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Characteristics of Chirped Fiber Gratings for Dispersion Compensation
OPTICAL FIBER TECHNOLOGY ARTICLE NO.
2, 213–215 (1996)
0026
Characteristics of Chirped Fiber Gratings for Dispersion Compensation SERGIO BARCELOS,∗ MICHAEL N. ZERVAS, AND RICHARD I. LAMING Optoelectronics Research Centre, University of Southampton, Southampton, SO17 1BJ, United Kingdom Received November 6, 1995
kept constant, will modify the index profile to We report a detailed characterization of the properties of a chirped fiber Bragg grating with respect to the amount of applied chirp. The results demonstrate the reflection and dispersion dependencies associated with any linearly chirped grating. The dispersion of the device tested could be continuously tuned to give a dispersion up to −2010 ps/nm. © 1996 Academic Press, Inc.
INTRODUCTION Chirped fiber Bragg gratings have recently received considerable attention due to their immense potential for use as dispersion equalizers in long haul fiber telecom links [1]. Some of their properties have been studied theoretically and demonstrated in a number of system trials [2]. We have implemented a variablechirp grating using the temperature gradient technique [3] and systematically measured its reflection and dispersion characteristics [4] for a wide range of applied chirp. The results clarify those properties and are in very good agreement with the theoretical predictions, which were calculated using coupled-mode theory applicable to nonuniform aperiodic structures [5, 6]. THE TEMPERATURE-GRADIENT TUNABLE CHIRPED FIBER GRATING The refractive index profile along a linearly chirped fiber Bragg grating is given by [5] µ ¶¸ · 2π n(z) = n 0 1 + 2h 0 cos z(1 + C z) , 30
(1)
where n 0 is the average fiber refractive index, h 0 and 30 are the amplitude and period of the refractive index modulation, C is the built-in chirp of the Bragg grating, and z is the axial distance. Applying a linear temperature gradient G [in ◦ C/mm] to this grating, with the temperature at the center of the grating (z = 0)
∗
Fax: +44 1703 593149. E-mail: [email protected].
µ ¶¸ · 2π ξG z + 2h 0 cos z(1 + (C − αG)z) , n(z) ≈ n 0 1 + n0 30 (2) where α and ξ are the expansion and the thermo-optic coefficients of the fiber. Both the grating period and the background refractive index vary linearly along the grating length and combine to induce a linear chirp in the grating [5]. The overall effect can then be represented by an effective chirp parameter Ceff = C − (ξ /2n 0 + α)G. RESULTS AND DISCUSSIONS The tested fiber grating was approximately 40 mm in length and slightly apodised at the edges, and, at room temperature (22◦ C), it had approximately 0.055 nm of built-in chirp. It was written with a frequency-doubled Excimer laser and scanning interferometer in hydrogenated standard telecommunications fiber. Linear temperature gradients were applied by mounting the grating in a 45-mm-long V-groove machined in an aluminium slab, the two ends of which were independently controlled in temperature by separate peltier elements. The center temperature was held constant at 25◦ C and the linearity of the temperature gradients was better than 3%. Figure 1 shows the measured reflectively and time delay response of the grating for different applied temperature gradients. The best-fitted straight line over the time delay and across the grating reflection bandwidth gives the mean dispersion, Dm . By applying a temperature gradient G of 13◦ C/45 mm to the grating (Fig. 1a), we were able to cancel the built-in chirp and achieve the minimum bandwidth (BW3dB = 0.036 nm) and maximum peak reflectivity (88%). In this case, the time delay does not exhibit any measurable slope over the grating bandwidth. Figure 1a also shows the calculated response of an unapodised unchirped grating of effective length l g = 36 mm and h 0 = 0.83 × 10−5 , which is in very good agreement with the experimental data. Applying a temperature gradient G = −25◦ C/45 mm (Fig. 1b) broadens the reflection spectrum to BW3dB = 0.219 nm, reduces the peak reflectivity to 29%, and induces a negative linear dispersion Dm = −1062 ps/nm. Reversing the temperature gradient to +30◦ C/45 mm (Fig. 1c) reverses the chirp and the
213 1068-5200/96 $18.00 Copyright © 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
214
BARCELOS, ZERVAS, AND LAMING
by fitting the theoretical and experimental curves and are in very good agreement with the measured values of a similar fiber [7]. Figure 2a shows that, away from the zero-chirp point, the grating bandwidth increases almost linearly with |Ceff | while the peak reflectivity drops rapidly. The mean dispersion, Dm , is observed to exhibit a 1/|Ceff | dependence, which maintains the dispersion-bandwidth product (Fig. 2b) near constant and proportional to twice the grating length. As anticipated, the total time delay difference across the grating bandwidth was found to be independent of Ceff and roughly equal to 380 ps (cf. Figs. 1b and 1c), which corresponds to the double passage of light through the fiber grating. The time delay curves were found to have linear variation across the 3-dB grating bandwidths for |Ceff | > ∼ 0.0012 m −1 , tending to become nonlinear and exhibiting stronger oscillations at the grating edges with decreasing |Ceff |. The maximum practical dispersion compensating capability of the device, observed to occur at Ceff ≈ −0.0012 m −1 , provides a useful negative slope Dm = −2010 ps/nm and 3-dB bandwidth BW3dB = 0.11 nm. FIG. 1. Measured grating power reflectivity and time delay response for three different temperature gradients G: (a) 13◦ C/45 mm (Ceff = 0), (b) −25◦ C/45 mm (Ceff = −0.0025), and (c) 30◦ C/45 mm (Ceff = +0.0011). The calculated response is also shown in (a).
