2526 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 15, AUGUST 1, 2013

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1 2526 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 15, AUGUST 1, 2013 Sensitivity Characteristics of Fabry-Perot Pressure Sensors Based on Hollow-Core Microstructured Fibers Long Jin, Bai-Ou Guan, Huifeng Wei Abstract In this paper, the sensitivity characteristics of Fabry-Perot (F-P) hydrostatic pressure sensor based on two different hollow-core (HC) microstructured optical fibers are experimentally theoretically investigated. The sensors are fabricated by simply splicing a length of HC fiber to singlemode fibers. Hydrostatic pressure is measured by monitoring the wavelength shifts of the interferometric fringes as a result of the two reflection beams at the splicing points. The measured pressure sensitivities of F-P sensors fabricated on the simplified HC microstructured fiber hollow-core photonic bgap fiber (HC-PBGF) are pm/mpa, respectively. Theoretical investigation is then carried out based on the analysis of elastic properties for the individual fibers. The calculated result suggests that the pressure sensitivities are dominantly determined by the induced changes in cavity length. In comparison, the contribution of mode-index change is slight. The mechanisms behind the mode-index changes for the two fibers are clarified by analyzing the deformation of the fiber structure under pressure. The holey microstructure is highly deformable compared to the solid fiber, which provide another dimension for the implementation of tunable photonic devices. Index Terms Fabry Perot sensors, fiber optic sensors, photonic bgap fibers, pressure sensors. I. INTRODUCTION HOLLOW-CORE photonic bgap fiber (HC-PBGF) is a kind of optical fiber which guides light in an air core relying on photonic bgap effect, rather than total internal reflection [1]. The establishment of the photonic bgap guiding depends on its periodic cladding which consists of a hexagonal array of air holes. Low-loss transmission can be realized within one or more spectral windows. The cladding can be also engineered to have a Kagome profile to obtain much wider transmission range [2]. Recently, an alternative air-core fiber has been proposed, which has only one ring of air-hole cladding Manuscript received January 22, 2013; revised April 16, 2013 May 27, 2013; accepted June 11, Date of publication June 17, 2013; date of current version June 28, This work was supported by National Natural Science Foundation of China (Grant No ), in part by the National High Technology Research Development Program of China under grant 2010CB735904, in part by the National High Technology Research Development Program of China under Grant 2012AA L. Jin B. O. Guan are with Institute of Photonics Technology, Jinan University, Guangzhou , China. H. Wei is with the State Key Laboratory of Optical Fiber Cable Manufacture Technology, Yangtze Optical Fiber Cable Company Ltd. R&D Center, Wuhan , China. Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JLT the transverse geometry is greatly simplified [3], [4]. Its guidance relies on the antiresonance between the core mode the mode of the silica wall around the core. HC-PBGFs have been exploited as photonic sensors in the recent years, taking advantage of their unique guidance mechanism microstructured geometry [5]. For example, an interferometric fiber optic gyro has been implementedbasedonthis fiber, which has reduced Kerr effect, temperature sensitivity Faraday effect [6]. Fiber grating sensors can be fabricated on the bgap fibers through heat treatment. The long period grating sensors, which contain periodic -laser-induced deformations, are sensitive to axial strain insensitive to environmental temperature [7], [8]. Hydrostatic pressure measurement has been realized with a HC-PBGF by monitoring the spectral shift of its transmission b or the change in phase difference between orthogonal polarizations [9] [11]. In-line Fabry-Perot sensors have also been implemented on HC-PBGFs for the measurement of temperature, axial stain vibration, ultrasound signal, even magnetic field [12] [16]. The sensors present advantages including low cost, simple fabrication process the ability to work under high temperature. The low-loss transmissioninthepbgfisbeneficial for its multiplexing capability. The air guiding also allow the F-P etalon to have a length of mm or cm order to obtain dense interferometric fringes. In contrast, the F-P cavities based on silica capillaries are typically tens of microns in length [17], [18]. F-P sensors based on simplified HC microstructured fibers have also been demonstrated for the measurement of refractive index [19], [20]. Note that the existence of the microstructure greatly changes the elasticity of a silica fiber the effect of the microstructure to the sensitivity is not totally clear so far. In this paper, the pressure sensitivities of F-P sensors based on the simplified bgap fiber HC-PBGF are experimentally theoretically investigated, respectively. Theoretical investigations