Efficient Writing of Fiber Bragg Gratings with Low Energy Focused fs Pulses Using a Two-Mask Interferometer

Abstract

We demonstrate fast writing of strong fiber Bragg grating (FBG) without hydrogen loading using 343 nm femtosecond pulses of only 7 $\mathsf{\mu }$J energy at 60 kHz repetition rates and a two-mask interferometer. The beam was focused to a 30–50 $\mathsf{\mu }$m diameter along the fiber axis, greatly enhancing the peak power while avoiding damage to the masks. A refractive index modulation of more than ${10}^{-3}$ could be obtained in less than one minute exposure. To avoid the observed strong temperature gradient observed in the SMF-28 fiber, a galvo scanner was used to rapidly move the beam back and forth laterally up to 1 mm. FBG were written in SMF-28, as well as 20/400 $\mathsf{\mu }$m fiber. In the latter fiber, better heat dissipation allowed us to write the FBG with the standard phase mask scanning technique, and a 0.28 mm Gaussian apodized FBG could be written.

1. Introduction

The use of femtosecond laser pulses to write fiber Bragg gratings (FBG) has been the subject of much development in recent years [1], as it has been shown to provide many practical benefits. One is that strong FBG can be written without loading the fiber with hydrogen, which greatly simplifies the manufacturing process [2,3,4,5,6]. The multi-photon nature of the inscription also allows the use of longer wavelengths where the fiber coating is transparent, thus removing the need for stripping and recoating and preserving the fiber mechanical integrity [7]. Focusing the pulses to a small point also allows point-by-point (PbP) writing [8,9], which gives full flexibility in choosing the FBG central wavelength and eliminates the need for costly phase masks.

While the PbP technique is advantageous, it nevertheless requires very high quality optics and translation stages to achieve wavelength precision and repeatability, which is otherwise easy to achieve with a phase mask. For mass production of identical FBG, the cost of the phase mask is negligible. However, using the phase mask with the standard technique, which is to position the fiber right behind the mask [10], poses other problems with femtosecond pulses. The peak intensity is very high, and both self-focusing and multi-photon absorption (MPA) can occur in the mask itself [4]. This can either damage the mask or limit the efficiency of the writing process.

To circumvent this problem, the fiber can be placed at some distance from the mask, and the beam remains unfocused along the fiber axis so that the two interfering beams still have significant spatial and temporal overlap in the fiber core [2,3]. To maintain a high peak intensity, the pulse energy has to be significant, of the order of 1 mJ. The broad spatial width of the beams also precludes the fabrication of FBG with complex apodization profiles.

Recently, we have theoretically demonstrated that a two phase mask interferometer allows the focusing of femtosecond pulses on the fiber down to a very small diameter, without affecting the pulse duration, contrary to a Talbot interferometer [11]. Since the fiber is at a significant distance from the masks, self-focusing and multi-photon absorption in the masks can be avoided. With such tight focusing, high peak intensity can be reached with very low pulse energy. Our review of the previous work using femtosecond pulses to write FBG indicated that the required peak power could be reached with such tightly focused pulses [11]. Thus lasers with low pulse energy but high repetition rates could be used for efficient FBG fabrication, even in non H₂-loaded fiber. The two-mask interferometer was used before to write FBGs with fs pulses by Livitziis et al. [5], but those authors did not take advantage of the possibility to focus the UV beams. Here we demonstrate this technique, using the third harmonic of an Yb-based solid state femtosecond laser at 343 nm and non-H₂ loaded SMF-28 fiber, as well as double clad fiber with a core diameter of 20 $\mathsf{\mu }$m and an external diameter of 400 $\mathsf{\mu }$m (20/400 fiber). The total energy impinging on the fiber of only 7 $\mathsf{\mu }$J, at a repetition rate of 60 kHz (average power 420 mW), was sufficient to reach refractive index modulations larger than ${10}^{-3}$ in less than one minute. The small diameter focused beam also allows very fine apodization patterns to be written.

