Abstract

Ultra-long fiber Bragg gratings (FBGs), i.e., FBGs of several tens of cm in length, have attracted much attention in the last few decades for their potential applications in advanced devices. Although numerous fabrication methods as well as ultra-long functionalized FBGs have been proposed and demonstrated successfully, such devices are difficult to reproduce. We have recently found that specialty optical fibers of the type required for these applications are highly non-uniform on a short length scale, severely affecting the characteristics of ultra-long FBGs. We propose here a new production technique that can be adapted to any non-uniform fiber for ultra-long FBG fabrication. This technique involves a fiber characterization prior to FBG inscription followed by the writing of a phase corrected ultra-long FBG. This technique has no limitations in terms of correction amplitude or FBG length. The results are quite astonishing, as near-perfect 1-m-length-scale FBGs are possible in fibers in which it was impossible to write uniform period gratings prior to phase correction.

© 2017 Optical Society of America

Fiber Bragg gratings (FBGs) have been used widely in numerous applications, from filters in telecommunications to sensors in many areas of photonics. Ultra-long FBGs, which we define as being longer than the length of commonly available phase masks, i.e., >15cm, have been studied over the last few decades, leading to numerous demonstrations in various applications such as lasers, dispersion compensation, and nonlinear optics. Stitched FBGs were first proposed, but those typically included phase errors [1,2]. Continuous writing schemes were then proposed to avoid such errors [37]. However, random phase errors were still frequently observed, which led to applications in random gratings [8]. Ultra-long distributed feedback FBGs (DFB-FBGs) have been also successfully used as Raman lasers [9]. Despite these numerous attempts and demonstrations, our own considerable experience has shown unequivocally that such ultra-long FBGs are not reproducible because they often show significant phase errors if examined at higher spectral resolution, and only the few “best-typical” results are normally seen in publications. For ultra-long FBGs to become widely deployable, the reasons for their lack of reproducibility need to be addressed.

A reproducible method has been shown recently in standard fiber (SMF-28) for up to 1-m-long FBGs [10], the longest all-in-phase FBGs ever produced with good reliability. This fabrication method was used to produce a 50-cm-long Brillouin DFB laser in SMF-28 [11]. Although ultra-long FBGs in SMF-28 do seem reproducible, such reproducibility is very hard to demonstrate in other types of fibers. We have recently demonstrated that the fibers themselves are not uniform over even short lengths in the order of cms (variation in the effective mode index) and cause large fluctuations in the FBG’s instantaneous Bragg wavelength along the fiber [12]. This random and unpredictable chirp effectively reduces the stop-band strength, enlarges the bandwidth, and causes unwanted mode resonances to appear within the stop band. Various techniques have been developed to characterize FBGs spatially: the refractive index modulation (coupling constant) can be determined by side diffraction [13,14], while all parameters can be determined by optical Fourier domain reflectometry (OFDR) [15], thermal iterative chirping [16], or inverse reconstruction [17]. These techniques can allow the observation of repetitive phase defects in the FBG during a specific writing cycle, which can be subsequently corrected, as shown by Miller et al. [15,18]. However, the latter method is limited in terms of FBG length and phase correction to variations in the order of 2π. We have seen in our investigations that in many fibers, the observed phase shift can be 20π radians or greater along 10cm, making this technique impossible to apply for correcting ultra-long FBGs.

We have implemented a modified correction scheme based on the one reported by Miller et al. and applied it to ultra-long FBG fabrication in our continuous direct writing technique, overcoming the limits in phase correction. Hence, in this Letter, we demonstrate ultra-long phase corrected FBGs. The final phase corrected FBGs show near theoretically perfect spectra, overcoming the problems of reproducibility. The method will be described, followed by a demonstration of a few phase corrected FBGs to highlight the power of this technique.

A continuous direct writing scheme was used [10], as shown in Fig. 1(a), based on a Q-switched 266 nm wavelength laser, a Talbot interferometer, and phase modulators to synchronize the fringe movement with the moving fiber. An air-bearing stage stabilized by a laser interferometer moves the fiber. The phase modulators are driven with a sawtooth wave function, the frequency of which determines the Bragg wavelength so long as the wavelength is within a certain bandwidth of the fringe pattern determined by the Talbot interferometer and spot size. The DFB-FBGs demonstrated here include a π-shift near the middle of the FBG through a speed variation [11]. The relationship between the Bragg wavelength λB and writing parameters is as follows [7]:

λB(z)=2neff(z)v(z)f,
where neff is the effective refractive index of the mode (around 1.45, dependent on fiber), v is the speed of the moving fiber (typ. 100μm/s), and f is the frequency of the sawtooth wave function on the modulators (selected for the target λB). Here, neff(z) needs to be corrected, and v is used to correct it.

 figure: Fig. 1.

