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Tunable chirped fiber Bragg grating based on the D-shaped fiber
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Optics Communications 281 (2008) 2077–2082 www.elsevier.com/locate/optcom
Tunable chirped fiber Bragg grating based on the D-shaped fiber Jinlong Zhou a, Xiaopeng Dong a,b,*, Zhidong Shi b a
Institute of Lightwave Technology, School of Information Science and Technology, Xiamen University, Xiamen, Fujian 361005, China b Shanghai Key Lab of Specialty Fiber Optics, Shanghai University, Shanghai 208100, China Received 18 September 2007; received in revised form 26 November 2007; accepted 9 December 2007
Abstract A novel tunable chirped fiber Bragg grating is realized by bending a piece of D-shaped fiber Bragg grating into a specific shape like the character ‘X’. The principle of tuning is demonstrated by numerical simulation. The dispersion of the grating can be tuned while the center wavelength is kept nearly no shift. The experimental results match well with the numerical analysis. The influence from D-shaped fiber’s birefringence and polarization dependent loss is discussed theoretically and experimentally as well. This proposed tuning technique has potential applications in the optical communications and other fiber optics systems. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Chirped fiber Bragg grating (CFBG) has been intensively studied for the compensation of chromatic dispersion in optical communications owing to its tunability, compatibility, low cost, etc. Generally, the dispersion of the CFBG can be tuned by temperature or strain. For example, Eggleton et al. deposited the metallic film with gradient thickness onto a uniform FBG. The film generated gradient temperature when it was applied electric current through [1]. Gradient strain could be generated in the grating with the help of a tapered cantilever [2] or a piezoelectric stack [3]. However, the center wavelength is changed simultaneously when the dispersion is tuned with such schemes, which will cause severe problems in the wavelength-division multiplexing (WDM) systems. Several improved methods [4–8] with various center wavelength shifts from 0.1 nm to 0.03 nm have been reported. All of them base on the principle of locating the center of the grating at the zero-strain
* Corresponding author. Address: Institute of Lightwave Technology, School of Information Science and Technology, Xiamen University, Xiamen, Fujian 361005, China. E-mail address: [email protected] (X. Dong).
0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.12.041
point and chirping the grating by gradient strain. However, because of the glue’s creep deformation and the mechanical difference between the materials of the beam and the optical fiber, sticking the grating on the hard surface of a beam or a rod with glue may cause ununiformity of the chirp, which will result in center wavelength shift and relatively high group delay ripple (GDR) in the dispersion spectrum. In this letter, we propose a tunable CFBG scheme by bending a piece of D-shaped fiber (D-fiber) grating into the ‘X’ shape. Since the D-fiber’s cross section is not circularly symmetrical, gradient longitudinal strain can be generated in the fiber core [9], thus the grating is chirped. The dispersion of such CFBG can be tuned by adjusting the curvature, while the center wavelength shift is kept nearly unchanged (less than 17 pm in our experiment) by locating the center of the initial uniform grating at the zero-strain point. Since in this scheme it is not necessary to stick the grating on any beam with glue, there should be no uniformity and center wavelength shift problem compared with previous schemes. Another advantage is its compact structure, which is important for the integrated optical devices and components. In the following parts, firstly, we analyze the strain distribution in the bent D-fiber theoretically with material mechanics. Secondly, the CFBG’s dispersion and reflection spectra under different bending are numerically simulated. Thirdly, the experimen-
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J. Zhou et al. / Optics Communications 281 (2008) 2077–2082
