Optical Vernier Effect: Recent Advances and Developments

Reconfigurable highly-sensitive interferometric sensor with Vernier effect and a virtually tunable reference cell

The optical Vernier effect magnifies the sensing capabilities of an interferometer, allowing for unprecedented sensitivities and resolutions to be achieved. Just like a caliper uses two different scales to achieve higher resolution measurements, the optical Vernier effect is based on the overlap in the responses of two interferometers with slightly detuned interference signals. Here, we present a novel approach in detail, which introduces optical harmonics to the Vernier effect through Fabry–Perot interferometers, where the two interferometers can have very different frequencies in the interferometric pattern. We demonstrate not only a considerable enhancement compared to current methods, but also better control of the sensitivity magnification factor, which scales up with the order of the harmonics, allowing us to surpass the limits of the conventional Vernier effect as used today. In addition, this novel concept opens also new ways of dimensioning the sensing structures, together with improved fabrication tolerances.

In this paper, dual-wavelength laser emission of an erbium-doped fiber laser (EDFL) with a tunable distinct wavelength selection of the simultaneously produced laser lines was achieved by applying a parallel comb filter configuration based on the optical Vernier effect. The intracavity inserted proposed comb filter consists of two parallel branches to generate the Vernier effect. Each branch is an in-line Mach-Zehnder interferometer (MZI) filter, which is composed of a polarization-maintaining fiber fusion spliced between single-mode fibers with sphere shapes at both ends. The tunability of the selected laser wavelength was realized by submerging the proposed filter in different sodium chloride/water mixtures. The proposed comb filter-based Vernier effect was used to independently achieve the selection of the dual-wavelength EDFL lines and for refractive index (RI) sensing applications. The in-line M Z I 1 and M Z I 2 structures show a wavelength shift sensitivity to RI variations of -88 and 79nm/RIU, respectively. Our proposed MZI structure presents a reliable, straightforward, and low-cost spectral comb filter for separate tunable dual-wavelength laser generation in the c-band region. Furthermore, the proposed filter structure-based Vernier effect presents a new perspective and method in the RI sensing application.

We have designed a highly sensitive optical fiber transverse load and axial strain sensor based on the cascaded Fabry–Perot (F–P) cavity and fiber Sagnac loop. F–P cavity is composed of an air-bubble formed by a Section of quartz capillary discharge. Fiber Sagnac loop is made by winding a Section of panda fiber (PF) through a 3 dB coupler. When the free spectral ranges (FSRs) of two interferometers are similar, they are cascaded to form the optical Vernier effect, which amplifies the sensitivity of the sensor. The experimental results show that the sensitivities of transverse load and axial strain of the sensor are up to 19.1 nm/N and 28.9 pm/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \varepsilon $ </tex-math></inline-formula> , respectively. The sensitivities of a single F–P cavity for measuring the transverse load and the axial strain are 1.5 nm/N and 2.4 pm/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \varepsilon $ </tex-math></inline-formula> , respectively. It can be seen that by using the optical Vernier effect, the sensitivity of the transverse load and axial strain of the sensor is improved by 12.7 and 12 times, respectively. The measurement matrix is constructed by using the sensitivities of a single F–P cavity and the cascaded structure to realize the simultaneous measurement of the transverse load and axial strain and eliminate the cross-sensitivity between them. The designed sensor has a certain attraction in small load and small strain monitoring.

A quasi-distributed fiber-optic sensitized sensing technique based on Fabry Perot (FP) microcavities is proposed by integrating frequency-modulated continuous-wave (FMCW) interferometry with the Vernier effect. An open-cavity structured FP sensor (FP-Sen) was fabricated for seawater salinity detection. Precise localization and interferometric spectral demodulation of multiple FP-Sens were achieved by compensating for the nonlinear tuning errors of the laser source using a digital signal processing (DSP) algorithm. The virtual interferometric spectrum (VIS) of multiple virtual sensors (V-Sens) was constructed according to the interferometric formula and superimposed with the interferometric spectrum of the FP-Sen to generate the optical Vernier effect. Sensitized salinity measurements were then realized by monitoring the drift of the Vernier envelope spectrum. Experimentally, a quasi-distributed FMCW system with three cascaded FP-Sens was employed to obtain high spatial resolution fiber-optic link information and to verify the feasibility of multipoint salinity sensitization. The sensitivity of the FP-Sen reached 2.235 nm/‰ within the salinity range of 25-30‰, achieving a 9-times sensitivity enhancement compared to a single sensor. Additionally, stability analysis using violin plots demonstrated that the fabricated FP-Sens exhibited good stability. The proposed technique offers clear advantages in practical applications requiring a large number of sensitized sensing points.