Fig. 1. (a) Experimental setup for FBG writing. The system is a continuous direct writing scheme. The fiber moves at speed v, while the phase modulator moves the fringe pattern using a sawtooth function with a frequency f. (b) A commercial OFDR characterization system is used to find the wavelength deviation along the fiber.

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The required correction was measured by probe FBGs using OFDR, as shown in Fig. 1(b), prior to the target FBG being written. Three weak probe FBGs were written at the same location as the final target FBG with Bragg wavelengths separated by 1 nm each and outside of the target bandwidth of the desired FBG. The wavelengths of the probe FBGs were set using the sawtooth wave frequency f. Because the probe FBGs are very weak (<10dB in transmission, κacL<0.3) and lie outside of the target FBGs bandwidth, their spectra do not interfere with the latter. The frequency shift along fiber position (phase derivative measured by OFDR) was then averaged for the three probe FBGs, and a correction profile was derived. The FBGs’ strength can be altered by the UV exposure (speed of writing and UV power) and apodization. A combination of these adjustments was used for the probe gratings depending on the FBG type and fabrication time needed for each grating.

Using more than a single probe FBG for characterization is essential because environmental fluctuation can easily mask the spectra through noise of a few pm (slow varying), as well as measurement errors causing peaks to appear in the OFDR phase derivative. Having several probe FBGs and comparing their respective wavelength deviations ensure that the correction is valid and truly represents defects in the fiber.

To demonstrate the ultra-long FBG writing technique, three high-NA fibers were tested, including one that was polarization maintaining. Such fibers have several applications in nonlinear optics but were found to be highly non-uniform even over short lengths [12], which poses serious issues for ultra-long FBGs. Of the three fibers, HNA1 is a high NA (0.25), germanium-boron co-doped and cladding mode suppressed fiber. HNA2 is a highly nonlinear fiber with a large NA (0.3) and small core (3 μm diameter). PMHNA is a polarization maintaining (PM) fiber with a small core (3 μm diameter) and large NA (0.3).

For the first demonstration of phase correction, a 95-cm-long FBG was written in HNA1. The wavelength deviation (difference from the target λB) resulting from a spatial variation in the refractive index of the fiber was first measured using the three probe FBGs. The average of these measurements is shown in Fig. 2(a). A required correction was then applied to the desired stronger FBG. The resulting change is shown in Fig. 2(b), in which the reflection spectrum of one of the three probe FBGs (all three probe FBGs had near identical spectra) is seen with the dramatically narrower spectrum of the corrected FBG in the background. The latter is shown in greater detail where it is compared to a theoretical fit yielding a κac of 3.9m1 (κacL=3.42) in Fig. 2(c). Theoretical calculation was performed using the transfer matrix method [7].

 figure: Fig. 2.

Fig. 2. Corrected 95-cm-long uniform FBG fabricated in HNA1 fiber at 1555.3 nm. (a) Measured wavelength deviation by OFDR from the average of the probe FBGs. (b) Comparison of one of the uncorrected probe FBG spectra with the corrected required FBG, a zoom of which is reproduced (c), along with the theoretically designed spectra.

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High Ge content fibers typically have a weak birefringence, intrinsic to fabrication or induced by UV writing, which generates two Bragg resonances separated by 5pm for this fiber. Since the dual spectra could not be observed in the probe FBGs, given that their bandwidths are >100pm, the testing laser’s polarization could not be aligned with one of the axes during the wavelength deviation characterization. We believe this is the reason why the correction was not quite perfect and generated stronger sidelobes.

To achieve better results, a PM fiber was used. As in the first case, a 95-cm-corrected FBG was written. This time, however, the polarization of the OFDR laser was aligned along one of the axes of the PM fiber, as the resonances of the two polarizations could be easily distinguished in the probe FBGs’ spectra. The average of the wavelength deviation along the length as measured by the OFDR of the three probe FBGs is shown in Fig. 3(a). The corresponding spectra of one of the probe FBGs is shown in Fig. 3(b). As can be observed once again, the probe FBG spectra is of poor quality. By correcting the wavelength deviation, we obtained the FBG shown in Fig. 3(b) (in the background), a close-up of which is shown in Fig. 3(c). As can be seen, this FBG is very close to a perfect theoretical FBG of 95 cm length over the full stop band and the first sidelobes.

 figure: Fig. 3.

