is thanked for fabricating the 1-3 //m injection laser used in these experiments. 2 STOLEN, R. H., and BJORKHOLM, j . E.: 'Parametric amplification and frequency in optical fibers', IEEE J. Quantum Electron., 1982, QE-18, pp. 1062-1072 3 PRABHU, v. K.: 'PSK performance with imperfect carrier phase recovery', IEEE Trans., 1976, AES-12, pp. 275-285 TRANSMISSION PROPERTIES OF LIGHTGUIDE FIBRES COATED AT A LINE SPEED OF 10 m/s Indexing terms: Optical fibres, Optical transmission We report the transmission characteristics of high-speedcoated lightguide fibres; the evaluation is based on a total length of 90 km of single-mode fibre. For this experiment the line speed was varied from 2 to 10 m/s, and each sample length obtained from a preform was ~ 10 km. We found that the average losses of the fibres coated at three different speeds (2, 5 and 10 m/s) are all ~0-4 dB/km at 1-32 /im. Introduction: It is known that the preform size depends primarily on its fabrication method (MCVD, LMCVD, VAD and OVD technique), and the diameter ranges normally between 1 and 2 cm. However, further improvement of the preform processes is likely to result in diameters larger than 2 cm and that will inevitably require high-speed coating. Fibre coating and drawing technology has progressed substantially, originally starting with line speeds of 1 m/s and recently achieving the coating speed in the excess of 10 m/s. 1 In the past, we first reported very high strength results of silica fibres in a long length coated at high speeds, 23 including proof-tested data as well as the Weibull distributions of the fibre strength. Highspeed coating has a major impact on lightguide fibre cost, since a significant portion of the cost is attributed to the fibre manufacturing processes.3 5 It should be pointed out that one of the noticeable differences in high-speed coating ( > 1 0 m/s) is the fibre draw tension, which is maintained at a much higher level than for the low-speed-coating case. The important fact that one has to remember is that the draw tension increases linearly with draw speed and will thus embed increased residual stresses in the composite-structured drawn fibre.6 Therefore, a major concern is the effect of this higher tension on the fibre loss and other propagation properties. No. 24 997 To characterise the transmission performance we examined a total of ~ 9 0 km length of depressed clad single-mode fibres that were coated at a rate of 10 m/s. This letter reports the experimental results for these fibres. in the case for the fibre drawn at 10 m/s. The cutoff point varies from sample to sample, ranging from ~ 1-25 to ~ 1-28 nm. It must be noted that this phenomenon was also observed in the loss curves of the fibres drawn with different furnace temperatures. Experiments: The high-speed coating was done on a modified high draw tower that is capable of applying a uniform thickness layer coating of UV-curable material with good concentricity.7 The draw tower is equipped with a high-frequency zirconia induction furnace to draw a certain size of an optical fibre from a silica glass preform. The suscepter surface of the furnace is constantly monitored at its midpoint by an optical pyrometer through an open port and maintained at a constant temperature within a few degrees fluctuation of the set point using feed-back control. Its temperature was set to 2250°C and is one of the major parameters for determining the draw tension that is the critical variable in yielding the desired results. Our tension measurements showed that with and without applying coating, both tensions are linearly increased as the draw speed increases.1 In this case, the tension without applying coating at the speed of 10 m/s was ~50 g. Using the fibre draw control system8 we have achieved the standard deviation for the fibre diameter variation less than 0-5 nm for 125 ^im fibre. 100 80 60 20 ' i-0r 5m/s 10"m/s 40 1 0-8 06 09 0-4 08 0-2 10m/s 0-1 E'0-6 1000 1100 1200 1300 1400 wavelength, nm 1500 1600 15777?! -0-5 Fig. 2 Spectral loss curves of a single-mode fibre drawn from a preform with three different coating speeds 0-4 For this particular experiment the furnace temperature was varied from 2300 to 2150°C in decrements of 50°C to increase the fibre draw tension at the constant pulling speed. We set the draw speed to be 5 m/s, and the spectral losses of the single-mode fibres obtained under this condition are shown in Fig. 3. It is seen in the Figure that, as the temperature 0-3 02 o o o , fibre drawn at 10 m/s fibre drawn at 5m/s 2m Is X X X , fibre drawn at 0-1 100 80 2 1-1. .3pQ 1-2 •2250" 1 . 