Suppression of parasitic interference in a fiber-tip Fabry-Perot interferometer for high- pressure measurements

We demonstrate a novel design and fabrication process for fiber-tip Fabry-Perot interferometric (FTFPI) pressure sensors which eliminates fringe envelopes in the reflection spectrum. The outer facet reflectivity and thickness of the FTFPI silica diaphragm were reduced through orthogonal rough-polishing of the fiber end facet. A silica FTFPI sample with a diaphragm thickness of ~10.7 μm was produced and tested under hydraulic pressures ranging from 0 to 30 MPa. The proposed sensor achieved a pressure sensitivity of −284 pm/MPa at 1555 nm and could be a valuable new tool for high pressure measurements. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Optical fiber Fabry-Perot interferometric (FPI) sensors exhibit several characteristics which have attracted attention in recent years.They have been widely investigated for applications in a variety of fields, such as environmental monitoring, biomedical instruments, and mechanical engineering [1][2][3][4][5][6][7].Among these, all-silica FPIs fabricated at the tip of an optical fiber are preferable for pressure measurements due to their small size, robust mechanical structure, and high sensitivity [8][9][10][11].Pressure sensitivity is one of the most important properties of a fiber-tip Fabry-Perot interferometric (FTFPI) sensor.As such, recent studies have mostly investigated optimal structure types for the reflecting mirrors at the fiber ends.FTFPI pressure sensitivity can be increased by reducing the mirror thickness [12][13][14].
Reflection occurs at three interfaces in the flat silica diaphragm, with a thickness of several to tens of microns, located at the end of a short hollow core fiber (HCF).This threewave interference could potentially modulate the fringe envelope, affecting the measurement of peak or dip wavelengths [9] and the observation of spectral shifts [10].To remove these unwanted reflections at the fiber end surface, Liu et al polished a single-mode fiber (SMF) facet to 8° [15].Smith et al reported an ultra-small Fabry-Perot cavity written into optical micro-fibers, they removed the parasitic interference by cleaving the end of the micro-fiber using a focused-ion beam at an angle of 45° [16].While oblique surfaces can reduce facet reflectivity, they can also affect the linear response of an FTFPI pressure sensor.In addition, tilting the fiber end facet is also a complex process.Hence, researchers proposed other ways to reduce the outer facet reflectivity, such as by increasing the roughness of the outer facet.For example, Xu et al proposed a novel diaphragm-based FPI pressure sensor which utilized hydrofluoric acid (HF) etching.Reflections from the exterior diaphragm surface can be neglected because the two surfaces are not parallel after cleaving.HF etching also produces a rough outside surface [17] and requires the use of hazardous chemicals.Sorin et al measured the absolute optical path differences (OPDs) between reflectors spaced along a single sensing fiber using a coherence-domain demodulation method [18].However, this method exhibits a limited spatial resolution of ~10 μm, which is not sufficient for discriminating the parasitic interference in the FTFPIs with thin diaphragms [18,19].Moreover, Shen et al proposed a frequency estimation-based signal processing algorithm for multiplexed FPIs, to estimate the absolute OPDs [20].Hence, the parasitic interference from different interfaces could easily be discriminated using this method.However, this approach always requires large computations, such as fast Fourier transformation (FFT) and/or digital filtering [21,22].
In this study, we propose a replicable technique for fabricating all-silica FTFPI highpressure sensors, avoiding fringe envelopes in the reflection spectrum.This device is produced by polishing the FTFPI end facet.This process not only decreases diaphragm thickness, which increases sensitivity, but also reduces diaphragm reflectivity which decreases noise.A polishing experiment demonstrated the facet reflectivity of a flat-end SMF, polished using a 9-μm-grit polishing paper, could be reduced below 5% compared with normal Fresnel reflection.The proposed sensor can also eliminate the influence of fringe envelopes.A silica diaphragm was produced with a thickness of 10.7 μm, achieving a pressure sensitivity of −284 pm/MPa over an applied pressure range of 0 to 30 MPa.

Principles
Figure 1(a) illustrates that there are three silica/air interfaces which can reflect light along the SMF.Surface 1 is the flat-end of the SMF, surface 2 and surface 3 are the inner and outer surfaces of the silica diaphragm, respectively.The reflectivity of the silica/air interface is so low (~3.5%) that we can neglect the impact of high-order FP interference.The total reflected electric field E and light intensity I can then be expressed as: where E 1 , E 2 , and E 3 are the field amplitudes of the light reflected by surface 1, surface 2, and surface 3, respectively.L is the length of the air cavity, n a and n s are the refractive indexes of air and silica, respectively, d is the thickness of the silica diaphragm, and λ is the wavelength of the light.
As shown in Eq. ( 1), the existence of E 3 will introduce the parasitic interference.E 3 can increase or decrease the intensity of the reflected light, modulating the reflection spectrum by inducing a fringe envelope.Fig. 1(b) illustrates the measured FTFPI spectrum from 1250 to 1650 nm, in which the 0 dB level corresponds to a fiber end facet Fresnel reflection of ~3.5%.The FTFPI spectrum has a periodic fringe envelope, clearly showing the modulation caused by E 3 [23,24].Unlike in two-beam interference, this envelope can be used to determine the thickness of the silica diaphragm [25].However, this modulated spectrum can lead to errors when estimating the actual cavity length L, by tracing the interfering minima or maxima in the spectrum [12].Furthermore, low fringe contrast near the envelope valley may limit the use of spectrum demodulation, which is commonly applied in optical signal processing.
The effects of the fringe envelope can be lessened by reducing the thickness of the silica diaphragm.When the silica is sufficiently thin, the envelope can be considered as the result of interference between surface 2 and surface 3. The interval between two adjacent valleys (or peaks) in the envelope can be expressed as λ 2 /2n s d [26].Recently, we reported an FTFPI silica diaphragm with a thickness of below 180 nm [13].The fringe envelope spacing in the reflection spectrum was larger than 2120 nm.The resulting modulated spectrum is difficult to measure using standard equipment.However, FTFPIs with ultra-thin diaphragms are not suitable for high-pressure applications.The ampli such as apply diaphragm to index matchin and the titled FTFPI.In thi polishing, and  ) can be reduc r end [27] or ap r, the temperat n the amplitude t the linear pr he fiber end fa tly reduced.

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Conclusion
The fabrication process for an FTFPI pressure sensor without a fringe envelope in its reflection spectrum was proposed and experimentally demonstrated.The reflectivity of the end surface was reduced by polishing the outer facet of an FTFPI silica diaphragm, using 9μm-grit polishing paper, to a thickness of 10.7 μm.A high pressure response was observed from 0 to 30 with a sensitivity of ~−284 pm/MPa.The benefits of this all-silica FTFPI include low fabrication cost, avoidance of a fringe envelope, high mechanical strength, and significant pressure endurance.As such, the proposed FTFPI device is an excellent candidate for performing pressure measurements in harsh environments.
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