Abstract

Ultra short long-period gratings (LPGs) fabricated using the electric arc discharge method are demonstrated with regular single-mode fibers. The gratings were as short as two periods, which were the shortest LPGs ever reported. The evolution of this short gratings and their characteristics are investigated in this paper. The excellent bending insensitivity and high temperature robustness demonstrated by this unique LPG make it particularly suitable for harsh environment sensing and communication.

©2005 Optical Society of America

1. Introduction

An electromagnetic interference (EMI)-immune, high-accuracy fiber-grating-based temperature sensing system has great potential to improve the operating efficiency by providing distributed temperature estimation in the power generation systems. A typical operating environment for temperature sensors in such systems will reach temperatures of 500 °C or higher and be accompanied by vibrations and turbulences. The need for achieving long-term stability for high temperature operations will require new grating fabrication techniques.

Recently, we have noticed a growing interest in non-ultraviolet (UV) based fabrication methods of long-period fiber gratings (LPFGs). The fiber gratings rely on periodic refractive index perturbation of the fibers. To induce the refractive index change in the fibers, conventionally, the photosensitivity of Ge-doped fibers to ultraviolet (UV) light has been utilized. Several non-UV based methods have shown the capability of inducing refractive index changes inside fibers by different types of writing mechanisms; thermal effects by CO2 laser or electric arc, photo-elastic effects by cladding etching, and femtosecond laser irradiation [14]. Each fabrication method has its own advantages, such as producing gratings that have high temperature stability and flexibility of fabrication. Since photosensitivity is no longer a requirement, these methods are also attractive for writing gratings in micro-structured specialty fibers [5]. The fabrication method based on electric arc discharge has drawn considerable attention due to its low fabrication cost, flexibility, and excellent grating quality. Most recently, however, gratings written using non-UV based methods have only aimed at achieving a spectral quality similar to those written with UV. Although strong gratings were fabricated in photonic crystal fiber using a CO2 based method in [6], the background loss was too big (~15dB) to be practical due to the collapse of the air holes.

In this letter, we report a unique bend insensitive LPFG fabricated by using a strong electric arc discharge. By intentionally increasing the arc duration, a large refractive index modulation is achieved in the fiber, and the unique LPFG is realized.

2. Fabrication and growth of very short LPFGs

The experimental setup we used for LPFG fabrication is similar to that described in [2] and is shown in Fig. 1. A standard single mode communication fiber (SMF-28e) with a short unjacketed section was placed in two fiber holders. Both ends of the fiber were clamped by the holders and held straight. Two electrodes were mounted in a fixture that was moved by a nano-precision translation stage. The grating spectrum was monitored while the arc discharge was being produced. The entire fabrication process was fully controlled by a computer. Two methods have been used to fabricate LPFGs by electric arc discharge. The first creates microbends by introducing a small lateral displacement at one end of the fiber [2]. The other tapers the fiber by attaching a mass to one end [7]. Both methods induce refractive index modulation along with mechanical deformation. Depending on the position of the fiber in the arc flame and the applied stress to the fiber, the induced refractive index profile inside the fiber can be greatly affected, which in turn, affects the coupling constant between core and cladding modes. For our experiment, the fiber sat in V-grooves made on the electrodes fixture. There was no lateral displacement at one end of the fiber, and no additional mass was attached. The arc current was ~15mA (rms) with 20 kHz frequency, and the arc duration was changed while keeping arc current constant.

 figure: Fig. 1.

Fig. 1. Experimental setup for LPFG fabrication.

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Figure 2 shows the evolution of a short LPFG as the number of arc discharges is increased. The arc duration was 357ms, and the period was 500µm for this grating. The resonant coupling rapidly grew and reached its deepest peak (-30dB) with 4 grating periods (5 arc discharge). The peak depth was reduced to -13.2dB with one more arc discharge due to over-coupling. The total grating length was 2mm when it reached the deepest peak. Using the measured peak depths, the number of periods, and the relation t ×,max=sin2(κL), the coupling constant for this mode was estimated to be in the order of 10 cm-1, which is over ten times larger than the typical coupling constant of LPFGs.

 figure: Fig. 2.

Fig. 2. Evolution of the short arc-written LPFG.

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 figure: Fig. 3.

Fig. 3. Optical microscope image of short arc-written LPFG.

