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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 18 — Sep. 1, 2008
  • pp: 14248–14254
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Optical loss mechanisms in femtosecond laser-written point-by-point fibre Bragg gratings

Mattias L. Åslund, Nemanja Jovanovic, Nathaniel Groothoff, John Canning, Graham D. Marshall, Stuart D. Jackson, Alexander Fuerbach, and Michael J. Withford  »View Author Affiliations


Optics Express, Vol. 16, Issue 18, pp. 14248-14254 (2008)
http://dx.doi.org/10.1364/OE.16.014248


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Abstract

Fibre Bragg gratings inscribed with the point-by-point method using a Ti-sapphire femtosecond laser operating at 800 nm are shown to display strong increasing attenuation towards shorter wavelengths with a large and spectrally sharp recovery observed below 400 nm. The origin of this loss is shown to be Mie scattering, and the sharp recovery in the transmission results from wavelength dependent scattering within the numerical aperture of the core. The permanent losses from these Type II gratings have implications for high temperature sensors and fibre lasers.

© 2008 Optical Society of America

1. Introduction

Type II fibre Bragg gratings (FBGs), i.e., those that are written above the damage threshold of glass, have been written using high intensity UV-lasers [1

1. C. G. Askins, T.-E. Tsai, G. M. Williams, M. A. Putnam, M. Bashkansky, and E. J. Friebele, “Fiber Bragg reflectors prepared by a single excimer pulse,” Opt. Lett. 17, 833–835 (1992). [CrossRef] [PubMed]

, 2

2. J.-L. Archambault, L. Reekie, and P. St. J. Russell, “100% reflectivity Bragg reflectors produced in optical fibres by single excimer laser pulses,” Electron. Lett. 29, 453–455 (1993). [CrossRef]

], as well as more recently, by femtosecond lasers [3

3. C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13, 5377–5386 (2005). [CrossRef] [PubMed]

-5

5. A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40, 1170 (2004). [CrossRef]

]. Both processes operate above the so-called damage threshold of the glass [6

6. E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, (1997). [CrossRef]

, 7

7. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nature Phot. 2, 219–225 (2008). [CrossRef]

], which for point-by-point (PbP) femtosecond laser written gratings is ~0.15 µJ for a ~120 fs pulse duration, as determined through microscope and annealing studies. This leads to structural changes that can withstand temperatures approaching 1000 °C [8

8. A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41, 176–178 (2005). [CrossRef]

]. The importance of the underlying processes has meant extensive applications within a number of fields demanding superior temperature performance as well as long-term stability, including sensors, lasers, laser written waveguide channels and other components [9

9. J. Canning, “New fibre and grating technologies for lasers and sensors,” 1, 1–62, Frontiers in lasers and electro optics research, Nova science publishers, (2006).

-12

12. L. Tong, R. R. Gattass, I. Z. Maxwell, J. B. Ashcom, and E. Mazur, “Optical loss measurements in femtosecond laser written waveguides in glass,” Opt. Commun. 259, 626–630 (2006). [CrossRef]

]. For example, we recently reported the use of femtosecond gratings for a high power fibre laser operating in excess of 100 W [13

13. N. Jovanovic, M. Åslund, A. Fuerbach, S. D. Jackson, G. D. Marshall, and M. J. Withford, “Narrow linewidth, 100W cw Yb3+-doped silica fiber laser with a point-by-point Bragg grating inscribed directly into the active core,” Opt. Lett. 32, 2804–2806 (2007). [CrossRef] [PubMed]

].

Short wavelength attenuation, i.e., attenuation stretching from the visible into the NIR is associated with all forms of grating writing, but the origins of the losses and the solutions to mitigate the losses are different for different types of gratings. For Type I gratings, written well below the damage threshold of the glass by excitation through defect absorptions, the losses are associated with photo-induced colour centres that can be annealed out at moderate temperatures [14

14. R. M. Atkins and V. Mizrahi, “Observations of changes in uv absorption bands of singlemode germanosilicate core optical fibers on writing and thermally erasing refractive index gratings,” Electron. Lett. 28, 1743–1744 (1992). [CrossRef]

, 15

15. J. Canning, A. L. G. Carter, and M. G. Sceats, “Correlation between photodarkening and index change during 193 nm irradiation of germanosilicate and phosphosilicate fibers,” J. Lightwave Technol. 15, 1348–1356 (1997). [CrossRef]

]. On the other hand, for Type II gratings, written above the damage threshold of the glass through bond breaking below the glass band edge [9

9. J. Canning, “New fibre and grating technologies for lasers and sensors,” 1, 1–62, Frontiers in lasers and electro optics research, Nova science publishers, (2006).

