Abstract

We report the spectral characteristics of CO2-laser inscribed long-period gratings (LPGs) in endlessly single mode photonic crystal fiber (PCF) subject to macro-bending. The coupling modes as a result of bending were studied by examining the shifts of resonant wavelengths, the splits of attenuation bands, and the variation in coupling strength of the transmission spectra. A bending coefficient of ~ 27.9 nm∙m was determined in the PCF at 180° rotational orientation relative to the point of laser inscription in the curvature range from 2.6 m-1 to 3.5 m-1. Compared with conventional fiber LPGs fabricated using the same method, the PCF-based LPGs possess higher sensitivity both to bending and orientation, making them promising for sensor applications.

©2007 Optical Society of America

1. Introduction

The experimental realization of both long-period gratings (LPGs) [1] and photonic crystal fibers (PCFs) [2] was demonstrated almost concurrently ten years ago. LPGs couple the fundamental core mode to a series of forward-propagating cladding modes at discrete wavelength and thus generate attenuation bands in the transmission spectrum. They have been explored as sensor components for bending detection [3], seismic measurement [4], and biomedical monitoring [5]. PCFs contain axially aligned wavelength-scale air channels in the cladding. They have excellent potential as sensors and communication components [6] for their many unique optical properties, such as endlessly single-mode guidance, unusual dispersion properties, and high birefringence. The integration of LPGs and PCFs, two promising photonic building blocks, into one component as a PCF-based LPG (PCF-LPG) was scarcely explored till it became feasible to fabricate LPGs without the need of photosensitive doping in fiber core. Micro-collapsing the PCF air channels periodically with heat from a CO2 laser gives rise to a new family of PCF-LPG devices [7]. Modifying refractive index based on the glass structure rearrangement in PCF locally by arc discharge can also result in a higher index difference core and cladding against wavelength and stronger core-cladding mode coupling [8]. The coupled resonance can be tuned by adjusting the LPG period and the pressure applied partly on the PCF, while the resonant wavelength is blue-shifted with the increase of periodicity, contrary to the usual case in conventional LPGs [9]. The bending properties of PCFs fabricated by the electric arc technique have been reported for curvature sensitivity [10]. In this paper, we show the transmission spectra of PCF-LPGs inscribed by CO2 laser under bending conditions with different axial rotational orientations. The results yield a strong relationship between the cladding-mode symmetry and mode coupling coefficient. Compared to the conventional fiber-based LPGs written with the same technique, PCF-LPGs are more sensitive to both macro-bending and orientation. This work provides some insights into the mechanisms that contribute to the measured properties of PCF-LPGs.

2. Fabrication of LPGs

To systematically analyze the effects of macro-bending on the transmission characteristics of mode-coupling resonance phase-matched by LPGs in PCF, we inscribed the LPGs by means of residual stress relaxation in a sol-gel derived PCF provided by OFS Laboratories [11] using a CO2 laser. The experimental setup is similar to that described elsewhere [12]. The laser operates at the frequency of 5 kHz. 0.5 W (about 5 % of the total power) was used for inscription. The exposure time was 200 ms and each period was exposed twice, the interval of which is half a second. The beam envelope is a round spot with Gaussian profile focused to a diameter of ~ 250 μm on the fiber. All these parameters were chosen on the basis of achieving fabrication reproducibility and high mode-coupling efficiency. No microstructure deformation was observed on the exposed section of the fiber according to our examination using scanning electron microscopy and optical microscopy.

The PCF used for LPG fabrication contains four rings of air channels arranged in a hexagonal pattern, extending to an air cladding diameter of 79 μm. The center-to-center distance between adjunct air channels is Λ ~ 9 μm. The average air-channel diameter is d ~ 3.7 μm. The core diameter, D core, is ~ 14.3 μm. The outer diameter of the PCF is 125 μm. The value of d/Λ is about 0.41 (< 0.45), indicating that this fiber is single mode at all wavelengths transparent for fused silica; thus termed endless single mode PCF (ESM-PCF). The LPG was written with a period length of 787.4 μm and total grating length of 18.11 mm. We also made the inscription of LPGs in conventional optical fiber (SMF-28) under the same fabrication condition for comparison of the transmission spectra of ESM-PCF-LPGs and SMF-28-LPGs subject to bending deformation. The period length and total grating length are 711.2 μm and 17.1 mm, respectively. By means of controlling the writing condition the wavelength of the strongest resonance can be predicted. The period length of each fiber was selected for the lowest attenuation band located at around 1560 nm, within the wavelength region (1450 – 1650 nm) of the broadband light source we used.

