Antiresonant reflecting guidance mechanism in hollow-core fiber for gas pressure sensing

A gas pressure sensor based on an antiresonant reflecting guidance mechanism in a hollow-core fiber (HCF) with an open microchannel is experimentally demonstrated for gas pressure sensing. The microchannel was created on the ring cladding of the HCF by femtosecond laser drilling to provide an air-core pressure equivalent to the external environment. The HCF cladding functions as an antiresonant reflecting waveguide, which induces sharp periodic lossy dips in the transmission spectrum. The proposed sensor exhibits a high pressure sensitivity of 3.592 nm/MPa and a low temperature cross-sensitivity of 7.5 kPa/°C. Theoretical analysis indicates that the observed high gas pressure sensitivity originates from the pressure induced refractive index change of the air in the hollow-core. 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Antiresonant reflecting fiber is a kind of waveguide that spectral characteristics are governed by the thickness of the first high-index layer rather than lattice constant, and has been identified to play an important role in near-infrared and THz optical signal transmission [15][16][17][18].Various structures of antiresonant reflecting fibers have been reported, including photonic crystal fibers (PCFs) [15,16], Kagome fibers [19,20], "negative curvature" fiber [21] and the simplest structure of ring-cladding hollow-core fiber (HCF) [22].Moreover, HCF coated with functional material films have been reported for biosensing, magnetic field sensing and humidity sensing [22][23][24].
In this letter, we present a gas pressure sensor based on an antiresonant reflecting guidance (ARRG) mechanism in an HCF.The pressure sensor is comprised of an HCF section with an open microchannel fabricated through the ring cladding of the HCF by femtosecond (fs) laser micromachining [25].Here, the HCF serves as an antiresonant reflecting waveguide, and the microchannel allows for an air-core pressure equivalent to that of the external pressure.The ARRG-based sensor exhibits sharp periodic lossy dips in the transmission spectrum, and the resonant lossy dips exhibit a wavelength shift with a linear sensitivity of 3.59 nm/MPa and a low temperature cross-sensitivity of 7.5 kPa/°C.Theoretical analyses indicate that the pressure sensitivities for the ARRG sensors mainly result from the refractive index change of air within the hollow-core.Moreover, the proposed device exhibits the advantage of novelty, simplicity and high sensitivity.sections and with a microchnnel passing through the ring cladding of the HCF in a direction perpendicular to its core.The HCF employed in the experiments (Polymicro Technologies, TSP025150) consisted of a 25 μm diameter (2r) of and a ring-cladding with a thickness (d) of 50 μm.The HCF section was spliced to the SMFs using a Fujikura 80S fusion splicer.

Fabrication
In the fs laser micromachining process employed for micro-channel fabrication, 800 nm wavelength fs laser pulses with duration of 120 fs and pulse energy of 2 μJ at a repetition rate of 1 kHz were focused onto the outside surface of the HCF through a 20 × microscope objective lens.The initially closed sensor specimen was fixed to a linear translation stage, and the laser beam was initially scanned parallel to the fiber axis at a speed of 2 μm/s over a total distance of 20 μm.After one scanning cycle, the laser beam focus point was shifted 10 μm perpendicular to the fiber axis, for the next scanning cycle.After four scanning cycles, a V shaped microchannel was successfully fabricated in the cladding of the HCF, which allows for an air-core pressure equivalent to that of the external pressure, as shown in Figs.1(b) and 1(c).
Figure 1(d) shows the transmission spectra of an L = 5 mm specimen before and after microchannel fabrication.The transmission spectra of the sample were collected with a broadband light source (BBS; Shenzhen Fiberlaker Technology Co., Ltd.) ranging from 1250 to 1650 nm and an optical spectrum analyzer (OSA; Yokogawa AQ6370C) with a resolution of 0.02 nm.Prior to microchannel fabrication, the initial insertion loss was approximately −7 dB, which mainly derived from the transmission loss of the HCF.After microchannel fabrication, the insertion loss increased to approximately −8 dB, and the resonance wavelengths remained unchanged.Five sharp resonance lossy dips were observed in the 100 nm wavelength range shown in Fig. 1(d).To explain the data presented in Fig. 1(d), a schematic diagram of the HCF cross-section is shown in Fig. 2(a).The air-core has an index of refraction n 1 and the ring cladding has an index of refraction n 2 .Air also resides external to the cladding, and has an index of refraction n 3 that is dependent on the external pressure.The optical guidance mechanism of the HCF can be explained according to the antiresonant reflecting optical waveguide (ARROW) model.In this model, the high refractive index cladding is regarded as a Fabry-Pérot etalon.Figure 2(b) illustrates multiple beams at the interfaces within the FP-etalon.The light intensity corresponding to the resonant condition can be easily interpreted by referring to geometrical optics.In the ARROW model, light passes out of the high refractive index cladding when its wavelengths is close to that of a resonant wavelength λ m , which results in the sharp periodic lossy dips in the transmission spectrum shown in Fig. 1(d).However, when the propagating wavelength is far away from a resonant wavelength (i.e. the antiresonant wavelengths region), the light is internally reflected, confined in the hollow core of the fiber as the guided core mode.The resonant wavelengths λ m can be expressed as follows [15]:

