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Based on reconstruction-equivalent-chirp (REC) technique, a novel solution for fabricating low-cost long fiber Bragg gratings (FBGs) with desired properties is proposed and initially studied. A proof-of-concept experiment is demonstrated with two conventional uniform phase masks and a submicron-precision translation stage, successfully. It is shown that the original phase shift (OPS) caused by phase mismatch of the two phase masks can be compensated by the equivalent phase shift (EPS) at the ±1st channels of sampled FBGs, separately. Furthermore, as an example, a π phase-shifted FBG of about 90mm is fabricated by using these two 50mm-long uniform phase masks based on the presented method.
©2012 Optical Society of America
1. Introduction
Fiber Bragg gratings (FBGs) with special responses are attractive devices for optical communication systems, such as the sampled FBGs for wavelength division (WDM) system [1], the phase-shifted FBGs for optical code-division multiple-access (OCDMA) system and optical Hilbert transformation system [2–4], and the chirped FBGs for dispersion or dispersion compensation [5,6]. However, the fabrication of FBGs with complex structure is a little difficult for the requirement of complicated phase masks or nanometer-precision translation stages. One of the low-cost solutions is using the reconstruction-equivalent-chirp (REC) technique. With REC technique and uniform phase masks, the FBGs with desired properties can be obtained only based on submicron-precision fabrication. Many kinds of physically realizable FBGs have been achieved with REC technique in previous works [7–12]. However, the lengths of FBGs have not been investigated yet, as the FBGs cannot be longer than the phase mask, traditionally. In some applications, long FBGs are required to achieve better performance or some special properties. For example, chirped FBGs with long length can be used for ultra-long distance dispersion compensation or used in the arbitrary-shaped optical filter system [13,14]. A wider range can be monitored with a longer FBG in the distributed FBG sensor system [15]. Specially designed long FBGs can be used to suppress the stimulated Brillouin scattering phenomenon occurring for high-energy Q-switched pulses [16]. There are several methods that can fabricate long FBGs. They can be achieved by writing a set of consecutive subgratings with interferometric control of the relative position of them [17]. However, this method needs complicated nanometer-precision fabrication. Another method is using several phase masks, but there are always uncontrolled phase mismatches among these phase masks [18]. Moreover, to obtain a desired long FBG, many specially designed phase masks are needed, which makes the fabrication of long FBGs expensive and inflexible.
In this paper, it is proposed that based on the REC technique long FBGs with desired properties can be fabricated with two uniform phase masks and a translation stage of submicron precision. The original phase shift (OPS) caused by the phase mismatch of phase masks can be compensated thoroughly. A proof-of-concept experiment is demonstrated with two 50mm-long uniform phase masks of the same period. Our experiment focuses on using the equivalent phase shift (EPS) to compensate and obtain the OPS, which is the key of this method. It is shown that the phase shift at the ±1st channels can be compensated separately with different EPS. In addition, an FBG of about 90mm with π phase shift at the −1st channel is written by using these two 50mm-long uniform phase masks. If more separate phase masks are used, longer FBGs with desired properties can be obtained. The length of such FBG is only limited by the working range of the submicron-precision translation stage and the overall performance of the spliced phase masks. The significance of the proposed method is that only based on submicron precision and uniform phase masks, long FBGs with desired properties can be achieved, which makes the fabrication simple, low-cost and flexible.
2. Principle and simulation
There are multiple channels in the reflection spectrum of a sampled FBG. The optical properties of a certain non-zero channel can be controlled by varying the sampling function. On the other hand, by applying appropriate sampling function, the optical properties desired can be achieved. The REC technique reveals the relationship between the sampling function and the desired optical properties, thus, with REC technique, the sampling function corresponding to the desired optical properties can be obtained. Traditionally, in the reconstruction algorithm only one phase mask is considered, however, the content presented in this paper is based on a system with two phase masks. It is an exploitation and extension of REC technique.
When two uniform phase masks with the same period are spliced together, there will be a phase shift in the grating, which is caused by the phase mismatch of the phase masks. The index modulation of the grating fabricated with two phase masks along z is given by
where S1(z) and S2(z) are sampling functions, Λ is the period of the grating, and β is the OPS caused by the phase mismatch of the phase masks at the kth sampling position zk.If the index modulation of the seed grating with desired properties is shown as
where Λs is the period of the seed grating, and As(z) and φs(z) are the profiles of apodization and phase. The desired properties can be phase-shifted, chirped, apodized and so on [7–12].To get the FBG with desired properties at the mth channel, S1(z) and S2(z) should be
where, and Fm are the sampling period, the apodization and the Fourier coefficient of the mth-order channel, respectively.Note that the OPS β of the two spliced phase masks is unknown to us, however, it can also be obtained with REC technique. The key is using the EPS to compensate and obtain the OPS, and the schematic diagram of it is shown in Fig. 1 .
When different EPS em is introduced into the mth channel by altering the change of sampling period Δzk at zk, the total phase shift (TPS) at this channel will change, because it is the summation of the OPS and EPS. An FBG without phase shift at the mth channel, which means the OPS is compensated thoroughly by the EPS, is achieved when the EPS is
where Δzk is the change of sampling period at zk, and N is an integer. On the other hand, when there is no phase shift at the mth channel, the OPS can be obtained according to the EPS.Two simulated examples with different parameters are presented. The parameters used in simulation are given in Table 1 .where neff, Δnmax and L are the effective refractive index, the maximum index modulation and the length of FBG, respectively.
