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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 19 — Sep. 14, 2009
  • pp: 16750–16755
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All-fiber bandwidth-tunable band-rejection filter based on a composite grating induced by CO2 laser pulses

T. Zhu, C. H. Shi, Y. J. Rao, L. L. Shi, and K. S. Chiang  »View Author Affiliations


Optics Express, Vol. 17, Issue 19, pp. 16750-16755 (2009)
http://dx.doi.org/10.1364/OE.17.016750


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Abstract

We propose an all-fiber band-rejection filter with a tunable bandwidth, which is realized by putting a normal long-period fiber grating in series with a rotary long-period fiber grating written in a twisted single-mode fiber by CO2 laser pulses. Bandwidth tuning is achieved by applying torsion to the composite grating. Our experimental filter shows a bandwidth tuning of ~16.3 nm at a rejection level of ~15 dB and a polarization-dependent loss lower than ~0.9 dB.

© 2009 OSA

1. Introduction

Long-period fiber gratings (LPFGs) have attracted much attention as all-fiber band-rejection filters, which can be used, for example, as gain equalizers or ASE filters for broadband optical amplifiers [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(1), 58–65 (1996). [CrossRef]

]. Several LPFG-based tunable filters have been reported [2

2. P. Steinvurzel, E. D. Moore, E. C. Mägi, and B. J. Eggleton, “Tuning properties of long period gratings in photonic bandgap fibers,” Opt. Lett. 31(14), 2103–2105 (2006). [CrossRef] [PubMed]

4

4. J. H. Lim, K. S. Lee, J. C. Kim, and B. H. Lee, “Tunable fiber gratings fabricated in photonic crystal fiber by use of mechanical pressure,” Opt. Lett. 29(4), 331–333 (2004). [CrossRef] [PubMed]

], where the filter response is tuned by the thermo-optic effect or the mechanical effect. However, most tunable LPFG-based filters allow tuning of only the resonance wavelength or the grating contrast. The possibility of tuning the bandwidth of the resonance band has not been much explored. Recently, the use of a helicoidal fiber grating pair with opposite helicities can offer bandwidth tuning [5

5. W. Shin, B. A. Yu, Y. C. Noh, J. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007). [CrossRef] [PubMed]

]. Acousto-optic filters can also provide bandwidth tuning, but they require active RF components and complicated flexural wave excitation and suffer from a large polarization-dependent loss (PDL) [6

6. A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windler, and T. A. Strasser, “Electrically Tunable Efficient Broad-Band Fiber Filter,” IEEE Photon. Technol. Lett. 11(4), 445–447 (1999). [CrossRef]

].

In this paper, we report a novel bandwidth-tunable band-rejection filter, which is realized by putting a normal LPFG in series with a rotary LPFG (R-LPFG). The R-LPFG is fabricated by exposing a twisted single-mode fiber to CO2 laser pulses. Unlike a helical LPFG [5

5. W. Shin, B. A. Yu, Y. C. Noh, J. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007). [CrossRef] [PubMed]

] and conventional CO2 laser written LPFGs [7

7. Y. J. Rao, T. Zhu, Z. L. Ran, Y. P. Wang, J. Jiang, and A. Z. Hu, “Novel long-period fiber gratings written by high-frequency CO2 laser pulses and applications in optical fiber communication,” Opt. Commun. 229(1-6), 209–221 (2004). [CrossRef]

9

9. 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(3), 302–303 (1998). [CrossRef]

], an R-LPFG can produce split resonance wavelengths when the twist applied to the fiber is removed after the formation of the grating [10

10. T. Zhu, Y. J. Rao, J. L. Wang, and Y. Song, “Strain sensor without temperature compensation based on a LPFG with strongly rotary refractive index modulation,” Electron. Lett. 43(21), 1132–1133 (2007). [CrossRef]