], the losses are due to diffractive Mie scattering [16

16. P. C. Hill, G. R. Atkins, J. Canning, G. C. Cox, and M. G. Sceats, “Writing and visualization of low-threshold type II Bragg gratings in stressed optical fibers,” Appl. Opt. 33, 7689–7694 (1995). [CrossRef]

], which can only be remedied by addressing the overlap integral between the grating and the incident mode by changing grating size and morphology [17

17. A. Othonos and K. Kalli, Fibre Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Boston London: Artech House, 1999).

]. A limited study of short wavelength attenuation induced by femtosecond gratings [18

18. M. Åslund, N. Jovanovic, N. Groothoff, J. Canning, G. D. Marshall, S. D. Jackson, A. Fuerbach, and M. J. Withford, “Photodarkening study of gratings written into rare-earth doped optical fibers using a femtosecond laser,” in Proc. SPIE 6800 , 32, Canberra, Australia, Dec., (2007). [CrossRef]

] and recent studies of these gratings employed in core pumped fibre lasers [19

19. N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster, and M. J. Withford, “Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization,” Photon. Technol. Lett. 20, 809–811 (2008). [CrossRef]

] indicate that the differences in confinement of the induced changes compared to long pulse UV Type II gratings give rise to significant differences in attenuation, either from scattering and/or defect absorption.

This paper reports on the observation of significant short wavelength attenuation associated with PbP written femtosecond Bragg gratings written in the high intensity Type II damage regime. To address both sensor and fibre laser applications, the studies are carried out for both Ge-doped as well as Yb/Al/Ge codoped (henceforth referred to as Yb-codoped) fibres. Moderate temperature annealing procedures are carried out to separate the contributions arising from scattering and photo-induced colour centres. A simulation is carried out to qualitatively confirm the origins of scattering.

2. Experiments and results

The fibres used in the experiments were fabricated by modified chemical vapour deposition (MCVD) and their properties summarised in Table 1. To fabricate the gratings, the fibre was mounted on a high-precision air bearing translation stage, the outer polymer cladding was stripped and femtosecond pulses were focused into the core using a 0.8 NA, 20× oil immersion objective lens. The pulses, which were generated by a regeneratively amplified Ti:sapphire laser operating at 800 nm, had ~120 fs pulse duration, a 1 kHz repetition rate and pulse energies between 160 and 300 nJ (the so-called “Type II-IR” regime). The gratings were 50 mm long and written in the 20th order for 1.55 µm light (Λperiod=10.7 µm). The scattering and absorption losses were grating period independent so a higher order period was used to remove coupling to cladding modes at shorter wavelengths, which can obscure the study of the losses associated directly with the structural changes. Optical micrographs of the gratings from top and side perspectives are presented in Fig. 1 showing that the changes are confined to well-defined cylinders across the core.

Table 1. Optical fibres used in the experiments.

table-icon
View This Table
Fig. 1. Femtosecond laser induced refractive index modulations written with a pulse energy of 260 nJ in SMF28. (a) Top view (laser pulse entered glass in the plane of the image), (b) Side view.

