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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 26 — Dec. 24, 2007
  • pp: 17645–17651
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Light coupling between two parallel CO2-laser written long-period fiber gratings

Yunqi Liu, Kin Seng Chiang, Yun Jiang Rao, Zeng Ling Ran, and Tao Zhu  »View Author Affiliations


Optics Express, Vol. 15, Issue 26, pp. 17645-17651 (2007)
http://dx.doi.org/10.1364/OE.15.017645


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Abstract

We demonstrate experimentally the light coupling effects between two parallel CO2-laser written long-period fiber gratings. For gratings written in standard single-mode fibers, the coupling efficiency depends strongly on the fiber orientation with the strongest coupling obtained when the exposed sides of the fibers face each other, while for gratings written in boron-doped fibers, the coupling efficiency is independent of the fiber orientation. We achieve a peak coupling efficiency of ~86% with gratings written in boron-doped fibers by using a suitable surrounding refractive index and offset distance between the two gratings. Our results suggest the possibility of realizing efficient broadband all-fiber couplers with CO2-laser written long-period fiber gratings.

© 2007 Optical Society of America

1. Introduction

A long-period fiber grating (LPFG) formed in a single-mode fiber (SMF) enables light coupling from the guided mode to selected cladding modes at specific wavelengths and is intrinsically a band-rejection filter [1

1. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996). [CrossRef]

]. To enhance the functionality of LPFGs, the structure of two parallel LPFGs has been proposed as a broadband optical coupler or optical add/drop multiplexer (OADM) for application in coarse wavelength division multiplexing (CWDM) systems [2

2. K. S. Chiang, Y. Liu, M. N. Ng, and S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000). [CrossRef]

6

6. Y. H. Han, S. B. Lee, C. S. Kim, and M. Y. Jeong, “Tunable optical add-drop multiplexer based on long-period fiber gratings for coarse wavelength division multiplexing systems,” Opt. Lett. 31, 703–705 (2006). [CrossRef] [PubMed]

], where light launched into one fiber is coupled into the other fiber through evanescent-field coupling between the cladding modes of the two parallel gratings. Recently, an optical coupler with an exceptionally large bandwidth (> 100 nm) has been realized by using two parallel specially designed gratings [7

7. M. J. Kim, Y. M. Jung, B. H. Kim, W. T. Han, and B. H. Lee, “Ultra-wide bandpass filter based on long-period fiber gratings and the evanescent field coupling between two fiber,” Opt. Express 15, 10855–10862 (2007). [CrossRef] [PubMed]

]. The coupling efficiencies that have been achieved with two parallel gratings are 50–65% [5

5. K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22, 1358–1366 (2004). [CrossRef]

7

7. M. J. Kim, Y. M. Jung, B. H. Kim, W. T. Han, and B. H. Lee, “Ultra-wide bandpass filter based on long-period fiber gratings and the evanescent field coupling between two fiber,” Opt. Express 15, 10855–10862 (2007). [CrossRef] [PubMed]

]. Using the structure of three parallel gratings, a six-port balanced coupler with a coupling efficiency of 85% [8

8. Y. Liu and K. S. Chiang, “Broadband optical coupler based on evanescent-field coupling between three parallel long-period fiber gratings,” IEEE Photon. Technol. Lett. 18, 229–231 (2006). [CrossRef]

] and a symmetric 3×3 power distributor with a total power throughput of 72% [9

9. Y. Liu, K. S. Chiang, and Q. Liu, “Symmetric 3×3 optical coupler using three parallel long-period fiber gratings,” Opt. Express 15, 6494–6499 (2007). [CrossRef] [PubMed]

] have been demonstrated. All these demonstrated couplers [2

2. K. S. Chiang, Y. Liu, M. N. Ng, and S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000). [CrossRef]

9

9. Y. Liu, K. S. Chiang, and Q. Liu, “Symmetric 3×3 optical coupler using three parallel long-period fiber gratings,” Opt. Express 15, 6494–6499 (2007). [CrossRef] [PubMed]

] employ gratings written by the conventional ultraviolet (UV) technique [1

1. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996). [CrossRef]

]. Over the years, there has been a number of non-UV techniques developed for the fabrication of LPFGs, such as the femosecond-pulse irradiation technique [10

10. Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. Kazansky, and K. Hirao, “Fabrication of long-period fibre gratings by focused irradiation of infrared femtosecond laser pulses,” Opt. Lett. 24, 646–648 (1999). [CrossRef]