Guiding mechanism
where m is an integer beginning with 1, d = 50 μm and n 2 = 1.4446 (around 1500 nm) and n 1 = 1 (under normal pressure).By using the commercial COMSOL software, the transmission spectrum of the HCF was simulated with full-vector finite element method (FEM) [23], as shown in Fig. 3(a).Given that the guided light is assumed as a Gaussian beam with a diameter of 9 μm.The theoretical resonant wavelengths were calculated as 1499.51nm and 1520.64 nm, around 1500 nm.
Moreover, Fig. 3(a) also presents the transmission spectra of three sensor specimens with L values of 1.5, 2, and 5 mm, where the locations of the sharp transmission lossy dips for the three samples exhibit slight deviations with the theoretical predictions.This might be related to the thickness of the silica cladding d, which is not very strictly uniform at different positions of the HCF.The transmission lossy dips of the three samples are −3.5, −4.8, and −7 dB, respectively, result from incomplete confine of light by the single layer ring cladding structure of HCF [16].The visibilities of the three samples are 4.4, 7.5, and 17.1 dB, respectively, which indicate that the resonant effect is accumulated along the length of the HCF at resonant wavelengths [26].Therefore, there is a tradeoff between the visibilities and the transmission lossy dips.It is noted that the transmission spectra are not particularly uniform but appear to include other periodic components, distributed throughout the antiresonance regions of the transmission spectra.We believe that the guide light is also reflected on the outer surface of the HCF, but the reflectivity is relative low, which results in the ripples in the transmission spectra [27].and 3(c) present the intensity distributions of near-mode field patterns observed at the wavelength of 1535.8 and 1538.08 nm for the L = 5 mm sensor.These wavelengths respectively correspond to an antiresonance peak and main resonance loss.Figure 3(b) shows the mode field for the antiresonant wavelength, which is confined in the hollow core of the fiber as the guided core mode.Figure 3(c) shows the mode field for the resonant wavelength, and the guided light would transmit out of the HCF section and completely lost.Therefore, the HCF can be described as an ARROW.The gas pressure responses of the ARRG-based sensors were tested by means of the experimental setup shown in Fig. 4. Sensors were fixed into a pressure chamber, where a commercial gas pressure generator (ConST-168) with a stability of ± 0.2 kPa and a high precision digital pressure meter (ConST-211) were employed to regulate the pressure in the chamber.The applied gas pressure in the chamber was increased from 0 to 2 MPa in interval of 0.1 MPa at room temperature, and the pressure was maintained for 5 min at each step.

