Regular and cascaded long period gratings (LPG, C-LPG) of periods ranging from 460 to 590 μm were inscribed in an endlessly single mode photonic crystal fiber (PCF) using CO2 laser for sensing measurements of helium, argon and acetylene. High index sensitivities in excess of 1700 nm/RIU were achieved in both grating schemes with a period of 460 μm. The sharp interference fringes in the transmission spectrum of C-PCF-LPG afforded not only greatly enhanced sensing resolution, but also accuracy when the phase-shift of the fringe pattern is determined through spectral processing. Comparative numerical and experimental studies indicated LP01 to LP03 mode coupling as the principal coupling step for both PCF-LPG and C-PCF-LPG with emergence of multi-mode coupling at shorter grating periods or longer resonance wavelengths.
©2012 Optical Society of America
The ability to accurately measure the type, composition and index of refraction of a gas medium is of great scientific and technological importance for diverse areas of applications. Such applications include chemical and mining safety, environmental monitoring, medical diagnosis, homeland security, as well as design and operation of modern laser systems. Conventional, all-solid optical fiber gas sensors have been broadly explored due to their small footprint, good chemical and thermal stability, immunity to electromagnetic interference, as well as the ability for distributed sensing. Common sensing modalities include absorption spectroscopy , fluorescence spectroscopy [2–4], interferometry , and grating-based index transductions [6–8]. High sensitivity often requires an enabling coating scheme that either physically entraps or chemically binds/reacts with the gas species of interest, potentially limiting response time and reusability of the sensing devices. Challenges remain using conventional optical fiber as the base platform for gas sensing and measurements.
The breakthrough in both the science and the manufacturing of photonic crystal fiber (PCF) has elevated fiber-optic sensing research and development to a new height [9–11]. The axially aligned air channels in PCF afford intimate light-analyte interaction over a path length spanning the entire fiber, making it an inherently far more sensitive platform than its conventional counterpart per Beer-Lambert law . The potential of PCF for gas sensing and detection has been demonstrated .
Periodic index perturbation on the order of hundreds of microns in period (also termed long-period grating (LPG)) further expands the sensing capabilities of PCF. At a fundamental level, LPG enables the coupling of the core mode (LP01) to co-propagating cladding modes (LP02 and higher orders) in PCF, leading to significant attenuation in transmission at specific resonance wavelengths. The phase-matching condition for LPG can be described by λi = (neffcore − neffclad(i))Λ, where λi is the resonance wavelength of the ith cladding mode coupled with the core mode, and neffcore and neffclad(i) are the respective effective refractive indices of the core mode and the ith cladding mode. The strong dependence of λi on neffclad(i) makes LPG inscribed in PCF (LPG-PCF) a refractive index transduction platform that is potentially very sensitive to minute changes in neffclad(i) (e.g., manifested via gas type, composition, and pressure) without deploying any coating. The marked dispersion of neffcore and neffclad(i) with wavelength further promotes high index sensitivity of LPG-PCF. There is a dearth of literature that deals with the use of LPG-PCF for gas measurements, though solution-based measurements are documented far more extensively [14–17]. We recently demonstrated a sensitivity of 517 nm/RIU using argon-filled LPG-PCF with applied pressure as a means of varying the index of refraction in the gas medium . This value is comparable to those reported using more complex index-transduction schemes such as photonic crystal nanocavity resonators (510 nm/RIU)  and localized surface plasmon resonance (200 nm/RIU) . Much remains to be done to extend the frontier of fiber-optic gas sensing using PCF-LPG and its derivative schemes.
We report here an integrated theoretical and experimental investigation of LPG inscribed in a commercial (NKT Photonics) index-guided endlessly single-mode PCF (ESM-12B) for sensing evaluations in helium (He), argon (Ar), and acetylene (C2H2). This is the first comprehensive PCF-LPG based gas sensing measurements using different gas types to the best of our knowledge. Further novel and unique in this study is the inscription and subsequent assessment of cascaded PCF-LPG (C-PCF-LPG) in their sensing characteristics. C-PCF-LPG has been reported to provide high performance for measurements of external perturbation such as humidity, strain and temperature [20–22]. C-PCF-LPG consists of two identical LPGs in PCF separated by a certain length . The first LPG couples part of the core mode to a forward-propagating cladding mode. The second LPG couples the cladding mode back to the core mode, resulting in sharp interference fringes which could lead to enhanced resolution . The key aim of this work is to compare and contrast PCF-LPG and its cascaded counterpart in their gas sensing capacities and to establish a basic and applied acknowledge foundation to guide further development of PCF-LPG and C-PCF-LPG as robust index-transduction platforms not only for gas sensing but for solution-based measurements as well.
