We demonstrate the fabrication of high-quality LPFGs in simplified hollow-core photonic crystal fibers, composed of a hollow hexagonal core and six crown-like air holes, using CO2-laser-irradiation method. Theoretical and experimental investigations indicate that the LPFGs are originated from the strong mode-coupling between the LP01 and LP11 core modes. And a dominant physical mechanism for the mode-coupling is experimentally confirmed to be the periodic microbends rather than the deformations of the cross-section or other common factors. In addition, the LPFGs are highly sensitive to strain and nearly insensitive to temperature, and are promising candidates for gas sensors and nonlinear optical devices.
© 2011 OSA
In recent years, much attention has been paid to long period fiber gratings (LPFGs) because they play a key role in modern optical communication, sensing, and other fiber-based devices. To continuously explore and develop LPFGs’ performance and applications, a large number of studies are devoted to fabricate LPFGs efficiently and conveniently. Many methods, such as ultraviolet laser exposure , electric-arc discharge , femtosecond laser irradiation , CO2 laser irradiation [4, 5], acousto-optic interaction , mechanically stress , and so on, have been innovated to fabricate LPFGs. Another considerable proportion of the studies are about fabricating LPFGs in all kinds of hosts, including single mode fibers (SMFs) , index-guiding photonic crystal fibers (IG-PCFs) , hollow-core photonic bandgap fibers (HC-PBGFs) , all-solid PBGFs , microfiber , and so on.
However, LPFGs inscribed in the hollow-core photonic crystal fibers (HC-PCFs) with the Kagomé-lattice are rarely reported. So-called “Kagomé-lattice” HC-PCF, whose typical repeating unit of the cladding is a Star of David pattern, is firstly demonstrated by F. Benabid et. al in 2002 . Another type of HC-PCF with a square-lattice , consists of two sets of orthogonal glass strips, is also demonstrated and investigated as a Kagomé-like HC-PCF. Differing from the HC-PBGFs and some other PCFs, the Kagomé HC-PCFs show no obvious bandgap and provide ultra-broad transmission bands with relatively low loss. Furthermore, the Kagomé-like HC-PCFs have other advantages, such as high air-filling fraction, no surface modes, low chromatic dispersion , and so forth, resulting in their useful applications in nonlinear optics in gas , gas spectroscopy  and fiber laser . However, both the Kagomé and square lattice HC-PCFs are difficult to fabricate for their complicate structures. Recently, a new type of simplified HC-PCF, which shows the similar guidance properties and mechanism to the Kagomé-lattice HC-PCF, is proposed by Frédéric Gérôme et.al in Ref . This fiber is composed of a hollow core and only one layer air-holes cladding, simplifying significantly the fabrication procedure in relation to the precursors.
In this paper, a simplified hollow-core photonic crystal fiber, which is very similar in structure to the fiber used in Ref , is firstly demonstrated to fabricate LPFGs by using CO2-laser-irradiation method. The LPFGs show very low additional insertion loss (~0.15 dB), high strain-sensitivity and near temperature-insensitivity. Furthermore, theoretical and experimental investigations illustrate that the LPFGs are originated from the strong mode-coupling between the fundamental core mode (LP01 mode) and the second-order core modes (LP11 modes) under the phase-matching condition. And the converted LP11 modes light are almost dissipated due to the larger attenuation and a significant recoupling loss from the HC-PCF to SMF, resulting in deep dips (>17 dB). Finally, through a comparative experiment, the dominant physical mechanism for the mode-coupling is confirmed to be the periodic microbends rather than the deformations of the cross-section or other common factors.
2. Mode analysis of the simplified HC-PCFs
The cross-section of the simplified HC-PCF used in our experiments, which is produced by Yangtze Optical Fiber and Cable Corporation, is shown as the inset in Fig. 1(a) . This pure silica HC-PCF is composed of a hollow hexagonal core surrounded by six crown-like air holes. The diameter of the core, air-holes-cladding and outer cladding is respectively about ~22 μm, 70 μm and 140 μm. And the thickness of the struts is about 370 nm. Figure 1 (a) also shows the measured transmission spectrum of a ~15 cm HC-PCF spliced with SMFs at both ends. As can be seen, a broad transmission band, from ~1100 nm to longer than 1750 nm, is provided by this HC-PCF. And it may guide light in a much longer wavelength range and visible even ultraviolet bands [15, 16], although they are not measured with the limits of the light source and optical spectrum analyzer (OSA). The attenuation of the transmission band is about 5.5 dB. By the cut-off method, the transmission loss of the HC-PCF is measured about 12 dB/m, and the insertion loss of each splice is about 2dB. It is mainly due to the mode mismatching in the splices, because the core diameter of the HC-PCF is much bigger than that of SMF.