tal results are presented and discussed. Finally, the influence from D-fiber’s birefringence and polarization dependent loss is discussed. 2. Longitudinal strain distribution of the bent D-fiber As shown in Fig. 1, one end of the D-fiber is mounted on a fixed stage, and the other end is mounted on a horizontally moveable translation stage. The D-fiber can be bent into ‘X’ shape when the translation stage is moved towards the fixed stage. According to the material mechanics, the neutral layer denotes the layer neither stretched nor compressed when the fiber is bent. To generate maximum longitudinal strain, the flat surface of the D-fiber is kept parallel to the neutral layer as shown in Fig. 2. The longitudinal strain, e, can be written as [10]: y e¼ ð1Þ q where q is the curvature radius, and y is the distance between the core center and the centroid as indicated in Fig. 2c, which is derived in Appendix A: cos arcsin dr þ 13 cos 3 arcsin dr y¼r ð2Þ p þ 2 arcsin dr þ sin 2 arcsin dr where r is the cladding radius, d is the distance between the core center and the flat surface of the D-fiber. From (1), it is obvious that if the curvature radius is kept no change, the strain will increase with y. So, the parameter y can be regarded as the D-fiber’s strain sensitivity vs the curvature. According to the analysis in [11], the local flexibility of the bent fiber, m(z), can be written as d 2pz 1 cos vðzÞ ¼ ð3Þ 2 L DL where d, L, and DL represent, respectively, the maximum flexibility, the total length of the D-fiber, and the moving distance of the translation stage as indicated in Fig. 1. Since the Young’s modulus of fused silica is as high as 7.2 1010 Pa, it is reasonable to assume that L is a constant during the bending process. As a result, the integral of the flexibility curve can be approximated to the fiber length: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Z LDL dv 1þ dz L ð4Þ dz 0
Fig. 2. Different bending of the D-fiber (a) towards the flat surface (b) against the flat surface (c) cross section of the D-fiber.
Therefore, d can be derived from (4) as the function of DL. Furthermore, the relationship between m(z) and DL can be obtained from Eq. (3). With the help of m(z) and (1), the longitudinal strain distribution can be obtained: 1 eðzÞ ¼ y ¼ y qz
d2 v dz2
2 3=2 1 þ dv dz p 2 2pz 2d LDL cos LDL ¼y dp 3=2 2pz 2 1 þ LDL sin LDL
ð5Þ
The D-fiber used in the experiment was designed and manufactured by ourselves. Its parameters are given as follows: L = 86 mm, r = 63.5 lm and d = 17.6 lm. y = 17.86 lm can be obtained from (2). The strain distribution with different DL can be calculated from (5) and the results are plotted in Fig. 3. By locating the center of the initial grating at the zero-strain point (L/4 or 3L/4), gradient strain form positive to negative value can be built along the grating, so, the uniform grating will become chirped. Since the center of the grating is neither stretched nor compressed, the center wavelength of the CFBG can be kept no shift. Furthermore, the dispersion of the CFBG can be tuned simply by adjusting the moving distance of the translation stage, DL. 3. Simulation of the spectrum and dispersion of the tunable CFBG The characteristics of the bent CFBG can be simulated with the software FOGS-BG which is produced by Apollo
Fig. 1. Scheme of the working principle of the tunable CFBG based on the D-fiber.
J. Zhou et al. / Optics Communications 281 (2008) 2077–2082
Fig. 3. Longitudinal strain distribution of the bent D-fiber with different DL.
Photonics Inc. in Canada. The practical parameters of the D-fiber grating are chosen in the simulation, which are given as follows: D-fiber’s total length L = 86 mm, initial grating length l = 28 mm, period K = 527.2 nm, without apodization, effective refractive index neff = 1.467, and UV-induced index change dn = 1.4 104. The simulated results are summarized in Table 1. When DL is increased from 0.25 mm to 12 mm, the bandwidth of the CFBG is changed from 0.347 nm to 2.133 nm, while the center wavelength change is kept within 5 pm. The dispersion can be tuned from 925.5 ps/nm to 130.1 ps/nm. The reflection spectra and group delays with different DL are shown in Figs. 4 and 5a, respectively. The relatively big group delay ripples (GDR) are due to non-apodization in the grating. Here, the GDR is defined as the difference between the group delay and the straight line fitting within the 1-dB bandwidth. The ripples can be eliminated by introducing Gaussian-shape apodization as shown in Fig. 5b. From Fig. 3, it can be seen that around the position of L/4 the strain distribution is not perfectly linear, which will result in nonlinearity in the group delay profile. The non-
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Fig. 4. Simulated reflection spectra of the CFBG with different DL.
