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Abstract
In a previous study, we proposed a measuring method for the reflectivity of weak-reflection large-mode-area fiber Bragg gratings by using scale gratings. We experimentally found that the interference between two scale fiber Bragg gratings (FBGs) is beneficial for increasing reflectivity scales, which can improve the measurement accuracy. Therefore, in this study, we designed and fabricated FBG-based Fabry–Perot cavities (FBG-FP) in single-mode fibers by two inscription methods, namely ultraviolet (UV) laser exposure and femtosecond-laser direct writing. Then, a large-mode-area double-clad (LMA-DC) FBG of weak reflectivity was measured by these two scales, and the experimental results show that the Bragg resonance reflectivity is less than 4.28% and 1.14% ∼ 2.28%, respectively. This method of measuring the weak grating reflectivity based on FBG-FP scales is convenient, efficient, and accurate. It is also worth mentioning that the method of femtosecond-laser direct writing eliminates the period limitation of the phase mask, thereby expanding the measurement wavelength range of FBGs. In the future, with the improvement of fiber grating fabrication technology, it is expected that more accurate results can be obtained.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-power fiber lasers have the advantages of compact structure, efficient conversion, and good beam quality; thus, they have important applications in industrial processing, communication, military, and national defense [1–6, 56]. In the past few years, high-power fiber oscillators have evolved rapidly owing to the development of large-mode-area double-cladding (LMA-DC) gain fibers and fiber Bragg gratings (FBGs) [6]. This structure employs a pair of high-reflectivity and weak-reflectivity FBGs that constitute a resonant cavity. Compared with a fiber laser based on a master oscillator power amplifier, the aforementioned oscillator is not only simple in terms of structure, good in terms of stability, and low-cost, but can also suppress the generation of high-order modes [7–10]. By optimizing the grating characteristics, the laser efficiency, transverse mode instability, and stimulated Raman scattering threshold of the laser can be significantly enhanced. In addition, the reflectivity of a weakly reflective fiber grating has an impact on the broadening of the laser output spectrum [11]. Therefore, it is necessary to accurately measure the reflectivity of weak reflection gratings.
The measurement of grating reflectivity is mainly based on the analysis of the transmission spectrum using a broadband light source and an optical spectrum analyzer (OSA). This method enables the accurate measurement of the reflectivity of single-mode FBGs, but accurate measurement of the reflectivity of LMA FBGs is still very difficult to achieve, especially for weak-reflectivity FBGs. Owing to the existing high-order modes in LMA fibers, different testing conditions lead to a multipeak or symmetric/asymmetric-convex distribution in the grating reflection spectrum and a ladder distribution of the transmission spectrum. In addition, the mode interference leads to fluctuations in the transmission spectrum. Therefore, the reflectivity of the LMA FBGs cannot be measured accurately by transmission spectrum. Recently, we proposed a novel measuring method for the reflectivity of weak-reflection LMA FBGs by using scale gratings [12]. These are a string of weak reflectivity gratings fabricated on single-mode fibers by ultraviolet exposure with a chirped phase mask. Then, the weak reflectivity of the measured FBGs could be obtained by comparing the intensity of the Bragg resonance peak with those of the scale gratings in the reflection spectrum. In the experiment, we found that the structure similar to FBG-FP can make scale grating with more reflectivity scales, which can greatly improve the measurement accuracy.
In previous studies, we found that interference phenomena similar to FBG-FP structures can greatly increase the number of reflectivity scales, in order to more accurately measure the reflectivity of the LMA-DC FBG. In this paper, on the one hand, we designed and fabricated FBG-FP in single-mode fibers as the new scale gratings. On the other hand, Phase masks are expensive and only correspond to specific wavelength ranges, so we try to get rid of the limitation of phase masks by direct femtosecond inscription. We also obtained ideal spectral characteristics by controlling the distance between the two FBGs and the cavity length. An output coupler (OC) FBG is a core device in high-power fiber laser oscillators [13,14,10]. We measured the reflectivity of an OC-FBG with an FBG-FP scale grating. The experimental results show that the Bragg resonance reflectivity of the OC-FBG, measured through comparison with the reflectivity of the two types of FBG-FP scale gratings, was less than 4.28% and 1.14% ∼ 2.28%, and a more accurate result of 1.31% was obtained through fitting. The results obtained using both measurement methods were consistent. Compared with the method based on the transmission spectrum, the proposed measurement method is simple, convenient, and accurate. It should be noted that compared with the method of Uexposure, which the period of FBGs is limited by the period of the phase mask, femtosecond direct writing has greatly flexibility and can theoretically fabricate FBG-FP working in any wavelength band [15–17].