Spectral transmission experiments

Normalised white light transmission spectra for gratings written with various pulse energies in both the Ge-doped and Yb-codoped fibre were taken in order to investigate the wavelength dependant losses as a function of pulse energy. A fibre-coupled, high brightness halogen light was used as the white light source. The fibres under test were cleaved to the same length (L~25 cm) and SMF 28 fibre pigtails were spliced to the input and output ends. An optical spectrum analyser (OSA) was used to measure the transmission properties of the gratings (s-n=~35 dB, res=5 nm, Δλ=350-1750 nm). Figures 2(a) and 2(b) show the normalised transmission spectra for the Ge-doped and the Yb-codoped fibres respectively. Figure 2(a) and 2(b) show significant short wavelength attenuation stretching to the NIR with no observable cladding mode losses around 1500 nm. Maximum loss occurs in the region 380-400 nm, depending on pulse energy, below which a sharp rise in transmission is observed. The losses above 400 nm exhibit a strong dependence on the grating writing pulse energy, with greater losses for increasing pulse energies [bottom inset of Fig. 2(a)]. The transmission minimum around 380-400 nm shifts to longer wavelengths with increasing pulse energy. For the Yb-codoped fibre, this begins at ~400 nm with a similar, small shift towards longer wavelengths for increasing pulse energies [see top inset of Fig. 2(a)]. The reduced losses observed in the transmission spectrum between ~900-1000 nm in Fig. 2(b) are due to normalisation of the results to a slightly longer Yb3+ -doped fibre. To ensure that the increased transmission observed below 400 nm was not due to detection limitations of the optical spectrum analyser, a narrow line-width CW frequency tripled Nd:YAG laser emitting at 355 nm was coupled into the fibre and the signal measured with a UV power meter and the OSA. Within experimental error, the transmissivity was identical to the results obtained with the white light source and OSA. It should be noted that in the transmission spectrum of pristine SMF28 fibre, shown in the inset to Fig. 2(b), there is a narrow weak loss band (0.18 dB/250 mm) around 370 nm, the origins of which are currently unknown.

Fig. 2. Normalised broad-band transmission spectra for femtosecond laser inscribed PbP FBGs written in (a) Ge-doped fibre and (b) 1.18 %wt Yb3+-, Ge-, Al-doped fibre for various pulse energies as a function of wavelength (red=160nJ, blue=180nJ, green=200nJ, yellow=220nJ, pink=260nJ and black=300nJ) shown in same scale. Top inset in (a) shows the transmission (T) minimum wavelength (red=Ge, black=Yb) and the bottom inset shows the respective transmission losses, both as a function of pulse energy. Inset in (b) shows the transmission spectra of pristine Ge-doped fibre (SMF 28) for the normalised L=25 cm.

Annealing experiments

PbP gratings written with 160 and 300 nJ pulses for both the Ge-doped and Yb-codoped fibres were annealed at 300 and 400 °C for one hour consecutively, and the transmission spectra were taken before and after each step. The normalised change in transmission, ΔT, is shown in Fig. 3(a)&(b) for the Ge-doped and Yb-codoped fibres respectively. Within experimental error, for the Ge-doped fibre, a slight decrease in transmission in the NIR for the 160 nJ grating after annealing at 300°C and for the 300 nJ grating after annealing at 400 °C is observed. For the Yb-doped fibre, no significant change in the transmission across the whole spectrum at any temperature can be seen. Overall, the results indicate no evidence of colour centre bleaching. The loss in transmission in the NIR for the Ge-doped fibre is attributed to increased scattering as a result of thermally-induced stress relaxations; the change in transmission from 1200 nm to 1070 nm is attributed to single mode cut-off.

Fig. 3. Change in spectral transmissivity (T) for gratings written in the Ge (a) and Yb, Al (b) fibres after 1hr annealing, including: 160 nJ gratings at 300 °C (green), 160 nJ at 400 °C (blue), 300 nJ at 300 °C (black), 300 nJ at 400 °C (red) shown in same scale. Inset shows the raw data for both the 300 nJ-400 °C experiments before and after heating (Ge: red→black; Yb:green→blue), compared with an identical annealing study of a UV 193 nm written grating (pink→ yellow).

For comparison, a typical example from an annealing study of a 193 nm written Type I grating (SMF28: 300 mJ/cm2/pulse, total 15kJ/cm2), which consists of photo induced colour centres, is shown in the inset of Fig. 3(b). In this case annealing reduced the amount of short wavelength attenuation by as much as 32 dB. From Fig. 3 it can be observed that this type of signal recovery does not occur in the IR written PbP FBGs.