are carried out for the individual fibers based on the analysis of their elastic properties. The calculated result suggests that the pressure sensitivities for the F-P sensors are mainly resulted from the changes in cavity length. In contrast, the effective-index change induced by the fiber deformation is extremely small. The difference in mode-index changes between the two fibers are analyzed based on the description of the deformations of the microstructures under pressure. Theoretical analysis suggests that the holey microstructure can be highly deformable, especially for directional stresses, as a result of the large air-filling ratios, which offers the feasibility of further implementation of tunable photonic devices based on the air-core fibers /$ IEEE

2 JIN et al.: SENSITIVITY CHARACTERISTICS OF FABRY-PEROT PRESSURE SENSORS BASED ON HOLLOW-CORE MICROSTRUCTURED FIBERS 2527 Fig. 1. Microscopic images of the transverse geometry of (a) simplified microstructure fiber (b) HC-PBGF. II. EXPERIMENT Fig. 1 shows the microscopic cross sections of the two HC fibers. Fiber I is a simplified bgap fiber, which is fabricated by Yangtze Optical Fiber Cable Company Ltd. The fiber has an air core surrounded by a ring of thin silica wall. The air core the outer silica cladding are connected with six bridges. Light can be guided in the air core due to the antiresonance between the core mode the modes of the inner silica wall. The outer inner radii of the outer silica cladding are, respectively. The distance from the fiber center axis to the wall of the air core is about 16.Thesimplified PBGF presents a loss peak at around 770 nm, as a result of the resonance of the thin wall. The loss wavelength is determined by the thickness of the wall between adjacent air holes via the the relation [4]. Substituting, we can obtain the thickness of the wall. Fiber II is the HC-PBGF (NKT Photonics, HC ). It has an air core surrounded by a holey cladding with periodic air holes. The spacing or pitch between the adjacent air holes is.theair-filling ratio, i.e., the ratio between the cladding-hole diameter the pitch is. The outer radius the holey-cladding radius are, respectively. The radius of the air core is about. The periodic structure establishes a photonic bgap therefore the fiber presents a transmission window ranges from 1400 to above 1700 nm. The transmission wavelength range is determined by the geometrical parameters of the air-silica cladding, including the pitch the air-filling ratio. F-P cavities are fabricated by splicing a section of HC fiber to singlemode fibers at both ends. The arc fusion parameters including arc duration strength have been optimized to obtain higher extinction ratio. The polymer jackets have been removed before the splicing. Three F-P sensors with cavity lengths of mm are fabricated with fibers I II, respectively. Fig. 2(a) shows the setup to measure the pressure responses of the individual F-P sensors. Hydrostatic pressure is subjected to the sensor by use of a pressure chamber with a maximum pressure of 10 MPa. A broadb light source an optical spectrum analyzer are used to record the fringe shift. The light is launched onto the sensor the reflection signal is retrieved via an optical circulator. Fig. 2(b) shows the measured spectra of the F-P cavities based on hollow-core fibers at around 1550 nm. Fig. 2. (a) Experimental setup for the measurement of the pressure response. (b) Measured reflection spectra for F-P cavities based on the two hollow core fibers. (c) Measured wavelength shifts as a function of applied pressure for the F-P sensors. Fig. 2(c) shows the measured wavelength shifts of the transmission dip closest to 1550 nm of the three sensors. The fringes

3 2528 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 15, AUGUST 1, 2013 blue shift with applied pressure for all the three sensors. The measured sensitivities for fibers I II are pm/mpa, respectively. III. THEORETICAL ANALYSIS The fringes in the reflection spectrum are a result of the interference between the two reflection beams at the two interfaces between the SMF the HC fibers. The spectrum is determined by the phase difference between the two beams where is the cavity length, is wavelength is the effective index of the fundamental mode of the HC fiber. The interference signal reaches its maximum intensity when the phase difference satisfies,where is integral, the peak wavelengths are determined by When the cavity is perturbed, the phase difference changes as a result of the changes in cavity length effective index. The pressure sensitivity for the th peak can be expressed by The former term in the bracket depicts the change in cavity length under pressure the latter one represents the index change. In the following text, these two effects are discussed, respectively. A. The Effect of Cavity-Length Change 1) FiberI: Fig. 3(a) shows the constructed transverse geometry for the simplified HC fiber to calculate the response of the F-P pressure sensor. Considering the extremely thin walls between the air holes, the deformation of