Open Access
Add to BibSonomyAbstract
A novel kind of Fabry–Pérot (FP) structure based on chirped sampled fiber Bragg grating (CSFBG) is proposed and demonstrated. In this structure, the regular chirped FBG (CFBG) that functions as reflecting mirror in the FP cavity is replaced by CSFBG, which is realized by chirping the sampling periods of a sampled FBG having uniform local grating period. The realization of such CSFBG-FPs having diverse properties just needs a single uniform pitch phase mask and sub-micrometer precision moving stage. Compared with the conventional CFBG-FP, it becomes more flexible to design CSFBG-FPs of diverse functions, and the fabrication process gets simpler. As a demonstration, based on the same experimental facilities, FPs with uniform FSR (~73pm) and chirped FSR (varying from 28pm to 405pm) are fabricated respectively, which shows good agreement with simulation results.
© 2014 Optical Society of America
1. Introduction
All-fiber Fabry–Pérot (FP) cavities based on fiber Bragg gratings (FBGs), which are realized by cascading or partly superimposing multiple FBGs on the fiber, have wide applications in optical fiber communication systems [1–9], optical fiber sensing systems [10–13] and photonic generation and processing of microwave signals [14–16], due to their unique advantages such as low insertion loss, low cost, and ease of fabrication with the flexible filtering spectrum. The FBG FPs can be mainly divided into two kinds: one is based on uniform FBGs and the other is based on chirped FBGs(CFBGs) (also called distributed FPs). Usually, the CFBG-based FP has wider spectrum range than the uniform FBG-based FP, which helps to extend the signal-processing ability of FBG FP. Moreover, the CFBG-based FP can provide more flexible functionality, since individual CFBG can be designed with different structure to constitute a variety of FP cavities.
Usually, a CFBG-based FP is formed either by writing multiple identical CFBGs successively into the same part of a fiber with only a small longitudinal offset between adjacent gratings, or by superimposing multiple CFBGs with different chirp-rates. The former has a uniform free spectral range (FSR), while the latter has an increased or decreased FSR. Thus, when fabricate a FP structure, one or two of the following three experimental procedures may be unavoidable: firstly, one or multiple specific chirped phase masks are needed; secondly, a precise longitudinal shift of phase-mask between two ultraviolet scans is required, which determines the FSR of FP resonator; thirdly, changing phase masks with different chirp-rates before each superimposing. However, this fabrication process arouses two problems: first, the FP’s property is overly dependent on the pattern of chirped phase mask, including the chirp-rate and wavelength band; second, the longitudinal shift of phase-mask or changing masks before each superimposing would result in additional alignment procedure to make the relative state (relative position and phase) between the phase mask and fiber keep consistent, which determines the uniformity of FBGs and FP’s performance consequently. Therefore, it would be a costly and challenging work to manufacture CFBG-based FPs of diverse functions.
In this letter, we propose a novel CFBG-FP structure based on chirped sampled FBGs (CSFBGs). In this structure, the conventional CFBGs forming FP resonant cavity are replaced by CSFBGs, i.e., chirping the sampling periods of a SFBG that has uniform local grating period. Owning to the introduction of sampling function, the realization of various CSFBG FPs only needs a single uniform phase mask, and no displacement between phase mask and fiber is required. Hence the relative state between the phase mask and fiber keep consistent all the procedure. In addition, to implement sampling structures, only the sub-micrometer control-precision is required. Compared with the conventional method, such CSFBG FPs have the advantages of increased flexibility and decreased fabrication complexity.
2. Principle
Figure 1 illustrates the CFBG-FPs structure of both the conventional and the proposed method. Two identical or different FBGs with varied chirp-rates are superimposed with a small longitudinal offset d. In the proposed FP structure, the regular CFBGs have been replaced by CSFBGs. For CSFBGs, the sampling periods are changed with the chirp-rate Cp, while the uniform local grating periods in all gratings keep constant. Based on the equivalent chirp (EC) principle [17] that makes use of the −1st or + 1st order reflective channel of SFBG by varying the sampling periods, it becomes feasible that the CSFBGs can take the place of regular CFBGs in specific wavelength region.
Fig. 1 Comparison between the conventional CFBG-FP and the proposed CSFBG-FP. (a) FP cavity consists of two identical FBGs. (b) FP cavity consists of two FBGs with different chirp-rates. Here d, Λ and P represent the longitudinal shift, the grating period and the sampling period respectively.