2. Theoretical analysis
The sensing performance of PCF-LPG, at the fundamental level, depends on mode field overlap and core-to-cladding mode coupling strength, which is dictated by the PCF microstructure and LPG parameters. We first attempted theoretical calculation to evaluate the interplay between these factors in general and the wavelength dependence of the effective index and mode field distribution in particular using a mode solver based on the Finite Element Method (FEM). The input parameters for the structure of ESM-12B in the calculations were acquired from the fiber cross-sectional SEM image (see inset in Fig. 1 ). Briefly, ESM-12B consists of six rings of hexagonally arrayed air channels of 3.38 μm in diameter and 7.77 μm in channel-channel separation (e.g., pitch Λ). Material dispersion of fused silica, given by the Sellmeier Eq , was included in the calculation. The refractive index of the air channels was set to 1.Taking into account the symmetry of the PCF and mode classes of the coupled modes, the computational window could be reduced to one-quarter of the fiber cross section with the perfect electric and magnetic conductor boundary conditions applied along symmetric planes. Moreover, in order to further reduce the computational window and eliminate a large number of outer cladding modes, perfectly-matched layers (PML) were implemented along the planes crossing the centers of the air channels in the outermost ring. It was justified by the fact that a shift of the PML layers towards the boundary of PCF outer cladding had no significant effect on the numerical calculation results. Analyzing 40 lowest modes, we numerically verified that the LP01 core mode (identical with HE11 notation for an conventional fiber) should be preferentially coupled into the LP0n (identical with HE1n) cladding modes. Note, that there is no complete correspondence between the modes in a conventional fiber and PCF due to different symmetries. The LP0n cladding modes in PCF are only similar to LP0n in a conventional fiber. The field distributions of the LP01 core mode and three lowest LP0n cladding modes are plotted over the computational window in Fig. 1. For easier identification of the coupled modes we plotted the y-component of electrical field. Note that the applied boundary conditions determined the vertical polarization of LP0n modes. It can be readily seen in Fig. 1(a) that the core mode is confined within the innermost ring of air channels in the absence of core mode to cladding mode coupling. Under this circumstance, gas phase present in the absolute majority of the cladding air channels will not participate in sensing interrogation. LP01 to LP0n coupling fundamentally changes the mode distribution, extending the mode field throughout the cladding air channels and availing the gas phase within for light-analyte interactions, despite the difference in detail, depending on the type of the cladding mode coupled, evident in Figs. 1(b)–1(d). The extension of the light field over the entire cladding structure enabled by PCF-LPG is the very premise of its expected high sensing capability.
The calculated dispersive characteristics of the LP0n modes are shown in Fig. 2 . The phase matching curves (PMC) in Fig. 2(a) illustrate the relationship between the grating period and the resonance wavelength for LP01-LP0n mode coupling governed by the phase matching condition. For LP01 coupling to a given cladding mode in the wavelength region considered, the resonance wavelength increases as the grating period decreases. At a given grating period, the resonance wavelength increases as the order of the coupled cladding mode decreases. The percentage power fractions (evanescent overlaps) in the cladding air channels of the LP0n cladding modes are shown in Fig. 2(b). The power overlap is generally low (below 0.2%) but increases with wavelength. While the difference is not substantial, the overlap increases as the order of the coupled cladding mode decreases. On the other hand, the coupling coefficient (κ) increases with the order of the cladding modes but decreases with the wavelength, as shown in Fig. 2(c). For the calculation of κ we assumed the grating area (over which the field overlap was integrated) as the fiber central circular area, having its diameter equal to 90% of the core diameter (2Λ-d) (see Figs. 1(a)–1(d)). For maximum LP01-LP0n mode conversion, coupling coefficient, κ, and LPG length, L, must satisfy the relation κL = π/2. Modal analysis of PCF was performed with the refractive indices of the chosen gas species as parameters. Since the resonance wavelength of interest are 1200 nm or longer, the dispersion of the refractive index of the gas is not considered here because the dispersion curve of the gas phase is known to plateau towards long wavelength beyond visible, making its influence on the sensitivity negligible. We have found a very good correspondence between the RI-sensitivities derived from the shifts of simulated phase matching curves due to changes in the refractive index of the gas phase and RI-sensitivities calculated using the perturbation expression derived elsewhere  and took full consideration of the effective and group indices, evanescent overlaps of the coupled modes and wavelength. As we were dealing with very tiny changes in PCF structure’s optical contrast, a perturbation theory approach used in  has proved adequate. Illustrated in Fig. 2(d) are calculated sensitivities to gas phase refractive index expressed as a shift in the resonance wavelength per refractive index unit (nm/RIU). It is evident from Fig. 2(d) that the sensitivity decreases with the order of the cladding mode, and it increases considerably with wavelength following the trend of the evanescent overlap in Fig. 2(b). The theoretical calculations and implications form a base for the interpretation of the subsequent experimental results.