2. Principle analysis
At present, the main method for measuring the reflectivity of FBGs is to analyze the transmission spectrum. Figure 1 shows a typical experimental setup for the transmission method.
The broadband light source is usually realized by amplified spontaneous emission (ASE) or a super-luminescent light emitting diode. The output of the light source enters port 1 of the circulator and then the fiber grating to be measured through port 2. The other end of the FBG is used to measure the transmission spectrum. The reflection spectrum is obtained from port 3 of the circulator.
Figures 2 (a) and (b) show the spectrum of the OC-FBG fabricated on single-mode and LMA fibers. In the transmission spectrum, light whose wavelength is not in the working band of the FBG is completely transmitted according to the definition of dB, $T = 10\lg \frac{1}{{{T_{FBG}}}}$, where T represents the valley depth of the working region in the FBG transmission spectrum, TFBG represents the transmittance of the grating, and ${\textrm{T}_{\textrm{FBG}}} = {10^{ - T\textrm{ / }10}} \times 100\%$. The reflectivity of the measured grating can be expressed as ${R_{FBG}} = 1 - {10^{ - T\textrm{ / }10}} \times 100\%$. . The transmission spectrum base of a single-mode FBG is a horizontal straight line, whereas that of an LMA FBG exhibits certain fluctuations. Because of the existing mode interference in LMA fibers, it is very difficult to measure the value of the valley depth. All in all, it can be concluded that the method based on the transmission spectrum is not accurate to calculate the reflectivity of LMA FBGs.
By comparing the peaks of the transmission and reflection spectrum, we found that the higher the reflectivity is, the higher the peak intensity becomes. The measurement of the spectrum of the LMA fiber is affected by different modes, but that of the single-mode fiber is not affected. Therefore, we can make a series of weakly reflective FBGs on single-mode fibers as scale gratings that can be used to measure the reflectivity of LMA gratings. The reflectivity can then be obtained by comparing the intensities of the reflection peaks.
In fibers, two identical FBGs separated by a certain distance can form an FBG-FP grating, the structure of which is illustrated in Fig. 3. When the transmitted and reflected light passing through the FBG-FP grating meets the coherence condition, a stable interference phenomenon emerges in the fiber space.
The FBG acts as a weak mirror in the FBG-FP grating. Owing to the interference effect of the F-P cavity, many resonance peaks are generated at the working wavelength of the grating. In the FBG-FP structure, the length of the FBG and the distance between the two FBGs affect the spectral characteristics of the FBG-FP grating. Figure 4 shows the effect on the transmission and reflection spectrum of the FBG-FP grating when the length of both FBGs was 1 mm and their mutual distances were 3, 6, 9, and 12 mm. Figure 5 shows the effect on the transmission and reflection spectrum of the FBG-FP grating when the distance between both FBGs was 10 mm and their lengths were 0.6, 0.8, 1, and 1.2 mm. The effective refractive index of the fiber grating core was neff = 1.4546, the grid period was Λ=532.79 nm, and the refractive index modulation depth was $\Delta n$=1.1 × 10−4.
Fig. 4. Spectrum of the FBG-FP grating with different cavity lengths: (a) LFP = 3 mm, (b) LFP = 6 mm, (c) LFP = 9 mm, and (d) LFP = 12 mm.
Fig. 5. Spectrum of the FBG-FP grating with different FBG lengths: (a) LBG = 0.6 mm, (b) LBG = 0.8 mm, (c) LBG = 1.0 mm, and (d) LBG = 1.2 mm.
Figure 4 shows that the reflection spectrum of the FBG-FP grating is modulated by the reflection spectrum of the FBG. Note also that there are multiple resonant peaks in the reflection bandwidth. As the distance between both FBGs was gradually increased, the number of resonant peaks in the reflection bandwidth of the FBG increased significantly, and the interval between adjacent interferences gradually decreased; however, the peak reflectivity and FBG bandwidth remained unchanged.