Fig. 3. Corrected 95-cm-long uniform FBG fabricated in PMHNA fiber at 1559.7 nm. (a) Measured wavelength deviation by OFDR derived from the average of spectra of the three probe FBGs. (b) Comparison of one of the uncorrected probe FBGs with the final corrected FBG, which is reproduced and zoomed in (c), where it is compared with the theoretical spectra of a 95-cm-long FBG.

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As near-perfect ultra-long uniform FBGs have been demonstrated with good reproducibility in difficult fibers, we now try to functionalize the FBG by adding a π-phase shift near the middle of the grating. The DFB-FBGs tested here were shorter because they were designed according to our Raman generation test bench, which limited the length. Stronger versions (<80dB in transmission) required for lasers, not shown here because the features cannot be resolved due to lack of spectral resolution, showed significant improvement in single-mode performance at 1578 nm when pumped at 1480 nm, details of which will be published elsewhere in a near future. A weaker DFB (55dB in transmission) is shown in Fig. 4 to demonstrate the effect of the correction on the quality of the FBG. Figure 4(a) shows the measured wavelength deviation of three probe FBGs, and Fig. 4(b) shows the corresponding reflection spectra of one of the probe FBGs. Since we are interested here in a DFB grating for a laser application, and since such FBGs are quite strong, transmission spectra are shown of the resulting corrected FBG in Figs. 4(b) and 4(c). To appreciate the difference between uncorrected and corrected FBGs, a simulated transmission spectrum of an uncorrected FBG is shown in Fig. 4(b). This simulation is based on the wavelength deviation measured in Fig. 4(a). This simulated uncorrected DFB grating loses stop-band strength due to nonlinearity and has multiple internal modes, which interfere with the desired π-shifted DFB mode. In contrast, the correction yields a theoretically near-perfect DFB-FBG, with a slight nonlinear chirp generating asymmetric sidelobes, which do not compromise the functionality of this DFB.

 figure: Fig. 4.

Fig. 4. Corrected DFB-FBG of 30 cm fabricated in HNA2 fiber at 1578.1 nm. (a) Measured wavelength deviation with OBR from three probe FBG average. (b) Comparison of one of the uncorrected probe FBGs (in reflection) with the final corrected DFB (in transmission). A simulated DFB with its final κac strength was calculated with the frequency deviation in (a) to show what the DFB would have looked like in transmission if not corrected. The final corrected DFB is reproduced in (c), where it is compared with a theoretically perfect DFB.

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Despite the significant observed gain in FBG quality, we do still observe some imperfections, manifesting mainly in the appearance of sidelobes. This is likely due to noise and errors in the characterization, as well as influence from environmental fluctuations during the final writing process. Because birefringence is typical of any high Ge photosensitive non-PM fibers, a better characterization of the wavelength deviation performed along one of the UV induced, or intrinsic, principal axes is necessary, especially for FBGs with a length of >50cm. A solution would be to make a second iteration in the characterization using corrected probe FBGs aligned with the principal axis, after the initial coarse correction. The characterization of the newly corrected probe FBGs will allow a finer correction for the final targeted FBG.

Typical FBGs of 10cm or less are not significantly affected by the fiber’s neff fluctuations. For 20–30 cm FBGs, the defects are not necessarily critical, but they do affect the reproducibility of high quality FBGs affecting overall yield. However, for 30 cm to 1 m ultra-long FBGs, these defects are quite critical, as shown in Figs. 2(b) and 3(b), because each fluctuation generates internal resonances and significantly enlarges the bandwidth.

It should be noted that ultra-long FBGs are extremely sensitive to the environment. Indeed, the spectrum can radically change (chirped, resonance modes) with the slightest bend or temperature gradient. Therefore, if the conditions change between the fiber characterization and the application, then the applied correction may not be adapted to the application, and the FBG spectrum may be of poorer quality. To avoid this, the OFDR characterization should take place with the probe FBGs in the operating conditions of the future desired FBG.

