Optimizing the net reflectivity of point-by-point fiber Bragg gratings: the role of scattering loss

We present an experimental and theoretical analysis of the influence of scattering losses on the net reflectivity of fiber Bragg gratings inscribed with a femtosecond laser and the point-by-point technique. We demonstrate that the ratio of the coupling strength coefficient to the scattering loss coefficient varies significantly with the inscribing laser pulse energy, and highlight that an optimal pulse-energy range exists for achieving highreflectivity gratings. These results are critical for exploiting high power fiber laser opportunities based on point-by-point gratings. ©2012 Optical Society of America OCIS codes: (060.3510) Lasers, fiber; (060.3735) Fiber Bragg gratings; (320.2250) Femtosecond phenomena. References and links 1. A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004). 2. E. Wikszak, J. Burghoff, M. Will, S. Nolte, A. Tunnermann, and T. Gabler, “Recording of fiber Bragg gratings with femtosecond pulses using a 'point by point' technique,” in Conference on Lasers and Electro-Optics (CLEO)(Optical Society of America, 2004), p. CThM7. 3. J. Thomas, C. Voigtländer, R. G. Becker, D. Richter, A. Tünnermann, and S. Nolte, “Femtosecond pulse written fiber gratings: a new avenue to integrated fiber technology,” Laser Photonics Rev., Early posting (2012). 4. Y. Lai, A. Martinez, I. Khrushchev, and I. Bennion, “Distributed Bragg reflector fiber laser fabricated by femtosecond laser inscription,” Opt. Lett. 31(11), 1672–1674 (2006). 5. N. Jovanovic, M. Åslund, A. Fuerbach, S. D. Jackson, G. D. Marshall, and M. J. Withford, “Narrow linewidth, 100 W cw Yb-doped silica fiber laser with a point-by-point Bragg grating inscribed directly into the active core,” Opt. Lett. 32(19), 2804–2806 (2007). 6. R. J. Williams, N. Jovanovic, G. D. Marshall, and M. J. Withford, “All-optical, actively Q-switched fiber laser,” Opt. Express 18(8), 7714–7723 (2010). 7. R. Goto, R. J. Williams, N. Jovanovic, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Linearly polarized fiber laser using a point-by-point Bragg grating in a single-polarization photonic bandgap fiber,” Opt. Lett. 36(10), 1872– 1874 (2011). 8. N. Jovanovic, J. Thomas, R. J. Williams, M. J. Steel, G. D. Marshall, A. Fuerbach, S. Nolte, A. Tünnermann, and M. J. Withford, “Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers,” Opt. Express 17(8), 6082–6095 (2009). 9. Y. Lai, K. Zhou, K. Sugden, and I. Bennion, “Point-by-point inscription of first-order fiber Bragg grating for C-band applications,” Opt. Express 15(26), 18318–18325 (2007). 10. R. J. Williams, C. Voigtländer, G. D. Marshall, A. Tünnermann, S. Nolte, M. J. Steel, and M. J. Withford, “Pointby-point inscription of apodized fiber Bragg gratings,” Opt. Lett. 36(15), 2988–2990 (2011). 11. G. D. Marshall, R. J. Williams, N. Jovanovic, M. J. Steel, and M. J. Withford, “Point-by-point written fiber-Bragg gratings and their application in complex grating designs,” Opt. Express 18(19), 19844–19859 (2010). 12. M. L. Åslund, N. Nemanja, N. Groothoff, J. Canning, G. D. Marshall, S. D. Jackson, A. Fuerbach, and M. J. Withford, “Optical loss mechanisms in femtosecond laser-written point-by-point fibre Bragg gratings,” Opt. Express 16(18), 14248–14254 (2008). #165556 $15.00 USD Received 27 Mar 2012; revised 21 May 2012; accepted 23 May 2012; published 31 May 2012 (C) 2012 OSA 4 June 2012 / Vol. 20, No. 12 / OPTICS EXPRESS 13451 13. J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: modal properties and transmission spectra,” Opt. Express 19(1), 325–341 (2011). 14. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). 15. C. Smelser, S. 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(14), 5377–5386 (2005). 16. C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008). 17. M. Janos, J. Canning, and M. G. Sceats, “Incoherent scattering losses in optical fiber Bragg gratings,” Opt. Lett. 21(22), 1827–1829 (1996). 18. D. Grobnic, C. W. Smelser, S. J. Mihailov, R. B. Walker, and P. Lu, “Fiber Bragg gratings with suppressed cladding modes made in SMF-28 with a femtosecond IR laser and a phase mask,” IEEE Photon. Technol. Lett. 16(8), 1864– 1866 (2004).