], the electric-discharge writing technique [11

11. G. Rego, O. Okhotnikov, E. Dianov, and V. Sulimov, “High-temperature stability of long-period fibre gratings using an electric arc,” J. Lightwave Technol. , 19, 1574–1579 (2001). [CrossRef]

], and different versions of the CO2-laser writing technique [12

12. D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser beams,” Electron. Lett. 34, 302–303 (1998). [CrossRef]

15

15. V. Grubsky and J. Feinberg, “Rewritable densification gratings in boron-doped fibers,” Opt. Lett. 30, 1279–1281 (2005). [CrossRef] [PubMed]

]. In this paper, we study experimentally the light coupling effects between two parallel LPFGs written by high-frequency CO2-laser pulses [14

14. Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, “Novel fiber-optic sensors based on the long-period fiber grating written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21, 1320–1327 (2003). [CrossRef]

]. Compared with the UV-writing technique, the CO2-laser writing technique is much more flexible, as it can be applied to practically any untreated glass fibers and the writing process can be computer-programmed to produce complicated grating profiles without using any masks. The primary objective of our study is to confirm whether efficient couplers can be realized with such CO2-laser written LPFGs. We study two kinds of fibers, a standard telecommunication SMF and a boron-doped SMF. We find that the light coupling effects between the LPFGs written in these two kinds of fibers are very different. For gratings written in the standard SMF, the coupling efficiency depends strongly on the fiber orientation, while for gratings written in the boron-doped fiber, the coupling efficiency is independent of the fiber orientation. We obtained a record-high coupling efficiency of ~86% using gratings written in the boron-doped fiber. LPFG couplers have emerged as a new class of all-fiber broadband couplers [2

2. K. S. Chiang, Y. Liu, M. N. Ng, and S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000). [CrossRef]

9

9. Y. Liu, K. S. Chiang, and Q. Liu, “Symmetric 3×3 optical coupler using three parallel long-period fiber gratings,” Opt. Express 15, 6494–6499 (2007). [CrossRef] [PubMed]

], which could be developed into bandpass filters and OADMs (fixed or tunable) for CWDM applications. The flexibility offered by the grating design can be exploited to generate sophisticated transmission characteristics [16

16. F. Y. M. Chan and K. S. Chiang, “Transfer-matrix method for the analysis of two parallel dissimilar non-uniform long-period fiber gratings”, J. Lightwave Technol. 24, 1008–1018 (2006). [CrossRef]

].

2. Grating fabrication and experimental setup

A coupler formed with two parallel LPFGs of equal length L is shown schematically in Fig. 1(a), which allows an offset distance s to be introduced between the two gratings. Light is launched into one of the fibers, called the transmission fiber, where the grating couples the light from the guided core mode to the cladding mode of the fiber. At the same time, the cladding mode of the adjacent fiber, called the tapping fiber, is excited through evanescent-field coupling between the two fibers and the grating in the tapping fiber couples the cladding mode to the guided core mode of the tapping fiber. The light that is rejected from the transmission fiber is collected by the tapping fiber, so the output spectra of the two fibers are complementary to each other. The efficiency of the whole process depends critically on the efficiency of evanescent-field coupling between the cladding modes, which depends on the spatial overlap of the cladding-mode fields of the two fibers [2

2. K. S. Chiang, Y. Liu, M. N. Ng, and S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000). [CrossRef]

,5

5. K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22, 1358–1366 (2004). [CrossRef]

]. In the case of a UV-written grating, the induced index change is present only across the photosensitive core and its spatial distribution is axially symmetric. In the case of a CO2-laser written grating, however, the induced index distribution is likely to be asymmetric across the fiber cross section due to the strong absorption of the 10.6-µm CO2-laser radiation on the exposed side of the fiber [12

12. D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser beams,” Electron. Lett. 34, 302–303 (1998). [CrossRef]

14

14. Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, “Novel fiber-optic sensors based on the long-period fiber grating written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21, 1320–1327 (2003). [CrossRef]

]. Therefore, when two such gratings are placed in parallel, it is likely that the coupling efficiency depends on the fiber orientation. Figure 1(b) shows four different orientations of the gratings (Configurations I-IV), where the red areas label the sides exposed to the CO2-laser radiation during the writing of the gratings (they do not represent the actual index distributions inside the fiber).