]. The wavelength-splitting effect can be made particularly sensitive to the axial strain applied to the grating when the CO2 laser power used is high enough to produce rotary grooves along the fiber [11

11. T. Zhu, Y. J. Rao, Y. Song, K. S. Chiang, and M. Liu, “Highly sensitive temperature-independent strain sensor based on a long-period fiber grating with a CO2-laser engraved rotary structure,” IEEE Photon. Technol. Lett. 21(8), 543–545 (2009). [CrossRef]

]. It is found recently that CO2 laser irradiation on a fiber under tension can generate a large frozen-in inelastic strain in the fiber, which significantly enhances the efficiency of CO2 laser writing of an LPFG [12

12. Y. Liu and K. S. Chiang, “CO(2) laser writing of long-period fiber gratings in optical fibers under tension,” Opt. Lett. 33(17), 1933–1935 (2008). [CrossRef] [PubMed]

]. In the case of writing an LPFG in a twisted fiber, since the fiber is subjected to large twisting tension during CO2 laser irradiation, a large frozen-in strain must be generated in the fiber [13

13. T. Zhu, K. S. Chiang, Y. J. Rao, C. H. Shi, and M. Liu, “Characterization of long-period fiber gratings written by CO2 laser in twisted single-mode fibers,” J. Lightwave Technol. (to be published).

]. When the applied twist is removed, the frozen-in strain turns into a torsion stress that rotates along the fiber [13

13. T. Zhu, K. S. Chiang, Y. J. Rao, C. H. Shi, and M. Liu, “Characterization of long-period fiber gratings written by CO2 laser in twisted single-mode fibers,” J. Lightwave Technol. (to be published).

]. We observe that each of the resonance peaks of the R-LPFG splits into two when the rotation rate is large enough, and the separation of the two peaks can increase or decrease, depending on the sense (clockwise or counter-clockwise) of the torsion applied to the grating. Applying torsion to an R-LPFG, therefore, provides a means of tuning the bandwidth of the rejection band. To compensate for a drop in the contrast of the rejection band due to wavelength splitting, we put a normal LPFG with matching characteristics in series with the R-LPFG. Using such a composite grating structure, we are able to tune the bandwidth over 16.3 nm at a rejection level of ~15 dB without introducing significant insertion loss and PDL. Our bandwidth-tunable filter could find applications in optical communication systems as a noise filter or a dynamic gain equalizer.

2. Principle and fabrication of the grating filter

Figure 1
Fig. 1 Schematic diagrams of (a) a normal LPFG and (b) an R-LPFG.
shows schematically the index modulations along a normal LPFG and a rotary LPFG. The phase-matching condition that relates the resonance wavelength λ 0 and the grating pitch of an LPFG ΛG is given by [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(1), 58–65 (1996). [CrossRef]

]:
λ0=(nco,effncl,eff)ΛG=δneffΛG
(1)
where δneff is the difference between the effective indexes of the guided core mode nco,eff and the coupled cladding mode ncl,eff. For a normal LPFG, as shown in Fig. 1(a), the index modulation is uniform along the fiber. For an R-LPFG, however, the index modulation due to torsion stress is rotated at a period ΛT with ΛT >> ΛG, where ΛT = 360ΛG with ϕ (in degree) being the twist angle between two adjacent periods of the grating, as shown in Fig. 1(b). The index modulation at any fixed point in the cladding along the fiber can be described as
n(z)~sin(2πΛTz)sin(2πΛGz)
(2)
which can be considered as the result of the beating of two gratings with slightly different periods Λ+andΛ, where [13

13. T. Zhu, K. S. Chiang, Y. J. Rao, C. H. Shi, and M. Liu, “Characterization of long-period fiber gratings written by CO2 laser in twisted single-mode fibers,” J. Lightwave Technol. (to be published).