3 _22PO_ , 2150 60 3 4 5 6 sample number 8 9 40 10 I6377T1 draw Fig. 1 Transmission losses of single-mode fibres at /. = 1-32 pm for three different coating speeds (2, 5 und 10 m/s) 20 For these experiments, nine single-mode preforms of germanium-doped core with fluorine-doped depressed cladding were used. These were fabricated by the MCVD technique, obtaining a A of 0-37% and designed to be a zero dispersion near 1-31 /mi region. The preform diameter is ~ 1-6 cm and approximately 10 km were drawn from each preform, producing a combined length of about 90 km of 125 /im-diameter fibre with 8-3 /im core. Fig. 1 shows the results of fibre transmission loss at the wavelength point of 1 -32 fim in the loss spectrum. As shown in the Figure, the data points scatter around the value of 0-4 dB/km. Except for an outlying point, the scattering of measured points is within measurement uncertainty. Thus it is indicated that there are practically no differences in the loss for three different coating speeds—2, 5 and 10 m/s. To eliminate any possible effect of variations in the properties of the preforms, fibres were drawn from each preform at the three different speeds. Fig. 2 shows the loss spectrums of the samples drawn at the different speeds. In all cases, the thickness of the applied coating is typically 50 jim. However, one peculiar characteristic we observed in the curves is that the width of the hump in the higher-order-mode region (denoted by W in the Figure) where the wavelength is less than ~ 1-25 ^m is appreciably narrower 10 998 speed = 5 m / s 1 08 0-6 0 4 02 0-1; 1000 1100 1200 1300 wavelength, nm 1400 1500 1600 I637/3I Fig. 3 Spectral loss curves of a single-mode fibre drawn at four different draw tensions by varying the furnace temperature from 2300 to 2150 C ELECTRONICS LETTERS 22nd November 1984 Vol. 20 No. 24 decreases, the width of the hump below the cutoff point also decreases. Thus we believe that this phenomenon is somehow related to fibre draw tension. More specifically, it seems likely that it is attributed to mode filtering. According to a periodic structured-waveguide theory, 9 a guiding condition of modes is determined by a relation among three parameters— wavelength, spatial periodicity and diameter fluctuation depth. For example, if the periodicity is greater than half the wavelength for a given modulation depth, the modes in the waveguide will be scattered out. For increasing tension the fibre diameter variation tends to be smoother and, therefore, the higher-order modes in the shorter-wavelength region will be less filtered out. We believe that this is a plausible explanation of the reason for the narrower width of the hump in the case of higher draw tension. In order to check any discrepancy in performance between low-speed- and high-speed-coated fibres, we also examined the other lightguide properties such as cutoff wavelength, zerodispersion wavelength etc. We found that there are no significant differences in the measured results. However, it must be noted that high-speed coating tends to provide a slightly lower value of the transmission loss, particularly in the longwavelength region (see Fig. 2). surements. We also acknowledge W. M. Flegal, AT&T Technologies, Atlanta Works, for providing the preforms. U. C. PAEK C. M. SCHROEDER A T& T Technologies Inc. Engineering Research Center PO Box 900 Princeton, XJ 08540, USA References 1 2 3 4 5 Conclusion: A total of approximately 90 km length of singlemode fibres was produced with coating at 2, 5 and 10 m/s. The investigation showed that the transmission characteristics of high-speed-coated fibres remain the same as those obtained at a low coating speed. Acknowledgments: The authors wish to express their gratitude to R. J. Klaiber and L. S. Watkins for their guidance and encouragement. We also thank T. L. Watros, L. D. L'Esperance and E. A. Sigety (BL-MH) for their help in mea- 24th October 1984 6 7 8 9 PAEK, LT. c , and SCHROEDER, c. M.: 'Optical fibres coated with a