Fig. 1. (a) Schematic diagram of two parallel identical LPFGs. (b) Four different fiber orientations for the two LPFGs, where the red areas represent the sides exposed to the CO2-laser pulses.
Fig. 2. Transmission spectrum of a LPFG written in (a) a standard SMF; (b) a boron-doped SMF.

Each of the LPFGs used in our experiments was written by irradiating a fiber (with its jacket removed) on one side with high-frequency CO2-laser pulses. The CO2 laser (CO2-H10, Han’s Laser) had a maximum average output power of 10 W. The pulse frequency and the average writing power were fixed at 5 kHz and ~0.6 W, respectively. The laser beam was focused onto a spot of ~50 µm, which was controlled by a computer to scan across the fiber in the transverse direction at a controllable speed. Transverse scanning was advanced along the fiber at steps with each step equal to the grating period. A scanning cycle was completed when the number of periods required was attained. The scanning cycle could be repeated as many times as desired. The transverse scanning speed was used to control the total CO2-laser energy irradiated on the fiber. The fibers used were standard telecommunication SMF (Sumitomo Electric G652) and boron-doped SMF (Fibercore PS 1250/1500).

The gratings written in the standard SMF had a period of 550 µm and a length of 33 mm (60 periods). The CO2-laser energy density and the number of scanning cycles used were 7.0 J/mm2 and 7, respectively. We inspected the surface of the exposed side of each grating with a microscope and observed no visible physical deformation or damage due to the CO2-laser exposure. The transmission spectrum of a typical grating is shown in Fig. 2(a), which consists of a number of overlapped resonance wavelengths due to coupling to both axially symmetric and non-axially symmetric cladding modes. Our results are in good agreement with those reported by others [18

18. V. Grubsky and J. Feinberg, “Fabrication of axially symmetric long-period fiber gratings with a carbon dioxide laser,” IEEE Photon. Technol. Lett. 18, 2299–2298 (2006). [CrossRef]

]. It is known that stress relaxation in the fiber core by CO2-laser irradiation is the dominant mechanism responsible for the formation of the grating [19

19. R. Slavik, “Coupling to circularly asymmetric modes via long-period gratings made in a standard straight fiber,” Opt. Commun. , 275, 90–93 (2007). [CrossRef]

,20

20. H. S. Ryu, Y. Park, S. T. Oh, Y. Chung, and D. Y. Kim, “Effect of asymmetric stress relaxation on the polarization-dependent transmission characteristics of a CO2 laser-written long-period fiber grating,” Opt. Lett. 28, 155–157 (2003). [CrossRef] [PubMed]

]. While stress relaxation in the core leads to an axially uniform index change [19

19. R. Slavik, “Coupling to circularly asymmetric modes via long-period gratings made in a standard straight fiber,” Opt. Commun. , 275, 90–93 (2007). [CrossRef]

], one-side exposure to a large dose of CO2-laser radiation can induce an additional, asymmetric index change across the cladding cross section and thus give rise to coupling to non-axially symmetric cladding modes [17

17. G. D. Van Wiggeren, T. K. Gaylord, D. D. Davis, E. Anemogiannis, B. D. Garrett, M. I. Braiwish, and E. N. Glytsis, “Axial rotation dependence of the resonances in the curved CO2-laser-induced long-period fiber gratings,” Electron. Lett. 36, 1354–1355 (2000). [CrossRef]

19

19. R. Slavik, “Coupling to circularly asymmetric modes via long-period gratings made in a standard straight fiber,” Opt. Commun. , 275, 90–93 (2007). [CrossRef]

]. In fact, when the cladding is irradiated on one side at a temperature below its fictive temperature, the refractive index of the exposed side can increase [21

21. K. Morishita and A. Kaino, “Residual stress effects on post-fabrication resonance wavelength trimming of long-period fiber gratings,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (OSA, Washington, DC, 2007), JWA18.

,22

22. A. K. Varshneya, Fundamentals of Inorganic Glasses, (Academic Press, Boston, 1994).

]. By inspecting the mode pattern with a CCD camera together with a C-band tunable laser, the large dip at the longest wavelength shown in Fig. 2(a) was identified to be the LP05 mode. For the two gratings used in the coupler experiments, the center wavelengths at the LP05-mode dips were 1558.0 nm and 1555.8 nm, respectively, and the corresponding contrasts and 3-dB bandwidths were 24 dB and 26 dB, and 26 nm and 29 nm, respectively. All were measured in air.