]
1Λ±=1ΛG1ΛT
(3)
From Eqs. (1)-(3), we can get the resonance wavelengths of the grating as:
λ±=λ0Λ±ΛG
(4)
As a result, each resonance wavelength splits into two with a separation given by:
Δλ0=(nco,effncl,eff)(Λ+Λ)2ΛGΛTλ0
(5)
Equation (5) is accurate only when the grating is sufficiently longer than the twist period. When the grating is too short, Eq. (5) is no longer accurate and the wavelength splitting effect may not arise.

Our composite grating is composed of a normal LPFG and an R-LPFG written along the same fiber. The setup for the fabrication of the composite grating is shown in Fig. 2
Fig. 2 Setup for the fabrication of the composite LPFG.
, which consists of a high frequency CO2 laser (Synrad, USA) with a maximum output power of 10 W and a maximum scanning frequency of 10 kHz, a broadband light source, and an optical spectrum analyzer (OSA, Agilent 68140A). A single-mode fiber (SMF) was mounted with its two ends fixed respectively at the left and right holders. Another fiber holder was placed in the middle to separate the fiber into two sections. The normal LPFG was written in the left section of the fiber using the conventional writing process [7-9], while the R-LPFG was written in the right section of the fiber. To fabricate the R-LPFG, the right end of the fiber was attached to a rotation disc. The distance between the middle holder and the right holder was fixed at L = 300 mm. The fiber was first twisted at an angle θ by rotating the disc. The twist rate and the twist period are given, respectively, by η = θ/L and ΛT = 360. The CO2 laser beam was focused onto the fiber at a spot of ~100 μm in diameter and advanced along the fiber at steps with the distance of each step equal to the grating period. The output power of the CO2 laser was set at ~0.4 W, whose power density was about 2.5 J/cm2. Finally, the fiber was untwisted, which resulted in a rotary refractive index modulation along the fiber axis, as shown in Fig. 1(b). Because of the generation of frozen-in strain in the fiber during the writing process [12

12. Y. Liu and K. S. Chiang, “CO(2) laser writing of long-period fiber gratings in optical fibers under tension,” Opt. Lett. 33(17), 1933–1935 (2008). [CrossRef] [PubMed]

], torsion stress was produced at the exposed locations of the R-LPFG [13

13. T. Zhu, K. S. Chiang, Y. J. Rao, C. H. Shi, and M. Liu, “Characterization of long-period fiber gratings written by CO2 laser in twisted single-mode fibers,” J. Lightwave Technol. (to be published).

].

In our experiment, a conventional SMF (Corning, SMF-28) was used. The grating period ΛG and the period number were 570 μm and 50, respectively. Figure 3
Fig. 3 Transmission spectra of R-LPFGs with different values of ΛT.
shows the transmission spectra of R-LPFGs with different twist periods. We observe clear wavelength splitting when the twist period is small enough. As an example, with ΛG = 0.57 mm, the calculated and experimental wavelength splits for λ 0 = 1431 nm and λ 0 = 1547 nm under different twist periods are shown in Fig. 4
Fig. 4 Wavelength split as a function of the twist period for (a) λ 0 = 1431 nm and (b) λ 0 = 1547 nm.
. Because of the overlapping of the two rejection bands and the finite length of the grating, the experimental wavelength split should be smaller than that of the calculated value. The experimental results and the simulation agree reasonably well.

From Fig. 3 and Fig. 4, we can see that the bandwidth between the two split peaks of an R-LPFG can be tuned by twisting the grating. However, the contrast of the rejection band drops when the wavelength splits (due to the appearance of a saddle-shaped region in the overlapped area of the two split rejection bands – see Fig. 3). To compensate for the drop in the grating contrast, we put a normal LPFG with a similar pitch in series with the R-LPFG, so that the contrast at the center wavelength can be kept large as the rejection band of the R-LPFG splits.