linearity increases with DL. For example, the nonlinear amplitude reaches about 5 ps when DL = 12 mm, as shown in the inset of Fig. 5b. Owing to the nonlinear effect in such CFBG, its linear bandwidth will be limited. However, one could also make use of such effect to compensate highorder dispersion by careful design and control of the bending. 4. Experimental results In the experiment, a piece of D-fiber with 86 mm in length was mounted as shown in Fig. 1. A uniform Bragg grating with 28 mm in length was inscribed in the D-fiber. According to the analysis above, the center of this grating was carefully located at the position of 21.5 mm (L/4) from the left end of the D-fiber before bending. A broadband source (BBS) at 1550 nm was used in the experiment, and the spectrum of the light reflected from the bent CFBG was measured with the optical spectrum analyzer (OSA, AQ6317B). The translation stage was moved with the precision of 62.5 lm. During the experiment the temperature of the grating is kept no change to avoid its influence on the wavelength measurement.
Table 1 Simulated results obtained with different DL DL (mm)
Center wavelength (nm)
Bandwidth (Bsim) (nm)
Dispersion ps (nm)
0.25 0.5 1 1.5 2 3 4 5 6 7 8 10 12
1546.752 1546.752 1546.752 1546.753 1546.753 1546.75 1546.751 1546.750 1546.751 1546.751 1546.75 1546.748 1546.753
0.347 0.450 0.580 0.697 0.799 0.974 1.132 1.280 1.415 1.535 1.650 1.899 2.133
925.5 613.4 462.9 371.7 330.1 268.4 233.6 210 192.9 177.8 165.7 144.1 130.1
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J. Zhou et al. / Optics Communications 281 (2008) 2077–2082 Table 2 Experimental results obtained with different DL DL (mm)
Center wavelength (nm)
Bandwidth (Bexp) (nm)
Bandwidth errora (%)
0.25 0.5 1 1.5 2 3 4 5 6 7 8 10 12
1546.762 1546.757 1546.756 1546.756 1546.758 1546.754 1546.757 1546.750 1546.749 1546.749 1546.751 1546.746 1546.745
0.299 0.407 0.569 0.685 0.805 0.998 1.156 1.293 1.426 1.547 1.657 1.878 2.057
13.8 9.6 1.9 1.8 0.8 2.5 2.1 1 0.8 0.8 0.4 1.1 3.6
a
Error = jBexp Bsimj/Bsim 100%.
17 pm while the bandwidth of the spectrum has changed significantly from 0.299 nm to 2.057 nm, when the translation stage moved from 0.25 mm to 12 mm. The relative errors of the bandwidths are within 3.6% when DL > 1 mm. The dispersion of the CFBG has not been measured because of the lack of the instruments. By comparing Table 2 with Table 1, it can be seen that the experimental results match well with the simulated data. The discrepancy between them is mainly attributed to the imperfection of the fiber and bending. The tuning range of the bandwidth and dispersion of this CFBG are limited by the length of the grating currently we can fabricate in the laboratory. With longer length of CFBG and improved grating writing technique, larger tunable CFBG with better specifications can be obtained. Fig. 5. Simulated group delay of the CFBG with different DL, inset is the GDR, (a) without apodization, (b) with Gaussian-shape apodization.
The measured reflection spectra of the tunable CFBG at different moving distances are shown in Fig. 6, and the data of center wavelengths and bandwidths are given in Table 2. The variation of the center wavelength can be kept within
Fig. 6. Experimental reflection spectra of the CFBG with different DL.
5. Discussion and conclusions Since the cross section of the D-fiber is deviated from the circular symmetry of conventional single mode fiber, the resulted birefringence and polarization dependent loss (PDL) of such fiber should be estimated and discussed. We have numerically calculated and experimentally measured the birefringence and PDL of the D-fiber used in the experiment. The calculated variation of the birefringence of D-fiber with different wavelength is shown in Fig. 7. The parameters used in the calculation are close to our practical Dfiber, which are given as follows: the radius of cladding and core are 63.5 lm and 4.5 lm, respectively; the distance between the core center and the flat surface is 17.6 lm; the refractive index of the core, cladding, and the surrounding materials are 1.467, 1.46, and 1.0, respectively. From Fig. 7, we can find that the birefringence is in the order of 107, which should have little influence on the characteristics of the gratings. To verify above theoretical analysis on the birefringence of D-fiber, we also measured the birefringence and PDL of such D-fiber by Mueller matrix method [12] with the instru-
J. Zhou et al. / Optics Communications 281 (2008) 2077–2082
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Fig. 7. Calculated birefringence of the D-fiber.