3. Fabrication of PCF-LPG and C-PCF-LPG
PCF-LPG and C-PCF-LPG were inscribed in ESM-12B using a high-stability CO2 laser (Synrad, water-cooled 48-1 10 W) within the general window of parameters of the aforementioned calculations for integrative theoretical and experimental investigation. A laser energy density of 0.5 joules/mm2 was used to induce relaxation of residual stress thus impart a change in the index of refraction in the irradiated region of the PCF due to the so-called photo-elastic effect without structural deformation . The fiber was firmly mounted on a high-precision motorized micro-translation stage under a nominal tensile stress of ~22 MPa to ensure reproducible inscription with the desired periodicity over the entire grating structure. Both the laser and the stage were synchronized via computer interface. A Super-K ultra broadband supercontinuum light source and an optical spectrum analyzer were used to monitor the transmission spectra in situ during fabrication of PCF-LPG and C-PCF-LPG. Specifically, five sets of PCF-LPGs of respective periods of 590, 540, 515, 490 and 460 μm were fabricated under the same laser power density and applied stress with respective lengths of 14.75, 12.96, 30.39, 18.13, and 22.54 mm to achieve maximum attenuations. The corresponding transmission spectra are shown in Fig. 3(a) . The measured resonance wavelengths for core mode to cladding mode coupling are 1224, 1349, 1495, 1575 and 1710 nm in air, respectively. The wavelengths at the deepest attenuation dips in LPGs spectra correspond well to the resonance wavelengths predicted by the simulated PMC of LP03-cladding mode for the experimental grating period. The correlation between the resonance wavelength and the period tracks well with the phase matching curve for LP01-LP03 coupling(Fig. 2(a)), suggesting LP03 being the predominant cladding mode in the PCF-LPG scheme in the wavelength region investigated. For large period of 590 μm, only LP03 cladding mode is coupled and there is only one attenuation band corresponding to LP03 mode in the spectrum. However, as the period decreases, additional attenuation bands arise in the spectrum indicating multi-mode coupling, likely to asymmetric cladding modes induced by an asymmetric LPG inscription. Note that towards longer wavelengths the coupling coefficient for LP03 cladding mode decreases (see Fig. 2(c)) and asymmetric mode coupling becomes more competitive. A narrow bandwidth of LPG with a grating period of 515 um, especially compared to other “single-dip” LPGs, corresponds to a larger number of periods over a longer coupling length. The grating periods relating to the PMCs correspond to the 1st harmonic of an inscribed LPG refractive-index profile. The higher order harmonics of the LPG profile might couple into very high lossy cladding modes, which would be eliminated during their propagation between C-LPGs.