Introduction
Fiber Bragg gratings (FBGs) inscribed with femtosecond lasers using the point-by-point (PbP) inscription technique [1,2] have proven to be highly versatile for a variety of fiber laser applications [3].The ability to inscribe directly into non-photosensitive fibers has enabled shortlength DBR fiber lasers [4], high power monolithic fiber lasers [5], novel all-optical active Qswitching architectures [6] and direct inscription into complex fiber geometries such as a polarized, all-solid photonic bandgap fiber [7].Furthermore, the tailorable polarization properties of these gratings have enabled polarized laser output from low-birefringence fiber lasers [8,9].Recent advances in PbP inscription-including phase-shifted, chirped, superstructured and apodized PbP gratings [10,11]-greatly increase the flexibility of the technique and will undoubtedly lead to a greater variety of applications for this grating platform.However, it is known that PbP gratings exhibit broadband scattering loss due to Mie scattering from their micro-void modifications [12], which is often viewed as an obstacle to their use in applications that are critically sensitive to reflection loss or out-of-band loss.The wavelengthdependent non-resonant loss due to scattering and the resonant coupling to cladding modes have been studied in detail [12,13].Nevertheless, the impact of the scattering loss on the net reflectivity of the grating-which is a key parameter for laser applications as it directly affects the threshold and slope efficiency-is not well understood.For example, while a grating with -50 dB transmission at the Bragg wavelength would ideally produce 99.999% reflectivity, a typical PbP grating of equal strength may also have broadband loss of -1 dB (79% transmission).Whether such a grating has a net reflectivity closer to 79% or 99% is not intuitively obvious because of the co-distributed reflective coupling and scattering loss.
In this work we present experimental analysis of PbP grating strength, scattering loss and net reflectivity as a function of the inscribing femtosecond pulse energy.We show that the scattering loss and coupling strength coefficients increase with pulse energy at different rates, giving rise to an optimum pulse energy range for inscribing high-reflectivity gratings.Although scattering losses at shorter wavelengths are important in fiber lasers as they contribute to loss at the pump wavelength, they can be avoided by minimizing the overlap of the pump with the grating modifications, such as by cladding-pumping.This work focusses on the influence of scattering loss on the net reflectivity at the Bragg wavelength.

Scattering losses in point-by-point gratings
Figure 1 shows the transmission and reflection spectra for a uniform PbP grating of length L = 5 mm, inscribed with 250 nJ pulses, which has a second-order resonance at 1549.6 nm.This grating exhibits broadband scattering loss of 19% (measured in transmission at the longwavelength side of the stop-band), and a strong Bragg resonance with -30.9 dB transmission at the Bragg wavelength.The measured peak reflectivity, 93%, is higher than the broadband transmission level (81%) because of the rapid decay of the field envelope along the grating due to the Bragg resonance: light at the Bragg wavelength penetrates less than 2 L and only experiences a small fraction of the single-pass scattering loss measured outside the stop-band.
In the case of uniform gratings we can treat the scattering loss as a simple distributed loss, such that the transmission loss measured out-of-band can be expressed as where  is the scattering loss coefficient.We included this scattering loss term in the standard grating coupled-mode equations [14] to calculate the net reflectivity of PbP gratings (see Section 4), determining  from normalized transmission measurements (such as that shown in Fig. 1).
Also, as we are investigating strong gratings ( 3 L   ) we can approximate the in-band field decay due to Bragg reflection as being exponential, such that where  is the coupling coefficient for the grating.The relative magnitudes of  and  will determine the impact of the scattering loss on the net reflectivity of the grating, as they determine the decay lengths due to scattering loss and Bragg reflection.In the case where ,

 
net reflectivity of the grating, as they determine the decay lengths due to scattering loss and ,   the decay length due to scattering is much longer than that due to Bragg reflection: most of the light is reflected before experiencing any significant scattering, thus the scattering loss becomes negligible.Conversely, if ,

 
than that due to Bragg reflection: most of the light is reflected before experiencing any ,

 
scattering loss dominates and the Bragg reflection becomes insignificant.Therefore, in order to maximize the reflectivity of PbP gratings, the ratio   must be maximized.Since the pulse energy of the femtosecond laser is the dominant experimental parameter in determining the coupling and scattering coefficients, we measured   for PbP gratings as a function of pulse energy, spanning three distinct grating inscription regimes.