3. Bending spectral characteristics

The bending experiments were carried out using a three-point bending system schematically illustrated in Fig. 1(a). The fiber samples with LPGs were attached to the center location of the bottom surface of a thin spring steel plate (0.5 × 18 × 150 mm). The fiber was bent through depressing the center of this plate with a micrometer drive. The fiber was so affixed that it followed the contour of the steel plate freely without axial straining. The fiber was placed in a V-groove to avoid traverse deformation, if any. The curvature (1/R) induced in the fiber can be obtained from the following expression:

1R=2d(d2+L2)

where R is the radius of the spring steel plate under bending deformation, d is the bending depth at the center of the grating as determined by the micrometer, and L is the half of the span distance of the deforming plate.

 

Fig. 1. (a) Schematic diagram of the three-point bending setup (2L = 100 mm, d = 0 - 25.4 mm, wavelength region of broadband light source λ = 1450 - 1650 nm); (b) 0° orientation; (c) 180° orientation; (d) 90° orientation; (e) 270° orientation.

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A broadband light source was employed to illuminate the grating, and an optical spectrum analyzer with a resolution of 50 pm was used to record the grating transmission spectra in situ as bending was applied to create curvature variation from 0 to 3.94 m-1 under different axial rotational orientations. Considering that the fiber was exposure to the CO2 laser only on one side that might induce azimuthally asymmetric refractive index change in the fiber cross section [13], we rotated the grating at 0°, 90°, and 180° within ± 5° to investigate the optical anisotropy. The angle of 0° corresponds to the side of fiber exposed to incident CO2 laser facing downwards during bending shown in Fig. 1(b), while an angle of 180° relates to the side facing upwards (see Fig. 1(c)). 90° directional orientation is perpendicular to 0° and 180°. There are two opposite directions, one at 90° and the other 270°, shown in Fig. 1(d) and (e) respectively. Their spectral features are expected to be the same due to fiber symmetry. The use of 90° and 270° is therefore interchangeable with respect to rotational orientations.

In an ESM-PCF-LPG, the resonant wavelength generated by the i-th cladding mode coupled to fundamental core mode abides by the phase-matching condition as expressed:

λi=ncoreeffλ0ncorencladnclad(i)effλ0ncladnextΛ

where neffcore (λ 0, ncore, nclad) and neff clad(i)(λ 0, nclad, next) are the effective indices of core and cladding; ncore, nclad, and next are the core, cladding, and external refractive indices, respectively; λ 0 is the wavelength of free space; and Λ is grating period. The change of refractive index in air-silica cladding predominantly contributes to the cladding mode profiles; hence the resonant wavelengths shift and the intensities vary. When the grating is bent, the resultant change in Δnclad can be derived from Eq. (2):

λinclad=(λincoreeffncoreeffncladλinclad(i)effnclad(i)effnclad)Λ

The variations of effective indices of core and cladding modes [14,15] determine whether the resonant wavelength of the grating experiences blue-shift or red-shift, according to Eq. (3). In order to know the slopes of effective indices of core mode and the i-th cladding mode, we assume that the Eq. (2) can be differential with grating curvature without the influence of other variables. The length of periodicity keeps unchanged so that the slope of resonance wavelength as a function of curvature can be given by

dλid(1R)=(dncoreeff(1R)d(1R)dnclad(i)eff(1R)d(1R))Λ

The effect of λ 0, ncore, nclad, next on neffcore, neff clad(i) can be negligible because the range of curvature in our bending experiments is relatively small (from 0 m-1 to 4 m-1). Thus, using experimental results, we can estimate the increase or decrease of effective indices of core mode and the i-th cladding mode with the change of curvature on ESM-PCF-LPGs.

Due to unidirectional laser inscription, symmetrical and asymmetrical cladding modes in the ESM-PCF-LPG are allowed to be coupled with the fundamental core mode at resonant wavelengths of 1578 nm and 1539 nm, respectively, as shown in Fig. 2(a) in the fiber without bending [16]. The later resonance is very weak, indicating probably only slight non-uniformity in the distribution of cladding refractive index. There is no resonance mode splitting in the curvature range investigated at 0° orientation. The cladding mode effective index at the downside of fiber decreases with curvature tension, while the cladding mode effective index at the upside of fiber increases with curvature compression. Likewise, the intensity field of cladding mode is azimuthally changed with the bending of the fiber. The resonant wavelength of symmetrical coupling is gradually shifted towards blue-side and the resonance of asymmetrical coupling disappears.