the fiber is dominantly determined by the outer silica cladding. The elasticity of fiber I, i. e., the simplified bgap fiber can be analyzed with a single-layer model with outer inner radii.the stress strain over silica can be expressed by [21] (See equation at bottom of page) where are the Young s Modulus Poisson s ratio of silica glass. We define (1) (2) (3) (4) Fig. 3. Ressembled fiber transverse geometries for the calculation of the stress strain distributions. (a) Simplified HC bgap fiber. (b) HC-PBGF. The holey cladding is considered as a uniform material in elasticity.. The parameter represents the ratio between the area defined by the outer radius the actual cross sectional area of the silica ring. With the conditions (6a) (6b) (6c) the constants A, C D can be found the stress strain field can be expressed as follows Based on (3) (8), the contribution of the cavity-length change to the pressure sensitivity is. Compared with the phase-change expression for a solid fiber, the sensitivity is enhanced by times. Substituting,,, the cavity-length change contribute 17.7 pm/mpa to the pressure sensitivity. 2) FiberII: For fiber II, i. e., the photonic bgap fiber, a two-layer model described in [22] [24] can be applied to calculate the stress strain fields, as shown in Fig. 3(b). The inner layer is the honeycomb cladding, with its inner outer radii of. The outer layer is silica glass with inner outer radii of. The holey cladding can be considered as a uniform material since it contains an air hole structure with (7) (8) (5)

4 JIN et al.: SENSITIVITY CHARACTERISTICS OF FABRY-PEROT PRESSURE SENSORS BASED ON HOLLOW-CORE MICROSTRUCTURED FIBERS 2529 tens of layers. The material is inhomogeneous its Young s modulus Poisson s ratio can be expressed by [22] (9) (10) The small amplitudes of suggest the fact that the honeycomb structure is highly compressible for a directional in-plane stress. is proportional to the actual cross sectional area of silica glass. indicates that the applied directional in-plane strain can induce identical strain along the orthogonal in-plane direction but can hardly induce a change in longitudinal strain. The stress over the individual regions can also be expressed by (11) Substituting their respective Young s Moduli Poisson s ratios, the strain field over the silica outer cladding can be expressed by over the holey cladding (12-a) (12-b) The amplitudes of,, canbefoundwiththefollowing conditions, including the boundary conditions at the inner outer surface the requirement of continuity the requirement at the end face With the plane strain approximation, (13-a) (13-b) (13-c) (13-d) (13-e) (13-f) With the found constants,, the longitudinal strain can be determined. We found that the change of cavity length contributes 21.2 pm/mpa out of the pressure sensitivity. We also found that if the holey cladding is removed, the sensitivity only changes by 0.5%, through further calculation. This is because the holey cladding has a large air-filling ratio small effective Young s modulus, the longitudinal strain is almost determined by the outer silica cladding. B. The Effect of Effective-Index Change The applied hydrostatic pressure subjected to the HC fiber can also induce a mode-index change, which can possibly contributes to the round-trip phase change the pressure sensitivity, according to (3). The mode-index change comes from the changes in fiber transverse geometry the refractive-index change of the silica walls. In this subsection, this effect is discussed for both fibers. 1) FiberI: For fiber I, considering the cell walls are too thin, the deformation of the microstructure the refractive-index change of the silica walls are determinedbythedeformationof the outer silica ring. The calculation of pressure-induced modeindex change is performed with the following steps: First, the deformation of the silica ring are calculated with the single-layer structure. Second, the geometrical parameters the material-index of the microstructure are determined by the deformed silica ring. Third, mode solving is carried out for the deformed microstructure. The radial strain at the inner boundary of the silica ring is calculated as 2.95 foranappliedpressureof1mpa,basedon (8). That means the diameter of the silica ring becomes slightly larger when the cavity is under pressure, because the longitudinal component of the applied pressure tends to enlarge it, due to the positive Poisson s ratio. The silica ring stretches the bridges between the core the ring, which causes a deformation of the microstructure corresponding material-index change of silica walls. Fig. 4 shows a one-sixth model for fiber I. The applied displacement at point C is determined by. Since the angles between AD, BD CD are all 120, the silica bridges the core walls experience normal stresses with identical amplitude.assumetheradialdisplacement at point D is. For section CD, we have For sections AD BD, (14) (15) With (14) (15), the amplitudes of can be obtained. Note that the thickness of the walls are also changed considering the Poisson s ratio. The mode index of the deformed microstructure is calculated its contribution to the pressure sensitivity is estimated as. We found that the contribution of the refractive-index change to mode-index change is about two orders lower than the effect of the microstructure deformation can be ignored. 2) FiberII: For fiber II, the bgap guidance in the air core relies on the cladding structure the mode property is largely determined by the geometry of the holey cladding. In addition,