3. Results and discussions

When a torsion η = Δθ/L (in degree per unit length of fiber) is applied to the R-LPFG, the twist rate of the grating is changed by η = 360/ΛT. According to Eq. (5), the wavelength separation Δλ 0 is given by [13

13. T. Zhu, K. S. Chiang, Y. J. Rao, C. H. Shi, and M. Liu, “Characterization of long-period fiber gratings written by CO2 laser in twisted single-mode fibers,” J. Lightwave Technol. (to be published).

]
Δλ0=2ΛGλ0(1ΛTη360)=2ΛG(360NLη)360Lλ0
(6)
which changes linearly with the applied torsion η. Here, η > 0 means that the direction of the applied torsion is the same as the twisting direction in the fabrication of the grating, while η < 0 means the opposite direction. Figure 5
Fig. 5 Torsion characteristics of a 50-period R-LPFG with ΛG = 0.57 mm and ΛT = 37.5 mm: (a) calculated and experimental wavelength separations and (b) measured transmission spectra.
shows the tuning characteristics of the R-LPFG with ΛG = 0.57 mm and ΛT = 37.5 mm. As shown in Fig. 5(a), the wavelength separation increases with the applied torsion when the direction of the applied torsion is opposite to that of the original twist applied to the fiber (η < 0). In this case, the applied torsion tends to enhance the original twisting effect. On the other hand, the wavelength separation decreases with an increase in the applied torsion when the direction of the applied torsion is the same as that of the original twist applied to the fiber (η > 0). The two bands merge completely when the applied torsion is more than ~2 °/mm, which is about the same twist rate used in the fabrication of the grating. Fig. 5(b) shows the changes in the transmission spectrum of the R-LPFG at different values of the applied torsion.

Figure 6
Fig. 6 Measured torsion characteristics of a 50-period normal LPFG with ΛG = 0.57 mm: (a) resonance wavelengths and (b) transmission spectra.
shows the torsion characteristics of the normal LPFG with ΛG = 0.57 mm and 40 periods. As shown in Fig. 6, the wavelength shift is only ~3.3 nm when the torsion rate varies from −1.2 °/mm to 1.2 °/mm, and the contrast changes by only ~2.5 dB. During the fabrication of the grating, we did not apply any twist to the fiber, but absolute zero twist could not be guaranteed. The fact that the wavelength shifts towards opposite directions by changing the sign of the applied torsion, as shown in Fig. 6(a), suggests the presence of a small residual twist. Nevertheless, the transmission characteristics of the grating are insensitive to the applied torsion and, therefore, can be used to compensate for the contrast drop of the R-LPFG.

To demonstrate an effective bandwidth-tunable filter, the normal LPFG used had a pitch of 0.57 mm and a length of 22.8 mm, and the R-LPFG had a pitch of 0.57 mm, a twist period of 37.5 mm, and a length of 28.5 mm. We controlled the dosage of the CO2 laser irradiation to achieve a sufficiently large contrast. We applied torsion to one end of the composite grating and measured the change in the transmission spectrum. Figure 7(a)
Fig. 7 Torsion characteristics of the composite grating for bandwidth tuning: (a) transmission spectra showing the bandwidths 25.0 nm and 41.3 nm at the torsion rates −1.5 °/mm and 1.5 °/mm, respectively, for a rejection level of ~15 dB, (b) bandwidth and PDL.
shows the measured transmission spectra at different torsion rates, where the bandwidth is defined as the wavelength range at a specific rejection level. As shown in Fig. 7(a), the combined spectra of the normal LPFG and the R-LPFG produce a flat-bottom rejection band over a range of applied torsion. The center wavelength of the rejection band is kept at ~1550 nm. Although the shape of the rejection band varies with the applied torsion and hence the bandwidth, our composite grating serves as a useful bandwidth-tunable filter as long as the rejection level over the tunable bandwidth can be kept larger than a high value, say, 15 dB. Figure 7(b) shows the bandwidth-tuning characteristics. The tuning range of the bandwidth is ~21.3 nm at a rejection level of ~9 dB and ~16.3 nm at a rejection level of ~15 dB. We expect better performance with a longer (and hence stronger) R-LPFG. The length of the grating we can fabricate is limited by our fabrication setup. As also shown in Fig. 7(b), the measured PDL of our filter is lower than 0.9 dB, which is smaller than that of a helical LPFG [5]. Our filter is practically polarization-insensitive.