The refractive index modulation of an SFBG can be expressed as
where is the average effective index (DC index), is the fringe visibility that also acts as the apodization function, is the grating-period that is determined by the phase mask, describes the spatially-varying phase, S(z) describes the sampling function. For a uniform SFBG with the sampling period of P, S(z) can be written aswhere Fm is the Fourier coefficient. Hence, the refractive index modulation of the SFBG can be rewritten asEquation (3) shows that the SFBG consists of a series of equivalent ghost gratings with the grating periods of . Generally speaking, both the + 1st and −1st order () ghost gratings, which are usually symmetrical, have the largest refractive index modulation strength among all the non-zero order ghost gratings. Hence, such two channels become the most appropriate candidates for realizing equivalent structures. For the + 1st order ghost grating, the refractive index modulation can be written as
The grating period of the + 1st order ghost grating (producing the + 1st order reflective channel) can be expressed as:
Expression (5) shows that different + 1st order ghost gratings can be produced just by varying the sampling period based on a single uniform phase mask. So, chirped + 1st order ghost grating can also be realized by chirping the sampling period. Suppose chirped Λ+1(z) is desired, then the sampling period P(z) should be designed as:
Similar to expression (6), for realizing chirped Λ-1(z), P(z) should be designed as:
Furthermore, only the sub-micrometer control-precision is required, since the sampling period is usually in the order of hundreds of microns.
Thus, distributed FPs can be equivalently formed in the + 1st order channel by superimposing two or more chirped SFBGs.
3. Demonstration and results
To validate the proposed principle, two FPs with uniform FSR and chirped FSR are demonstrated respectively. For the FP with uniform FSR, two identical CSFBGs are superimposed with a small longitudinal offset d that determines FSR value. The local grating period is constant, and the sampling periods vary from P0 to Pend. Table 1 lists the detailed simulation parameters.
Table 1. Parameters for FP with Uniform FSR
The refractive index modulation depth (AC index) i.e., Δneff, is set to be a medium value, which is limited by the fiber photosensitivity available in our lab. The simulated results are shown in Fig. 2. The sampling periods (P(z)) of CSFBGs and corresponding grating periods (Λ+1(z)) of + 1st order ghost gratings are plotted in Fig. 2(a). We can see that + 1st order ghost gratings are designed to be linearly-chirped. The relationship between P(z) and Λ+1(z) has been revealed by Eq. (6). Such two equivalent chirped grating are identical except for a longitudinal offset of 11.4mm, which forms a FP structure with uniform FSR that is about 73pm. The sampling on a uniform grating creates multiple resonant orders in the resulting grating spectrum, and the spectrum of two CSFBGs superimposition are shown in Fig. 2(b). Either + 1st or −1st order channel is suitable for forming distributed FP structure. Here the + 1st order channel is chosen, as shown in Figs. 2(c) and 2(d). Figure 2(c) exhibits a typical spectrum of a FP structure. The FSR is also calculated, which shows good uniformity. Figure 2(d) shows linear group delay with multiple dips or peaks that locate in the position of notches in Fig. 2(c). The linearity with special slope proves that linear chirped equivalent gratings are realized just based on uniform-period seed grating. For comparison, such a CSFBG-based FP cavity is fabricated according to the same parameters. The FBGs are fabricated using a frequency-doubled argon-ion laser emitting at 244 nm. The sampling is implemented by switching on and off the UV scanning beam using an electrically controlled optical shutter. The half-width at half-maximum (FWHM) of the UV beam along the direction of the fiber measured at the fiber is ~90 µm. The hydrogen-loaded normal single mode fiber (SMF, G.652D) is used, and the pitch of uniform phase mask is 1070nm. The 0.1µm–precision moving stage used in this experiment can ensure the accurate realization of sampling function of the CSFBG. The experimental results which are measured by Optical Vector Analyzer (OVA) are shown in Fig. 3. The FSR differences between the experiment and simulation are calculated and drawn in Fig. 3(c). It can been seen that the FSR differences are less than ± 4pm.The results show that the reflection and group delay agree well with the simulation results. The minor variation of reflection peak ( ± 1.5dB) and FSR differences ( ± 4pm) are caused partly by phase or pitch errors of phase mask and partly by the non-uniformity of fiber itself. Being one kind of sampling structure, the phase or pitch errors induced by phase mask can be corrected by Reconstruction Equivalent Chirp (REC) technology that was proposed in [18]. The non-uniformity of fiber can be improved by using hydrogen-loaded photo-sensitive fiber as well as increased ultraviolet power and exposure time. It also should be noted that the increase of Δneff could increase the peak reflectivity of + 1st order channel. For example, when Δneff goes up to 3.5 × 10−4, the peak reflectivity of FP locating in the + 1st order channel will increase to as high as 99%.