Figure 5 shows that when the FBG length was gradually increased, the reflectivity of the FBG-FP grating also increased. The bandwidth of the FBG gradually decreased and the number of interference fringes within the bandwidth gradually decreased, but the interval between adjacent resonant fringes remained unchanged.
In general, the number of resonant peaks in the reflection spectrum is essentially the number of interference phenomena in the FP cavity, so the longer the LFP is, the more interference can meet the optical path difference condition, and the more number of resonant peaks. The envelope width of the reflection spectrum is actually the working bandwidth of the two FBGs in the FBG-FP, so the longer the LBG is, the smaller the working bandwidth of the FBG will be, and the envelope width of the reflection spectrum will become smaller.
In the reflection spectrum, each interference peak corresponds to a reflectance scale. Therefore, in the subsequent grating fabrication process, the most appropriate distance between the two FBGs, LFP, and the grating length, LFBG, should be set according to the simulations described above.
3. FBG-FP fabrication and measurements
3.1 By UV laser with a uniform phase mask
According to the available laboratory equipment and technology, we used a UV laser beam and a phase mask method to fabricate the FBG-FP grating. Figure 6 shows the experimental device employed for grating fabrication. In front of the focus lens, we set a diaphragm with an adjustable width to control the size of the beam, which was installed on an electronic displacement platform. During the fabrication process, the position of the light spot irradiating the phase mask can be controlled by moving the diaphragm. In this experiment, the width of the diaphragm was 0.4 mm. Given that the period of the phase mask was uniform, the period of the FBG produced by irradiating any position of the phase mask was the same. We irradiated the two ends of the phase mask by controlling the diaphragm with an electric displacement platform, and two FBGs with the same period but with a certain interval were fabricated in the same fiber.
During the fabrication process, a broadband light source, an OSA, and a circulator were used to connect the optical path and establish a monitoring optical path. The UV laser, which inputs KrF gas, outputs a 248-nm wavelength with an operating frequency of 10 Hz and a single pulse energy of 7 mJ. The fiber used for fabrication was HI1060, which was hydrogen-loaded for 10 days at 12 MPa. The period of the phase mask was 740 nm. The test light source was an ASE, which was connected to the OSA through a circulator. All the optical fibers were HI1060.
We fabricated two FBG-FP gratings between 1075-1077 nm. During the fabrication, the valley depth of the transmission was controlled by the total exposure energy. Figures 7 and 8 show the transmission and reflection spectrum of the FBG-FP grating after annealing at 150 °C for 15 h. The data are detailed in Tables 1 and 2. Note that the spectrum has evident interference characteristics of the FBG-FP structure. The black dotted line represents the wavelength position with the scale function, and the calibrated reflection resonance peak is a function of the reflectivity scale. Grating A has 8 positions that can be used as reflectance scales, and the corresponding range of reflectivity is 4.28%-23.79%. Grating B has 13 positions that can be used as reflectance scales, and the corresponding range of reflectivity is 4.50%-10.26%.
Fig. 7. Transmission and reflection spectrum of the FBG-FP grating (LFP = 4 mm): (a) overall and (b) partial spectrum.
Fig. 8. Transmission and reflection spectrum of the FBG-FP grating (LFP = 8 mm): (a) overall and (b) partial spectrum.
Table 1. Detailed data of the resonance wavelength and reflectivity of the FBG-FP grating (LFP = 4 mm)
Table 2. Detailed data of the resonance wavelength and reflectivity of the FBG-FP grating (LFP = 8 mm)
3.2 By femtosecond-laser direct writing
In the femtosecond-laser direct writing method, we can control the moving speed of the electric displacement platform to change the interval of the laser scribe lines, and then change the period of the FBG. Meanwhile, this method does not need to carry hydrogen in the fiber, and does not require annealing after fabricating [18,19]. The experimental setup for the femtosecond-laser direct fabrication of the FBG-FP grating is shown in Fig. 9.