4. Conclusion

We propose an all-fiber bandwidth-tunable filter based on a composite grating formed with an R-LPFG connected to a normal LPFG, both written by CO2 laser pulses. The wavelength-splitting effect of the R-LPFG allows the bandwidth of the rejection band to be varied by applying torsion to the grating, while the rejection band of the normal LPFG compensates for the drop in the rejection level due to wavelength splitting in the R-LPFG. The combined spectra of the two gratings offer bandwidth tunability while maintaining a large rejection level. We demonstrate such a composite grating experimentally. It shows a bandwidth tuning of ~16.3 nm at a rejection level of ~15 dB and a PDL lower than ~0.9 dB. The filter is easy to fabricate and could find applications in optical communication and sensing systems, where bandwidth tuning is needed.

Acknowledgements

This work was supported by the Project of Natural Science Foundation of China under Grant No.60807019, Program for NCET under Grant No. NCET-08-0602, Natural Science Foundation Project of CQ CSTC Grant No. CSTC2008BB2165, and a 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(1), 58–65 (1996). [CrossRef]

2.

P. Steinvurzel, E. D. Moore, E. C. Mägi, and B. J. Eggleton, “Tuning properties of long period gratings in photonic bandgap fibers,” Opt. Lett. 31(14), 2103–2105 (2006). [CrossRef] [PubMed]

3.

K. R. Sohn and K. T. Kim, “Thermo-optically tunable band-rejection filters using mechanically formed long-period fiber gratings,” Opt. Lett. 30(20), 2688–2690 (2005). [CrossRef] [PubMed]

4.

J. H. Lim, K. S. Lee, J. C. Kim, and B. H. Lee, “Tunable fiber gratings fabricated in photonic crystal fiber by use of mechanical pressure,” Opt. Lett. 29(4), 331–333 (2004). [CrossRef] [PubMed]

5.

W. Shin, B. A. Yu, Y. C. Noh, J. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007). [CrossRef] [PubMed]

6.

A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windler, and T. A. Strasser, “Electrically Tunable Efficient Broad-Band Fiber Filter,” IEEE Photon. Technol. Lett. 11(4), 445–447 (1999). [CrossRef]

7.

Y. J. Rao, T. Zhu, Z. L. Ran, Y. P. Wang, J. Jiang, and A. Z. Hu, “Novel long-period fiber gratings written by high-frequency CO2 laser pulses and applications in optical fiber communication,” Opt. Commun. 229(1-6), 209–221 (2004). [CrossRef]

8.

T. Zhu, Y. J. Rao, and Q. J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultra-long-period fiber grating,” IEEE Photon. Technol. Lett. 17(12), 2700–2702 (2005). [CrossRef]

9.

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(3), 302–303 (1998). [CrossRef]

10.

T. Zhu, Y. J. Rao, J. L. Wang, and Y. Song, “Strain sensor without temperature compensation based on a LPFG with strongly rotary refractive index modulation,” Electron. Lett. 43(21), 1132–1133 (2007). [CrossRef]

11.

T. Zhu, Y. J. Rao, Y. Song, K. S. Chiang, and M. Liu, “Highly sensitive temperature-independent strain sensor based on a long-period fiber grating with a CO2-laser engraved rotary structure,” IEEE Photon. Technol. Lett. 21(8), 543–545 (2009). [CrossRef]

12.

Y. Liu and K. S. Chiang, “CO(2) laser writing of long-period fiber gratings in optical fibers under tension,” Opt. Lett. 33(17), 1933–1935 (2008). [CrossRef] [PubMed]

13.