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For this short grating, a mechanical deformation was observed by an optical microscope as shown in Fig. 3. The magnitude of deformation was estimated to be approximately 10µm. To investigate the effect of the arc duration on resonant wavelength, several LPFGs with different arc durations were fabricated with the grating period 500µm. Figure 4 shows the spectrums obtained with the following arc durations and number of grating periods: (a) 278ms, 11 periods, (b) 313ms, 7 periods, (c) 357ms, 4 periods, (d) 417ms, 2 periods. The spectra shown were taken when the resonant depths reached their maximal values. Notice that in spectrum (d), the LPFG is composed of only 2 periods. To the best knowledge of authors, this is the shortest LPFG ever reported. Also, notice that the resonant peaks shifted to longer wavelength as the arc duration increased, and the magnitude of the shift between (a) and (d) was ~160nm. For weak arc-written LPFGs, the resonant wavelength is independent of the arc duration [2], and is obtained from the phase matching condition as given by Eqs. (1)(3) [8],

(βco+σcoco)(βνjclad+σνjνj)=πΛ
σcoco(z)=ωεon2δn(z)¯dxdyδn(x,y)eco(x,y)·eco*(x,y)
σνjνj(z)=ωεon2δn(z)¯dxdyδn(x,y)eνj(x,y)·eνj*(x,y)

where βco and βνjclad are the propagation constants of the core mode and the ν j cladding mode, respectively, Λ is the grating period, and σco-co and σν j-ν j are the dc (period-averaged) selfcoupling coefficients of the core mode and the ν j cladding mode, respectively. In Eqs. (2) and (3), we used Δε(x, y, z)≅2nδn, where δn(x, y, z)=δn(z)δn(x,y). Since δnn, δn(x, y, z) cannot be assumed uniform across entire cross section of the fiber.

 figure: Fig. 4.

Fig. 4. LPFG spectra with different arc durations. (a) 278ms, 11 periods (b) 313ms, 7 periods (c) 357ms, 4 periods (d) 417ms, 2 periods

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If we further define the effective index perturbation for core mode and cladding mode by Eqs. (4) and (5),

δncoeff(x,y)=dxdyδn(x,y)ecoco(x,y)·ecoco(x,y)dxdyecoco(x,y)·ecoco(x,y)
δnνjeff(x,y)=dxdyδn(x,y)eνjνj(x,y)·eνjνj(x,y)dxdyeνjνj(x,y)·eνjνj(x,y)

the resonant wavelength can be expressed by Eq. (6).

λmax=[neff,co(λmax)(neff,cln(λmax)+δn(z)¯(δncoeffδnνjeff)]Λ

In Eq. (6), the relative effective index perturbation between core and cladding mode, δncoeffδnνjeff , can have different values depending on the method of grating fabrication. For UV-written LPFGs, δncoeffδnνjeff , since the refractive index perturbation is only in the core [8]. As the gratings grow, δncoeff becomes bigger, and the resonant wavelength shifts to the longer wavelength unless res/dΛ is negative. In the latter case, the resonant wavelength shifts to shorter wavelengths [9]. For weak arc written gratings, the results obtained in [2] and our experimental results seem to imply that δncoeffδnνjeff since the resonant wavelength doesn’t change with arc duration. This means that arc discharge can alter the refractive index of the cladding as well as that of the core, and the magnitudes of both are approximately equal. As shown in Fig. 2, however, the relative effective index perturbation, δncoeffδnνjeff , can become larger as the arc duration increases.

3. Bending sensitivity and high temperature characterization of the very short LPFGs

3.1 Bending sensitivity

To investigate the bending sensitivity of the short LPFGs, we prepared samples with 5 periods and 530µm grating period. One end of the fiber was clamped and the other end was translated toward the clamped end by a moving stage to induce fiber bending. The curvature of the bend was calculated by considering the bent fiber as the arc of a circle [10]. The range of curvature was from 0~10.9 m-1. Also, fiber was wound around cylinders with four different curvatures (6.25, 11.1, 18.2, and 27.8 m-1) to get tight bending. For all cases, the orientation of the fiber was kept constant using scotch tape flags attached to the fiber. Figure 5(a) shows the result of the bending experiment for the short LPFG with 0 degree orientation. Note that the bend curvatures tested are much bigger than previous bending experiments [10, 11]. Previous bending experiments were conducted with less than 5m-1 due to LPFG’s high sensitivity to bending. Typical responses of LPFGs to bending are resonant wavelength shifts, reduction of the resonant peak’s depth, and resonant peak splitting [10, 11]. The short LPFG showed a reduction in resonant peak depth but very little spectral shift. The central wavelength remained relatively constant until the curvature reached ~10 m-1, and only showed small shifts at some curvatures, which were within ±2nm. These small shifts were mainly due to the ambiguity of peak position. Even with very tight bending (18.2 m-1), the spectral shape was preserved, and the peak shifted to shorter wavelength by 10nm as shown in Fig. 5(a). The LPFG also showed sensitivity to the orientation of the bending. Figure 5(b) shows the peak’s depth change with different fiber orientation. The resonant peak depth was more sensitive with the 0° orientation (arc discharge direction) than with the 90° orientation. This result is believed to be due to the asymmetry of refractive index modulation induced by electric arc, which is similar to CO2 laser-written LPFGs [12]. We stress that, in many cases, the high sensitivity of typical LPFGs to bending is not desirable, unless bending itself is being measured. The sensitivity to bending imposes tight packaging requirements on the LPFGs to prevent cross-sensitivity. The bending insensitivity of the short LPFGs could benefit the stability of the devices in fiber sensors and communication applications, in particular, in a harsh environment.