The gratings written in the boron-doped SMF had a period of 345 µm and a length of 34.5 mm (100 periods). The CO2-laser energy density used was 3.5 J/mm2, which was much lower than that used for the standard SMF. The number of scanning cycles used was 5. The transmission spectrum of a typical grating is shown in Fig. 2(b), which is much cleaner than that of the grating written in the standard SMF. In fact, the transmission spectrum is similar to that of a UV-written grating, which couples light only to symmetric cladding modes. Because boron-doped silica has a significantly lower fictive temperature than silica [22

22. A. K. Varshneya, Fundamentals of Inorganic Glasses, (Academic Press, Boston, 1994).

], it takes a much lower dose of CO2-laser radiation to relax the mechanical stress in the core [13

13. C. S. Kim, Y. Han, B. H. Lee, W. T. Han, U. C. Paek, and Y. Chung, “Induction of the refractive index changes in B-doped optical fibers through relaxation of the mechanical stress,” Opt. Commun. 185, 337–342 (2000). [CrossRef]

,15

15. V. Grubsky and J. Feinberg, “Rewritable densification gratings in boron-doped fibers,” Opt. Lett. 30, 1279–1281 (2005). [CrossRef] [PubMed]

]. This explains why an efficient grating could be written in the boron-doped fiber with a much lower CO2-laser energy density and a smaller number of scanning cycles. Moreover, because the CO2-laser dosage used was too low to induce a significant asymmetric index distribution in the cladding, there was no significant coupling to non-axially symmetric cladding modes and the resultant transmission spectrum was clean. Our results agree with those reported in Ref.15. By inspection of the mode pattern, the dip at the longest wavelength shown in Fig. 2(b) was identified to be the LP08 mode and the two other dips should correspond, respectively, to the LP07 and LP06 modes. For the two gratings used in the coupler experiments, the center wavelengths at the LP08-mode dips were 1578.8 nm and 1578.5 nm, respectively, and the corresponding contrasts and the 3-dB bandwidths were 23 dB and 28 dB, and 29 nm and 27 nm, respectively. All were measured in air.

In the coupler experiments, the two gratings were kept straight and placed in close contact with each other by applying a suitable tension along the fibers. Slightly different tensions were applied to the two gratings to equalize their center wavelengths. The two gratings were allowed to displace from each other by an offset distance. If necessary, an index-matching liquid was applied to the gratings to change the surrounding refractive index. Light from a commercial (C+L)-band amplified spontaneous emission source was launched into the transmission fiber and the output spectra of the two fibers were measured with an optical spectrum analyzer. The coupling efficiency of the device is defined as the ratio of the output power from the tapping fiber to the input power launched into the transmission fiber.

3. Experimental results and discussions

Table 1. Peak coupling efficiencies of the coupler formed with gratings written in the standard SMF measured for the four fiber orientations with the surrounding index n fixed at 1.0, 1.420, or 1.448.

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Fig. 3. (a) Normalized output spectra from the tapping fiber measured in air for the four fiber orientations. (b) The dependence of the peak coupling efficiency on the offset distance for Configurations I and IV with the surrounding index fixed at 1.448.

Figure 3(a) shows the normalized output spectra of the tapping fiber measured in air for the four fiber orientations. The side-lobe suppression ratio, defined as the ratio of the peak coupling efficiency to the coupling efficiency of the most significant side lobe in the coupled spectrum, varies between 9.0 dB and 17.0 dB. The 3-dB bandwidths of the output spectra of the tapping fiber are 30.2, 34.4, 35.2, and 35.7 nm for Configurations I, II, III, and IV, respectively. Figure 3(b) shows the variation of the peak coupling efficiency with the offset distance s for Configurations I and IV with the surrounding index fixed at 1.448. The peak coupling efficiency varies periodically with s, which is typical of evanescent-field coupling between two fibers [5

5. K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22, 1358–1366 (2004). [CrossRef]

]. The maximum peak coupling efficiency, measured at s=40 mm for Configuration I with the surrounding index 1.448, was -4.27 dB (37.4%). The maximum peak coupling efficiency for Configuration IV, measured at s=45 mm with the surrounding index 1.448, was -5.57 dB (27.7%). These results further confirm that Configuration I is the preferred fiber orientation. In practice, it is difficult to further increase the coupling efficiency because it is difficult to ensure a perfect face-to-face alignment (and evanescent-field coupling is highly sensitive to such an alignment). The coupling to non-axially symmetric cladding modes around the LP05-mode dip, as shown in Fig. 2(a), contributes an additional insertion loss of 1 to 2 dB.