mean dispersion. Spectral broadening to B3dB = 0.096 nm and decrease in the peak reflectivity to 58% are also observed (cf. Fig. 1a). Although the measured mean dispersion is increased to approximately +2270 ps/nm, the time delay response is now nonlinear across the grating bandwidth and exhibits large oscillations at the bandwidth edges. Figures 1b and 1c show that the reflectivity spectra are asymmetric, which is probably due to variations of the coupling constant along the grating length. Several different temperature gradients were studied, and the results are summarized in Fig. 2. The effective chirp parameter Ceff is given by (ξ /2n 0 + α) · (G 0 − G), where G 0 (≈ 13◦ C/45 mm) is the temperature gradient giving zero chirp. The parameters α ≈ 0.42 × 10−6 /◦ C and ξ ≈ −9.73 × 10−6 /◦ C were obtained
CONCLUSIONS We have implemented a variable-chirp fiber grating and conducted an accurate characterization of its reflectivity and time delay response for several levels of chirp. The experimental data are in very good agreement with the theoretical predictions. The reflectivity and bandwidth have a symmetric behavior, whereas the mean dispersion depends on the sign of the chirp parameter C. With increasing |C|, the grating bandwidth increases quasi-linearly and the reflectivity drops. On the other hand, the mean dispersion, which represents the dispersion experienced on average by the transmitted data in an optical transmission system, varies maintaining the dispersion-bandwidth product constant and proportional to twice the grating length. It is shown that high induced dispersion (low chirp) is accompanied by increased nonlinearity in the time delay slope, which degrades the dispersion characteristics and can be associated with BER degradation in system applications of the device, while an
FIG. 2. Measured (°), (¥) and calculated (—) 3-dB reflection bandwidth and maximum reflectivity of grating as a function of the effective chirp parameter (a) and mean dispersion as a function of the grating 3-dB reflection bandwidth (b). For the calculated data, we assumed l g = 36 mm and h 0 = 0.83 × 10−5 .
CHARACTERISTICS OF CHIRPED FIBER GRATINGS FOR DISPERSION COMPENSATION
increased chirp linearises the dispersion characteristic, but at the expense of reducing the mean dispersion. The 40-mm grating evaluated offered a practical dispersion compensating capability up to −2010 ps/nm with a 3-dB bandwidth of 0.11 nm. ACKNOWLEDGMENTS
215
[2] R. I. Laming, M. N. Zervas, S. Barcelos, M. J. Cole, L. Reekie, N. Robinson, and P. L. Scrivener, “Dispersion compensating chirped fiber gratings,” in 13th Annual Conference on European Fiber Optic Communications & Networks, invited paper, Brighton, UK, June 1995. [3] J. Lauzon, S. Thibault, J. Martin, and F. Ouellette, “Implementation and characterization of fiber Bragg gratings linearly chirped by a temperature gradient,” Opt. Lett., vol. 19, No. 23, 2027 (1994). [4] S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. McKee, F. Sladen, and B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett., vol. 31, no. 15 (1995).
The authors acknowledge L. Reekie for fabricating the grating. S. Barcelos acknowledges the support of the Brazilian National Council for Science and Technology (CNPq). This work was supported by Pirelli Cavi SpA.
[5] L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E, vol. 48, no. 4, 4758 (1993).
REFERENCES
[6] J. E. Sipe, L. Poladian, and C. M. de Sterke, “Propagation through nonuniform grating structures,” J. Opt. Soc. Am. A, vol. 11, no. 4, 1307 (1994).
[1] F. Ouellette, “All-fiber filter for efficient dispersion compensation,” Opt. Lett., vol. 16, no. 5, 303 (1991).
[7] J.-L. Archambault, “Photorefractive gratings in optical fibers,” Ph.D. Thesis, Optoelectronics Research Centre/Dept. of Electronics and Computer Science, University of Southampton, Nov. 1994.