2. Experiment

The laser used in this work was a Pharos 6W laser (Light Conversion, Vilnius, Lithuania) that provides up to 24 $\mathsf{\mu }$J pulses at the third harmonic (343 nm), with a duration of 237 fs and a repetition rate of up to 60 kHz. An internal attenuator could be used to reduce the average power, and the repetition rate could also be reduced to any integer divider of 60 kHz. Our choice of the 343 nm wavelength was guided by two factors. One is that the threshold for MPA is much lower as one approaches the bandgap. Multi-photon absorption at 343 nm only involves 2 or 3 photons rather than 4 or 5 at longer wavelengths, such as 800 nm or 1030 nm. Since the conversion efficiency of the nonlinear crystal is very high, it makes more sense to use a shorter wavelength to reduce the peak power requirement. Another choice would be the fourth harmonic at 257 nm. However, we wanted to avoid linear absorption in the core to interfere with the MPA process. Another important factor is that lasers operating at the third harmonic are commonly used in industry and thus have a higher reliability, and components such as the galvo scanner are readily available for this standard wavelength. Our results nevertheless indicated that the fourth harmonic would also be well suited, since the actual linear absorption at 257 nm is quite small compared with the MPA that we observed.

A schematic of the writing setup is shown in Figure 1. The UV beam is first reshaped with a 3× cylindrical telescope, composed of lenses with 75 mm and −25 mm focal lengths, so as to make its diameter smaller in the direction of the fiber axis and, thus, wider after focusing. The beam is then redirected by a galvo scanner (GS), for reasons explained below, itself mounted on a motorized translation stage (TS) and focused with the spherical 100 mm focal length lens (SL), also mounted on the stage. The beam then passes through the two-mask interferometer, with the fiber (OF) positioned at the crossing of the two beams diffracted by the mask M2. The distance between the lenses of the telescope could also be fine tuned to minimize the beam diameters on the fiber. The fiber itself could be moved along the y- and z-directions to be positioned at the crossing point of the beams. Focusing resulted in beam widths of 30–50 $\mathsf{\mu }$m in the longitudinal direction (which could be adjusted by varying the lens spacing of the telescope) and approximately 16 $\mathsf{\mu }$m in the transverse direction. Having a wider beam in the longitudinal direction results in a full spatial and temporal overlap of the interfering beams in the fiber core, which is also less critical to the fiber z-position. A pen-sized microscope (PM) connected to the PC computer is positioned above the fiber to visualize the beams and optimize the alignment.

The classic design of a two-mask interferometer involves a first phase mask (M1) diffracting the beam equally into the +1 and −1 orders at normal incidence, followed by a second mask (M2) with half the period of the first mask that diffracts the incident beam into the +1 order. Although the configuration analyzed in Ref. [11] uses two separate M2 masks, to allow for angle tuning, our configuration uses a single M2 mask. The requirement that the period of M2 be half that of M1 is, however, not absolute. In fact, many period combinations can be used, as long as the beams incident on the fiber have the proper angle to give the required grating period. Thus, we used an M2 mask of period 508.4 nm, in combination with a mask M1 of period 1040.8 nm to make FBG at 1550 nm, as well as a mask M1 of period 1743 nm with the same M2 mask to make FBG at 1080 nm. FBG across a wide range of wavelengths can thus be made by only changing the first mask. All the masks used were 25 mm long. The M2 mask was designed and fabricated for maximum diffraction efficiency (by Ibsen, Denmark). The M1 mask was obtained from Phasemask Technology (Fremont, CA, USA). The diffraction efficiency of both M1 masks was 35%, and that of the M2 mask was 65%. Thus the compound diffraction efficiency was 22%, with 44% of the incident energy reaching the fiber.

The distance between the two masks was set to approximately 25 mm. The distance from M2 to the fiber was approximately the same for FBG at 1550 nm but only approximately 10 mm for the FBG at 1080 nm, due to the larger diffraction angle. The length of the FBG was limited mostly by the length of M2, in our case, 25 mm. Keeping the distance between the two masks small allowed us to make FBG up to approximately 13 mm long. It is important to ensure that the grooves of the two phase masks are parallel and perpendicular to the fiber axis, otherwise the two diffracted beams are not at the same height on the fiber. Thus, each mask had an independent tilt adjustment. The masks must also be parallel to the fiber and perpendicular to the beam, or else the distance to the crossing point changes along the mask. This is carried out by ensuring that the beam is reflected by the mask back on itself. For this, mask M2 is installed and aligned this way first, followed by M1.

At the highest pulse energy available, significant two-photon absorption and self-focusing were still readily observed in M1, which sees the highest peak power. However, as is explained, we only used approximately 30% of the available pulse energy, which was sufficient for fast writing of strong FBG. In such conditions, the pulse energy required from the laser was only $7\mathsf{\mu }$J, while $4\mathsf{\mu }$J total energy was actually incident on the fiber. This is more than 100 times less than the typical 800–1000 $\mathsf{\mu }$J required when the beam is not focused horizontally or longer wavelengths are used. Considering the pulse energy, the pulse duration of 237 fs, and the focused beams diameter, the peak power on the crest of the interference pattern was $2.1\times {10}^{12}$ W/cm². This is in line with the prediction made in our previous paper [11], considering the different writing wavelength.