 figure: Fig. 5.

Fig. 5. Bending response of the short LPFG. (a) spectrums of the short LPFG with different bending curvatures (unit: m-1) (b) The change of the resonant peaks’ depth with different bending orientation

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3.2 High temperature characterization

The high temperature characteristics of arc-written LPFGs are a major research interest since their thermal stability makes them excellent candidates for applications in harsh, high temperature environments, like boilers in the power plants, where few temperature sensors can survive. For our experiments, a 530 µm grating with four periods was used. The LPFG was positioned in the chamber of a furnace. Due to the limited size of the chamber, the fiber was bent with the bending curvature approximately 10 m-1. The effect of fiber bending on the grating spectrum was negligible. The experimental temperature range extended from room temperature to 1100 °C. The spectrum change was measured as a function of temperature increase, as shown in Fig. 6. Note that the depth of the resonant peak was reduced as the peak wavelength shifted to longer wavelengths. The LPFG’s overall response to temperature was slightly non-linear. The temperature sensitivity increased at higher temperatures. At low temperatures, room temperature to 200 °C, the temperature sensitivity was estimated about 0.054 nm/°C. From 200 °C to 1000 °C, the sensitivity was approximately 0.135 nm/°C, which is similar to those of typical arc-written LPFGs previously reported [7]. These experimental results demonstrated that this unique ultra short LPG was not only insensitive to bending but also could survive at high temperature (~1000 °C), which made it a very good candidate for harsh environment high temperature distributed sensing.

 figure: Fig. 6.

Fig. 6. The high temperature response of the ultra short LPFG.

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4. Conclusion

We demonstrated that very short long-period gratings with a deep spectral peak could be made by the electric arc discharge method. The fabricated LPFGs were as short as 2 periods with ~25dB depth from the background level. By using longer arc periods, the resonant peaks of LPFGs shifted toward longer wavelengths. Bending properties and high temperature characterization were also conducted with the short arc-written LPFGs. The short LPFGs were very insensitive to bending. Although there was a reduction in peak depth, the peak wavelength shift was within ±2 nm even with a ~10 m-1 curvature. The high temperature characteristics of the short LPFGs were similar to regular arc-written LPFGs. The bend-insensitive short arc-written LPFGs could be very useful for broad band filtering and harsh environment high temperature sensing.

References and links

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

2. In Kag Hwang, Seok Hyun Yun, and Byoung Yoon Kim, “Long-period fiber gratings based on periodic microbends,” Opt. Lett. 24, 1263–1265 (1999) [CrossRef]  

3. C. Y. Lin and Lon A. Wang, “A Wavelength- and loss- tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13, 332–334 (2001) [CrossRef]  

4. Francis Hindle et al., “Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation,” IEEE Photon. Technol. Lett. 16, 1861–1863 (2004) [CrossRef]  

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

6. Yinian Zhu, Ping Shum, Joo-Hin Chong, M. K. Rao, and Chao Lu, “Deep-notch, ultracompact long-period grating in a large-mode-area photonic crystal fiber,” Opt. Lett. 28, 2467–2469 (2003) [CrossRef]   [PubMed]  

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

8. Turan Erdogan, “Fiber Grating Sectra,” J. Lightwave. Technol. 15, 1277–1294 (1997) [CrossRef]  

9. Trevor W. MacDougall, Saeed Pilevar, Charles W. Haggans, and Marvin A. Jackson, “Generalized expression for the growth of long period gratings,” IEEE Photon. Technol. Lett. 10, 1449–1451 (1998) [CrossRef]  

10. H. J. Patrick, C. C. Chang, and S. T. Vohra, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998) [CrossRef]  

11. C. C. Ye, S. W. James, and R. P. Tatam, “Simultaneous temperature and bend sensing with long-period fiber gratings,” Opt. Lett. 25, 1007–1009 (2000) [CrossRef]  