 

Fig. 2. (a) Resonance evolution of the ESM-PCF-LPG transmission spectrum corresponding to different curvature at rotational orientation of 0°; (b) resonant wavelength shift and intensity change of the tested grating as bending curvature increases.

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The coupled-mode theory can be applied in the intensity of resonance in a PCF-LPG [17–20], which is determined by the coupling coefficient κ and grating length L. The minimum transmission is proportional to cos2(κL), while the coupling coefficient is the function of the effective index change and the mode overlap between the guided core mode and the coupled cladding mode over the region of perturbation. When the tested ESM-PCF-LPG experiences a bending process, both effective index of core and cladding will change. The trend of resonance strength in Fig. 2(b) reveals that the slope of effective index change is larger in cladding than in core because of the micro-deformation of air channel at fiber curvature, which causes the oscillation of resonant intensity to become shorter. It can be seen that, as the curvature increases up to 2.5 m-1, the resonant wavelength shifts towards blue-side linearly. With further bending, the resonance shits to red-side. This trend implies that the influence of curvature on the effective index of cladding mode would be less than that of core mode, likely caused by greater change of cladding refractive index at higher curvature.

 

Fig. 3. (a) Resonance evolution of ESM-PCF-LPG transmission spectrum corresponding to different curvature at rotational orientation of 90°, resonance splitting to occur at higher bending curvature; (b) resonant wavelength shift, and intensity change of the tested grating as bending curvature increases, insets: optical micrographs of an LPG section (left) and a cleaved cross-section of the fiber (right).

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Fig. 4. (a) Resonance evolution of ESM-PCF-LPG transmission spectrum corresponding to different curvature at rotational orientation of 180°, resonance splitting to occur at higher bending curvature; (b) resonant wavelength shift, and intensity change of the tested grating as the bending curvature increases, inset: evolution of two closed resonances at 1554 nm and 1603 nm for wavelength separation as a function of curvature.

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The resonance evolution of ESM-PCF-LPG at orientation of 90° and 180° is shown in Fig. 3(a) and Fig. 4(a), respectively. The symmetric cladding modes are split into two resonances in both cases. The splitting can be attributed to the breaking of the cladding-mode symmetry [14]. In addition, the resonant strength of the symmetrical cladding mode decreases with curvature, implying that the overlap of the core mode with the field of symmetrical cladding mode tends to decrease. The strength of the asymmetrical cladding mode at 90° orientation remains unchanged. It shifts towards red-side with symmetrical resonance as the bending curvature increases. The relationship of wavelength and transmission intensity via curvature is shown in Fig. 3(b). Insets in the figure are photographs of a section of the ESM-PCF-LPG and a cleaved end of this fiber. The asymmetrical cladding at 180° orientation diminishes with curvature and finally, the symmetrical resonance splits into two attenuation bends at the wavelengths of 1554 nm and 1603 nm as plotted in inset of Fig. 4(b). In fact, two higher order cladding modes with azimuthally symmetrical field are coupled with guided core mode, leaving two resonances at individual wavelength. The azimuthal asymmetry of cladding mode in PCF-LPG is induced due to micro-deformation of air channels during fiber bending as well as unidirectional LPG fabrication. A bending coefficient of ~ 27.9 nm∙m in the ESM-PCF-LPG was found at rotational orientation of 180° within the curvature range from 2.6 m-1 to 3.5 m-1.

 

Fig. 5. Shift in resonant wavelength and change in intensity of SMF-28-LPG at rotational orientation of 0° and 180°, respectively, as bending curvature increases, inset: an optical micrograph of a section of SMF-28-LPG.