To examine the nature of the scattering process, HeNe light (632.5nm) was launched into the fibre core containing a grating and the scattered light was captured by a screen placed parallel to the fibre. Scattering occurred over the entire length of the grating, so a small 1.5 mm section of the grating was apertured off to show the diffraction orders with greater clarity. Figure 4 shows a photograph of the screen. The angular distribution of these diffraction orders correspond to the diffraction angles that were calculated using the Bragg equation for diffraction [16

16. P. C. Hill, G. R. Atkins, J. Canning, G. C. Cox, and M. G. Sceats, “Writing and visualization of low-threshold type II Bragg gratings in stressed optical fibers,” Appl. Opt. 33, 7689–7694 (1995). [CrossRef]

]. Identical experiments using white light also produced spectrally dependent diffraction orders, thus confirming diffractive scattering as the dominant source for the losses in the visible wavelength region.

Fig. 4. Photo of diffraction orders of 632.8 nm light emanating from a 20th order PbP FBG onto a screen parallel to the fibre.

3. Discussion

The transmission losses for wavelengths longer than 400 nm are consistent with the expectations from a grating written with a process that exceeds the damage threshold of glass [16

16. P. C. Hill, G. R. Atkins, J. Canning, G. C. Cox, and M. G. Sceats, “Writing and visualization of low-threshold type II Bragg gratings in stressed optical fibers,” Appl. Opt. 33, 7689–7694 (1995). [CrossRef]

]. The observed recovery in the transmission for wavelengths <400 nm can be explained if the strong wavelength dependency of the longitudinal angular Mie scattering crossection is taken into consideration. From scattering theory, light incident on particles of the order of the wavelength and larger is predominantly back-scattered within a small solid angle, Ω, whereas light incident on particles significantly smaller than the wavelength scatter less, but into a much larger Ω [20

20. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, Cambridge, 2002).

]. It is expected, therefore, that short wavelength light (i.e., λ < 400 nm) is scattered from the refractive index modulations into solid angles that are within the NA of the fibre and continue to be guided. The micrographs in Fig. 1 indicate that the maximum diameter of the tubular refractive index modulations is, Ø~1.8 µm, which is comparable to the relevant wavelengths.

The results of the transmission measurements in Fig. 2 show that the Yb-codoped fibre has significantly more induced attenuation than the Ge-doped fibre; however, Bragg gratings in the Yb-codoped fibre have been measured to be stronger, so the losses are similar for a given strength Bragg grating.

Fig. 5. Theoretical simulation of the transmitted unscattered light for a single spherical scatterer in bulk media (black) compared with the sum of the transmitted unscattered light and the light scattered within the NA of the fibre core (red).

Our simulations indicate that the diffractive losses can be reduced significantly, perhaps by as much as three orders of magnitude, by producing larger and transversely flatter gratings. This result concurs with standard grating theory [17

17. A. Othonos and K. Kalli, Fibre Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Boston London: Artech House, 1999).

]. The use of an astigmatic lens with a lower NA in the transverse direction compared with the longitudinal direction [11

11. G. Cerullo, R. Osellame, S. Taccheo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Femtosecond micromachining of symmetric waveguides at 1.5 µm by astigmatic beam focusing,” Opt. Lett. 27, 1938–1940 (2002). [CrossRef]

] may facilitate the required grating shape; however, the femtosecond laser will need to produce greater pulse energy. If the current focusing geometry is retained to write FBGs for fibre lasers, issues such as core pumping need consideration since the pump light will be scattered substantially [19

19. N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster, and M. J. Withford, “Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization,” Photon. Technol. Lett. 20, 809–811 (2008). [CrossRef]

].

4. Conclusion

References and links

1.

C. G. Askins, T.-E. Tsai, G. M. Williams, M. A. Putnam, M. Bashkansky, and E. J. Friebele, “Fiber Bragg reflectors prepared by a single excimer pulse,” Opt. Lett. 17, 833–835 (1992). [CrossRef] [PubMed]

2.