The beams produced a strong fluorescence in both core and cladding, which made them easily visible with the microscope. The cladding produced mostly red fluorescence, due to the creation of non-bridging oxygen hole centers in the silica glass [12,13], while the core also produced violet fluorescence (400 nm) [14] from germanium defects. A color filter glued to the microscope could filter out the red fluorescence and only show the beams inside the core. Figure 2 shows the red fluorescence of the two focused beams in the 20/400 fiber. The microscope made it easy to optimize the position of the fiber and adjust the telescope lenses and the spherical lens positions to obtain the narrowest beams on the fiber. Supplementary Material S1: Alignment is a short video showing the fiber being moved forward and backward into the beam crossing and how the optimum position with the two beams crossing in the core can be achieved. The intensity of the red fluorescence was observed to quickly increase upon exposure. As observed previously in non-H₂ loaded fibers, the blue fluorescence decreased upon exposure by approximately 40% [14]. As Figure 2 clearly shows, one advantage of the two-mask interferometer is that the beams have perfect overlap in the fiber core, which maximizes the interference contrast, while any zero order light from the first mask is negligible, as well as being temporally separated. The multi photon nature of the process could be confirmed by the more than doubled fluorescence intensity where the beams interfere.

Under the writing conditions described above, and with stationary beams, a broad FBG was readily obtained in a few seconds, reaching a few percent reflectivity and with a bandwidth determined by the width of the interference pattern. A longer grating is typically made by translating the incoming beam along the mask, the so-called phase mask scanning technique [15]. However, we found that in SMF-28 fiber, we could never obtain a grating as strong as with the stationary beams, unless we reduced the repetition rate by approximately a factor of 10, which lengthens the writing time. Upon investigation, it was found that the temperature in the fiber was very high and easily exceeding 500 °C. This was readily seen by the shift in central wavelength when the beams were turned off, which could be in excess of 5–6 nm. There is, therefore, a very strong temperature gradient across the narrow writing beam. When translating the beam, the phase of the written grating changes significantly with temperature, and part of the already written grating is erased as the beam is moved and the phase of the newly written grating is different. This was most important in the 125 $\mathsf{\mu }$m SMF-28 fiber. In the 20/400 $\mathsf{\mu }$m fiber, heat seemed to be more easily dissipated by the larger volume of glass, and the temperature did not exceed 150 °C. Thus, the scanning beam method could only be used in that larger diameter fiber.

In order to resolve this problem, we made use of the galvo scanner to rapidly scan the beam back and forth over a predetermined length along the fiber, thus distributing the heat uniformly. This allowed us to write relatively short uniform gratings (0.5–1 mm) without translating the beam at all, using the full laser repetition rate, as well as only 30% of the laser power. Figure 3a shows the spectrum of a uniform, 0.69 mm long FBG written in this manner in SMF-28 fiber, with a reflectivity of 47%. The writing time was typically approximately 45 s. The reflected spectrum was fitted to the well-known response of the reflectivity R of a uniform fiber Bragg grating:

$$R\left(\lambda \right)=\frac{sinh\left(\sqrt{{\kappa }^2-{\delta }^2}L\right)}{{cosh}^2\left(\sqrt{{\kappa }^2-{\delta }^2}L\right)-({\delta }^2/{\kappa }^2)}$$

(1)

where $\kappa$ is the coupling constant, L is the length, and

$$\delta =2\pi n_{eff}\left(\frac{1}{\lambda }-\frac{1}{{\lambda }_0}\right),$$

(2)

where $n_{eff}$ is the effective refractive index of the optical fiber, $\lambda$ is the wavelength, and ${\lambda }_0$ is the central wavelength.

Gratings up to approximately 1 mm could be written this way, which may be limited by our use of a spherical lens instead of an f-theta lens. Such f-theta lenses are typically used with galvo scanners for engraving applications to produce a linear lateral displacement with angle, resulting in a flat field on the image plane.