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For comparison, SMF-28-LPGs inscribed by CO2 laser under the same condition as for fabrication of ESM-PCF-LPGs was measured upon bending to different curvatures at rotational orientations of 0° and 180°. The respective transmission spectra are shown in Fig. 5. Resonance mode splitting was absent in both orientations, which indicates uniform perturbation in the conventional fiber for the field of cladding modes. Only azimuthally symmetrical mode profiles can be coupled to the guided core mode when the fiber is bent. The shifts of resonant wavelengths and changes of transmission intensity of SMF-28-LPG have the same trend with curvature at 0° and 180° orientations, according to the plots presented in Fig. 5. Shown in the inset of Fig. 5 is the photograph of a section of SMF-28-LPG. In other words, modulation of core and cladding refractive indices induced by CO2 laser exposure is azimuthally symmetric. Unlike the ESM-PCF-LPG at 90° and 180° orientation, but similar with that grating at 0° orientation, the resonant wavelengths of two orientations shift toward blue-side, and the resonance intensities decrease with the increase of bending curvature. These results indicate that the effective refractive index of cladding increases with the formation of asymmetrical cladding mode while the mode coupling coefficient becomes small with less mode-coupling overlap. Additionally, no cladding mode splitting was observed in SMF-28-LPG at bending curvature from 0 to 4 m-1 according to our experiments, contrary to reported studies [21,22] due probably to variation in LPG fabrication methods. Compared with normal LPGs, the high sensitivity of ESM-PCF-LPGs to bending and orientation is meanly attributed to the significant change of evanescent field profile of cladding modes and slight deformation of air channels in cladding with the curvature of the fiber, hence the change of effective refractive indices of cladding modes.

4. Conclusion

We have experimentally studied the spectral characteristics of ESM-PCF-LPGs subject to macro-bending. In addition to predictable changes in resonant wavelength and intensity as a function of bending curvature, the gratings also exhibit resonant mode splitting and orientation dependence due to asymmetrical nature of the unidirectionally inscribed gratings. In contrast, no mode splitting and directional nature at bending are presented for LPGs fabricated in conventional fiber using the same method. ESM-PCF-LPGs are more sensitive both to the curvature and orientation. These grating components with tunable resonant wavelength have excellent potential for sensing applications.

Acknowledgments

We thank Dr. Ryan T. Bise of OFS Laboratories for providing us with ESM-PCFs. This work was partially supported by the National Science Foundation under grant number ECS-0404002.

References and links

1. A. N. Vengsakar, 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. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., 22,961–963, (1997). [CrossRef]  

3. B. Culshaw, “Optical fiber sensor technologies: opportunities and-perhaps-pitfalls,” J. Lightwave Technol. 22,39–50 (2004). [CrossRef]  

4. U. Willer, C. Bohling, and W. Schade, “Using laser spectroscopy and fiber optic sensors to monitor volcanoes,” Opt. Photon. News 15,18–23 (2004).

5. T. Allsop, T. E. Gound, D. J. Webb, and I. Bennion, “Embedded progressive-three-layered fiber long-period gratings for respiratory monitoring,” J. Biomed. Opt. 8,552–558 (2003). [CrossRef]   [PubMed]  

6. J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fiber: A new class of optical waveguides,” Opt. Fiber Technol. 5,305–330 (1999). [CrossRef]  

7. G. Kakarantzas, T. A. Birks, and P. S. J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27,1013–1015 (2002). [CrossRef]  

8. K. Morishita and Y. Miyake, “Fabrication and resonance wavelengths of long-period gratings written in a pure-silica photonic crystal fiber by the glass structure change,” J. Lightwave Technol. 22,625–630 (2004). [CrossRef]  

9. J. K. 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. 29,331–333 (2004). [CrossRef]   [PubMed]  

10. H. Dobb, K. Kalli, and D. J. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fiber,” Opt. Commun. 260,184–191 (2006). [CrossRef]  

11. R. T. Bise and D. Trevor, “Solgel-Derived Microstructured Fibers: Fabrication and Characterization,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OWL6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2005-OWL6. [PubMed]  

12. Y. Zhu, P. Shum, J. H. Chong, M. K. Rao, and C. Lu, “Deep-notch, ultracompact long-period grating in a large-mode-area photonic crystal fiber,” Opt. Lett. 28,2467–2469 (2003). [CrossRef]   [PubMed]  

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

14. K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 14,58–65 (1996).

15. M. Nielsen and N. Mortensen, “Photonic crystal fiber design based on the V-parameter,” Opt. Express 11,2762–2768 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-21-2762. [CrossRef]   [PubMed]  

16. G. Rego, O. V. Ivano, and P. V. S. Marques, “Demonstration of coupling to symmetric and antisymmetric cladding modes in arc-induced long-period fiber gratings,” Opt. Express 14,9594–9599 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9594. [CrossRef]   [PubMed]  

17. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15,1277–1294 (1997). [CrossRef]  

18. B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler, and G. L. Burdge, “Cladding-mode-resonances in air-silica microstructure optical fiber,” J. Lightwave Technol. 18,1084–1100 (2000). [CrossRef]  