Experiment
PbP fiber Bragg gratings were inscribed in Corning SMF-28e fiber by focusing 800 nm femtosecond laser pulses into the core using a 0.8 N.A. oil-immersion objective lens while translating the fiber at a constant velocity.The inscription technique used here, which includes a fiber-guiding system with submicrometer transverse control, is described in detail elsewhere [11].The polarization state of the inscribing beam is linear and orthogonal to the fiber axis.The gratings were analyzed in transmission and reflection using a high-resolution (3 pm) swept wavelength system (JDSU 15100).Reflectivity measurements were made using a C-band fiber circulator and were normalized to a broadband fiber mirror.Figure 2(a) shows grating strength, scattering loss and reflectivity data for a series of 5 mmlong PbP gratings inscribed with 2 nd order resonances in the range 1520-1570 nm and with different femtosecond pulse energies.In this graph, the grating strength is expressed as the transmission extinction at the Bragg wavelength in dB; the broadband scattering loss in dB was measured at a point far from resonance on the long-wavelength side of the stop-band; and the measured reflectivity of the gratings is plotted as a 'net grating strength',   10 10 log 1 , such that it can be directly compared with the grating strength data on the same graph.Therefore the separation between the red and black data points is the 'penalty' in reflectivity due to the scattering loss in the grating.The data in Fig. 2(a) fall into three distinct regimes according to inscription pulse energy.For pulse energies <110 nJ, the grating strength is vanishingly small.These gratings can be characterized as Type I-IR gratings [15] as they do not contain micro-void modifications.Figure 2(b) shows a differential-interference-contrast (DIC) micrograph of the grating that was inscribed with 90 nJ: the refractive index modifications are faintly visible in the center of the core.The gratings inscribed with pulse energies between 110 nJ and 250 nJ are Type II-IR PbP gratings and the grating strength increases dramatically with pulse energy in this range.Microvoid formation was confirmed by the observed plasma glow generated at the focal point of the femtosecond laser during inscription, radiative scattering of guided visible light from the core observed post-inscription, and imaging of the gratings with a DIC microscope (see Fig. 2(c)).For pulse energies of 300 nJ and higher, the modifications overlap each other, reducing the 'visibility' of each grating period (and thus the index contrast in the grating), resulting in increased scattering loss and reduced grating strength.Figure 2(d) shows a DIC micrograph of a Type-II IR overlapping grating which was inscribed with 350 nJ.
The data in Fig. 2(a) show that the penalty due to scattering loss increases with the inscription pulse energy in the Type II-IR regime and that the highest reflectivity is not achieved with the strongest grating, but at a balance between grating strength and scattering losses.As mentioned previously, the key figure of merit for high-reflectivity PbP gratings (provided 3 L   ) is the ratio of the coupling strength and scattering loss coefficients.Figure 3 shows the value of  for the gratings in Fig. 2(a), as well as for another set of gratings inscribed on a (C) 2012 OSA different day.The gratings in data set #2 have higher corresponding values of  than for data set #1, which is most likely due to small variations in femtosecond laser beam parameters from day to day.Variations in beam quality can affect the threshold for Type II-IR modification, as well as the peak  values (translating the curve horizontally or vertically).Nevertheless, it does not affect the trend towards lower  values for both low pulse energies (in the Type I- IR modification regime) and high pulse energies within the Type II-IR modification regime.
Both data sets show a consistent trend that  reduces at high pulse energies (>150 nJ in both cases).The highest value of  in data set #1 corresponds to an inscription pulse energy of 120 nJ, indicating that a longer grating at this pulse energy would produce higher reflectivity than the grating inscribed at 200 nJ.Pulse Energy (nJ) Fig. 3.The ratio of coupling strength coefficient to scattering loss coefficient as a function of the inscribing pulse energy.Two data sets are shown from different days (higher ratios for data set #2 are most likely due to variation in femtosecond laser beam parameters from day to day).The uncertainty in these data arises from the measurement of the scattering loss which includes up to 0.02 dB splice loss from splicing the grating into the swept wavelength system.
We note that although we observe random fluctuations in the grating periodicity, this is unlikely to affect the coupling strength of the gratings, as high-frequency random fluctuations in grating period have been shown to have negligible impact on coupling strength [16]; whereas low-frequency fluctuations in the period, which impact on long-range order, result in multiple reflection peaks, which we do not observe in any of these gratings.