When using the galvo scanner, the entire grating is inscribed simultaneously and the evolution of the spectrum can be monitored on the optical spectrum analyzer (OSA). Figure 4 shows the fluorescence of the two beams in the 20/400 fiber when the galvo scanner is activated. When turning the writing beams off, we could confirm the large temperature of the fiber observed with stationary beams, typically 500 °C. At a higher power and temperature, the quality of the grating started to degrade. Measuring the grating bandwidth at different exposure times provides a good measure of the refractive index modulation, since there is a direct and monotonous relationship between the two. It is, therefore, more convenient, accurate, and reliable than a measurement of the absolute maximum reflection. Such a measurement is shown in Figure 5, showing that up to $1.6\times {10}^{-3}$ can be reached. The growth is well-fitted by an exponential with a characteristic time of 38 s and a saturated index change of $1.85\times {10}^{-3}$. Using both the galvo scanner to produce a 0.7 mm beam and then translating the scanner, we could write longer gratings, such as are shown in Figure 3b. That grating could be written in approximately 30 s. It is fitted to a 7.2 mm long uniform grating and $1.5\times {10}^{-4}$ index modulation, a 89% reflectivity, and a 0.19 nm 3 dB bandwidth.

In the 20/400 $\mathsf{\mu }$m fiber, the temperature rise was much smaller, due to the more efficient heat dissipation in the large volume of glass. Thus, slightly higher power could be used but, this time, limited by the onset of MPA in mask M1. The small focused beams allowed for writing gratings with a fine apodized profile. The contrast of the interference pattern is controlled by dithering the phase masks with a piezo stage at a determined amplitude, resulting in a constant average exposure but varying grating strength [16]. One example is the writing of a 1 nm bandwidth low reflector for high-power fiber lasers with a Gaussian profile, resulting in a smooth spectral profile with low side lobes. Shown in Figure 6 is the spectrum of a 0.8 mm long, Gaussian profile FBG with a 0.28 mm full-width at half maximum, along with the simulated spectrum. The grating has a reflectivity of 13% corresponding to a refractive index modulation of $5.6\times {10}^{-4}$, and was written in 40 s. The side lobes are suppressed down to 20 dB below the peak, and the small side lobe on the short wavelength side may actually be due to residual higher order mode light. Such fine control of the apodization profile is made possible by the strong focusing and perfect beam overlap of the two-mask interferometer.

3. Discussion and Conclusions

Albert et al. [17] were the first to point out that electrons excited above the bandgap through MPA at 193 nm could result in index changes of the order of ${10}^{-3}$ in low-Ge fiber such as SMF-28. Lancry et al. [18] have studied the dynamics of electron thermalization under femtosecond excitation into the conduction band at 800 nm. A complete model for fiber photosensitivity has also been proposed by Janer et al. [19]. In our case, excitation into the conduction band would involve three-photon absorption (10.8 eV). The large temperature rise in the fiber indicates significant multi-photon absorption.Such a rise was not observed in ref. [17] (or other works, to the best of our knowledge), but the much slower rate of index change in that case (10–20 min compared with 1 min in our case) indicates a much smaller MPA. While it is difficult to measure the exact amount of absorbed light, because the transmitted beams expand rapidly out of the fiber, we nevertheless could estimate that absorption was at least 30% and was decreasing upon exposure. The high temperature poses a limit to the speed of the writing process. Writing at such high temperatures, however, means that the grating is, to a large extent, self-annealed. Indeed, preliminary measurements have shown negligible change in the grating strength after 24 h in an oven at 120 °C. It is also known that type 1 fs FBG in non-H₂ loaded fibers have greater thermal stability than those written with longer pulses in H₂-loaded fiber [20]. In H₂-loaded fiber, such high temperatures are never reached, despite the similar or faster writing speed. This indicates that despite the large MPA, the process leading to defect formation and permanent index change, starting with electrons excited into the conduction band, has a very low yield in the absence of H₂, and most of the absorbed energy is dissipated as heat [18]. Nevertheless, the fast writing speed remains advantageous since it both removes the H₂-loading requirement, and may also eliminate the need for subsequent grating annealing. Manufacturing then becomes a one-step efficient process.

The low pulse energy also means that either a lower average power laser can be used, or that a single laser can be divided for use in multiple writing stations simultaneously, in either case bringing significant cost reduction since the laser is by far the most expensive part of the manufacturing station. Even lower pulse energies could be used and the smaller resulting MPA be compensated with a higher repetition rate. Such lasers with repetition rates in the MHz range are readily available.

In conclusion, we have shown that the use of a two-mask interferometer allows for efficient fiber Bragg grating production in non-H₂-loaded fiber with a femtosecond laser. Pulses of only 7 $\mathsf{\mu }$J energy at 343 nm could be used to obtain 0.7 mm gratings with up to $1.6\times {10}^{-3}$ index change in less than one minute. Gratings could be written in both small core SMF-28 and large core 20/400 $\mathsf{\mu }$m fiber. This approach represents a significant progress in FBG writing technology, by greatly simplifying the manufacturing process.