19. K. L. Reichenbach and C. Xu, “Independent core propagation in two-core photonic crystal fibers resulting from structural nonuniformities,” Opt. Express 13,10336–10348 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10336. [CrossRef]   [PubMed]  

20. M. Antkowiak, R. Kotynski, K. Panajotov, F. Berghmans, and H. Thienpont, “Numerical, analysis of highly birefringent photonic crystal fibers with Bragg reflectors,” Opt. Quan. Electron. 38,535–545 (2006). [CrossRef]  

21. Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Resonance peak shift and dual peak separation of long-period fiber gratings for sensing applications,” IEEE Photon. Technol. Lett. 13,699–701 (2001). [CrossRef]  

22. U. L. Block, V. Dangui, M. J. F. Digonnet, and M. M. Fejer, “Origin of apparent resonance mode splitting in bent long-period fiber gratings,” J. Lightwave Technol. 24,1027–1034 (2006). [CrossRef]  

References

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  1. A. N. Vengsakar, 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. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., 22,961–963, (1997).
    [Crossref]
  3. B. Culshaw, “Optical fiber sensor technologies: opportunities and-perhaps-pitfalls,” J. Lightwave Technol. 22,39–50 (2004).
    [Crossref]
  4. U. Willer, C. Bohling, and W. Schade, “Using laser spectroscopy and fiber optic sensors to monitor volcanoes,” Opt. Photon. News 15,18–23 (2004).
  5. T. Allsop, T. E. Gound, D. J. Webb, and I. Bennion, “Embedded progressive-three-layered fiber long-period gratings for respiratory monitoring,” J. Biomed. Opt. 8,552–558 (2003).
    [Crossref] [PubMed]
  6. J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fiber: A new class of optical waveguides,” Opt. Fiber Technol. 5,305–330 (1999).
    [Crossref]
  7. G. Kakarantzas, T. A. Birks, and P. S. J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27,1013–1015 (2002).
    [Crossref]
  8. K. Morishita and Y. Miyake, “Fabrication and resonance wavelengths of long-period gratings written in a pure-silica photonic crystal fiber by the glass structure change,” J. Lightwave Technol. 22,625–630 (2004).
    [Crossref]
  9. J. K. 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. 29,331–333 (2004).
    [Crossref] [PubMed]
  10. H. Dobb, K. Kalli, and D. J. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fiber,” Opt. Commun. 260,184–191 (2006).
    [Crossref]
  11. R. T. Bise and D. Trevor, “Solgel-Derived Microstructured Fibers: Fabrication and Characterization,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OWL6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2005-OWL6.
    [PubMed]
  12. Y. Zhu, P. Shum, J. H. Chong, M. K. Rao, and C. Lu, “Deep-notch, ultracompact long-period grating in a large-mode-area photonic crystal fiber,” Opt. Lett. 28,2467–2469 (2003).
    [Crossref] [PubMed]
  13. G. M. VanWiggeren, T. K. Gaylord, D. D. Davis, E. Anemogiannis, B. D. Garrett, M. I. Braiwish, and E. N. Glytsis, “Axial rotation dependence of resonances in curved CO2-laser-induced long-period fiber gratings,” Electron. Lett. 36,1354–1355 (2000).
    [Crossref]
  14. K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 14,58–65 (1996).
  15. M. Nielsen and N. Mortensen, “Photonic crystal fiber design based on the V-parameter,” Opt. Express 11,2762–2768 (2003). http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-21-2762.
    [Crossref] [PubMed]
  16. G. Rego, O. V. Ivano, and P. V. S. Marques, “Demonstration of coupling to symmetric and antisymmetric cladding modes in arc-induced long-period fiber gratings,” Opt. Express 14,9594–9599 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9594.
    [Crossref] [PubMed]
  17. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15,1277–1294 (1997).
    [Crossref]
  18. B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler, and G. L. Burdge, “Cladding-mode-resonances in air-silica microstructure optical fiber,” J. Lightwave Technol. 18,1084–1100 (2000).
    [Crossref]
  19. K. L. Reichenbach and C. Xu, “Independent core propagation in two-core photonic crystal fibers resulting from structural nonuniformities,” Opt. Express 13,10336–10348 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10336.
    [Crossref] [PubMed]
  20. M. Antkowiak, R. Kotynski, K. Panajotov, F. Berghmans, and H. Thienpont, “Numerical, analysis of highly birefringent photonic crystal fibers with Bragg reflectors,” Opt. Quan. Electron. 38,535–545 (2006).
    [Crossref]
  21. Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Resonance peak shift and dual peak separation of long-period fiber gratings for sensing applications,” IEEE Photon. Technol. Lett. 13,699–701 (2001).
    [Crossref]
  22. U. L. Block, V. Dangui, M. J. F. Digonnet, and M. M. Fejer, “Origin of apparent resonance mode splitting in bent long-period fiber gratings,” J. Lightwave Technol. 24,1027–1034 (2006).
    [Crossref]