J.-L. Archambault, L. Reekie, and P. St. J. Russell, “100% reflectivity Bragg reflectors produced in optical fibres by single excimer laser pulses,” Electron. Lett. 29, 453–455 (1993). [CrossRef]

3.

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13, 5377–5386 (2005). [CrossRef] [PubMed]

4.

E. Wikszak, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Recording of fiber Bragg gratings with femtosecond pulses using a “point by point” technique,” Conference on Lasers and Electro-Optics, 2004. (CLEO) , 2, pp 2. CThM7, (2004).

5.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40, 1170 (2004). [CrossRef]

6.

E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett. 71, (1997). [CrossRef]

7.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nature Phot. 2, 219–225 (2008). [CrossRef]

8.

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41, 176–178 (2005). [CrossRef]

9.

J. Canning, “New fibre and grating technologies for lasers and sensors,” 1, 1–62, Frontiers in lasers and electro optics research, Nova science publishers, (2006).

10.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996). [CrossRef] [PubMed]

11.

G. Cerullo, R. Osellame, S. Taccheo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Femtosecond micromachining of symmetric waveguides at 1.5 µm by astigmatic beam focusing,” Opt. Lett. 27, 1938–1940 (2002). [CrossRef]

12.

L. Tong, R. R. Gattass, I. Z. Maxwell, J. B. Ashcom, and E. Mazur, “Optical loss measurements in femtosecond laser written waveguides in glass,” Opt. Commun. 259, 626–630 (2006). [CrossRef]

13.

N. Jovanovic, M. Åslund, A. Fuerbach, S. D. Jackson, G. D. Marshall, and M. J. Withford, “Narrow linewidth, 100W cw Yb3+-doped silica fiber laser with a point-by-point Bragg grating inscribed directly into the active core,” Opt. Lett. 32, 2804–2806 (2007). [CrossRef] [PubMed]

14.

R. M. Atkins and V. Mizrahi, “Observations of changes in uv absorption bands of singlemode germanosilicate core optical fibers on writing and thermally erasing refractive index gratings,” Electron. Lett. 28, 1743–1744 (1992). [CrossRef]

15.

J. Canning, A. L. G. Carter, and M. G. Sceats, “Correlation between photodarkening and index change during 193 nm irradiation of germanosilicate and phosphosilicate fibers,” J. Lightwave Technol. 15, 1348–1356 (1997). [CrossRef]

16.

P. C. Hill, G. R. Atkins, J. Canning, G. C. Cox, and M. G. Sceats, “Writing and visualization of low-threshold type II Bragg gratings in stressed optical fibers,” Appl. Opt. 33, 7689–7694 (1995). [CrossRef]

17.

A. Othonos and K. Kalli, Fibre Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Boston London: Artech House, 1999).

18.

M. Åslund, N. Jovanovic, N. Groothoff, J. Canning, G. D. Marshall, S. D. Jackson, A. Fuerbach, and M. J. Withford, “Photodarkening study of gratings written into rare-earth doped optical fibers using a femtosecond laser,” in Proc. SPIE 6800 , 32, Canberra, Australia, Dec., (2007). [CrossRef]

19.

N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster, and M. J. Withford, “Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization,” Photon. Technol. Lett. 20, 809–811 (2008). [CrossRef]

20.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, Cambridge, 2002).

OCIS Codes
(140.3390) Lasers and laser optics : Laser materials processing
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 15, 2008
Revised Manuscript: August 21, 2008
Manuscript Accepted: August 25, 2008
Published: August 27, 2008

Citation
Mattias L. Åslund, Nemanja Nemanja, Nathaniel Groothoff, John Canning, Graham D. Marshall, Stuart D. Jackson, Alexander Fuerbach, and Michael J. Withford, "Optical loss mechanisms in femtosecond laser-written point-by-point fibre Bragg gratings," Opt. Express 16, 14248-14254 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-14248