Fig. 9. Birefringence and PDL of the D-fiber measured by the Mueller matrix method.
Acknowledgements The authors would like to thank the financial supports of the ‘985’ Project of Xiamen University, the Key Disciplinary Development Program of Shanghai (T0102), and the Natural Science Foundation of China under Grant Nos. 60177026, 60777031. Fig. 8. Experimental measurement of the birefringence and PDL of the Dfiber.
ments of tunable laser (MG9638A) and the polarimeter (TXP5004) as shown in Fig. 8. The measured data are plotted in Fig. 9. From Fig. 9, we can see that the measured birefringence is below 5.5 107, which agrees with the theoretic calculation. The measured PDL is less than 0.8 dB/m corresponding to 0.05 dB for the length of 86 mm of the D-fiber used in the experiment. So, with the practical parameters of such D-fiber, the birefringence and PDL should have little effect on the characteristics of the tunable CFBG. In conclusion, we have demonstrated theoretically and experimentally a novel tunable CFBG by bending a piece of uniform D-fiber grating into the specific shape. The problem of center wavelength shift can be overcome by properly locating the center of the grating at the quarter length of the D-fiber. The experimental results agree well with the theoretical analysis. The proposed tunable CFBG, which is simple, easy to implement, and capable of tuning both of the bandwidth and dispersion dynamically in a large range, should have potential applications in optical communications and other fiber optics devices and systems.
Appendix A In this appendix, the distance between the core center and the centroid, Eq. (2), will be discussed. The cross section of D-fiber can be created in x–y plane of a Cartesian coordinates shown in Fig. A1. The centroid is denoted by (xc, yc), and the cladding radius, the distance between the core center and the flat surface, are r and d. The position of the centroid is given as [9]:
Fig. A1. Cross section of the D-fiber.
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R xc ¼
A
x dA ; A
R yc ¼
A
y dA A
ðA:1Þ
where A is the area of the cross section. xc = 0 can be obtained directly because the cross section is symmetrical about the y-axis. The surface area element can be written as pffiffiffiffiffiffiffiffiffiffiffiffiffiffi dA ¼ 2 r2 y 2 dy ðA:2Þ Since y = rsin h, (A.2) will be rewritten as ðA:3Þ dA ¼ 2r2 cos2 h dh Thus, Z Z p2 y dA ¼ 2r3 sin h cos2 h dh A
h0 3
r ¼ 2
1 cos h0 þ cos 3h0 3
ðA:4Þ
where h0 ¼ arcsin dr . The area of the cross section can be calculated as 1 2 p þ j h0 j þ jsin 2h0 j A¼r ðA:5Þ 2 2 From (A.4) and (A.5), the y-position of the centroid in (A.1) can be rewritten as cos h0 þ 13 cos 3h0 ðA:6Þ yc ¼ r p þ 2 j h0 j þ j sin 2h0 j
Consequently, the distance between the core center and the centroid, y, can be obtained.