Fig. 2 Simulation results of CSFBG FP with uniform FSR. (a) The sampling periods of CSFBGs and corresponding grating periods of linearly chirped + 1st order ghost gratings. (b) Spectrum of two CSFBGs superimposition. (c) Spectrum of + 1st order channel exhibiting FP characteristic, the red circles represent FSR values. (d) Group delay of + 1st order channel.
Fig. 3 Experimental results of CSFBG FP with uniform FSR. (a) Spectrum of + 1st order channel exhibiting FP characteristic, the red circles represent FSR values. (b) Group delay of + 1st order channel. (c) FSR difference between simulation and experiment.
The second demonstration is for the FP with chirped FSR. Two different CSFBGs are superimposed with no initial longitudinal offset, i.e., d = 0. The local grating period is constant, while the two sampling functions have different chirp rates. Table 2 lists the detailed simulation parameters.
Table 2. Parameters for FP with Chirped FSR
The sampling periods (P(z)) of CSFBGs and corresponding grating periods (Λ+1(z)) of linearly chirped + 1st order ghost gratings are plotted in Fig. 4(a). It can be seen that the equivalent-chirped gratings have two different chirp rates, which can form a FP cavity with chirped FSR. We also choose the + 1st order channel, and the simulated spectrum are shown in Figs. 4(b) and 4(c). The FSR is also calculated and plotted in Fig. 4(b), which shows FSR varies from 28pm to 405pm. Figure 4(c) also indicates that linearly-chirped ghost gratings are realized indeed. For comparison, such a CSFBG-based FP cavity is fabricated according to the same parameters listed in Table 2. The experimental results measured by OVA are shown in Fig. 5. The FSR differences between the experiment and simulation are calculated and drawn in Fig. 5(c). It can been seen that the FSR differences are less than ± 6pm.The results show that the reflection and group delay agree well with the simulation results. The minor variations between the simulation and experiment are caused by the same reasons that are analyzed in the uniform-FSR FP and can be improved by the same methods.
Fig. 4 Simulation results of CSFBG FP with chirped FSR. (a) The sampling periods of CSFBGs and corresponding grating periods of linearly chirped + 1st order ghost gratings. (b) Spectrum of + 1st order channel exhibiting FP characteristic, the red circles represent FSR values. (c) Group delay of + 1st order channel.
Fig. 5 Experimental results of CSFBG FP with chirped FSR. (a) Spectrum of + 1st order channel exhibiting FP characteristic, the red circles represent FSR values. (b) Group delay of + 1st order channel. (c) FSR difference between simulation and experiment.
4. Conclusion
In this paper, a novel kind of FBG-FP structure, i.e., the CSFBG FP, is proposed and demonstrated both in simulation and experiment. Based on a single uniform pitch phase mask, various equivalent chirped gratings can be designed to form different FP structures. Furthermore, to realize sampling functions only needs a sub-micrometer-precision moving stage. Without any operation on phase mask or fiber, the relative state between the phase mask and fiber keep consistent all the procedure. Therefore, such CSFBG structures can make the realization of FP cavity more flexible and simplify its fabrication process. As a demonstration, based on the same experimental facilities, FPs with uniform and chirped FSR are fabricated respectively, which shows good agreement with simulation results. To improve performance using the methods discussed in aforementioned section would be another significant work to make such CSFBG FPs more powerful and practical. In addition, further research towards, among other things, the applications of such novel CSFBG FP cavities, such as multi-wavelength fiber laser or photonic generation of chirped microwave pulses, are expected.
Acknowledgments
This work is partly supported by the Nature Science Foundation of Jiangsu Province under (BK2012058) and China Postdoctoral Science Foundation (2013M531326) and the Key Programs of the Ministry of Education of China under Grant: 20100091110005, and National Nature Science Foundation of China under (61177065), (61090392) and (61032005). The authors would like to thank the anonymous reviewers for their careful reading and helpful comments.