12. Gregory D. Van Wiggeren et al., “Tuning, attenuating, and switching by controlled flexure of long-period fiber gratings,” Opt. Lett. 26, 61–63 (2001) [CrossRef]  

References

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  1. D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Longperiod fibre grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302–303 (1998)
    [Crossref]
  2. In Kag Hwang, Seok Hyun Yun, and Byoung Yoon Kim, “Long-period fiber gratings based on periodic microbends,” Opt. Lett. 24, 1263–1265 (1999)
    [Crossref]
  3. C. Y. Lin and Lon A. Wang, “A Wavelength- and loss- tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13, 332–334 (2001)
    [Crossref]
  4. Francis Hindle et al., “Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation,” IEEE Photon. Technol. Lett. 16, 1861–1863 (2004)
    [Crossref]
  5. G. Kakarantzas, T. A. Birks, and P. St. J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27, 1013–1015 (2002)
    [Crossref]
  6. Yinian Zhu, Ping Shum, Joo-Hin Chong, M. K. Rao, and Chao Lu, “Deep-notch, ultracompact long-period grating in a large-mode-area photonic crystal fiber,” Opt. Lett. 28, 2467–2469 (2003)
    [Crossref] [PubMed]
  7. G. Rego, O. Okhotnikov, E. Dianov, and V. Sulimov, “High-temperature stability of long-period fiber gratings produced using an electric arc,” J. Lightwave. Technol. 19, 1574–1579 (2001)
    [Crossref]
  8. Turan Erdogan, “Fiber Grating Sectra,” J. Lightwave. Technol. 15, 1277–1294 (1997)
    [Crossref]
  9. Trevor W. MacDougall, Saeed Pilevar, Charles W. Haggans, and Marvin A. Jackson, “Generalized expression for the growth of long period gratings,” IEEE Photon. Technol. Lett. 10, 1449–1451 (1998)
    [Crossref]
  10. H. J. Patrick, C. C. Chang, and S. T. Vohra, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998)
    [Crossref]
  11. C. C. Ye, S. W. James, and R. P. Tatam, “Simultaneous temperature and bend sensing with long-period fiber gratings,” Opt. Lett. 25, 1007–1009 (2000)
    [Crossref]
  12. Gregory D. Van Wiggeren et al., “Tuning, attenuating, and switching by controlled flexure of long-period fiber gratings,” Opt. Lett. 26, 61–63 (2001)
    [Crossref]

2004 (1)

Francis Hindle et al., “Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation,” IEEE Photon. Technol. Lett. 16, 1861–1863 (2004)
[Crossref]

2003 (1)

2002 (1)

2001 (3)

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

C. Y. Lin and Lon A. Wang, “A Wavelength- and loss- tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13, 332–334 (2001)
[Crossref]

Gregory D. Van Wiggeren et al., “Tuning, attenuating, and switching by controlled flexure of long-period fiber gratings,” Opt. Lett. 26, 61–63 (2001)
[Crossref]

2000 (1)

1999 (1)

1998 (3)

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

Trevor W. MacDougall, Saeed Pilevar, Charles W. Haggans, and Marvin A. Jackson, “Generalized expression for the growth of long period gratings,” IEEE Photon. Technol. Lett. 10, 1449–1451 (1998)
[Crossref]

H. J. Patrick, C. C. Chang, and S. T. Vohra, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998)
[Crossref]

1997 (1)

Turan Erdogan, “Fiber Grating Sectra,” J. Lightwave. Technol. 15, 1277–1294 (1997)
[Crossref]

Birks, T. A.

Chang, C. C.

H. J. Patrick, C. C. Chang, and S. T. Vohra, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998)
[Crossref]

Chong, Joo-Hin

Davis, D. D.

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

Dianov, E.

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

Erdogan, Turan

Turan Erdogan, “Fiber Grating Sectra,” J. Lightwave. Technol. 15, 1277–1294 (1997)
[Crossref]

Gaylord, T. K.

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

Glytsis, E. N.

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

Haggans, Charles W.

Trevor W. MacDougall, Saeed Pilevar, Charles W. Haggans, and Marvin A. Jackson, “Generalized expression for the growth of long period gratings,” IEEE Photon. Technol. Lett. 10, 1449–1451 (1998)
[Crossref]

Hindle, Francis

Francis Hindle et al., “Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation,” IEEE Photon. Technol. Lett. 16, 1861–1863 (2004)
[Crossref]

Hwang, In Kag

Jackson, Marvin A.