From our results, we can see a significant improvement in the spectral characteristics of ultra-long FBGs after correcting for intrinsic fiber non-uniformity. As can be seen from the wavelength deviation measurements and from our previously reported measurements [12], optical fibers, especially specialty optical fibers, are surprisingly non-uniform, which makes it impossible to generate or replicate perfect ultra-long FBG without correction. This phase correction technique can be applied to any continuous writing scheme for ultra-long FBG, including femtosecond laser writing. The ultimate limitation of the corrected gratings length is currently seen to be from the temperature gradient across the grating during testing and fabrication. Although the correction does place an overhead on production since a prior characterization must be performed, all the results of our correcting scheme show excellent reproducibility. The advantages of a near 100% yield in FBG production perhaps outweigh this overhead. This solution therefore allows high quality functionalized long and ultra-long FBGs to be highly reproducible and therefore commercially viable. Also, instead of directly correcting FBG frequency, this technique could also be used to flatten fiber refractive index by controlled exposure.

Funding

Natural Sciences and Engineering Research Council of Canada (NSERC); Canada Research Chairs Programs.

REFERENCES

1. R. Kashyap, H. G. Froehlich, A. Swanton, and D. J. Armes, Electron. Lett. 32, 1807 (1996). [CrossRef]  

2. B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001). [CrossRef]  

3. I. Petermann, B. Sahlgren, S. Helmfrid, A. T. Friberg, and P.-Y. Fonjallaz, Appl. Opt. 41, 1051 (2002). [CrossRef]  

4. M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997). [CrossRef]  

5. R. Kashyap, A. Swanton, and R. P. Smith, Electron. Lett. 35, 1871 (1999). [CrossRef]  

6. K. M. Chung, L. Dong, C. Lu, and H. Y. Tam, Opt. Express 19, 12664 (2011). [CrossRef]  

7. R. Kashyap, Fiber Bragg Gratings (Academic, 2010).

8. N. Lizárraga, N. P. Puente, E. I. Chaikina, T. A. Leskova, and E. R. Méndez, Opt. Express 17, 395 (2009). [CrossRef]  

9. J. Shi, S.-U. Alam, and M. Ibsen, in International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim (Optical Society of America, 2011), paper C1174.

10. M. Gagné, S. Loranger, J. Lapointe, and R. Kashyap, Opt. Express 22, 387 (2014). [CrossRef]  

11. S. Loranger, V. Lambin-Iezzi, M. Wahbeh, and R. Kashyap, Opt. Lett. 41, 1797 (2016). [CrossRef]  

12. S. Loranger and R. Kashyap, Opt. Lett. 42, 1832 (2017). [CrossRef]  

13. P. Ingemar, H. Sten, and F. Pierre-Yves, J. Opt. A 5, 437 (2003). [CrossRef]  

14. P.-Y. Fonjallaz and P. Börjel, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (Optical Society of America, 1999), pp. 179–182.

15. G. A. Miller, G. M. H. Flockhart, and G. A. Cranch, Electron. Lett. 44, 1399 (2008). [CrossRef]  

16. G. A. Miller, J. R. Peele, C. G. Askins, and G. A. Cranch, Appl. Opt. 50, 6617 (2011). [CrossRef]  

17. A. Sherman, A. Rosenthal, and M. Horowitz, Opt. Lett. 32, 457 (2007). [CrossRef]  

18. G. A. Miller, G. M. Flockhart, and G. A. Cranch, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThE6.

References

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  1. R. Kashyap, H. G. Froehlich, A. Swanton, and D. J. Armes, Electron. Lett. 32, 1807 (1996).
    [Crossref]
  2. B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001).
    [Crossref]
  3. I. Petermann, B. Sahlgren, S. Helmfrid, A. T. Friberg, and P.-Y. Fonjallaz, Appl. Opt. 41, 1051 (2002).
    [Crossref]
  4. M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
    [Crossref]
  5. R. Kashyap, A. Swanton, and R. P. Smith, Electron. Lett. 35, 1871 (1999).
    [Crossref]
  6. K. M. Chung, L. Dong, C. Lu, and H. Y. Tam, Opt. Express 19, 12664 (2011).
    [Crossref]
  7. R. Kashyap, Fiber Bragg Gratings (Academic, 2010).
  8. N. Lizárraga, N. P. Puente, E. I. Chaikina, T. A. Leskova, and E. R. Méndez, Opt. Express 17, 395 (2009).
    [Crossref]
  9. J. Shi, S.-U. Alam, and M. Ibsen, in International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim (Optical Society of America, 2011), paper C1174.
  10. M. Gagné, S. Loranger, J. Lapointe, and R. Kashyap, Opt. Express 22, 387 (2014).
    [Crossref]
  11. S. Loranger, V. Lambin-Iezzi, M. Wahbeh, and R. Kashyap, Opt. Lett. 41, 1797 (2016).
    [Crossref]
  12. S. Loranger and R. Kashyap, Opt. Lett. 42, 1832 (2017).
    [Crossref]
  13. P. Ingemar, H. Sten, and F. Pierre-Yves, J. Opt. A 5, 437 (2003).
    [Crossref]
  14. P.-Y. Fonjallaz and P. Börjel, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (Optical Society of America, 1999), pp. 179–182.
  15. G. A. Miller, G. M. H. Flockhart, and G. A. Cranch, Electron. Lett. 44, 1399 (2008).
    [Crossref]
  16. G. A. Miller, J. R. Peele, C. G. Askins, and G. A. Cranch, Appl. Opt. 50, 6617 (2011).
    [Crossref]
  17. A. Sherman, A. Rosenthal, and M. Horowitz, Opt. Lett. 32, 457 (2007).
    [Crossref]
  18. G. A. Miller, G. M. Flockhart, and G. A. Cranch, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThE6.