Table 2. Peak coupling efficiencies of the coupler formed with gratings written in the boron-doped SMF measured for the four fiber orientations with the surrounding index n fixed at 1.0 or 1.420.

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Fig. 4. (a) Dependence of the peak coupling efficiency on the offset distance with the surrounding index n fixed at 1.0 (air) and 1.420. (b) Normalized output spectra from the tapping fiber measured with the surrounding index 1.420 at the offset distances: s=0, 10, 20, 30, 40, 50, and 60 mm.

Figure 4(a) shows the variation of the peak coupling efficiency with the offset distance s with the surrounding index fixed at 1.0 (air) and 1.420. As expected, the peak coupling efficiency increases with the offset distance. The maximum peak coupling efficiency, measured at s=60 mm with the surrounding index 1.420, was -0.66 dB, which corresponds to a power conversion efficiency of 85.9%. To the best of our knowledge, this is the highest experimental coupling efficiency that has ever been reported for an optical coupler using two parallel LPFGs. Figure 4(b) shows the normalized output spectra from the tapping fiber measured with the surrounding index 1.420 at different offset distances. The side-lobe suppression ratio varies between 12.5 dB and 17.5 dB. The 3-dB bandwidths of the output spectra of the tapping fiber are 33.8, 25.1, 21.2, 19.9, 18.7, 18.3 and 17.4 nm for s=0, 10, 20, 30, 40, 50 and 60 mm, respectively. The reduction in the 3-dB bandwidth with s can be attributed to the fact that the bandwidth of evanescent-field coupling decreases with an increase in the interaction length. Similar effects have been observed with the couplers using UV-written gratings [3

3. K. S. Chiang, M. N. Ng, Y. Liu, and S. Li, “Evanescent-field coupling between two parallel long-period fiber gratings,” in Proc. IEEE Lasers Electro-Op. Soc. Conf., Puerto Rico (2000), pp. 836–837.

,8

8. Y. Liu and K. S. Chiang, “Broadband optical coupler based on evanescent-field coupling between three parallel long-period fiber gratings,” IEEE Photon. Technol. Lett. 18, 229–231 (2006). [CrossRef]

].

4. Conclusion

We investigated experimentally an all-fiber coupler formed by two parallel LPFGs written by high-frequency CO2-laser pulses. For gratings written in the standard SMF, the performance of the coupler depends strongly on the fiber orientation with the best performance obtained when the exposed sides of the fibers face each other. The highest peak coupling efficiency we can obtain with such gratings is ~37%. For gratings written in the boron-doped SMF, the performance of the coupler is independent of the fiber orientation. With such gratings, we achieve a record-high peak coupling efficiency of ~86% by using a suitable surrounding refractive index and offset distance. Our results confirm that high-frequency CO2-laser written LPFGs with the boron-doped fiber can be employed potentially for the realization of efficient broadband optical couplers, which could be further developed into a range of bandpass filters and OADMs for application in CWDM systems.

Acknowledgements

This research was supported jointly by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China, under Project CityU 111907, and a research grant from the University of Electronic Science and Technology of China under the Chang Jiang Scholars Program.

References and links

1.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996). [CrossRef]

2.

K. S. Chiang, Y. Liu, M. N. Ng, and S. Li, “Coupling between two parallel long-period fibre gratings,” Electron. Lett. 36, 1408–1409 (2000). [CrossRef]

3.

K. S. Chiang, M. N. Ng, Y. Liu, and S. Li, “Evanescent-field coupling between two parallel long-period fiber gratings,” in Proc. IEEE Lasers Electro-Op. Soc. Conf., Puerto Rico (2000), pp. 836–837.

4.

V. Grubsky, D. S. Starodubov, and J. Feinberg, “Wavelength-selective coupler and add-drop multiplexer using long-period fiber gratings,” in Tech. Dig. Opt. Fiber Commun. Conf., vol. 4, (2000), pp. 28–30.

5.

K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22, 1358–1366 (2004). [CrossRef]

6.

Y. H. Han, S. B. Lee, C. S. Kim, and M. Y. Jeong, “Tunable optical add-drop multiplexer based on long-period fiber gratings for coarse wavelength division multiplexing systems,” Opt. Lett. 31, 703–705 (2006). [CrossRef] [PubMed]

7.