2, 213–215 (1996)
0026
Characteristics of Chirped Fiber Gratings for Dispersion Compensation SERGIO BARCELOS,∗ MICHAEL N. ZERVAS, AND RICHARD I. LAMING Optoelectronics Research Centre, University of Southampton, Southampton, SO17 1BJ, United Kingdom Received November 6, 1995
kept constant, will modify the index profile to We report a detailed characterization of the properties of a chirped fiber Bragg grating with respect to the amount of applied chirp. The results demonstrate the reflection and dispersion dependencies associated with any linearly chirped grating. The dispersion of the device tested could be continuously tuned to give a dispersion up to −2010 ps/nm. © 1996 Academic Press, Inc.
INTRODUCTION Chirped fiber Bragg gratings have recently received considerable attention due to their immense potential for use as dispersion equalizers in long haul fiber telecom links [1]. Some of their properties have been studied theoretically and demonstrated in a number of system trials [2]. We have implemented a variablechirp grating using the temperature gradient technique [3] and systematically measured its reflection and dispersion characteristics [4] for a wide range of applied chirp. The results clarify those properties and are in very good agreement with the theoretical predictions, which were calculated using coupled-mode theory applicable to nonuniform aperiodic structures [5, 6]. THE TEMPERATURE-GRADIENT TUNABLE CHIRPED FIBER GRATING The refractive index profile along a linearly chirped fiber Bragg grating is given by [5] µ ¶¸ · 2π n(z) = n 0 1 + 2h 0 cos z(1 + C z) , 30
(1)
where n 0 is the average fiber refractive index, h 0 and 30 are the amplitude and period of the refractive index modulation, C is the built-in chirp of the Bragg grating, and z is the axial distance. Applying a linear temperature gradient G [in ◦ C/mm] to this grating, with the temperature at the center of the grating (z = 0)
∗
Fax: +44 1703 593149. E-mail: [email protected].
µ ¶¸ · 2π ξG z + 2h 0 cos z(1 + (C − αG)z) , n(z) ≈ n 0 1 + n0 30 (2) where α and ξ are the expansion and the thermo-optic coefficients of the fiber. Both the grating period and the background refractive index vary linearly along the grating length and combine to induce a linear chirp in the grating [5]. The overall effect can then be represented by an effective chirp parameter Ceff = C − (ξ /2n 0 + α)G. RESULTS AND DISCUSSIONS The tested fiber grating was approximately 40 mm in length and slightly apodised at the edges, and, at room temperature (22◦ C), it had approximately 0.055 nm of built-in chirp. It was written with a frequency-doubled Excimer laser and scanning interferometer in hydrogenated standard telecommunications fiber. Linear temperature gradients were applied by mounting the grating in a 45-mm-long V-groove machined in an aluminium slab, the two ends of which were independently controlled in temperature by separate peltier elements. The center temperature was held constant at 25◦ C and the linearity of the temperature gradients was better than 3%. Figure 1 shows the measured reflectively and time delay response of the grating for different applied temperature gradients. The best-fitted straight line over the time delay and across the grating reflection bandwidth gives the mean dispersion, Dm . By applying a temperature gradient G of 13◦ C/45 mm to the grating (Fig. 1a), we were able to cancel the built-in chirp and achieve the minimum bandwidth (BW3dB = 0.036 nm) and maximum peak reflectivity (88%). In this case, the time delay does not exhibit any measurable slope over the grating bandwidth. Figure 1a also shows the calculated response of an unapodised unchirped grating of effective length l g = 36 mm and h 0 = 0.83 × 10−5 , which is in very good agreement with the experimental data. Applying a temperature gradient G = −25◦ C/45 mm (Fig. 1b) broadens the reflection spectrum to BW3dB = 0.219 nm, reduces the peak reflectivity to 29%, and induces a negative linear dispersion Dm = −1062 ps/nm. Reversing the temperature gradient to +30◦ C/45 mm (Fig. 1c) reverses the chirp and the
213 1068-5200/96 $18.00 Copyright © 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
214
BARCELOS, ZERVAS, AND LAMING
by fitting the theoretical and experimental curves and are in very good agreement with the measured values of a similar fiber [7]. Figure 2a shows that, away from the zero-chirp point, the grating bandwidth increases almost linearly with |Ceff | while the peak reflectivity drops rapidly. The mean dispersion, Dm , is observed to exhibit a 1/|Ceff | dependence, which maintains the dispersion-bandwidth product (Fig. 2b) near constant and proportional to twice the grating length. As anticipated, the total time delay difference across the grating bandwidth was found to be independent of Ceff and roughly equal to 380 ps (cf. Figs. 1b and 1c), which corresponds to the double passage of light through the fiber grating. The time delay curves were found to have linear variation across the 3-dB grating bandwidths for |Ceff | > ∼ 0.0012 m −1 , tending to become nonlinear and exhibiting stronger oscillations at the grating edges with decreasing |Ceff |. The maximum practical dispersion compensating capability of the device, observed to occur at Ceff ≈ −0.0012 m −1 , provides a useful negative slope Dm = −2010 ps/nm and 3-dB bandwidth BW3dB = 0.11 nm. FIG. 1. Measured grating power reflectivity and time delay response for three different temperature gradients G: (a) 13◦ C/45 mm (Ceff = 0), (b) −25◦ C/45 mm (Ceff = −0.0025), and (c) 30◦ C/45 mm (Ceff = +0.0011). The calculated response is also shown in (a).