2017 (1)

2016 (1)

2014 (1)

2011 (2)

2009 (1)

2008 (1)

G. A. Miller, G. M. H. Flockhart, and G. A. Cranch, Electron. Lett. 44, 1399 (2008).
[Crossref]

2007 (1)

2003 (1)

P. Ingemar, H. Sten, and F. Pierre-Yves, J. Opt. A 5, 437 (2003).
[Crossref]

2002 (1)

2001 (1)

B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001).
[Crossref]

1999 (1)

R. Kashyap, A. Swanton, and R. P. Smith, Electron. Lett. 35, 1871 (1999).
[Crossref]

1997 (1)

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[Crossref]

1996 (1)

R. Kashyap, H. G. Froehlich, A. Swanton, and D. J. Armes, Electron. Lett. 32, 1807 (1996).
[Crossref]

Alam, S.-U.

J. Shi, S.-U. Alam, and M. Ibsen, in International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim (Optical Society of America, 2011), paper C1174.

Allison, S. G.

B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001).
[Crossref]

Armes, D. J.

R. Kashyap, H. G. Froehlich, A. Swanton, and D. J. Armes, Electron. Lett. 32, 1807 (1996).
[Crossref]

Askins, C. G.

Batten, C. F.

B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001).
[Crossref]

Börjel, P.

P.-Y. Fonjallaz and P. Börjel, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (Optical Society of America, 1999), pp. 179–182.

Chaikina, E. I.

Childers, B. A.

B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001).
[Crossref]

Chung, K. M.

Cole, M. J.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[Crossref]

Cranch, G. A.

G. A. Miller, J. R. Peele, C. G. Askins, and G. A. Cranch, Appl. Opt. 50, 6617 (2011).
[Crossref]

G. A. Miller, G. M. H. Flockhart, and G. A. Cranch, Electron. Lett. 44, 1399 (2008).
[Crossref]

G. A. Miller, G. M. Flockhart, and G. A. Cranch, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThE6.

Dong, L.

Durkin, M.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[Crossref]

Flockhart, G. M.

G. A. Miller, G. M. Flockhart, and G. A. Cranch, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThE6.

Flockhart, G. M. H.

G. A. Miller, G. M. H. Flockhart, and G. A. Cranch, Electron. Lett. 44, 1399 (2008).
[Crossref]

Fonjallaz, P.-Y.

I. Petermann, B. Sahlgren, S. Helmfrid, A. T. Friberg, and P.-Y. Fonjallaz, Appl. Opt. 41, 1051 (2002).
[Crossref]

P.-Y. Fonjallaz and P. Börjel, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides (Optical Society of America, 1999), pp. 179–182.

Friberg, A. T.

Froehlich, H. G.

R. Kashyap, H. G. Froehlich, A. Swanton, and D. J. Armes, Electron. Lett. 32, 1807 (1996).
[Crossref]

Froggatt, M. E.

B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001).
[Crossref]

Gagné, M.

Hare, D. A.

B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001).
[Crossref]

Helmfrid, S.

Horowitz, M.

Ibsen, M.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[Crossref]

J. Shi, S.-U. Alam, and M. Ibsen, in International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim (Optical Society of America, 2011), paper C1174.

Ingemar, P.

P. Ingemar, H. Sten, and F. Pierre-Yves, J. Opt. A 5, 437 (2003).
[Crossref]

Jegley, D. C.

B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001).
[Crossref]

Kashyap, R.