Table 1. Parameters used in simulation
In the first example, the seed grating is a uniform FBG at 1553nm and the −1st channel is chosen for reconstruction. In Figs. 2(a) -2(c), it can be found that there are dips at the stopbands of all these channels, when the EPSs at all channels are integer multiples of 2π. In such case, the EPSs have no effect on all channels, and the TPSs at all channels are equal to the OPS. Therefore, the relative positions of these dips in the stopbands are the same. Figure 2(b) and Fig. 2(c) also show that the relative positions of the dips in the stopbands of the non-zero channels change with different EPS. Since the OPS is −0.4π, when the EPS at the −1st channel is 8.4π, the dip in the stopband of it disappears in accordance with Eq. (4). Hence, it is proved that the OPS can be compensated by the EPS. Other EPSs which satisfy Eq. (4), can also be used for compensation. In the second example, the desired seed grating is a π phase-shifted FBG at 1548nm and the +1st channel is chosen for reconstruction. As the OPS is 0.7π, when the EPS at the +1st channel is −41.7π, the π phase shift we need is achieved as shown in Fig. 2(f).
3. Experiment and results
Our experiment will focus on using the EPS to compensate and obtain the OPS, which is the key of this method. The schematic configuration of the fabrication system with two uniform phase masks is depicted in Fig. 3 . Two uniform phase masks are held on two adjusting stages separately to adjust the symmetry and alignment of them. Once the two adjusting stages are adjusted to the most appropriate states, they cannot be moved to ensure that the OPS is not changed throughout the experiment. A section of fiber is fixed on two clips. The grating is imprinted into the fiber through the phase masks by scanning the focused 244-nm UV beam from a frequency-doubled argon ion laser. The sampling function of the FBG is controlled by a shutter, a submicron-precision electric translation stage and a computer. The structure of the FBG desired is input into the fabrication program in the computer, and then the computer controls the movement of the electric translation stage and the shutter. The optical responses of the FBG are monitored by an optical vector analyzer. In the experiment, two phase masks with the same period of 1070 nm are used. Both of them are 50mm long with about 4mm of margin at each edge.
First of all, the value of OPS should be obtained. A sampled FBG with the sampling period of 0.4mm is fabricated by using 40mm of each phase mask with 8.8mm of blank at the center. When Δzk is 8.8mm, the EPSs at all channels are integer multiples of 2π, thus the EPSs have no effect on all channels. In such case, the TPSs at all channels are equal to the OPS β. Figures 4(a) -4(c) show the reflection spectrums of the 0th, −1st and +1st channels. There are dips in all these stopbands of the reflection spectrums. As the TPSs at all these channels are the same, the relative positions of these dips in the stopbands are the same as expected. The −1st channel is selected for compensation, firstly. Several FBGs are fabricated with different Δzk, which means different EPS, in essence. In the experiment, the step of Δzk is 0.01mm, thus, the precision of the OPS obtained is 0.05π. It is found that the dip in the stopband of the −1st channel disappears when Δzk is 9.03mm, corresponding to the EPS of 45.15π and it is shown in Fig. 4(b). Therefore, the OPS is −45.15π according to Eq. (4) and it can be written as 0.85π. The TPS at the +1st channel is also changed but not compensated as Fig. 4(c) shows. If the OPS is indeed 0.85π, it can be compensated by an EPS of −44.85π at the +1st channel. Hence, to verify the accuracy of the OPS obtained, Δzk is chosen to be 8.97mm and it can be found that the dip in the stopband of the +1st channel disappears as shown in Fig. 4(c). Figure 4(a) shows that the phase shift at the 0th channel is not changed throughout the experiment, which indicates that the system is stable enough.
Fig. 4 (a) Reflection spectrum of the 0th channel at different EPS, (b) Reflection spectrum of the −1st channel at different EPS, (c) Reflection spectrum of the +1st channel at different EPS, (d) Reflection spectrum of the fabricated FBG with π phase shift at the −1st channel.
When a certain seed grating is needed, the OPS obtained and the index modulation of the seed grating are substituted into Eq. (3a) and Eq. (3b), and then the FBG with desired properties is reconstructed. As an example, in the experiment, the desired property of the seed grating is assumed to be π phase-shifted, therefore, Δzk is chosen to be 8.83mm, corresponding to the EPS of 44.15π. After the reconstruction process mentioned above, a π phase-shifted FBG of about 90mm is fabricated by using these two 50mm-long phase masks with this scheme, as shown in Fig. 4(d). It can be found that the experimental result is in good agreement with the simulation result.
4. Conclusion
In conclusion, we have presented that long FBGs with desired properties can be fabricated with two uniform phase masks and a translation stage of submicron precision based on the REC technique. The phase mismatch between the two phase masks can be compensated with the EPS, thoroughly. The length of FBG is not restricted by the length of phase mask anymore. In the proof-of-concept experiment, it is obtained that the OPS caused by phase mismatch of the two phase masks is 0.85π, and it keeps unchanged throughout the experiment. The phase shifts in the ±1st channels can be compensated with different EPS. Moreover, as an example, a 90mm-long FBG with π phase shift at the −1st channel is written by using these two 50mm-long phase masks. It should be mentioned that more than two phase masks can be used in the fabrication, and the phase shifts caused by the phase mismatches among them can all be compensated with REC technique. Therefore, FBGs can be as long as needed. The proposed solution is simple, low-cost and flexible. This method shows its promising applications in fabricating high-performance fiber laser, dispersion compensator, OCDMA en/decoder and so on.
Acknowledgments
This work was supported in part by the National Nature Science Foundation of China under Grants 60877043 and 61090392, the National High Technology Research and Development Program of China under Grant 2011AA010300, the Fundamental Research Funds for the Central Universities, and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
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