UV-curable material at a speed of 12 m s\ Electron. Lett., 1984, 20, pp. 304-305 PAEK, L\ c , and SCHROEDER, C. M.: 'High speed coating of optical fibers with UV curable materials at a rate of greater than 5 m sec', Appl. Opt., 1981, 20, pp. 4028-4034 PAEK, u. c , and SCHROEDER, C. M.: 'High strength in a long length for fiber coated at a speed of 5 m,'s\ J. Lightwave Techno!., 1984, LT-2, pp. 354-357 CHIDA, K., SAKAGUICHI, s., WAGATSUMA, M., and KiMLRA, T.: 'High- speed coating of optical fibres with thermally curable silica resin using a pressurised die', Electron. Lett., 1982, 18, pp. 713-715 INAGAKI, N., and CHIDA, N.: 'High speed fiber drawing'. Technical Digest of IOOC83, Japan 1983, paper 27A4-1 PAEK, u. c , and KURKJIAN, C. R.: 'Calculation of cooling rate and induced stresses in drawing of optical fibers', J. Am. Ceram. Soc, 1975, 58, pp. 330-335 SMITHGALL, D. H., and FRAZEE, R. E. : 'High speed measurement and control of fibre-coating concentricity', Bell Syst. Tech. J., 1981, 60, pp. 2065-2080 SMITHGALL, D. H.: 'Application of optimization theory to the control of the fiber drawing process', ibid., 1979, 58, pp. 1425-1436 DABBY, F. w., KESTENBAUM, A., and PAEK, u. c : 'Periodic dielectric waveguides', Opt. Commun., 1972, 6, pp. 125-130 Piezoresistance: For a gauge made in isotropic material the gauge factor (fractional change in resistance AR/R per unit strain e) is given by PIEZORESISTANCE IN POLYSILICON Indexing term: Piezoelectric devices and materials A theoretical model for piezoresistance in polysilicon is described. Grain size, orientation and doping dependence effects are included. Predictions of gauge factor using the model give reasonable agreement with experimental results and enable optimum processing parameters to be chosen for a given grain size. Introduction and theoretical model: Recent studies in piezoresistance of polysilicon1'2 have shown that it has the advantage of high gauge factor and ease of deposition on insulator coated substrates. However, the dependence of gauge factor on structure is not well understood. In this letter a theoretical estimate of gauge factor is made, taking into account grain size, texture and doping level, which is in reasonable agreement with experimental results. The model used allows the optimum doping level to be predicted for a given grain size. The p-type polysilicon material is assumed to have grains of length L, separated by thin grain boundaries with associated depletion regions. These barriers are assumed to be trapping centres and insensitive to strain. 3 Ap G = 1 + 2v + — pe where v is Poisson's ratio. Eqn. 2 can be expressed in terms of compliance coefficients S^5 and piezoresistance coefficients nd (where nd incorporates high doping effects6). In the case of an anisotropic homogeneous material eqn. 2 becomes (3) where i = 1 and d = / for longitudinal strain, and i = 2 and d = t for transverse strain. The values of nd and So- can be calculated for an arbitrary direction using the following equations: 5 S,j = Si2 + ( S t l - Sl2 - |S 44 K/, 2 / 2 + mfm] + nf n]) Su = S , , + (S 44 + 2Sl2 - 2Sl iX/f mf + If "if + mf nf) n, = nli Resistivity calculations: Doping segregation was assumed not to be present and thus the depletion widths w are given by QJ2N (for LN > Qt), where N is the average doping concentration (centimetre" 3 ) and Qt is the density of trapping states (centimetre" 2 ). Using the assumptions of this model the following equation for resistivity of the films can be found: Pg + Pb ELECTRONICS LETTERS 22nd November 1984 + l\ n\ + m\n\) m\ m\ (4) n\n\) The current is assumed to be in the x' direction in the transformed co-ordinate system, defined by 6, <j>, if/ as shown in Fig. 1. The direction cosines /,-, mh nt of the transformation are defined by (1) where p, pg and pb are the resistivities of the film, grain and barrier, respectively, and S is the grain boundary thickness. Numerical values used in eqn. 1 were taken from Mandurah's experimental work.4 + 2(TT44 + nl2 ~ niXil\m\ n, = nl2 + ( 7 i n - 7r12 - TI (2w + d) [L P= (2) x' mt y' = l2 m2 ./ 3 "1 K n 2 y "3. z (5) Piezoresistance in polysilicon: Using the assumptions of this model in conjunction with eqn. 1, the fractional change in Vol. 20 No. 24 999

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