S. Loranger and R. Kashyap, Opt. Lett. 42, 1832 (2017).
[Crossref]

S. Loranger, V. Lambin-Iezzi, M. Wahbeh, and R. Kashyap, Opt. Lett. 41, 1797 (2016).
[Crossref]

M. Gagné, S. Loranger, J. Lapointe, and R. Kashyap, Opt. Express 22, 387 (2014).
[Crossref]

R. Kashyap, A. Swanton, and R. P. Smith, Electron. Lett. 35, 1871 (1999).
[Crossref]

R. Kashyap, H. G. Froehlich, A. Swanton, and D. J. Armes, Electron. Lett. 32, 1807 (1996).
[Crossref]

R. Kashyap, Fiber Bragg Gratings (Academic, 2010).

Lambin-Iezzi, V.

Laming, R. I.

M. Durkin, M. Ibsen, M. J. Cole, and R. I. Laming, Electron. Lett. 33, 1891 (1997).
[Crossref]

Lapointe, J.

Leskova, T. A.

Lizárraga, N.

Loranger, S.

Lu, C.

Méndez, E. R.

Miller, G. A.

G. A. Miller, J. R. Peele, C. G. Askins, and G. A. Cranch, Appl. Opt. 50, 6617 (2011).
[Crossref]

G. A. Miller, G. M. H. Flockhart, and G. A. Cranch, Electron. Lett. 44, 1399 (2008).
[Crossref]

G. A. Miller, G. M. Flockhart, and G. A. Cranch, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThE6.

Moore, S. T. C.

B. A. Childers, M. E. Froggatt, S. G. Allison, S. T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, Proc. SPIE 4332, 133 (2001).
[Crossref]

Peele, J. R.

Petermann, I.

Pierre-Yves, F.

P. Ingemar, H. Sten, and F. Pierre-Yves, J. Opt. A 5, 437 (2003).
[Crossref]

Puente, N. P.

Rosenthal, A.

Sahlgren, B.

Sherman, A.

Shi, J.

J. Shi, S.-U. Alam, and M. Ibsen, in International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim (Optical Society of America, 2011), paper C1174.

Smith, R. P.

R. Kashyap, A. Swanton, and R. P. Smith, Electron. Lett. 35, 1871 (1999).
[Crossref]

Sten, H.

P. Ingemar, H. Sten, and F. Pierre-Yves, J. Opt. A 5, 437 (2003).
[Crossref]

Swanton, A.

R. Kashyap, A. Swanton, and R. P. Smith, Electron. Lett. 35, 1871 (1999).
[Crossref]

R. Kashyap, H. G. Froehlich, A. Swanton, and D. J. Armes, Electron. Lett. 32, 1807 (1996).
[Crossref]

Tam, H. Y.

Wahbeh, M.

Appl. Opt. (2)

Electron. Lett. (4)

G. A. Miller, G. M. H. Flockhart, and G. A. Cranch, Electron. Lett. 44, 1399 (2008).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. (a) Experimental setup for FBG writing. The system is a continuous direct writing scheme. The fiber moves at speed v, while the phase modulator moves the fringe pattern using a sawtooth function with a frequency f. (b) A commercial OFDR characterization system is used to find the wavelength deviation along the fiber.
Fig. 2.
Fig. 2. Corrected 95-cm-long uniform FBG fabricated in HNA1 fiber at 1555.3 nm. (a) Measured wavelength deviation by OFDR from the average of the probe FBGs. (b) Comparison of one of the uncorrected probe FBG spectra with the corrected required FBG, a zoom of which is reproduced (c), along with the theoretically designed spectra.
Fig. 3.
Fig. 3. Corrected 95-cm-long uniform FBG fabricated in PMHNA fiber at 1559.7 nm. (a) Measured wavelength deviation by OFDR derived from the average of spectra of the three probe FBGs. (b) Comparison of one of the uncorrected probe FBGs with the final corrected FBG, which is reproduced and zoomed in (c), where it is compared with the theoretical spectra of a 95-cm-long FBG.
Fig. 4.
Fig. 4. Corrected DFB-FBG of 30 cm fabricated in HNA2 fiber at 1578.1 nm. (a) Measured wavelength deviation with OBR from three probe FBG average. (b) Comparison of one of the uncorrected probe FBGs (in reflection) with the final corrected DFB (in transmission). A simulated DFB with its final κac strength was calculated with the frequency deviation in (a) to show what the DFB would have looked like in transmission if not corrected. The final corrected DFB is reproduced in (c), where it is compared with a theoretically perfect DFB.

Equations (1)

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λB(z)=2neff(z)v(z)f,

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