2006 (4)

H. Dobb, K. Kalli, and D. J. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fiber,” Opt. Commun. 260,184–191 (2006).
[Crossref]

G. Rego, O. V. Ivano, and P. V. S. Marques, “Demonstration of coupling to symmetric and antisymmetric cladding modes in arc-induced long-period fiber gratings,” Opt. Express 14,9594–9599 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9594.
[Crossref] [PubMed]

M. Antkowiak, R. Kotynski, K. Panajotov, F. Berghmans, and H. Thienpont, “Numerical, analysis of highly birefringent photonic crystal fibers with Bragg reflectors,” Opt. Quan. Electron. 38,535–545 (2006).
[Crossref]

U. L. Block, V. Dangui, M. J. F. Digonnet, and M. M. Fejer, “Origin of apparent resonance mode splitting in bent long-period fiber gratings,” J. Lightwave Technol. 24,1027–1034 (2006).
[Crossref]

2005 (1)

2004 (4)

2003 (3)

2002 (1)

2001 (1)

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Resonance peak shift and dual peak separation of long-period fiber gratings for sensing applications,” IEEE Photon. Technol. Lett. 13,699–701 (2001).
[Crossref]

2000 (2)

B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler, and G. L. Burdge, “Cladding-mode-resonances in air-silica microstructure optical fiber,” J. Lightwave Technol. 18,1084–1100 (2000).
[Crossref]

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

1999 (1)

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fiber: A new class of optical waveguides,” Opt. Fiber Technol. 5,305–330 (1999).
[Crossref]

1997 (2)

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., 22,961–963, (1997).
[Crossref]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15,1277–1294 (1997).
[Crossref]

1996 (2)

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 14,58–65 (1996).

A. N. Vengsakar, 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]

Allsop, T.

T. Allsop, T. E. Gound, D. J. Webb, and I. Bennion, “Embedded progressive-three-layered fiber long-period gratings for respiratory monitoring,” J. Biomed. Opt. 8,552–558 (2003).
[Crossref] [PubMed]

Anemogiannis, E.

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

Antkowiak, M.

M. Antkowiak, R. Kotynski, K. Panajotov, F. Berghmans, and H. Thienpont, “Numerical, analysis of highly birefringent photonic crystal fibers with Bragg reflectors,” Opt. Quan. Electron. 38,535–545 (2006).
[Crossref]

Barkou, S. E.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fiber: A new class of optical waveguides,” Opt. Fiber Technol. 5,305–330 (1999).
[Crossref]

Bennion, I.

T. Allsop, T. E. Gound, D. J. Webb, and I. Bennion, “Embedded progressive-three-layered fiber long-period gratings for respiratory monitoring,” J. Biomed. Opt. 8,552–558 (2003).
[Crossref] [PubMed]

Berghmans, F.

M. Antkowiak, R. Kotynski, K. Panajotov, F. Berghmans, and H. Thienpont, “Numerical, analysis of highly birefringent photonic crystal fibers with Bragg reflectors,” Opt. Quan. Electron. 38,535–545 (2006).
[Crossref]

Bhatia, V.

A. N. Vengsakar, 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]

Birks, T. A.

G. Kakarantzas, T. A. Birks, and P. S. J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27,1013–1015 (2002).
[Crossref]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., 22,961–963, (1997).
[Crossref]

Bise, R. T.

R. T. Bise and D. Trevor, “Solgel-Derived Microstructured Fibers: Fabrication and Characterization,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OWL6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2005-OWL6.
[PubMed]

Bjarklev, A.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fiber: A new class of optical waveguides,” Opt. Fiber Technol. 5,305–330 (1999).
[Crossref]

Block, U. L.

Bohling, C.

U. Willer, C. Bohling, and W. Schade, “Using laser spectroscopy and fiber optic sensors to monitor volcanoes,” Opt. Photon. News 15,18–23 (2004).

Braiwish, M. I.

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

Broeng, J.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fiber: A new class of optical waveguides,” Opt. Fiber Technol. 5,305–330 (1999).
[Crossref]

Burdge, G. L.