Theory
In order to further investigate the practicality of  as a figure of merit for high-reflectivity PbP gratings, we calculated the net reflectivity of gratings with the same coupling and loss coefficients as the gratings presented in Fig. 2(a), but with varying length L such that each grating had a coupling strength 4 L   .A lossless grating with this coupling strength would have 99.9% reflectivity.By including the scattering loss term  in the standard grating coupled- mode equations, we can express the net reflectivity at the Bragg wavelength as Figure 4 shows the reflectivity and length of each grating, with grating length plotted on a logarithmic scale.The trends of the reflectivity values in Fig. 4 closely resemble the  values of data set #1 in Fig. 3, confirming the validity of the figure of merit as well as highlighting a range of pulse energies from 110-200 nJ that produce higher reflectivity gratings.If we compare, for instance, the projected reflectivity of the gratings inscribed with 120 nJ and 200 nJ pulses, the former has a higher value of  and a net reflectivity of 96.8% for a 28.4 mm grating, whereas the latter has a slightly lower value of  and net reflectivity of 96.0% for a 6.9 mm grating.In our setup we routinely inscribe strong gratings of length up to 50 mm, therefore the length required to achieve a strong grating at a pulse energy of 120 nJ is not a limiting factor.Clearly in this instance the ratio of  is not sufficiently high that scattering loss can be ignored, as there is still a 3.1% penalty in reflectivity due to scattering loss (the ideal for 4 L   is 99.9%).However it is clear that the highest reflectivity PbP gratings are achieved with pulse energies above but near to the threshold for Type II-IR modifications.It is important to note that these considerations are particular to PbP gratings, as scattering losses in conventional UV laserinscribed gratings are orders of magnitude lower than PbP gratings [17], and gratings inscribed with femtosecond lasers and a phase-mask (typically Type I-IR with much greater mode overlap) have almost order of magnitude higher values of  [18].

Conclusions
We have characterized the dependence of the coupling strength and scattering loss in PbP gratings on the inscribing femtosecond pulse energy, as it is the key determinant of the shape, size and morphology of the modifications in the grating [8].We have identified the ratio of the coupling strength coefficient  to the scattering loss coefficient  as a figure of merit for determining the maximum reflectivity achievable with a PbP grating.We demonstrated that this ratio ( ) varies strongly with the inscribing pulse energy and consequently identified an optimal pulse-energy range for achieving maximum reflectivity from PbP gratings.We also highlight that high-reflectivity PbP gratings are possible (R > 95%), which should facilitate further implementation in fiber laser applications, particularly for those based on nonlinear processes such as stimulated Raman scattering, which demand high Q cavities.

Fig. 2 .
Fig. 2. (a) Grating strength (black squares), scattering loss (blue triangles) and net reflectivity (red circles) of 5 mm-long PbP gratings inscribed with different pulse energies.Each grating has a 2 nd order resonance in the C-band.Differential-interference-contrast micrographs of the PbP gratings inscribed with (b) 90 nJ, (c) 200 nJ and (d) 350 nJ are shown on the right (viewed from the direction of the inscribing beam).The measurement uncertainty of the data in (a) is 0.02 dB due to splices between the grating and the swept wavelength system.

Fig. 4 .
Fig. 4. Calculated net reflectivity and length of gratings with κL = 4 and with κ/α values corresponding to data set #1 in Fig. 3. Grating length is plotted on a logarithmic scale.