Gas pressure experiments and discussion
The resonance wavelengths of two ARRG-based sensors with L of 5 and 2 mm gas pressures are shown in Figs.5(a) and 5(c), respectively.The resonance transmission lossy dips of the sensors shift toward shorter wavelengths with increasing applied pressure, while the loss intensities exhibit no significant deviations, as a function of pressure.From Figs. 5(b) and 5(d), the two sensors with L = 5 mm and L = 2 mm both exhibit good linear wavelength responses with similar sensitivities of −3.592 nm/MPa and −3.585 nm/MPa, respectively.Compared with previously reported optical fiber pressure sensors, such as the inflated LPG (1.68 nm/MPa) [4], dual-core PCF (21 pm/MPa) [5], and optical fiber tip micro-bubble (1.036 nm/MPa) [11], the ~3.592 nm/MPa sensitivity of the proposed ARRG-based pressure sensor is much greater.For an opened ARRG-based sensor, the pressure sensitivity may be attributed to three factors: (i) refractive index change of air within the hollow-core S air , (ii) structural deformation of the silica cladding S structure , and (iii) refractive index change of silica cladding due to strain-optic effect S silica .The pressure sensitivity ∂ λ m /∂P can be derived from Eq. (1) as Firstly, we concern the contribution from the refractive index change of air.From an updated Edlén equation, at room temperature (15-25 °C), the index of refraction of air is a function of the pressure and temperature T (°C) [28]: As such, if the temperature remains unchanged, a linear relationship exists between n 1 and P. For T = 25°C, the pressure sensitivity S air can be calculated to be approximately −3.398 nm/MPa at 1500 nm.This value is very close to the experimental results (−3.592, −3.585 nm/MPa), indicating that the air-index change played a major role in the observed pressure sensitivity.
To estimate the magnitude of S structure and S silica , the structural deformation and strain distributions over the silica cladding region, need to be evaluated.The elasticity of HCF can be analyzed with a single-layer model with outer and inner radii r 11 and r 12 [9].The stress expression in silica cladding regions can be written as [29]: where A, C and D are constants.By substituting the above equations into the Hooke's law, we obtain the strain tensor for the silica cladding as [30]: Considering the situation of the opened ARRG sensor, the boundary conditions may be written as: Since the sensor is fixed in the chamber, the pressure applied from the two ends would have little or no effect on its length, the pressure-induced longitudinal strain εz is also negligible [31].With Eqs.(4)-Eqs.(6), A, C and D, and hence the stress and strain fields over the silica cladding region can be obtained.For different applied pressures in the hollow-core, the radial and azimuthal strains (ε r and ε θ ), and the radial displacement (u r = rε θ ) distribution for the entire cladding region are plotted in Fig. 6.The maximum strain happen near the wall where n 0 = 1.4446 is the refractive index of silica under strain-free condition, and p 11 = 0.121 and p 12 = 0.27 are strain-optic tensor for bulk silica material.We calculated the changes of refractive index in silica cladding for 2 MPa, as shown in Fig. 7.It is shown that the change of the longitudinal component Δn z is a constant while radial components reduce quickly with increasing radius.The maximum refractive index changes occur in the inner surface of the cladding with a value of ~2.4 × 10 −5 .
By importing the calculated results into Eq.( 2), as shown in Figs.(6) and Figs.(7), we can estimate the structural deformation induced pressure sensitivity S structure , and strain-optic effect induced pressure sensitivity S silica .When the pressure level is increased to 2 MPa, the maximum deformation is about −1.25 nm, and S structure can be estimated to be −0.019nm/MPa.Meanwhile, the maximum refractive index changes change of the mode index is ~2.4 × 10 −5 , corresponding to S silica of ~0.022 nm/MPa.Noting that the S structure and S silica are far less than the pressure-induced refractive index change of air within the hollow-core S air (−3.398 nm/MPa).Furthermore, the pressure sensitivity S structure will counteract most strainoptic effect induced pressure sensitivity S silica .This is an advantage of the proposed sensor, which greatly enhance its working pressure range.

Temperature experiment
The influence of temperature on the proposed ARRG-based sensor has been investigated by placing the sensor (L = 5 mm) into an electrical oven and gradually increasing T from room temperature to 500°C, while monitoring the shift in a resonance transmission loss.

Fig. 1 .
Fig. 1.(a) Pictorial view of the designed pressure sensor based on an antiresonant reflecting guidance (ARRG) mechanism in a hollow-core fiber (HCF).(b) Side-view and (c) top-view optical microscopy images of the microchannel created by femtosecond laser micromachining.(d) Transmission spectra of the ARRG-based pressure sensor with an HCF length of 5 mm before and after microchannel fabrication.