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References

  1. C. G. Askins, T.-E. Tsai, G. M. Williams, M. A. Putnam, M. Bashkansky, and E. J. Friebele, "Fiber Bragg reflectors prepared by a single excimer pulse," Opt. Lett. 17, 833-835 (1992). [CrossRef] [PubMed]
  2. J.-L. Archambault, L. Reekie, and P. St.J. Russell, "100% reflectivity Bragg reflectors produced in optical fibres by single excimer laser pulses," Electron. Lett. 29, 453-455 (1993). [CrossRef]
  3. C. W. Smelser, S. J. Mihailov, and D. Grobnic, "Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask," Opt. Express 13, 5377-5386 (2005). [CrossRef] [PubMed]
  4. E. Wikszak, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, "Recording of fiber Bragg gratings with femtosecond pulses using a "point by point" technique," Conference on Lasers and Electro-Optics, 2004. (CLEO), 2, pp 2. CThM7, (2004).
  5. A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, "Direct writing of fibre Bragg gratings by femtosecond laser," Electron. Lett. 40, 1170 (2004). [CrossRef]
  6. E. N. Glezer and E. Mazur, "Ultrafast-laser driven micro-explosions in transparent materials," Appl. Phys. Lett.71, (1997). [CrossRef]
  7. R. R. Gattass and E. Mazur, "Femtosecond laser micromachining in transparent materials," Nature Photo. 2, 219-225 (2008). [CrossRef]
  8. A. Martinez, I. Y. Khrushchev, and I. Bennion, "Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser," Electron. Lett. 41, 176-178 (2005). [CrossRef]
  9. J. Canning, "New fibre and grating technologies for lasers and sensors," 1, 1-62, Frontiers in lasers and electro optics research, Nova science publishers, (2006).
  10. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett. 21, 1729-1731 (1996). [CrossRef] [PubMed]
  11. G. Cerullo, R. Osellame, S. Taccheo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, "Femtosecond micromachining of symmetric waveguides at 1.5 μm by astigmatic beam focusing," Opt. Lett. 27, 1938-1940 (2002). [CrossRef]
  12. L. Tong, R. R. Gattass, I. Z. Maxwell, J. B. Ashcom, and E. Mazur, "Optical loss measurements in femtosecond laser written waveguides in glass," Opt. Commun. 259, 626-630 (2006). [CrossRef]
  13. N. Jovanovic, M. ?slund, A. Fuerbach, S. D. Jackson, G. D. Marshall, and M. J. Withford, "Narrow linewidth, 100W cw Yb3+-doped silica fiber laser with a point-by-point Bragg grating inscribed directly into the active core," Opt. Lett. 32, 2804-2806 (2007). [CrossRef] [PubMed]
  14. R. M. Atkins and V. Mizrahi, "Observations of changes in uv absorption bands of singlemode germanosilicate core optical fibers on writing and thermally erasing refractive index gratings," Electron. Lett. 28, 1743-1744 (1992). [CrossRef]
  15. J. Canning, A. L. G. Carter, and M. G. Sceats, "Correlation between photodarkening and index change during 193 nm irradiation of germanosilicate and phosphosilicate fibers," J. Lightwave Technol. 15, 1348-1356 (1997). [CrossRef]
  16. P. C. Hill, G. R. Atkins, J. Canning, G. C. Cox, and M. G. Sceats, "Writing and visualization of low-threshold type II Bragg gratings in stressed optical fibers," Appl. Opt. 33, 7689-7694 (1995). [CrossRef]
  17. A. Othonos and K. Kalli, Fibre Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Boston London: Artech House, 1999).
  18. M. ?slund, N. Jovanovic, N. Groothoff, J. Canning, G. D. Marshall, S. D. Jackson, A. Fuerbach, and M. J. Withford, "Photodarkening study of gratings written into rare-earth doped optical fibers using a femtosecond laser," in Proc. SPIE 6800, 32, Canberra, Australia, Dec., (2007). [CrossRef]
  19. N. Jovanovic, G. D. Marshall, A. Fuerbach, G. E. Town, S. Bennetts, D. G. Lancaster, and M. J. Withford, "Highly-narrow linewidth, CW, all-fiber oscillator with a switchable linear polarization," Photon. Technol. Lett. 20, 809-811 (2008). [CrossRef]
  20. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, Cambridge, 2002).

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