5 2530 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 15, AUGUST 1, 2013 Fig. 4. Calculated deformation of the silica walls first order principle stress over the microstructure for fiber III when the radial displacement of the inner boundary of the silica ring is 1. the mode index is also affected by the size shape of the air core. Generally speaking, larger core results in higher mode index (closer to 1). The microstructure change under pressure is quite complicated for the two-layer structure. The strain distribution can be characterized by (11) (12). With the calculated,, we found that the amplitude of the latter terms are much smaller than the former ones the in-plane strain distribution can be approximately expressed by (16) Fig. 5. Left: The ressembled fiber transverse geometry for the calculation of mode indexes for fiber II. Right: Schematic deformations of two selected cladding cells. The dashed curves define the orignal cells the solid curves represents the deformed ones. of The effective index of the fundamental mode is first calculated by use of finite element method. Then the mode solving process is performed for a fiber structure with a slightly reduced core, but the cladding structure remains unchanged, in order to estimate the index change under pressure. The pressure sensitivity contributed from the index change is estimated as only. where is calculated based on (11) (13). Eq. (16) suggests that the in-plane strain is nonuniform over the holey cladding. The region near the core experiences much higher strain than at near the silica outer cladding, since the strain is proportional to. For example, both the radial azimuth strain at (at the inner boundary of the holey cladding) is about 30 times higher than at (at the outer boundary). Since has a negative value, the cladding cells are compressed along the azimuth direction stretched along the radial direction. Fig. 5 demonstrates the schematic deformation of two selected cells when the cavity is under hydrostatic pressure. However, since the in-plane strain is of microstrain order with an applied pressure of 1 MPa, the deformation can hardly affect the bgap. The cell walls are bent when the holey cladding is deformed the refractive index of the silica walls may change as a result of the elasto-optic effect. However, this change is relatively small, compared with the silica-air index difference which is a critical parameter in the determination of the profile of the bagp. This analysis indicates that the induced deformation of the holey cladding is too small to induce the bgap shift mode-index change. On the other h, the air core also deforms when the cavity is under pressure. The calculated radial strain at the inner wall of the air core is based on (16), which suggests that the core shrinks due to the deformation of the holey cladding. With the composed transverse fiber geometry in Fig. 5, we calculated the mode index for the HC-PBGF. The core has a radius IV. DISCUSSION We found that the cavity-length change plays a dominate role for both the sensors by comparing the calculated measured result in Fig. 2(c). The pressure-induced cavity length is largely determined by the cross sectional area of the outer silica cladding. The enhancement can be measured with the amplification factor. The definition of indicates that the pressure sensitivity can be effectively enhanced by reducing the thickness of the silica outer cladding. In contrast, contributions of mode-index change to the sensitivities are much smaller. Note that the simplified bgap fiber presents a much higher positive index change rate than the HC-PBGF we intend to discuss the different mechanisms of mode-index changes between the two fibers. The elementary unit of the microsturcture is the hexagonal air-hole cell for the both fibers. This difference is mainly due to the existence of the defect core for fiber II, which is created by omitting seven air holes from the holey structure. If the air core is excluded in the microstructure, i. e., the fiber contains an ideally uniform hexagon array, all the cell walls experience normal stresses strains when the fiber is under pressure, like the case for fiber I. The air-hole cells can keep their hexagonal profile rather than deforms like those in Fig. 5. The introduction of the defect core significantly changes the elasticity of the fiber. The longitudinal component of the applied pressure tends to induce expansion of the holey cladding. The defect core provides a freedom for the expansion. As a result, the air holes surrounding the core can not hold ideal hexagonal shape.