T. Zhu, K. S. Chiang, Y. J. Rao, C. H. Shi, and M. Liu, “Characterization of long-period fiber gratings written by CO2 laser in twisted single-mode fibers,” J. Lightwave Technol. (to be published).

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2340) Fiber optics and optical communications : Fiber optics components

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 21, 2009
Revised Manuscript: August 28, 2009
Manuscript Accepted: September 2, 2009
Published: September 4, 2009

Citation
T. Zhu, C. H. Shi, Y. J. Rao, L. L. Shi, and K. S. Chiang, "All-fiber bandwidth-tunable band-rejection filter based on a composite grating induced by CO2 laser pulses," Opt. Express 17, 16750-16755 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-19-16750


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References

  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(1), 58–65 (1996). [CrossRef]
  2. P. Steinvurzel, E. D. Moore, E. C. Mägi, and B. J. Eggleton, “Tuning properties of long period gratings in photonic bandgap fibers,” Opt. Lett. 31(14), 2103–2105 (2006). [CrossRef] [PubMed]
  3. K. R. Sohn and K. T. Kim, “Thermo-optically tunable band-rejection filters using mechanically formed long-period fiber gratings,” Opt. Lett. 30(20), 2688–2690 (2005). [CrossRef] [PubMed]
  4. J. H. Lim, K. S. Lee, J. C. Kim, and B. H. Lee, “Tunable fiber gratings fabricated in photonic crystal fiber by use of mechanical pressure,” Opt. Lett. 29(4), 331–333 (2004). [CrossRef] [PubMed]
  5. W. Shin, B. A. Yu, Y. C. Noh, J. Lee, D. K. Ko, and K. Oh, “Bandwidth-tunable band-rejection filter based on helicoidal fiber grating pair of opposite helicities,” Opt. Lett. 32(10), 1214–1216 (2007). [CrossRef] [PubMed]
  6. A. A. Abramov, B. J. Eggleton, J. A. Rogers, R. P. Espindola, A. Hale, R. S. Windler, and T. A. Strasser, “Electrically Tunable Efficient Broad-Band Fiber Filter,” IEEE Photon. Technol. Lett. 11(4), 445–447 (1999). [CrossRef]
  7. Y. J. Rao, T. Zhu, Z. L. Ran, Y. P. Wang, J. Jiang, and A. Z. Hu, “Novel long-period fiber gratings written by high-frequency CO2 laser pulses and applications in optical fiber communication,” Opt. Commun. 229(1-6), 209–221 (2004). [CrossRef]
  8. T. Zhu, Y. J. Rao, and Q. J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultra-long-period fiber grating,” IEEE Photon. Technol. Lett. 17(12), 2700–2702 (2005). [CrossRef]
  9. 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(3), 302–303 (1998). [CrossRef]
  10. T. Zhu, Y. J. Rao, J. L. Wang, and Y. Song, “Strain sensor without temperature compensation based on a LPFG with strongly rotary refractive index modulation,” Electron. Lett. 43(21), 1132–1133 (2007). [CrossRef]
  11. T. Zhu, Y. J. Rao, Y. Song, K. S. Chiang, and M. Liu, “Highly sensitive temperature-independent strain sensor based on a long-period fiber grating with a CO2-laser engraved rotary structure,” IEEE Photon. Technol. Lett. 21(8), 543–545 (2009). [CrossRef]
  12. Y. Liu and K. S. Chiang, “CO(2) laser writing of long-period fiber gratings in optical fibers under tension,” Opt. Lett. 33(17), 1933–1935 (2008). [CrossRef] [PubMed]
  13. T. Zhu, K. S. Chiang, Y. J. Rao, C. H. Shi, and M. Liu, “Characterization of long-period fiber gratings written by CO2 laser in twisted single-mode fibers,” J. Lightwave Technol. (to be published).

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