Figure 1 (
Figure1(a) shows a pictorial illustration of the designed open ARRG-based pressure sensor, comprised of an HCF section of length (L) spliced between two single-mode fiber (SMF) sections and with a microchnnel passing through the ring cladding of the HCF in a direction perpendicular to its core.The HCF employed in the experiments (Polymicro Technologies, TSP025150) consisted of a 25 μm diameter (2r) of and a ring-cladding with a thickness (d) of 50 μm.The HCF section was spliced to the SMFs using a Fujikura 80S fusion splicer.In the fs laser micromachining process employed for micro-channel fabrication, 800 nm wavelength fs laser pulses with duration of 120 fs and pulse energy of 2 μJ at a repetition rate of 1 kHz were focused onto the outside surface of the HCF through a 20 × microscope objective lens.The initially closed sensor specimen was fixed to a linear translation stage, and the laser beam was initially scanned parallel to the fiber axis at a speed of 2 μm/s over a total distance of 20 μm.After one scanning cycle, the laser beam focus point was shifted 10 μm perpendicular to the fiber axis, for the next scanning cycle.After four scanning cycles, a V shaped microchannel was successfully fabricated in the cladding of the HCF, which allows for an air-core pressure equivalent to that of the external pressure, as shown in Figs.1(b) and 1(c).Figure1(d) shows the transmission spectra of an L = 5 mm specimen before and after microchannel fabrication.The transmission spectra of the sample were collected with a broadband light source (BBS; Shenzhen Fiberlaker Technology Co., Ltd.) ranging from 1250 to 1650 nm and an optical spectrum analyzer (OSA; Yokogawa AQ6370C) with a resolution of 0.02 nm.Prior to microchannel fabrication, the initial insertion loss was approximately −7

Fig. 2 .
Fig. 2. (a) Schematic diagram of an HCF cross section with cladding of thickness d and index of refraction n 2 .The indices of refraction of the hollow core and external environment are n 1 and n 3 , respectively.(b) The optical pathways at the HCF interfaces.

Fig. 3 .
Fig. 3. (a) Simulation and measured transmission spectra.(b) and (c) Intensity distributions of near-mode field patterns corresponding to the wavelengths of 1535.8 and 1538.08 nm for the specimen with an HCF length of 5 mm.

Figures
Figures 3(b) and 3(c) present the intensity distributions of near-mode field patterns observed at the wavelength of 1535.8 and 1538.08 nm for the L = 5 mm sensor.These wavelengths respectively correspond to an antiresonance peak and main resonance loss.Figure3(b) shows the mode field for the antiresonant wavelength, which is confined in the hollow core of the fiber as the guided core mode.Figure3(c) shows the mode field for the resonant wavelength, and the guided light would transmit out of the HCF section and completely lost.Therefore, the HCF can be described as an ARROW.
Figures 3(b) and 3(c) present the intensity distributions of near-mode field patterns observed at the wavelength of 1535.8 and 1538.08 nm for the L = 5 mm sensor.These wavelengths respectively correspond to an antiresonance peak and main resonance loss.Figure3(b) shows the mode field for the antiresonant wavelength, which is confined in the hollow core of the fiber as the guided core mode.Figure3(c) shows the mode field for the resonant wavelength, and the guided light would transmit out of the HCF section and completely lost.Therefore, the HCF can be described as an ARROW.

Fig. 4 .
Fig. 4. Experiment setup for gas pressure measurements employing a broadband light source ranging from 1250 to 1650 nm and an optical spectrum analyzer.

Fig. 7 .
Fig. 7.The changes for individual refractive index component of silica cladding region for a 2 MPa pressure applied.
Figure 8(a)   shows the transmission spectrum evolution of the pressure sensor with respect to T, where a red shift is clearly observed with increasing T. The wavelength shift was recorded with respect to increasing T, and is given in Fig.8 (b).Here, a linear relation is observed, with temperature coefficients of 26.97 pm/°C.The temperature response of the sensor is mainly