The fabrication system consisted of a femtosecond-laser amplifier, mirror, energy attenuation sheet, and microscope objective lens. The fiber was fixed on a mobile platform that could be automatically controlled in three dimensions using a fixture; the platform movement accuracy was 1 nm. The optical monitoring route comprised an ASE light source and an OSA. The center wavelength of the femtosecond laser was 515 nm, the pulse width was 190 fs, the repetition frequency was 1 kHz, and the maximum pulse energy was 30 nJ. The laser pulse was shaped by various devices, such as circular attenuators and diaphragms. After attenuation, the laser was focused on the HI1060 fiber core through a 100x objective lens; keep in mind that LFP denotes the length of the F-P cavity and LBG is the length of the FBG. Figure 10 shows the process of fabricating a FBG with a femtosecond laser. When the laser is on, the fiber fixed on the displacement platform moves vertically with speed velocities V1, then the laser is turned off and moved the displacement platform oblique upward with velocities V2 to the starting point of the second line, Therefore, we change the period of FBG by controlling the velocities V1 and V2 of the displacement platform
Two identical FBGs were fabricated on the same fiber at a certain interval; the structure diagram is shown in Fig. 9. We used the femtosecond line-by-line fabrication method to fabricate two identical FBGs on a single-mode fiber by changing the F-P cavity length LFP, FBG length LBG, and exposure energy to control the spectral properties of the FBG-FP grating. Figure 11 shows the transmission and reflection spectrum of the FBG-FP gratings fabricated at a wavelength of 1070 nm. It can be observed that the interference phenomenon is evident at approximately that wavelength, i.e., 1070 nm. The lengths of both FBG1 and FBG2 (LBG) were 345.55 µm, the distance between FBGs (LFP) was 2.5 mm. The reflectivity data are detailed in Table 3. The black dotted lines represent the wavelength position with the scale function, and the reflection resonance peak calibrated using the black circle can play the role of reflectivity scale. It should be noted that the left part of the resonant peak is due to the coupling between the core mode and the cladding mode, and the reflectivity of the FBG describes the transmission characteristics of the fundamental mode in the fiber core. So, the left resonance peak was not chosen as the reflectivity scale.
Fig. 11. Transmission and reflection spectrum of FBG-FP gratings fabricated by a femtosecond laser (LBG = 345.55 µm and LFP = 2.5 mm): (a) overall and (b) partial spectrum.
Table 3. Detailed data of the resonance wavelength and reflectivity of FBG-FP gratings
4. Measurement results and discussion
4.1 Measurement setup
Figure 12 shows the experimental setup for the measurement of OC-FBG reflectivity using the FBG-FP scale grating. ASE was used as the light source. In the two experiments conducted to measure the OC-FBG grating, FBG-FP scale gratings were placed between the measured OC-FBG and port 2. Angled physical contact connectors were used to reduce the influence of the end feedback. The reflection spectrum was obtained from port 3 of the circulator. A mode-field adapter (MFA) can filter out the high-order mode and thus ensure the transmission of the fundamental mode in the LMA fiber.
4.2 Using FBG-FP fabricated by UV laser
The measured grating was fabricated on an LMA fiber (LMA-GDF-20/400-HP-M fiber produced by Coherent Corporation). Figure 13 shows the transmission and reflection spectrum of the OC-FBG. The working wavelength was 1079.63 nm, and the bandwidth was 0.8 nm. Owing to the mode interference, clear fluctuations can be observed, which make it difficult to obtain an accurate weak reflectance in the transmission spectrum. According to the transmission-spectrum analysis method for reflectivity calculation, the measured T value at 1079.6 nm was 0.236 dB, and the reflectivity was 5.26%.
Figures 14 (a) and (b) show the transmission and reflection spectrum of the two FBG-FP scale gratings connected to the OC-FBG. It can be seen that the Bragg resonance peak of the OC-FBG is much lower than the reflectance scales of the FBG-FP scale grating. From Fig. 14 (a), it can be concluded that the reflectivity of the OC-FBG should be significantly less than 4.28%. From Fig. 14 (b), it can be concluded that the reflectivity of the OC-FBG should be much less than 4.50%.
Fig. 14. Transmission and reflection spectrum of the OC-FBG with different FBG-FP scale gratings: (a) FBG-FP grating (LFP = 4 mm) and (b) FBG-FP grating (LFP = 8 mm).
4.3 Using FBG-FP fabricated by femtosecond laser
Figure 15 shows the transmission and reflection spectrum of the FBG-FP grating connected to the OC-FBG. The horizontal dotted line in the figure represents the highest value of the OC-FBG reflection resonance peak. The Bragg resonance peak of the OC-FBG was located between the two interference peaks of the FBG-FP grating. According to the data of the resonance wavelength and reflectivity of the FBG-FP grating provided in Table 3, the reflectivity at these positions were 1.14% and 2.28%, respectively. According to the experimental results, the reflectivity of the OC-FBG measured by the FBG-FP grating should range between 1.14% and 2.28%.