References [1] B.J. Eggleton, J.A. Rogers, P.S. Westbrook, T.A. Strasser, IEEE Photon. Technol. Lett. 11 (1999) 854. [2] M.L. Blanc, S.Y. Huang, M.M. Ohn, R.M. Measures, Electron. Lett. 30 (1994) 2163. [3] M.M. Ohn, A.T. Alavie, R. Maaskant, M.G. Xu, F. Bilodeau, K.O. Hill, Electron. Lett. 32 (1996) 2000. [4] T. Imai, T. Komukai, M. Nakazawa, IEEE Photon. Technol. Lett. 10 (1998) 845. [5] X.Y. Dong, B.O. Guan, S.Z. Yuan, X.Y. Dong, H.Y. Tam, Opt. Commun. 202 (2002) 91. [6] W.G. Zhang, Y.G. Liu, G.Y. Kai, Q.D. Zhao, S.Z. Yuan, X.Y. Dong, Opt. Commun. 216 (2003) 343. [7] J. Kim, J. Bae, Y. Han, S.H. Kim, J. Jeong, S.B. Lee, IEEE Photon. Technol. Lett. 16 (2004) 849. [8] J. Kwon, B. Lee, IEEE Photon. Technol. Lett. 17 (2005) 408. [9] J.L. Zhou, X.P. Dong, Z.D. Shi, Acta Photonica Sinica 35 (2006) 1734. [10] C.P. Zheng, Mechanics of Materials, Beijing University of Technology Publisher, Beijing, 1993. [11] Y.G. Luo, L.X. Gao, G.L. Liu, Theory of Material Mechanics, Science Press of China, Beijing, 2004. [12] H. Dong, P. Shum, J.Q. Zhou, G.X. Ning, Y.D. Gong, C.Q. Wu, Opt. Express 14 (2006) 5067.
Optics Communications 281 (2008) 2077–2082 www.elsevier.com/locate/optcom
Tunable chirped fiber Bragg grating based on the D-shaped fiber Jinlong Zhou a, Xiaopeng Dong a,b,*, Zhidong Shi b a
Institute of Lightwave Technology, School of Information Science and Technology, Xiamen University, Xiamen, Fujian 361005, China b Shanghai Key Lab of Specialty Fiber Optics, Shanghai University, Shanghai 208100, China Received 18 September 2007; received in revised form 26 November 2007; accepted 9 December 2007
Abstract A novel tunable chirped fiber Bragg grating is realized by bending a piece of D-shaped fiber Bragg grating into a specific shape like the character ‘X’. The principle of tuning is demonstrated by numerical simulation. The dispersion of the grating can be tuned while the center wavelength is kept nearly no shift. The experimental results match well with the numerical analysis. The influence from D-shaped fiber’s birefringence and polarization dependent loss is discussed theoretically and experimentally as well. This proposed tuning technique has potential applications in the optical communications and other fiber optics systems. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Chirped fiber Bragg grating (CFBG) has been intensively studied for the compensation of chromatic dispersion in optical communications owing to its tunability, compatibility, low cost, etc. Generally, the dispersion of the CFBG can be tuned by temperature or strain. For example, Eggleton et al. deposited the metallic film with gradient thickness onto a uniform FBG. The film generated gradient temperature when it was applied electric current through [1]. Gradient strain could be generated in the grating with the help of a tapered cantilever [2] or a piezoelectric stack [3]. However, the center wavelength is changed simultaneously when the dispersion is tuned with such schemes, which will cause severe problems in the wavelength-division multiplexing (WDM) systems. Several improved methods [4–8] with various center wavelength shifts from 0.1 nm to 0.03 nm have been reported. All of them base on the principle of locating the center of the grating at the zero-strain
* Corresponding author. Address: Institute of Lightwave Technology, School of Information Science and Technology, Xiamen University, Xiamen, Fujian 361005, China. E-mail address: [email protected] (X. Dong).