Three C-PCF-LPGs of respective periods of 590, 515 and 460 μm were successfully fabricated despite the generally recognized challenge in achieving high-quality cascaded gratings in PCF . For the C-PCF-LPG, the lengths of the first LPGs are respectively 4.13, 6.18, 5.98 mm, while the lengths of the second LPGs are respectively 11.8, 8.76, 27.6 mm. The high loss of the cladding mode propagating in the 150 mm long PCF cladding makes it impossible to couple ~50% power back to the core mode by the second LPG with the same length as the first LPG. We always need to introduce longer second LPG to ensure the beating between the two arms is optimized. For each C-PCF-LPG, the pair of LPGs are separated by a fixed distance of 15 cm. The resultant transmission spectra are illustrated in Figs. 3(b)–3(d). The spectral features of C-PCF-LPG are striking in that many fine-scaled fringes are present in the otherwise broad attenuation band of the regular PCF-LPG scheme. The full width at half maximum (FWHM) of the individual fringes is several times narrower than that of the broad spectrum in PCF-LPG, suggesting significantly higher sensing resolution. In addition, the transmission spectrum in C-PCF-LPG can be analyzed in terms of the phase shift in the fringe pattern. C-PCF-LPG clearly should yield more accurate sensing measurements as the phase shift is a direct result of the change in optical path length induced by changing gas properties.
4. Gas measurement using PCF-LPG and C-PCF-LPG
He, Ar and C2H2 of respective indices of refraction of 1.000032 , 1.000278  and 1.000579  at wavelength λ = 1570 nm, were employed to measure the sensitivity of the PCF-LPG and C-PCF-LPG structures. A custom-build optically coupled microfluidic system, details of which are provided elsewhere , was used for the sensing experiments. Briefly, it consists of a gas delivery chamber and fiber self-alignment assembly that enables both gas flow through the cladding air channels of the PCF-LPG and C-PCF-LPG and acquisition of optical transmission through the fiber. Before each measurement, the chamber (thus the cladding air channels) was vacuum-pumped and back-filled with the desired gas at a pressure up to 1.38 MPa. This cycle was repeated three times to ensure purity of the gas inside of the PCF-LPG and C-PCF-LPG. The Super-K ultra broadband supercontinuum light source and optical spectrum analyzer for monitoring LPG inscription were also used to measure the transmission spectra of gas-filled PCF-LPG and C-PCF-LPG.
Depicted in Figs. 4(a) –4(e) are the transmission spectra of the five PCF-LPGs with the gas type as a parameter. The resonance wavelength of each PCF-LPG experienced a red shift as the gas inside of the cladding air channels were changed from He, to Ar, and to C2H2. This red shift is consistent with the phase matching condition since both the core mode and the cladding mode are wavelength-dependent in PCF. An increase in the refractive index of the gas within the cladding air channels will result in an increase in the contrast between the effective refractive indices of the core and cladding mode (neffcore-neffclad (i)), giving arise to an increase in the resonance wavelength .
Plotted in Fig. 4(f) is the measured index sensitivity of the five PCF-LPGs based on the transmission spectra as a function of the resonance wavelength. The sensitivities are calculated by taking the maximum shift with respect to the introduction of acetylene in the LPGs or C-LPGs using He as a reference. According to this Fig., the sensitivity improved monotonically from 548 to 1737 nm/RIU as the resonance wavelength increased from 1224 to 1710 nm. This trend is in agreement with our theoretical analysis (Fig. 2(d)). We note that our experimental sensitivity values are significantly higher than those predicted (Fig. 2(d)). This discrepancy will be dealt with as we attempt to analyze the C-PCF-LPG results.
Shown in Figs. 5(a) –5(c) are the transmission spectra of the three C-PCF-LPGs filled with He, Ar, and C2H2. The spectral features are clearly very rich compared to those from the regular PCF-LPG structures (Figs. 4(a)–4(e)). The respective interference fringes (as such the transmission spectrum will be referred to as IF spectrum thereafter) at around the center of each transmission band are presented in Figs. 5(d)–5(f), indicating well resolved red shift as the index of refraction of the gas medium increases. Significantly, the shift in trend and in wavelength is independent of the particular interference fringe chosen for a given C-PCF-LPG within the broad transmission, suggesting well-behaved and highly-predictable nature of the mode interferences.
The interference fringes and their shift in response to changing property of the gas medium allow phase shift analysis as a means of more precisely determining the sensitivity as well as resolution of C-PCF-LPG. The analysis was carried out by considering the shift as the phase difference of corresponding complex analytical signals that possess a real part (i.e., the original spectra) as well as an imaginary part (i.e., Hilbert transform of the original spectra). Hilbert transform was implemented using the Fast Fourier Transforms (FFT) .