To obtain more accurate experimental results, using the data in Fig. 15, we fit a curve based on the height of the FBG-FP scale grating reflection resonance peak and its representative reflectivity value in Fig. 16. Subsequently, the heights of the different reflection resonance peaks of the OC-FBG were substituted into the curve to obtain a fitting value, resulting in a OC-FBG reflectivity of 1.31%. This fitting result is consistent with the range of 1.14% to 2.28% obtained from the experimental measurement.
We used the FBG-FP scale grating fabricated by the UV laser to measure the OC-FBG reflectivity, which was less than 4.28%. The OC-FBG reflectivity measured using the FBG-FP scale grating fabricated by the femtosecond laser ranged between 1.14% and 2.28%, and a more accurate result of 1.31% was obtained through fitting. The results obtained using both measurement methods were consistent.
5. Discussion
The main difference between the two inscription methods is that the femtosecond laser method can get rid of the fixed period of the phase mask, and can flexibly inscribe more wavelength range of FBG-FP. And use femtosecond laser writing FBG does not need annealing, so there is no wavelength shift or depth change due to annealing, which improves the accuracy. Secondly, in the process of writing FBG-FP, in order to ensure that the two FBGS are exactly the same, UV laser inscribing needs to control the same exposure time of each FBG, but the laser beam is cut by the aperture so that the laser state of two exposure positions is not exactly the same, so it’s difficult to control the spectral characteristics of FBG-FP. As a result, the FBG-FP reflectivity scale inscribed by UV laser is not weak enough, and the measurement result of OC-FBG reflectance less than 4.28% is not as expected. Femtosecond laser inscribing FBG-FP can better control the consistency of two FBGs, only need to set the same number of lines can get a very ideal FBG-FP spectrum, and then inscribe FBG-FP with lower reflectivity scale. In the measurement results, the FBG-FP (via fs laser) obtained the reflectivity of the large-mode-area double-clad FBG from 1.14% to 2.28% by comparing the height of the reflection peak, we also obtained the accurate value of 1.31% by fitting method, and the two results are consistent. There is no doubt that both types of FBG-FP measurements results are better than the 5.26% result obtained by the traditional method. According to the inscribed minimum reflectivity scale of FBG-FP, the measurement results using femtosecond FBG-FP are more convincing.
There are two main advantages, on the one hand, the scale grating method avoids the large base fluctuation of the large-mode-area double-clad FBG transmission spectrum, thus reducing the measurement error and improving the accuracy of the results. meanwhile, the way to determine the reflectivity by comparing the height of the reflection peak is very straightforward. On the other hand, after each scale grating or FBG-FP is written, it can be used repeatedly, which is very convenient and efficient.
6. Conclusions
Based on the phase mask method and a femtosecond laser, we fabricated FBG-FP scale gratings to measure the reflectivity of an OC-FBG fabricated on an LMA fiber. The weak reflectivity of the OC-FBG can be obtained indirectly by comparing the peak heights from the weak reflection grating and the fabricated FBG-FP scale grating. The experimental results show that the reflectivity of the OC-FBG measured by the FBG-FP grating made by the UV laser was less than 4.28%. The results obtained using the FBG-FP scale grating made by the femtosecond laser ranged between 1.14% and 2.28%; and a more accurate result of 1.31% was obtained through fitting. The results obtained using both measurement methods were consistent. In the future, with the flexibility of femtosecond direct writing, it is theoretically possible to fabricate a scale grating capable of measuring reflectivity in any wavelength band, and then accurately measure the reflectivity of low-reflection LMA FBGs in all wavelengths. Meanwhile, fiber laser oscillators play a very important role in the field of fiber laser, and the output-coupling FBG is the core device of the structure. The method of measuring the low reflectivity of FBG with scale grating and FBG-FP can be used as a tool to optimize and improve the spectral characteristics of output-coupling FBG, and optimize the quality of the laser output from the oscillator.
Funding
National Natural Science Foundation of China (11974427, 12004431); Science and Technology Innovation Program of Hunan Province (2021RC4027); State Key Laboratory of Pulsed Power Laser Technology (SKL2020ZR05, SKL2021ZR01).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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