Optical Fiber Flowmeter Based on a Michelson Interferometer

. In this work, an optical fiber flowmeter based on a Michelson interferometer is presented. The Michelson interferometer uses a long period fiber grating (LPFG) to couple light to the cladding modes followed by a section of a GO-coated single mode fiber (SMF). By radiating the GO thin film, it will increase its temperature changing the effective refractive index of the optical cavity of the Michelson interferometer. By placing the sensor on a gas flow, its temperature surface will decrease in a proportional manner to the flow rate. The sensor was studied in both static and dynamic dry nitrogen flow, attaining an absolute sensitivity of 17.4 ± 0.8 pm/(L.min -1 ) and a maximum response time of 1.1 ± 0.4 s.


Introduction
Liquid and gas flow measurements are of paramount importance in many scientific and industrial applications [1,2].Different sensing configurations have been developed considering each application such as differential pressure, ultrasonic, and thermal flowmeters.
The properties of optical fiber have made it into an interesting alternative its traditional counterpart due to their immunity to electromagnetic interference, compactness, and ability to withstand harsh environments such as high temperatures or chemical corrosive atmospheres [3].Several techniques have emerged in recent years to monitor gas flow using optical fiber such as surface plasmon resonance [4], bending losses [5], and interferometry [6,7].
In this work, a thermal optical fiber flowmeter based on a graphene-oxide (GO) coated Michelson interferometer is presented.The Michelson interferometer is created using a long period fiber grating (LPFG) proceeded by a segment of single mode fiber (SMF) coated with GO.By radiating the LPFG, the light that is coupled to the cladding modes will heat up the GO thin film coating changing the effective refractive index of the cladding modes of the Michelson interferometer.The response of the sensor was studied regarding the static and dynamic responses to dry nitrogen gas flow.

Operation principle
The sensor is composed of a Michelson interferometer coated with GO.The Michelson interferometer is achieved by creating a LPFG with an attenuation band of 3 dB that allows the coupling of light between the core and the cladding modes.Following the LPFG is a section of SMF with a total length of 11 cm, that serves as optical cavity of the interferometer.The structure of the sensor is presented in Fig. 1.The section of the optical cavity is coated with GO that, by being radiated with the infrared light, heats up due to the photothermic effect.The optical cavity works as a "hot-wire", and when exposed to a gas flow will experience a decrease in its temperature dependent on the flow rate.
Due to the thermo-optic effect, the temperature changes on the GO coating will induce a variation on the effective refractive index (RI) of the cladding modes affecting the optical path difference of the interferometer inducing a phase shift of the reflected spectrum.

Sensor fabrication
The fabrication of the sensor starts by writing the LPFG on a SMF using the induced electric-arc discharge technique [8].The LPFG was fabricated with a period of 412  corresponding to a resonance band centered at 1553 nm with an attenuation band of 3 dB.The SMF is, then, cleaved to a length that enables to attain a significant number of fringes on the range of the attenuation band, by inspecting the reflected light as the section of SMF is cleaved.
Afterwards, the SMF section is coated with GO by following a similar protocol as presented by Xiao et al. [9].The coating process starts by cleaning the fiber using ethanol to remove any residues present on the surface.This is followed by a hydroxylation process, by immersing the fiber on a 1.0 M sodium hydroxide (NaOH) solution for 1 hour.The fiber is, then, washed three times using ethanol and distilled water.Next, the fiber is immersed on a 5 % (3-Aminopropyl) trimethoxysilane (APTMS) solution in ethanol for 1 hour.The unbounded APTMS was washed using ethanol and the fiber was dried on an oven for 30 minutes at 70 °C.The GO coating was, then, applied by immersing the fiber on a GO solution with a concentration of 1 mg/mL for 3 hours at 42 °C.The unbounded GO was washed using Milli-Q water, and the fiber was dried in an oven for 1 hour at 70 °C.The resultant reflected spectrum is presented in Fig. 2.

Experimental setup
The experimental setup was composed by an erbiumdoped fiber amplifier (EDFA, model IPG Laser GmbH EAD-1K-C3-W), an optical circulator, that allows to direct the reflected light to the optical spectrum analyzer (OSA, model AQ6370C, Yokogawa Electric).For the gas flow measurements, the fiber was placed on an air-tight gas chamber connected to a dry nitrogen (N2) bottle (Linde, ≤ 99.99 %) with a gas inlet controlled by high-resolution mass-flow controllers (Brooks, SLA5800 Series).

Experimental Results
The performance of the sensor was studied in static and dynamic conditions.In a first study, the sensor was placed on the gas chamber and a constant gas flow was applied to the fiber sensor.The gas flow induces a blueshift corresponding to a higher decrease of temperature with a higher flow rate, as presented in Fig. 3, with a sensitivity of -17.4 ± 0.8 /(. −1 ).The dynamic response of the sensor was studied by placing the sensor on the gas chamber and changing the gas flow rate between 0 and 8 L/min, while attaining the optical power at 1551 nm.The response time of the sensor was estimated to be 1.1 ± 0.4 s.

Conclusions
In summary, in this work a GO-coated Michelson interferometer was presented for gas flow sensing.The response of the sensor was studied considering its static response to gas flow, attaining a linear response with a sensitivity of -17.4 ± 0.8 /(. −1 ).The dynamic response of the sensor was also studied, achieving a time response of 1.1 ± 0.4 s.The proposed sensor presents promising potential for real-time flow measurements in different scientific and industrial applications., 09040 (2023)

Fig. 3 .
Fig. 3. Wavelength shift caused by gas flow on the Michelson interferometer.