mean dispersion. Spectral broadening to B3dB = 0.096 nm and decrease in the peak reflectivity to 58% are also observed (cf. Fig. 1a). Although the measured mean dispersion is increased to approximately +2270 ps/nm, the time delay response is now nonlinear across the grating bandwidth and exhibits large oscillations at the bandwidth edges. Figures 1b and 1c show that the reflectivity spectra are asymmetric, which is probably due to variations of the coupling constant along the grating length. Several different temperature gradients were studied, and the results are summarized in Fig. 2. The effective chirp parameter Ceff is given by (ξ /2n 0 + α) · (G 0 − G), where G 0 (≈ 13◦ C/45 mm) is the temperature gradient giving zero chirp. The parameters α ≈ 0.42 × 10−6 /◦ C and ξ ≈ −9.73 × 10−6 /◦ C were obtained
CONCLUSIONS We have implemented a variable-chirp fiber grating and conducted an accurate characterization of its reflectivity and time delay response for several levels of chirp. The experimental data are in very good agreement with the theoretical predictions. The reflectivity and bandwidth have a symmetric behavior, whereas the mean dispersion depends on the sign of the chirp parameter C. With increasing |C|, the grating bandwidth increases quasi-linearly and the reflectivity drops. On the other hand, the mean dispersion, which represents the dispersion experienced on average by the transmitted data in an optical transmission system, varies maintaining the dispersion-bandwidth product constant and proportional to twice the grating length. It is shown that high induced dispersion (low chirp) is accompanied by increased nonlinearity in the time delay slope, which degrades the dispersion characteristics and can be associated with BER degradation in system applications of the device, while an
FIG. 2. Measured (°), (¥) and calculated (—) 3-dB reflection bandwidth and maximum reflectivity of grating as a function of the effective chirp parameter (a) and mean dispersion as a function of the grating 3-dB reflection bandwidth (b). For the calculated data, we assumed l g = 36 mm and h 0 = 0.83 × 10−5 .
CHARACTERISTICS OF CHIRPED FIBER GRATINGS FOR DISPERSION COMPENSATION
increased chirp linearises the dispersion characteristic, but at the expense of reducing the mean dispersion. The 40-mm grating evaluated offered a practical dispersion compensating capability up to −2010 ps/nm with a 3-dB bandwidth of 0.11 nm. ACKNOWLEDGMENTS
215
[2] R. I. Laming, M. N. Zervas, S. Barcelos, M. J. Cole, L. Reekie, N. Robinson, and P. L. Scrivener, “Dispersion compensating chirped fiber gratings,” in 13th Annual Conference on European Fiber Optic Communications & Networks, invited paper, Brighton, UK, June 1995. [3] J. Lauzon, S. Thibault, J. Martin, and F. Ouellette, “Implementation and characterization of fiber Bragg gratings linearly chirped by a temperature gradient,” Opt. Lett., vol. 19, No. 23, 2027 (1994). [4] S. Barcelos, M. N. Zervas, R. I. Laming, D. N. Payne, L. Reekie, J. A. Tucknott, R. Kashyap, P. F. McKee, F. Sladen, and B. Wojciechowicz, “High accuracy dispersion measurements of chirped fiber gratings,” Electron. Lett., vol. 31, no. 15 (1995).
The authors acknowledge L. Reekie for fabricating the grating. S. Barcelos acknowledges the support of the Brazilian National Council for Science and Technology (CNPq). This work was supported by Pirelli Cavi SpA.
[5] L. Poladian, “Graphical and WKB analysis of nonuniform Bragg gratings,” Phys. Rev. E, vol. 48, no. 4, 4758 (1993).
REFERENCES
[6] J. E. Sipe, L. Poladian, and C. M. de Sterke, “Propagation through nonuniform grating structures,” J. Opt. Soc. Am. A, vol. 11, no. 4, 1307 (1994).
[1] F. Ouellette, “All-fiber filter for efficient dispersion compensation,” Opt. Lett., vol. 16, no. 5, 303 (1991).
[7] J.-L. Archambault, “Photorefractive gratings in optical fibers,” Ph.D. Thesis, Optoelectronics Research Centre/Dept. of Electronics and Computer Science, University of Southampton, Nov. 1994.