References and links
1. R. Slavik, S. Doucet, and S. LaRochelle, “High-performance all-fiber Fabry-Perot filters with superimposed chirped Bragg gratings,” J. Lightwave Technol. 21(4), 1059–1065 (2003). [CrossRef]
2. Q. J. Wang, Y. Zhang, and Y. C. Soh, “Efficient structure for optical interleavers using superimposed chirped fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17(2), 387–389 (2005). [CrossRef]
3. Y. G. Han, X. Y. Dong, C. S. Kim, M. Y. Jeong, and J. H. Lee, “Flexible all fiber Fabry-Perot filters based on superimposed chirped fiber Bragg gratings with continuous FSR tenability and its application to a multiwavelength fiber laser,” Opt. Express 15, 2921–2926 (2007).
4. X. P. Cheng, P. Shum, C. H. Tse, J. L. Zhou, M. Tang, W. C. Tan, R. F. Wu, and J. Zhang, “Single-longitudinal-mode erbium-doped fiber ring laser based on high finesse fiber Bragg grating Fabry–Pérot etalon,” IEEE Photon. Technol. Lett. 20(12), 976–978 (2008). [CrossRef]
5. Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006). [CrossRef] [PubMed]
6. X. W. Dong, W. K. Liu, D. Y. Wang, and M. L. Wu, “Study on Fabry–Perot cavity consisting of two chirped fiber Bragg gratings,” Opt. Fiber Technol. 18(4), 209–214 (2012). [CrossRef]
7. X. W. Shu, K. Sugden, and K. Byron, “Bragg-grating-based all-fiber distributed Gires-Tournois etalons,” Opt. Lett. 28(11), 881–883 (2003). [CrossRef] [PubMed]
8. X. F. Yang, C. L. Zhao, J. H. Ng, J. Zhang, X. Y. Dong, K. H. Ng, X. Guo, X. Q. Zhou, and C. Lu, “Simultaneous dispersion slope compensation for WDM channels using a Fabry-Perot etalon formed by double FBGs,” Opt. Commun. 231(1-6), 227–231 (2004). [CrossRef]
9. J. Magné, J. Bolger, M. Rochette, S. LaRochelle, L. R. Chen, B. J. Eggleton, and J. Azaña, “Generation of a 4×100 GHz pulse-train from a single-wavelength 10-GHz mode-locked laser using superimposed fiber Bragg gratings and nonlinear conversion,” J. Lightwave Technol. 24(5), 2091–2099 (2006). [CrossRef]
10. P. C. Won, Y. Lai, W. Zhang, J. S. Leng, and J. A. R. Williams, “Distributed temperature measurement using a Fabry–Perot effect based chirped fiber Bragg gratings,” Opt. Commun. 265(2), 494–499 (2006). [CrossRef]
11. W. Du, X. Tao, and H. Y. Tam, “Temperature independent strain measurement with a fiber grating tapered cavity sensor,” IEEE Photon. Technol. Lett. 11(5), 596–598 (1999). [CrossRef]
12. Y. J. Rao, C. X. Zhou, Z. L. Ran, T. Zhu, and R. R. Chen, “SFDM/WDM for large number of fiber-optic F-P sensors based on chirped fiber Bragg gratings,” Chin. J. Lasers 33, 631–635 (2006).
13. B. O. Guan, H. Y. Tam, S. T. Lau, and H. L. W. Chan, “Ultrasonic hydrophone based on distributed Bragg reflector fiber laser,” IEEE Photon. Technol. Lett. 17(1), 169–171 (2005). [CrossRef]
14. C. Wang and J. P. Yao, “Photonic generation of chirped microwave pulses using superimposed chirped fiber Bragg gratings,” IEEE Photon. Technol. Lett. 20(11), 882–884 (2008). [CrossRef]
15. P. Ou, Y. Zhang, and C. X. Zhang, “Optical generation of binary-phase-coded, direct-sequence ultra-wideband signals by polarization modulation and FBG-based multi-channel frequency discriminator,” Opt. Express 16(7), 5130–5135 (2008). [CrossRef] [PubMed]
16. M. M. Sisto, M. E. M. Pasandi, and S. Doucet, “Optical phase and amplitude control for beamforming with multiwavelength Gires-Tournois Bragg grating cavities,” the Fourth IASTED International Conference Antennas, Radar, and Wave Propagation, 238–243(2007).
17. X. F. Chen, Y. Luo, C. C. Fan, T. Wu, and S. Z. Xie, “Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system,” IEEE Photon. Technol. Lett. 12(8), 1013–1015 (2000). [CrossRef]
18. Y. T. Dai, X. F. Chen, Y. Yao, D. J. Jiang, and S. Z. Xie, “Correction of the repeatable errors in the fabrication of sampled Bragg gratings,” in Proceedings of OFC2005, paper OME20(2005).