The spectral analysis results following the approach above are summarized in Table 1 and Fig. 6 . For easier discerning we plotted only the spectra for He and C2H2 which are most far apart. The phase shifts (φ-shifts) calculated as average values over one IF-period, symmetrically around the wavelengths 1220, 1450 and 1680 nm, respectively, represent primary information in Table 1. The wavelength shifts derived from the phase shifts by relating to fringes’ periods are auxiliary data for comparison with the wavelength-shifts read out from Figs. 5(d), 5(e) and 5(f). (λ-shift ↔ φ-shift/2/π*IF-period). For this purpose, we calculated the IF fringes’ periods from the main frequency components, obtained from the FFT of pre-processed  IF spectra plotted in Figs. 6(a), 6(c) and 6(e). The FFT spectra are plotted in Figs. 6(b), 6(d) and 6(f) with a horizontal-axis unit defined as a number of cycles per wavenumber.
It is evident from Fig. 6(a) that the C-PCF-LPG with a resonance wavelength of 1220 nm exhibits high-quality interference patterns. On the other hand, the interference patterns for C-PCF-LPGs with longer resonance wavelengths (1450 and 1690 nm) are affected by multimode coupling, manifested through the presence of other frequency components in the FFT spectra (Figs. 6(d) and 6(f)). This illustrates one of the benefits from using C-PCF-LPGs. An envelope of interference fringes was strongly perturbed by multi-mode coupling while the interference fringes’ phase shift remains regular over wavelength range as it does not depend on LPG’s spectra but only on the difference in optical paths of core-mode and cladding-mode interferometer arms. We suppose that multi-mode coupling, not included into the numerical PCF model, could contribute to RI-sensitivity, which may explain why the measured RI-sensitivity values are higher than those numerically predicted.
Besides coupling into more cladding modes with distant resonance wavelengths (as obvious from Fig. 3(a)), we speculate about a possible contribution from multi-mode coupling into close neighboring (almost degenerate) modes. In such case, the resonance (not extremely narrow) curves of two cladding modes can overlap at some wavelength and both modes might be coupled at the same time at that wavelength. This might not be distinctly manifested in the FFT spectra and therefore it may be the case even for the best IF pattern around a resonant wavelength of 1220 nm. where an experimentally found RI-sensitivity also significantly overcomes a numerically predicted value. Multi-mode coupling might also adversely affect the linearity of the IF fringes shifts which can be seen when comparing the shifted spectra for He and C2H2, An effect of parasitic multi-mode coupling on RI-sensitivity of C-PCF-LPG will be numerically investigated in the next work.
We have carried out a comprehensive investigation of PCF-LPG and its cascaded counterpart for sensing measurements of He, Ar, and C2H2. An index sensitivity over 1700 nm/RIU, the highest known for a fiber-optic gas sensor, has been achieved using both schemes. The index sensitivity of PCF-LPG and C-PCF-LPG increases with mode-coupling resonance wavelength. While C-PCF-LPG does not seem to markedly increase the sensitivity, the sharp interference fringes in the transmission spectrum serve two important purposes. First, it leads to significantly enhanced sensing resolution due to the narrow FWHM of individual fringes. Second, it allows analysis of the phase shift through spectral processing which further enhances the sensing resolution and accuracy. The comparison of the experimentally measured correlation between the grating period and the resonance wavelength in PCF-LPG with theoretical prediction suggests core mode to LP03 cladding mode coupling in the resultant PCF-LPGs. The detailed spectral analysis of the IF spectra of the C-PCF-LPGs offers additional support for this mode coupling mechanism. The spectral analysis also strongly suggests multi-mode coupling especially at longer resonance wavelength. This investigation should prove valuable in the design, selection, and fabrication of PCF-LPG and C-PCF-LPG platforms for advanced sensing applications at both high sensitivity and high resolution not only in gas phase, but in solution medium as well.
The authors thank Dr. Zonghu He for helpful suggestions and Dr. Dennis J. Trevor of OFS Laboratories for insightful discussions in the course of this investigation. This work was sponsored by the US National Science Foundation under grant number ECCS-0922175 and by the Ministry of Education, Youth and Sport of the Czech Republic under grant number LH 11038 within the U.S.-Czech S&T Cooperation agreement.
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