6 JIN et al.: SENSITIVITY CHARACTERISTICS OF FABRY-PEROT PRESSURE SENSORS BASED ON HOLLOW-CORE MICROSTRUCTURED FIBERS 2531 In comparison, the F-P pressure sensors fabricated in solidcore microstructured optical fibers present much lower pressure sensitivities than the HC ones [25] [27]. This can be attributed to two reasons. First, the solid-core fibers have lower air-filling ratios. Second, the mode-index change induced by applied pressure significantly compensates the effect of cavity length change. It is now interesting to discuss how to enhance the microstructure deformation induce higher mode-index rates for the two fibers. Note that the honeycomb structure is highly deformable by in-plane stress due to the thin cell walls the consequent low effective Young s modulus. That means one can possibly induce significant deformation of the microstructure with much lower pressure in principle. The main limitation factor is the silica outer cladding. Due to its high stiffness, the silica region acts like a shield greatly reduces the effect of the applied pressure. For the microstructure of fiber I, the method is to increase the radial displacement at point C, i. e., the inner boundary of the silica ring. Based on (8), the radial strain at point C can be expressed by.thisindicates that the mode-index change rate can be enhanced by increasing the amplitude of, by reducing the thickness of the silica ring while keeping the inner radius constant. In contrast, the change rate of the core radius of fiber II is determined by multiple parameters, based on the two-layer model. The reduction in thickness of the outer silica cladding does not necessarily induce higher index change. An alternative method is to increase the air-filling ratio therefore a lower effective Young s modulus, based on (14). Note that the calculated result for HC bgap fiber is different with the polymer-jacketed ones described in [23], due to the significant difference in elasticity between silica glass the polymer. The jacketed fibers elongate with applied pressure, the bare ones are shortened in contrast. On the other h, the holey cladding of the jacketed fiber experiences positive radial strain the air core is enlarged. V. CONCLUSION In conclusion, we have investigated the sensitivity characteristics of F-P pressure sensors based on two different hollow core microstructured optical fibers. Despite their respective microstructure profile, the pressure sensitivities are dominantly determined by the cavity-length change, which is relevant with an amplification factor. In contrast, the mode-index change induced by the applied pressure is extremely small. However, we intended to give a detailed investigation on the physical mechanisms behind the mode-index changes for the HC bgap fibers. Due to the highly deformable holey structure, the air-core bgap fibers may offer a new dimension for the implementation of tunable photonic devices. ACKNOWLEDGMENT The authors would like to thank J. Ma, F. Yang, Z. Quan M.Linfortheirkindhelp fruitful discussion. REFERENCES [1] C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, K. W. Koch, Low-loss hollow-core silica/air photonic bgap fibre, Nature, vol. 424, no. 6949, pp , Aug [2]F.Couny,F.Benabid,P.S.Light, Large-pitchkagome-structured hollow-core photonic crystal fiber, Opt. Lett., vol. 31, no. 24, pp , Dec [3] S.Février,B.Beaudou,P.Viale, Understing origin of loss in large pitch hollow-core photonic crystal fibers their design simplification, Opt. Exp., vol. 18, no. 5, pp , Mar [4] F. Gérôme, R. Jamier, J. Auguste, G. Humbert, J. Blondy, Simplified hollow-core photonic crystal fiber, Opt. Lett., vol. 35, no. 8, pp , Apr [5] W. Jin, H. F. Xuan, H. L. 