0030-4018/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.12.041
point and chirping the grating by gradient strain. However, because of the glue’s creep deformation and the mechanical difference between the materials of the beam and the optical fiber, sticking the grating on the hard surface of a beam or a rod with glue may cause ununiformity of the chirp, which will result in center wavelength shift and relatively high group delay ripple (GDR) in the dispersion spectrum. In this letter, we propose a tunable CFBG scheme by bending a piece of D-shaped fiber (D-fiber) grating into the ‘X’ shape. Since the D-fiber’s cross section is not circularly symmetrical, gradient longitudinal strain can be generated in the fiber core [9], thus the grating is chirped. The dispersion of such CFBG can be tuned by adjusting the curvature, while the center wavelength shift is kept nearly unchanged (less than 17 pm in our experiment) by locating the center of the initial uniform grating at the zero-strain point. Since in this scheme it is not necessary to stick the grating on any beam with glue, there should be no uniformity and center wavelength shift problem compared with previous schemes. Another advantage is its compact structure, which is important for the integrated optical devices and components. In the following parts, firstly, we analyze the strain distribution in the bent D-fiber theoretically with material mechanics. Secondly, the CFBG’s dispersion and reflection spectra under different bending are numerically simulated. Thirdly, the experimen-
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J. Zhou et al. / Optics Communications 281 (2008) 2077–2082
tal results are presented and discussed. Finally, the influence from D-fiber’s birefringence and polarization dependent loss is discussed. 2. Longitudinal strain distribution of the bent D-fiber As shown in Fig. 1, one end of the D-fiber is mounted on a fixed stage, and the other end is mounted on a horizontally moveable translation stage. The D-fiber can be bent into ‘X’ shape when the translation stage is moved towards the fixed stage. According to the material mechanics, the neutral layer denotes the layer neither stretched nor compressed when the fiber is bent. To generate maximum longitudinal strain, the flat surface of the D-fiber is kept parallel to the neutral layer as shown in Fig. 2. The longitudinal strain, e, can be written as [10]: y e¼ ð1Þ q where q is the curvature radius, and y is the distance between the core center and the centroid as indicated in Fig. 2c, which is derived in Appendix A: cos arcsin dr þ 13 cos 3 arcsin dr y¼r ð2Þ p þ 2 arcsin dr þ sin 2 arcsin dr where r is the cladding radius, d is the distance between the core center and the flat surface of the D-fiber. From (1), it is obvious that if the curvature radius is kept no change, the strain will increase with y. So, the parameter y can be regarded as the D-fiber’s strain sensitivity vs the curvature. According to the analysis in [11], the local flexibility of the bent fiber, m(z), can be written as d 2pz 1 cos vðzÞ ¼ ð3Þ 2 L DL where d, L, and DL represent, respectively, the maximum flexibility, the total length of the D-fiber, and the moving distance of the translation stage as indicated in Fig. 1. Since the Young’s modulus of fused silica is as high as 7.2 1010 Pa, it is reasonable to assume that L is a constant during the bending process. As a result, the integral of the flexibility curve can be approximated to the fiber length: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Z LDL dv 1þ dz L ð4Þ dz 0
Fig. 2. Different bending of the D-fiber (a) towards the flat surface (b) against the flat surface (c) cross section of the D-fiber.
Therefore, d can be derived from (4) as the function of DL. Furthermore, the relationship between m(z) and DL can be obtained from Eq. (3). With the help of m(z) and (1), the longitudinal strain distribution can be obtained: 1 eðzÞ ¼ y ¼ y qz
d2 v dz2
2 3=2 1 þ dv dz p 2 2pz 2d LDL cos LDL ¼y dp 3=2 2pz 2 1 þ LDL sin LDL
ð5Þ
The D-fiber used in the experiment was designed and manufactured by ourselves. Its parameters are given as follows: L = 86 mm, r = 63.5 lm and d = 17.6 lm. y = 17.86 lm can be obtained from (2). The strain distribution with different DL can be calculated from (5) and the results are plotted in Fig. 3. By locating the center of the initial grating at the zero-strain point (L/4 or 3L/4), gradient strain form positive to negative value can be built along the grating, so, the uniform grating will become chirped. Since the center of the grating is neither stretched nor compressed, the center wavelength of the CFBG can be kept no shift. Furthermore, the dispersion of the CFBG can be tuned simply by adjusting the moving distance of the translation stage, DL. 3. Simulation of the spectrum and dispersion of the tunable CFBG The characteristics of the bent CFBG can be simulated with the software FOGS-BG which is produced by Apollo
Fig. 1. Scheme of the working principle of the tunable CFBG based on the D-fiber.
J. Zhou et al. / Optics Communications 281 (2008) 2077–2082
Fig. 3. Longitudinal strain distribution of the bent D-fiber with different DL.