M. J. Kim, Y. M. Jung, B. H. Kim, W. T. Han, and B. H. Lee, “Ultra-wide bandpass filter based on long-period fiber gratings and the evanescent field coupling between two fiber,” Opt. Express 15, 10855–10862 (2007). [CrossRef] [PubMed]

8.

Y. Liu and K. S. Chiang, “Broadband optical coupler based on evanescent-field coupling between three parallel long-period fiber gratings,” IEEE Photon. Technol. Lett. 18, 229–231 (2006). [CrossRef]

9.

Y. Liu, K. S. Chiang, and Q. Liu, “Symmetric 3×3 optical coupler using three parallel long-period fiber gratings,” Opt. Express 15, 6494–6499 (2007). [CrossRef] [PubMed]

10.

Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. Kazansky, and K. Hirao, “Fabrication of long-period fibre gratings by focused irradiation of infrared femtosecond laser pulses,” Opt. Lett. 24, 646–648 (1999). [CrossRef]

11.

G. Rego, O. Okhotnikov, E. Dianov, and V. Sulimov, “High-temperature stability of long-period fibre gratings using an electric arc,” J. Lightwave Technol. , 19, 1574–1579 (2001). [CrossRef]

12.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fibre grating fabrication with focused CO2 laser beams,” Electron. Lett. 34, 302–303 (1998). [CrossRef]

13.

C. S. Kim, Y. Han, B. H. Lee, W. T. Han, U. C. Paek, and Y. Chung, “Induction of the refractive index changes in B-doped optical fibers through relaxation of the mechanical stress,” Opt. Commun. 185, 337–342 (2000). [CrossRef]

14.

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, “Novel fiber-optic sensors based on the long-period fiber grating written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21, 1320–1327 (2003). [CrossRef]

15.

V. Grubsky and J. Feinberg, “Rewritable densification gratings in boron-doped fibers,” Opt. Lett. 30, 1279–1281 (2005). [CrossRef] [PubMed]

16.

F. Y. M. Chan and K. S. Chiang, “Transfer-matrix method for the analysis of two parallel dissimilar non-uniform long-period fiber gratings”, J. Lightwave Technol. 24, 1008–1018 (2006). [CrossRef]

17.

G. D. Van Wiggeren, T. K. Gaylord, D. D. Davis, E. Anemogiannis, B. D. Garrett, M. I. Braiwish, and E. N. Glytsis, “Axial rotation dependence of the resonances in the curved CO2-laser-induced long-period fiber gratings,” Electron. Lett. 36, 1354–1355 (2000). [CrossRef]

18.

V. Grubsky and J. Feinberg, “Fabrication of axially symmetric long-period fiber gratings with a carbon dioxide laser,” IEEE Photon. Technol. Lett. 18, 2299–2298 (2006). [CrossRef]

19.

R. Slavik, “Coupling to circularly asymmetric modes via long-period gratings made in a standard straight fiber,” Opt. Commun. , 275, 90–93 (2007). [CrossRef]

20.

H. S. Ryu, Y. Park, S. T. Oh, Y. Chung, and D. Y. Kim, “Effect of asymmetric stress relaxation on the polarization-dependent transmission characteristics of a CO2 laser-written long-period fiber grating,” Opt. Lett. 28, 155–157 (2003). [CrossRef] [PubMed]

21.

K. Morishita and A. Kaino, “Residual stress effects on post-fabrication resonance wavelength trimming of long-period fiber gratings,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (OSA, Washington, DC, 2007), JWA18.

22.

A. K. Varshneya, Fundamentals of Inorganic Glasses, (Academic Press, Boston, 1994).

23.

K. S. Chiang, Y. Liu, M. N. Ng, and X. Dong, “Analysis of etched long-period fibre grating and its response to external refractive index,” Electron. Lett. 36, 966–967 (2000). [CrossRef]

OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.2340) Fiber optics and optical communications : Fiber optics components
(350.2770) Other areas of optics : Gratings

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: November 1, 2007
Revised Manuscript: December 2, 2007
Manuscript Accepted: December 4, 2007
Published: December 12, 2007

Citation
Yunqi Liu, Kin Seng Chiang, Yun Jiang Rao, Zeng Ling Ran, and Tao Zhu, "Light coupling between two parallel CO2-laser written long-period fiber gratings," Opt. Express 15, 17645-17651 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-17645


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References

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