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7 2532 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 15, AUGUST 1, 2013 [22] V. Dangui, H. Kim, M. Digonnet, G. Kino, Phase sensitivity to temperature of the fundamental mode in air-guiding photonic-bgap fibers, Opt. Exp., vol. 13, no. 18, pp , Sep [23] M. Pang W. Jin, Detection of acoustic pressure with hollow-core photonic bgap fiber, Opt. Exp., vol. 17, no. 13, pp , Jul [24] M. Pang, H. Xuan, J. Ju, W. Jin, Influence of strain pressure to the effective refractive index of the fundamental mode of hollow-core photonic bgap fibers, Opt. Exp., vol. 18, no. 13, pp , Jul [25] C. Wu, B. O. Guan, Z. Wang, X. Feng, Characterization of pressure response of Bragg gratings in grapefruit microstructured fibers, J. Lightw. Technol., vol. 28, no. 9, pp , May [26] C. Wu, H. Y. Fu, K. K. Qureshi, B. O. Guan, H. Y. Tam, Highpressure high-temperature characteristics of a Fabry-Perot interferometer based on photonic crystal fiber, Opt. Lett., vol. 36, no. 3, pp , Feb [27] S. H. Aref, M. I. Zibaii, M. Kheiri, H. Porbeyram, H. Latifi, F.M. Araújo,L.A.Ferreira,J.L.Santos,J.Kobelke,K.Schuster,O. Frazão, Pressure temperature characterization of two interferometric configurations based on suspended-core fibers, Opt. Commun., vol. 285, no. 3, pp , Feb Bai-Ou Guan received the B.Sc. degree in applied physics from Sichuan University, Chengdu, China, in 1994, the M.Sc. Ph.D. degrees in optics from Nankai University, Tianjin, China, in , respectively. From 2000 to 2005, he was with the Department of Electrical Engineering, the Hong Kong Polytechnic University, Hong Kong, first as a Research Associate, then as a Postdoctoral Research Fellow. From 2005 to 2009, he was with School of Physics Optoelectronic Engineering, Dalian University of Technology, Dalian, China, as a full professor, where he established the PolyU-DUT Joint Research Center for Photonics. In 2009 he joined Jinan University, Guangzhou, China, where he founded the Institute of Photonics Technology. His current research interests include fiber-optic biochemical sensors, micro/nanofiber optical sensors, polarimetric fiber grating laser sensors, microstructured optical fiber sensors, photonic microwave generators, photonic components for sensing telecommunication. He has authored coauthored more than 160 technical papers presented more than 10 invited talks at international conferences. He is a member of IEEE OSA, served as the General Co-Chair of the 10th International Conference on Optical Communications Networks (ICOCN2011), the General Co-Chair of the 2nd Asia-Pacific Optical Sensors Conference (APOS2010), the Technical Program Committee Co-Chair of the 5th Asia-Pacific Microwave Photonics Conference 2010 (APMP2010). Long Jin received the B.S. degree in applied physics the Ph.D. degree in fiber optics from Nankai University, China, in , respectively. He joined the Department of Electrical Engineering, Hong Kong Polytechnic University in 2008, as a research assistant then a Postdoctoral Research Fellow. Since 2010, he has been with Institute of Photonics Technology, Guangzhou, China as an associate professor. He has published more than 50 journal conference papers. His research interests include fiber grating devices, photonic crystal fibers optical fiber sensors. Huifeng Wei received the M.S. degree from the College of Physics Science, Nankai University, Tianjin, China, in Currently, he is with the State Key Laboratory of Optical Fiber Cable Manufacture Technology, Yangtze Optical Fiber Cable Company Ltd. (YOFC), Wuhan, China, he is the leader of photonic crystal fiber project with YOFC, the executive leader of the project of the national Key Basic Research Development Program of China under Grant 2010CB His research interests include fabrication characterization of photonic crystal fiber, photonic crystal fiber-based super continuum source, research development of Rare Earth-doped fiber fiber laser.