Chong, J. H.

Chung, Y.

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Resonance peak shift and dual peak separation of long-period fiber gratings for sensing applications,” IEEE Photon. Technol. Lett. 13,699–701 (2001).
[Crossref]

Culshaw, B.

Dangui, V.

Davis, D. D.

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

Digonnet, M. J. F.

Dobb, H.

H. Dobb, K. Kalli, and D. J. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fiber,” Opt. Commun. 260,184–191 (2006).
[Crossref]

Eggleton, B. J.

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15,1277–1294 (1997).
[Crossref]

A. N. Vengsakar, 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]

Fejer, M. M.

Garrett, B. D.

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

Gaylord, T. K.

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

Glytsis, E. N.

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

Gound, T. E.

T. Allsop, T. E. Gound, D. J. Webb, and I. Bennion, “Embedded progressive-three-layered fiber long-period gratings for respiratory monitoring,” J. Biomed. Opt. 8,552–558 (2003).
[Crossref] [PubMed]

Han, W.-T.

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Resonance peak shift and dual peak separation of long-period fiber gratings for sensing applications,” IEEE Photon. Technol. Lett. 13,699–701 (2001).
[Crossref]

Han, Y.-G.

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Resonance peak shift and dual peak separation of long-period fiber gratings for sensing applications,” IEEE Photon. Technol. Lett. 13,699–701 (2001).
[Crossref]

Ivano, O. V.

Judkins, J. B.

A. N. Vengsakar, 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]

Kakarantzas, G.

Kalli, K.

H. Dobb, K. Kalli, and D. J. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fiber,” Opt. Commun. 260,184–191 (2006).
[Crossref]

Kerbage, C.

Kim, J. C.

Knight, J. C.

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., 22,961–963, (1997).
[Crossref]

Koshiba, M.

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 14,58–65 (1996).

Kotynski, R.

M. Antkowiak, R. Kotynski, K. Panajotov, F. Berghmans, and H. Thienpont, “Numerical, analysis of highly birefringent photonic crystal fibers with Bragg reflectors,” Opt. Quan. Electron. 38,535–545 (2006).
[Crossref]

Lee, B. H.

J. K. 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. 29,331–333 (2004).
[Crossref] [PubMed]

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Resonance peak shift and dual peak separation of long-period fiber gratings for sensing applications,” IEEE Photon. Technol. Lett. 13,699–701 (2001).
[Crossref]

Lee, K. S.

Lemaire, P. J.

A. N. Vengsakar, 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]

Lim, J. K. H.

Lu, C.

Marques, P. V. S.

Miyake, Y.

Mogilevstev, D.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fiber: A new class of optical waveguides,” Opt. Fiber Technol. 5,305–330 (1999).
[Crossref]

Morishita, K.

Mortensen, N.

Nielsen, M.

Paek, U.-C.

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Resonance peak shift and dual peak separation of long-period fiber gratings for sensing applications,” IEEE Photon. Technol. Lett. 13,699–701 (2001).
[Crossref]

Panajotov, K.

M. Antkowiak, R. Kotynski, K. Panajotov, F. Berghmans, and H. Thienpont, “Numerical, analysis of highly birefringent photonic crystal fibers with Bragg reflectors,” Opt. Quan. Electron. 38,535–545 (2006).
[Crossref]

Rao, M. K.

Rego, G.

Reichenbach, K. L.

Russell, P. S. J.

Russell, P. St. J.

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., 22,961–963, (1997).
[Crossref]

Saitoh, K.

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 14,58–65 (1996).

Schade, W.

U. Willer, C. Bohling, and W. Schade, “Using laser spectroscopy and fiber optic sensors to monitor volcanoes,” Opt. Photon. News 15,18–23 (2004).

Shum, P.

Sipe, J. E.

A. N. Vengsakar, 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]

Thienpont, H.

M. Antkowiak, R. Kotynski, K. Panajotov, F. Berghmans, and H. Thienpont, “Numerical, analysis of highly birefringent photonic crystal fibers with Bragg reflectors,” Opt. Quan. Electron. 38,535–545 (2006).
[Crossref]

Trevor, D.

R. T. Bise and D. Trevor, “Solgel-Derived Microstructured Fibers: Fabrication and Characterization,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OWL6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2005-OWL6.
[PubMed]

VanWiggeren, G. M.

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

Vengsakar, A. N.

A. N. Vengsakar, 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]

Webb, D. J.