Photonics Inc. in Canada. The practical parameters of the D-fiber grating are chosen in the simulation, which are given as follows: D-fiber’s total length L = 86 mm, initial grating length l = 28 mm, period K = 527.2 nm, without apodization, effective refractive index neff = 1.467, and UV-induced index change dn = 1.4 104. The simulated results are summarized in Table 1. When DL is increased from 0.25 mm to 12 mm, the bandwidth of the CFBG is changed from 0.347 nm to 2.133 nm, while the center wavelength change is kept within 5 pm. The dispersion can be tuned from 925.5 ps/nm to 130.1 ps/nm. The reflection spectra and group delays with different DL are shown in Figs. 4 and 5a, respectively. The relatively big group delay ripples (GDR) are due to non-apodization in the grating. Here, the GDR is defined as the difference between the group delay and the straight line fitting within the 1-dB bandwidth. The ripples can be eliminated by introducing Gaussian-shape apodization as shown in Fig. 5b. From Fig. 3, it can be seen that around the position of L/4 the strain distribution is not perfectly linear, which will result in nonlinearity in the group delay profile. The non-
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Fig. 4. Simulated reflection spectra of the CFBG with different DL.
linearity increases with DL. For example, the nonlinear amplitude reaches about 5 ps when DL = 12 mm, as shown in the inset of Fig. 5b. Owing to the nonlinear effect in such CFBG, its linear bandwidth will be limited. However, one could also make use of such effect to compensate highorder dispersion by careful design and control of the bending. 4. Experimental results In the experiment, a piece of D-fiber with 86 mm in length was mounted as shown in Fig. 1. A uniform Bragg grating with 28 mm in length was inscribed in the D-fiber. According to the analysis above, the center of this grating was carefully located at the position of 21.5 mm (L/4) from the left end of the D-fiber before bending. A broadband source (BBS) at 1550 nm was used in the experiment, and the spectrum of the light reflected from the bent CFBG was measured with the optical spectrum analyzer (OSA, AQ6317B). The translation stage was moved with the precision of 62.5 lm. During the experiment the temperature of the grating is kept no change to avoid its influence on the wavelength measurement.
Table 1 Simulated results obtained with different DL DL (mm)
Center wavelength (nm)
Bandwidth (Bsim) (nm)
Dispersion ps (nm)
0.25 0.5 1 1.5 2 3 4 5 6 7 8 10 12
1546.752 1546.752 1546.752 1546.753 1546.753 1546.75 1546.751 1546.750 1546.751 1546.751 1546.75 1546.748 1546.753
0.347 0.450 0.580 0.697 0.799 0.974 1.132 1.280 1.415 1.535 1.650 1.899 2.133
925.5 613.4 462.9 371.7 330.1 268.4 233.6 210 192.9 177.8 165.7 144.1 130.1
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J. Zhou et al. / Optics Communications 281 (2008) 2077–2082 Table 2 Experimental results obtained with different DL DL (mm)
Center wavelength (nm)
Bandwidth (Bexp) (nm)
Bandwidth errora (%)
0.25 0.5 1 1.5 2 3 4 5 6 7 8 10 12
1546.762 1546.757 1546.756 1546.756 1546.758 1546.754 1546.757 1546.750 1546.749 1546.749 1546.751 1546.746 1546.745
0.299 0.407 0.569 0.685 0.805 0.998 1.156 1.293 1.426 1.547 1.657 1.878 2.057
13.8 9.6 1.9 1.8 0.8 2.5 2.1 1 0.8 0.8 0.4 1.1 3.6
a
Error = jBexp Bsimj/Bsim 100%.
17 pm while the bandwidth of the spectrum has changed significantly from 0.299 nm to 2.057 nm, when the translation stage moved from 0.25 mm to 12 mm. The relative errors of the bandwidths are within 3.6% when DL > 1 mm. The dispersion of the CFBG has not been measured because of the lack of the instruments. By comparing Table 2 with Table 1, it can be seen that the experimental results match well with the simulated data. The discrepancy between them is mainly attributed to the imperfection of the fiber and bending. The tuning range of the bandwidth and dispersion of this CFBG are limited by the length of the grating currently we can fabricate in the laboratory. With longer length of CFBG and improved grating writing technique, larger tunable CFBG with better specifications can be obtained. Fig. 5. Simulated group delay of the CFBG with different DL, inset is the GDR, (a) without apodization, (b) with Gaussian-shape apodization.
The measured reflection spectra of the tunable CFBG at different moving distances are shown in Fig. 6, and the data of center wavelengths and bandwidths are given in Table 2. The variation of the center wavelength can be kept within
Fig. 6. Experimental reflection spectra of the CFBG with different DL.