Using the full-vector finite-element method, the modes guided in the simplified HC-PCF are theoretically investigated. To simplify the computing process, a perfect symmetrical and uniform structure model with the same geometric size as the actual fiber is employed in our simulations, although the structure of the actual fiber shows slight asymmetry and nonuniformity in the size of air holes and the length and thickness of the struts. Figure 1 (b) shows the calculated effective refractive indices (ERIs) of some typical core modes, such as LP01 mode (black), LP11 modes (wine, pink and blue), LP21 modes (navy, orange, and olive), LP02 mode (dark cyan) and LP31 modes (magenta). And their corresponding mode profiles are shown as Fig. 1 (c~j), respectively.
Moreover, around the core modes, we also find many cladding modes located in the air holes, struts and the outer cladding. For example, the representative mode profiles in the air holes and silica struts are respectively shown in Fig. 1 (k) and (l). Some cladding modes even have very similar ERIs to core modes. However, the confinement losses of the core modes are still low. This characteristic is due to the guidance mechanism of Kagomé-like fibers, which is known as “inhibited interaction” [11, 13] –couplings between the core modes and the cladding modes are effectively inhibited.
3. Fabrication and characteristics of the LPFGs
An experimental setup that is similar to that in [4, 8] is used to fabricate LPFGs in the simplified HC-PCFs. A ~10 cm section of the HC-PCF is spliced with SMFs at both ends. Since the simplified HC-PCF can support many modes, it is very important to align the cores of the HC-PCF and SMFs as accurately as possible to reduce energy loss and intermodal interferences. Light from a supercontinuum source (600 nm~1750 nm) is launched into the HC-PCF and the output spectra are measured with OSA. The main parameters of the CO2 laser (CO2-H10, Han’s laser) are listed as follows: maximum average output power of 1W, repeat frequency of 5 KHz, effective vector step of 1.5μm, delay time of effective step of 180 μs, and Q-release time of 30 μs, diameter of laser spot of ~50 μm. And the fiber is axially tensioned with a 100-g weight. It needs to emphasize that the applied axial tension is crucial to fabricate LPFGs in HC-PCFs, just as discussed as in Ref .
Based on the calculated ERIs and the phase-matching condition of LPFGs, , the resonant coupling between the LP01 core mode and high-order core or cladding modes can be computed one by one. Here, Λ is the grating pitch, λis the resonant wavelength, and andare the ERIs of the LP01 core mode and one of the high-order modes, respectively. Solid curves in Fig. 2(a) show the calculated grating pitches against wavelength for mode-coupling between the LP01 core mode and the LP11 core modes.
With the indication of the phase-matching curves in Fig. 2 (a), an appropriate grating pitch should be around 800 μm if the anticipated resonant wavelength is around 1550 nm. Thus, we firstly fabricate a LPFG with the pitch of 815 μm and 40 periods. Its transmission spectrum is shown as the pink curve in Fig. 2 (b). As can be seen, an obvious resonant dip with the depth over 17 dB and 3-dB width of ~16 nm is achieved. Then, more LPFGs with different pitches, including 850 μm, 900 μm, and 1000 μm, are fabricated with the same setup and parameters. Their transmission spectra are also shown in Fig. 2 (b). By contrasting the Fig. 2 (b) with Fig. 2 (a), the experimental results agree well with the simulations except for a certain deviation. Additional, the resonant dip of every LPFG is over 13dB, indicating an over 90% efficiency of mode conversion. It is also noteworthy that the additional insertion loss induced by the LPFG is as low as ~0.15 dB.
Besides the low additional loss, the LPFGs also show interesting sensing characteristics. Figure 2(h) and (i) show respectively the central wavelength and minimum transmission responses to strain and temperature of the LPFG with the pitch of 815 μm. The strain sensitivity of the resonant wavelength and minimum transmission are respectively −2.09 pm/με and 1.38 × 10−3 dB/με. The wavelength response to strain is about 3 times higher than that of LPFGs in HC-PBGFs reported in Ref . and 5 times higher than that of LPFGs in SMFs reported in Ref , which might be related to the lager microbends induced in the fabrication process. Moreover, the temperature sensitivity of the resonant wavelength and minimum transmission are about 0.59 pm/°C and −0.00089 dB/°C, which are only about 1/6 of those in Ref . and three orders of magnitude less than those reported in Ref . This temperature-insensitivity might be due to the fact that two modes involved in the mode-coupling are both guided in the air core and quite small thermo-optical coefficient of air. Yet, we also notice that the degree of fitting in Fig. 2(h) is relatively low, which may be caused by modal noise and interference.