Ultra-high sensitivity methane gas sensor based on vernier effect in double D-shaped and cryptophane-A film-coated photonic crystal fiber: Design and FEM simulation

In this study, a highly sensitive gas pressure sensor based on two Fabry–Perot interferometers (FPIs) in parallel with the Vernier effect is designed and demonstrated. In the sensor, FPI1 and FPI2 were used as the detection and reference units, respectively. FPI1 and FPI2 have similar structures, both comprising a single-mode fiber and capillary splicing. However, the microaperture is processed on the capillary of the FPI1 with a femtosecond laser, enabling the external gas to enter the FPI1 cavity through the microaperture channel to realize the gas pressure measurement. The Vernier effect is achieved by superimposing the reflective spectra of FPI1 and FPI2, which have a small cavity length. The gas pressure response, repeatability, and stability of the sensor structures were investigated. The sensitivity of the sensor was improved owing to the Vernier effect. Experimental results indicate that the sensor sensitivity is up to 47.76 nm MPa−1, which is 11.9 times that of a single FPI1 sensor without the Vernier effect. The measured temperature cross-sensitivity of the sensor is approximately 5.1 kPa/ °C. In addition, the sensor has the advantages of simple manufacturing, robust structure, and stable operation. Finally, the manufacturing method of FPI and the parallel connection mode of FPIs could also be used in other sensing fields, providing an alternative design scheme for high-sensitivity sensors.

Optical fiber sensor with a lateral-offset structure assisted by virtual vernier effect for stretching strain measurement

Temperature measuring is a daily procedure carried out worldwide in practically all environments of human activity, but it takes particular relevance in industrial, scientific, medical, and food processing and production areas. The characteristics and performance of the temperature sensors required for such a large universe of applications have opened the opportunity for a comprehensive range of technologies and architectures capable of fulfilling the sensitivity, resolution, dynamic range, and response time demanded. In this work, a highly sensitive fiber optic temperature sensor based on a double-cavity Fabry-Perot interferometer (DCFPI) is proposed and demonstrated. Taking advantage of the Vernier effect, we demonstrate that it is possible to improve the temperature sensitivity exhibited by the polymer-capped fiber Fabry-Perot interferometer (PCFPI) up to 39.8 nm/°C. The DCFPI is sturdy, reconfigured, and simple to fabricate, consisting of a semi-spherical polymer cap added to the surface of the ferrule of a commercial single-mode fiber connector (SMF FC/PC) placed in front of a mirror at a proper distance. The length of the air cavity (Lair) was adjusted to equal the thickness of the polymer cap (Lpol) plus a distance δ to generate the most convenient Vernier effect spectrum. The DCFPI was packaged in a machined, movable mount that allows the adjustment of the air cavity length easily but also protects the polymer cap and simplifies the manipulation of the sensor head.

Purpose The purpose of this paper is to design a high-sensitivity temperature sensor based on the vernier effect (VE) of dual-parallel Fabry-Perot interferometers (FPIs). Design/methodology/approach Initially, ultraviolet (UV) glue is coated on the end-face of a smooth single-mode fiber (SMF) and then tapered using a charged coupled device (CCD) precision displacement platform. Once the UV glue solidified, it is cut flat with a cutting tool to create FPI1. Subsequently, an SMF with a smooth end-face is inserted into a ceramic ferrule, and the other end-face of the ceramic ferrule is coated with polydimethylsiloxane (PDMS) to form FPI2 and FPI3. By adjusting the distance between the end-face of the SMF and the end-face of the ceramic ferrule, FPI2 and FPI3 are made to have different cavity lengths and free-spectral ranges (FSRs). In addition, the FSR of FPI2 is approximately equal to that of FPI1, while the FSR of FPI3 is roughly twice that of FPI1. When the temperature increases, the interference spectral lines of FPI1 gradually red-shift, whereas those of FPI2 and FPI3 gradually blue-shift. The parallel combination of FPI1 and FPI2 results in an enhanced traditional vernier effect (TVE), and the parallel combination of FPI1 and FPI3 leads to an enhanced harmonic vernier effect (HVE). Findings Experiments demonstrate that the temperature sensitivity of FPI1 is 0.17 nm/°C. The temperature sensitivities of FPI2 and FPI3 are −0.46 nm/°C and −1.90 nm/°C, respectively. Within the 30–37 °C temperature range, the enhanced traditional vernier effect sensor S1, formed by the parallel connection of FPI1 and FPI2, attains a temperature sensitivity of 9.42 nm/°C. The enhanced harmonic vernier effect sensor S2, constructed by the parallel combination of FPI1 and FPI3, reaches a temperature sensitivity of −29.59 nm/°C, respectively. These sensitivities represent a significant improvement over those of a single FPI. Originality/value These experimental results validate that the enhanced VE and the enhanced HVE represent an effective approach for enhancing sensor sensitivity. Moreover, compared with the enhanced VE, the enhanced HVE exhibits a more pronounced impact.