H. Dobb, K. Kalli, and D. J. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fiber,” Opt. Commun. 260,184–191 (2006).
[Crossref]

T. Allsop, T. E. Gound, D. J. Webb, and I. Bennion, “Embedded progressive-three-layered fiber long-period gratings for respiratory monitoring,” J. Biomed. Opt. 8,552–558 (2003).
[Crossref] [PubMed]

Westbrook, P. S.

White, C. A.

Willer, U.

U. Willer, C. Bohling, and W. Schade, “Using laser spectroscopy and fiber optic sensors to monitor volcanoes,” Opt. Photon. News 15,18–23 (2004).

Windeler, R. S.

Xu, C.

Zhu, Y.

Electron. Lett. (1)

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

IEEE Photon. Technol. Lett. (1)

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, and Y. Chung, “Resonance peak shift and dual peak separation of long-period fiber gratings for sensing applications,” IEEE Photon. Technol. Lett. 13,699–701 (2001).
[Crossref]

J. Biomed. Opt. (1)

T. Allsop, T. E. Gound, D. J. Webb, and I. Bennion, “Embedded progressive-three-layered fiber long-period gratings for respiratory monitoring,” J. Biomed. Opt. 8,552–558 (2003).
[Crossref] [PubMed]

J. Lightwave Technol. (7)

Opt. Commun. (1)

H. Dobb, K. Kalli, and D. J. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fiber,” Opt. Commun. 260,184–191 (2006).
[Crossref]

Opt. Express (3)

Opt. Fiber Technol. (1)

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fiber: A new class of optical waveguides,” Opt. Fiber Technol. 5,305–330 (1999).
[Crossref]

Opt. Lett. (3)

Opt. Lett., (1)

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., 22,961–963, (1997).
[Crossref]

Opt. Photon. News (1)

U. Willer, C. Bohling, and W. Schade, “Using laser spectroscopy and fiber optic sensors to monitor volcanoes,” Opt. Photon. News 15,18–23 (2004).

Opt. Quan. Electron. (1)

M. Antkowiak, R. Kotynski, K. Panajotov, F. Berghmans, and H. Thienpont, “Numerical, analysis of highly birefringent photonic crystal fibers with Bragg reflectors,” Opt. Quan. Electron. 38,535–545 (2006).
[Crossref]

Other (1)

R. T. Bise and D. Trevor, “Solgel-Derived Microstructured Fibers: Fabrication and Characterization,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OWL6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2005-OWL6.
[PubMed]

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic diagram of the three-point bending setup (2L = 100 mm, d = 0 - 25.4 mm, wavelength region of broadband light source λ = 1450 - 1650 nm); (b) 0° orientation; (c) 180° orientation; (d) 90° orientation; (e) 270° orientation.
Fig. 2.
Fig. 2. (a) Resonance evolution of the ESM-PCF-LPG transmission spectrum corresponding to different curvature at rotational orientation of 0°; (b) resonant wavelength shift and intensity change of the tested grating as bending curvature increases.
Fig. 3.
Fig. 3. (a) Resonance evolution of ESM-PCF-LPG transmission spectrum corresponding to different curvature at rotational orientation of 90°, resonance splitting to occur at higher bending curvature; (b) resonant wavelength shift, and intensity change of the tested grating as bending curvature increases, insets: optical micrographs of an LPG section (left) and a cleaved cross-section of the fiber (right).
Fig. 4.
Fig. 4. (a) Resonance evolution of ESM-PCF-LPG transmission spectrum corresponding to different curvature at rotational orientation of 180°, resonance splitting to occur at higher bending curvature; (b) resonant wavelength shift, and intensity change of the tested grating as the bending curvature increases, inset: evolution of two closed resonances at 1554 nm and 1603 nm for wavelength separation as a function of curvature.
Fig. 5.
Fig. 5. Shift in resonant wavelength and change in intensity of SMF-28-LPG at rotational orientation of 0° and 180°, respectively, as bending curvature increases, inset: an optical micrograph of a section of SMF-28-LPG.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

1 R = 2 d ( d 2 + L 2 )
λ i = n core eff λ 0 n core n clad n clad ( i ) eff λ 0 n clad n ext Λ
λ i n clad = ( λ i n core eff n core eff n clad λ i n clad ( i ) eff n clad ( i ) eff n clad ) Λ
d λ i d ( 1 R ) = ( dn core eff ( 1 R ) d ( 1 R ) dn clad ( i ) eff ( 1 R ) d ( 1 R ) ) Λ

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