4. Mechanism of the LPFGs
In order to verify further the mode-coupling mechanism of the LPFGs, mode profiles transmitted through the LPFG with are measured with a setup composed of a tunable laser diode (LD) (1530~1630 nm) and an IR CCD. The Fig. 2 (c~g) are the mode profiles located at the wavelength of 1542 nm (A), 1554 nm (B), 1601.2 nm (C), 1605.2 nm (D), and 1624 nm (E). By tuning the incident wavelength, we find that the light is guided with the LP01 core mode in most cases, just as shown in Fig. 2 (c) and (g). However, the mode profiles near B, C and D are obviously the second-order like modes by comparing them with the Fig. 1(d~g), which confirm that the light is converted from the LP01 core mode into LP11 core modes at the resonant wavelengths with the modulation of the LPFGs. And the converted lights with second-order modes are almost dissipated due to the larger attenuation and a significant recoupling loss from the HC-PCF to SMF, resulting in the resonant dips. Furthermore, the mode profiles (d), (e) and (f) have the similar shape but different directions, which indicate that they might come from different second-order modes.
Moreover, the physical mechanism for the mode-coupling in the LPFGs is discussed here. As well known, typical mechanisms of LPFGs fabricated by CO2-laser irradiation include residual stress relaxation , glass molecular structure change , physical deformation, and so on. Since most of light is guided in the air core, changes of glass internal stresses, material density or molecular structure will impact a little to core modes. A possible interpretation to the LPFGs’ formation is the physical deformation, such as changes of the cross-section [4, 19], microtaper  and microbend . Comparing the cross-sections of the HC-PCF before and after inscribing the LPFG with (see the inset (a) in Fig. 1 and Fig. 3 (a) ), we find an obvious ablation in the outer-layer cladding. Perhaps there are some kinds of slight deformations in the inner air-holes cladding or the struts, although they are not visible under the optical microscopy. Moreover, it is noteworthy that the HC-PCF is curved after inscribing the LPFG when it is set free (see Fig. 3 (d)). It is an accumulation consisting of a series of microbends [17, 21, 22], which are generated when the fiber is asymmetrically heated to the fictive temperature, even molten, and simultaneously tensioned by a certain axial tension. Thereby, both the periodic microbends and the deformations of the cross-section are possibly responsible for the mode-coupling in the LPFGs.
To make clear which one is dominant, a comparative experiment is designed. Two stages of HC-PCFs with the similar length are employed to fabricate the LPFGs with the same pitch () and periods. The first LPFG (signed as LPFGI) is fabricated with a ~33% (only increasing the Q-release time to 40 μs) more than the dose of CO2-laser irradiation used in section 3 but without the axial tension, which is design to highlight the effect of the deformations of the cross-section; whereas the second one (signed as LPFGII) is fabricated with a only 67% dose of laser irradiation used in section 3 (lower the Q-release time to 20 μs) but a tension as large as 250-g weight, which is used to strengthen the effect of the microbends and weaken the impact of the deformations of the cross-section. The numbers of scanning cycles are respectively 20 and ~200, determined by when their resonant dips are saturated. As expected, the HC-PCFs with the LPFGIand LPFGIIundergo different physical deformations. Firstly, as shown in Fig. 3 (b) and (c), not only the outer-layer cladding but also two air holes of the former are significantly deformed, while those of the latter are nearly no changes. Secondly, the latter is laterally bent but the former is not, as shown in Fig. 3 (d). However, their transmitted spectra, shown as Fig. 3 (e), illustrate the difference of the contribution to the LPFGs’ formation between two different physical deformations. As can be seen, the depth of resonant dip of the LPFGI is no more than 4dB; whereas that of the LPFGII is over 15dB. And the insertion loss of the former is much higher than that of the latter. Therefore, we prefer the periodic microbends rather than the deformations of the cross-section to be the dominant factor for the formation of the LPFGs.
High-quality LPFGs fabricated in the simplified HC-PCFs using CO2-laser-irradiation method have been demonstrated. Both numerical simulations and observations of mode profiles illustrate that the origination of the LPFGs is the mode-coupling from the LP01 core mode to LP11 core modes. And the lights with LP11 core modes are then dissipated due to the larger attenuation and a significant recoupling loss from the HC-PCF to SMF, generating the resonant dips. Moreover, through a comparative experiment, the physical mechanism for the mode-coupling is confirmed to depend a little on the deformations of the cross-section but highly on the periodic microbends. Finally, the LPFGs perform not only low additional insertion loss but also high sensitivity to strain and nearly insensitivity to temperature. Since the LPFGs in the simplified HC-PCFs combine the merits of the Kagomé like HC-PCFs with those of LPFGs, they hold the promise of significant applications in such fields as gas nonlinearity, gas sensing and mode convertors. In addition, the discussion about the physical mechanism of the LPFGs in section 4 is helpful to understand further the actual mechanism of LPFGs’ formation, especially for the cases of the mode-coupling between two core modes.
This work was supported by the National Key Basic Research and Development Program of China under grant 2010CB327605, the National Natural Science Foundation of China under grants 50802044, 60736039, 11004100 and Program for New Century Excellen Talents in University (NCET-09-0483).
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