A novel highly sensitive airflow sensor based on Fabry–Perot interferometer (FPI) and Vernier effect is proposed and demonstrated. The sensor is fabricated by splicing a section of hollow-core fiber (HCF) between a lead-in single mode fiber (SMF) and a section of SMF, which is almost one-fifteenth the length of the HCF. Airflow changes the cavity length of the FPI, which leads to the shift of the reflection spectrum. The reflection beam from the last end of the SMF is utilized to generate the Vernier effect, which enlarges the shift of the spectrum for 9.57 times than that of a single FPI. According to the experimental results, when the airflow ranges from ${\text{0 to 7 m/s}}$ , the spectrum of the sensor shifts as high as 7.9 nm which is almost eight times more than that of the self-heating sensor based on silver-coated FBG. And the highest airflow velocity sensitivity of the sensor can reach ${\text{1.541 nm/(m/s)}}$ in the region of ${\text{3m/s} \sim {7m/s}}$ . Besides, the sensor has a series of advantages such as fast response, low cost, compact size, and reflection measurement.

The Vernier effect is often utilized to boost the sensing ability of optical fiber sensors. In this paper, theoretical model of cascaded Fabry-Perot interferometer (FPI) with thin film based on Vernier effect is established. The sensitivities of the envelope spectra, thin film cavity and mixed cavity of air-thin film are analyzed qualitatively. According to the theoretical analysis, although sensitivity from mixed cavity of air-thin film is amplified, the value is equal to the sensitivity of sing thin film cavity. Experimental verification is carried out by an example of thin film named polydimethylsiloxane (PDMS) polymer. Herein, a new FPI constructed by air cavity from a hollow-core fiber, PDMS cavity, and air-PDMS mixed cavity is proposed and demonstrated. In order to facilitate the generation of the Vernier effect, the length of the PDMS cavity is intentionally designed shorter than the air cavity, making the free spectral range of the air-PDMS cavity and air cavity is approximately equal. The temperature change makes the refractive index and thermal expansion of PDMS change, while gas pressure change results in elastic deformation of PDMS. The Vernier envelope wavelength shifts with the temperature and gas pressure change. The proposed FPI features high temperature and gas pressure sensitivities of 3.07 nm/℃, and 23.07 nm/MPa, and a high magnification factor of 17 when the lengths of HCF and PDMS are 82.5 and 3.7 μm, respectively. The experimental results show that the temperature and pressure sensitivities of the cascaded FPI’s envelope spectra are equal to the sensitivity of a single thin film microcavity, and the theoretical calculation is in good agreement with the experimental verification. The theoretical model is also applicable to thin film prepared by other polymer materials. Additionally, the proposed FPI has good stability, reversibility, and repeatability, which is a good choice in the field of optical fiber sensing.

A highly sensitive fiber temperature sensor based on in-line Mach-Zehnder interferometers (MZIs) and Vernier effect was proposed and experimentally demonstrated. The MZI was fabricated by splicing a section of hollow core fiber between two pieces of multimode fiber. The temperature sensitivity obtained by extracting envelope dip shift of the superimposed spectrum reaches to 528.5 pm/°C in the range of 0 °C-100 °C, which is 17.5 times as high as that without enhanced by the Vernier effect. The experimental sensitivity amplification factor is close to the theoretical predication (18.3 times).The proposed sensitivity enhancement system employs parallel connecting to implement the Vernier effect, which possesses the advantages of easy fabrication and high flexibility.

Fabry-Perot parallel type high sensitivity fiber optic temperature sensor based on vernier effect beyond free spectral range measurement

We propose and experimentally demonstrate a refractive index (RI) sensor based on cascaded microfiber knot resonators (CMKRs) with Vernier effect. Deriving from high proportional evanescent field of microfiber and spectrum magnification function of Vernier effect, the RI sensor shows high sensitivity as well as high detection resolution. By using the method named "Drawing-Knotting-Assembling (DKA)", a compact CMKRs is fabricated for experimental demonstration. With the assistance of Lorentz fitting algorithm on the transmission spectrum, sensitivity of 6523nm/RIU and detection resolution up to 1.533 × 10(-7)RIU are obtained in the experiment which show good agreement with the numerical simulation. The proposed all-fiber RI sensor with high sensitivity, compact size and low cost can be widely used for chemical and biological detection, as well as the electronic/magnetic field measurement.