5. Discussion and conclusions Since the cross section of the D-fiber is deviated from the circular symmetry of conventional single mode fiber, the resulted birefringence and polarization dependent loss (PDL) of such fiber should be estimated and discussed. We have numerically calculated and experimentally measured the birefringence and PDL of the D-fiber used in the experiment. The calculated variation of the birefringence of D-fiber with different wavelength is shown in Fig. 7. The parameters used in the calculation are close to our practical Dfiber, which are given as follows: the radius of cladding and core are 63.5 lm and 4.5 lm, respectively; the distance between the core center and the flat surface is 17.6 lm; the refractive index of the core, cladding, and the surrounding materials are 1.467, 1.46, and 1.0, respectively. From Fig. 7, we can find that the birefringence is in the order of 107, which should have little influence on the characteristics of the gratings. To verify above theoretical analysis on the birefringence of D-fiber, we also measured the birefringence and PDL of such D-fiber by Mueller matrix method [12] with the instru-
J. Zhou et al. / Optics Communications 281 (2008) 2077–2082
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Fig. 7. Calculated birefringence of the D-fiber.
Fig. 9. Birefringence and PDL of the D-fiber measured by the Mueller matrix method.
Acknowledgements The authors would like to thank the financial supports of the ‘985’ Project of Xiamen University, the Key Disciplinary Development Program of Shanghai (T0102), and the Natural Science Foundation of China under Grant Nos. 60177026, 60777031. Fig. 8. Experimental measurement of the birefringence and PDL of the Dfiber.
ments of tunable laser (MG9638A) and the polarimeter (TXP5004) as shown in Fig. 8. The measured data are plotted in Fig. 9. From Fig. 9, we can see that the measured birefringence is below 5.5 107, which agrees with the theoretic calculation. The measured PDL is less than 0.8 dB/m corresponding to 0.05 dB for the length of 86 mm of the D-fiber used in the experiment. So, with the practical parameters of such D-fiber, the birefringence and PDL should have little effect on the characteristics of the tunable CFBG. In conclusion, we have demonstrated theoretically and experimentally a novel tunable CFBG by bending a piece of uniform D-fiber grating into the specific shape. The problem of center wavelength shift can be overcome by properly locating the center of the grating at the quarter length of the D-fiber. The experimental results agree well with the theoretical analysis. The proposed tunable CFBG, which is simple, easy to implement, and capable of tuning both of the bandwidth and dispersion dynamically in a large range, should have potential applications in optical communications and other fiber optics devices and systems.
Appendix A In this appendix, the distance between the core center and the centroid, Eq. (2), will be discussed. The cross section of D-fiber can be created in x–y plane of a Cartesian coordinates shown in Fig. A1. The centroid is denoted by (xc, yc), and the cladding radius, the distance between the core center and the flat surface, are r and d. The position of the centroid is given as [9]:
Fig. A1. Cross section of the D-fiber.
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R xc ¼
A
x dA ; A
R yc ¼
A
y dA A
ðA:1Þ
where A is the area of the cross section. xc = 0 can be obtained directly because the cross section is symmetrical about the y-axis. The surface area element can be written as pffiffiffiffiffiffiffiffiffiffiffiffiffiffi dA ¼ 2 r2 y 2 dy ðA:2Þ Since y = rsin h, (A.2) will be rewritten as ðA:3Þ dA ¼ 2r2 cos2 h dh Thus, Z Z p2 y dA ¼ 2r3 sin h cos2 h dh A
h0 3
r ¼ 2
1 cos h0 þ cos 3h0 3
ðA:4Þ
where h0 ¼ arcsin dr . The area of the cross section can be calculated as 1 2 p þ j h0 j þ jsin 2h0 j A¼r ðA:5Þ 2 2 From (A.4) and (A.5), the y-position of the centroid in (A.1) can be rewritten as cos h0 þ 13 cos 3h0 ðA:6Þ yc ¼ r p þ 2 j h0 j þ j sin 2h0 j
Consequently, the distance between the core center and the centroid, y, can be obtained.
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