Trevor W. MacDougall, Saeed Pilevar, Charles W. Haggans, and Marvin A. Jackson, “Generalized expression for the growth of long period gratings,” IEEE Photon. Technol. Lett. 10, 1449–1451 (1998)
[Crossref]

James, S. W.

Kakarantzas, G.

Kim, Byoung Yoon

Kosinski, S. G.

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

Lin, C. Y.

C. Y. Lin and Lon A. Wang, “A Wavelength- and loss- tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13, 332–334 (2001)
[Crossref]

Lu, Chao

MacDougall, Trevor W.

Trevor W. MacDougall, Saeed Pilevar, Charles W. Haggans, and Marvin A. Jackson, “Generalized expression for the growth of long period gratings,” IEEE Photon. Technol. Lett. 10, 1449–1451 (1998)
[Crossref]

Mettler, S. C.

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

Okhotnikov, O.

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

Patrick, H. J.

H. J. Patrick, C. C. Chang, and S. T. Vohra, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998)
[Crossref]

Pilevar, Saeed

Trevor W. MacDougall, Saeed Pilevar, Charles W. Haggans, and Marvin A. Jackson, “Generalized expression for the growth of long period gratings,” IEEE Photon. Technol. Lett. 10, 1449–1451 (1998)
[Crossref]

Rao, M. K.

Rego, G.

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

Russell, P. St. J.

Shum, Ping

Sulimov, V.

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

Tatam, R. P.

Van Wiggeren, Gregory D.

Vengsarkar, A. M.

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

Vohra, S. T.

H. J. Patrick, C. C. Chang, and S. T. Vohra, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998)
[Crossref]

Wang, Lon A.

C. Y. Lin and Lon A. Wang, “A Wavelength- and loss- tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13, 332–334 (2001)
[Crossref]

Ye, C. C.

Yun, Seok Hyun

Zhu, Yinian

Electron. Lett. (2)

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

H. J. Patrick, C. C. Chang, and S. T. Vohra, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998)
[Crossref]

IEEE Photon. Technol. Lett. (3)

Trevor W. MacDougall, Saeed Pilevar, Charles W. Haggans, and Marvin A. Jackson, “Generalized expression for the growth of long period gratings,” IEEE Photon. Technol. Lett. 10, 1449–1451 (1998)
[Crossref]

C. Y. Lin and Lon A. Wang, “A Wavelength- and loss- tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13, 332–334 (2001)
[Crossref]

Francis Hindle et al., “Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation,” IEEE Photon. Technol. Lett. 16, 1861–1863 (2004)
[Crossref]

J. Lightwave. Technol. (2)

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

Turan Erdogan, “Fiber Grating Sectra,” J. Lightwave. Technol. 15, 1277–1294 (1997)
[Crossref]

Opt. Lett. (5)

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Figures (6)

Fig. 1.
Fig. 1. Experimental setup for LPFG fabrication.
Fig. 2.
Fig. 2. Evolution of the short arc-written LPFG.
Fig. 3.
Fig. 3. Optical microscope image of short arc-written LPFG.
Fig. 4.
Fig. 4. LPFG spectra with different arc durations. (a) 278ms, 11 periods (b) 313ms, 7 periods (c) 357ms, 4 periods (d) 417ms, 2 periods
Fig. 5.
Fig. 5. Bending response of the short LPFG. (a) spectrums of the short LPFG with different bending curvatures (unit: m-1) (b) The change of the resonant peaks’ depth with different bending orientation
Fig. 6.
Fig. 6. The high temperature response of the ultra short LPFG.

Equations (6)

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( β co + σ co co ) ( β ν j clad + σ ν j ν j ) = π Λ
σ co co ( z ) = ω ε o n 2 δ n ( z ) ¯ dx dy δ n ( x , y ) e co ( x , y ) · e co * ( x , y )
σ ν j ν j ( z ) = ω ε o n 2 δ n ( z ) ¯ dx dy δ n ( x , y ) e ν j ( x , y ) · e ν j * ( x , y )
δ n co eff ( x , y ) = dx dy δ n ( x , y ) e co co ( x , y ) · e co co ( x , y ) dx dy e co co ( x , y ) · e co co ( x , y )
δ n ν j eff ( x , y ) = dx dy δ n ( x , y ) e ν j ν j ( x , y ) · e ν j ν j ( x , y ) dx dy e ν j ν j ( x , y ) · e ν j ν j ( x , y )
λ max = [ n eff , co ( λ max ) ( n eff , cl n ( λ max ) + δ n ( z ) ¯ ( δ n co eff δ n ν j eff ) ] Λ

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