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.

The optical analog of the Vernier effect applied to fiber interferometers is a recent tool to enhance the sensitivity and resolution of optical fiber sensors. This effect relies on the overlap between the signals of two interferometers with slightly detuned interference frequencies. The Vernier envelope modulation generated at the output spectrum presents magnified sensing capabilities (i.e., magnified wavelength shift) compared to that of the individual sensing interferometers that constitute the system, leading to a new generation of highly sensitive fiber sensing devices. This review analyses the recent advances and developments of the optical Vernier effect from a fiber sensing point‐of‐view. Initially, the fundamentals of the effect are introduced, followed by an extensive review on the state‐of‐the‐art, presenting all the different configurations and types of fiber sensing interferometers used to introduce the optical Vernier effect. This paper also includes an overview of the complex case of enhanced Vernier effect and the introduction of harmonics to the effect.

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.

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.

In this work, we present a high-sensitivity fiber-optic temperature sensor based on the enhanced Vernier effect. The sensor consists of a cascade of three Fabry–Perot interferometers (FPIs), where FPI1 contains a polydimethylsiloxane (PDMS) cavity, FPI2 contains an air microcavity, and FPI3 contains a PDMS–air hybrid cavity. Since the effective lengths of the PDMS cavity and the PDMS–air hybrid cavity are close to each other, the superposition of the reflection spectra of FPI1 and FPI3 produces the traditional Vernier effect. Due to the thermo-optic effect and thermal expansion effect of PDMS and air, the reflection spectra of FPI1 and FPI3 will vary in the opposite direction with the temperature change, to achieve the enhanced Vernier effect. A temperature sensitivity of −35.45 nm/°C much higher than that of the fiber FPI sensor based on conventional Vernier effect is achieved, in good agreement with the theoretical analysis. The proposed sensor has the advantages high stability, mechanical strength, small size, and low cost, which has a great potential for marine environment detection and bioscience.

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.

We have proposed and experimentally demonstrated an ultrasensitive fiber-optic temperature sensor based on two cascaded Fabry-Perot interferometers (FPIs). Vernier effect that significantly improves the sensitivity is generated due to the slight cavity length difference of the sensing and reference FPI. The sensing FPI is composed of a cleaved fiber end-face and UV-cured adhesive while the reference FPI is fabricated by splicing SMF with hollow core fiber. Temperature sensitivity of the sensing FPI is much higher than the reference FPI, which means that the reference FPI need not to be thermally isolated. By curve fitting method, three different temperature sensitivities of 33.07, -58.60, and 67.35 nm/°C have been experimentally demonstrated with different cavity lengths ratio of the sensing and reference FPI, which can be flexibly adjusted to meet different application demands. The proposed probe-type ultrahigh sensitivity temperature sensor is compact and cost effective, which can be applied to special fields, such as biochemical engineering, medical treatment, and nuclear test.

A white-light interferometry based on the Fourier transform method is proposed to measure the optical path difference (OPD) of the high-finesse fiber optic extrinsic Fabry–Pérot interferometric (EFPI) sensor. The Fourier spectrum of the transmission spectrum signal consists of multiple frequency components because of the multiple-beam interference occurring in the high-finesse EFPI sensor. The high-order frequency component of the Fourier spectrum can be extracted by the Fourier transform method to recover the OPD in order to overcome the spectrum overlapping, which happens when the OPD of the EFPI sensor is short. In the experiment, a high-finesse fiber optic EFPI sensor with the cavity length of 120 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(\mu \) </tex-math></inline-formula> m is measured, and the second-order frequency component was extracted to recover the cavity length. The standard deviation of the measurement results was 9.132 nm. The measurement range of the Fourier transform method was effectively extended to the short OPD.

In this paper, we report a sensitivity-controllable refractive index (RI) sensor based on a reflective θ-shaped microfiber resonator cooperated with Vernier effect. The θ-shaped microfiber resonator is a reflective all-fiber device with comb spectrum under weak coupling condition. By cascading it with a fiber Fabry-Perot interferometer, Vernier effect is generated to demodulate surrounding RI with enhanced sensitivity. Theoretical analysis reveals that RI sensitivity of the combined structure with Vernier effect is m times higher than the sensitivity of singular θ-shaped microfiber resonator. Moreover, by adjusting cavity length of the θ-shaped microfiber resonator, magnification factor M = (m + 1) can be tuned which enables the RI sensitivity to be controlled. Experimental result demonstrates that the RI sensitivity can be widely tuned from 311.77 nm/RIU (Reflective index unit) to 2460.07 nm/RIU when the cavity length of the θ-shaped microfiber resonator is adjusted from 9.4 mm to 8.7 mm. The θ-shaped microfiber resonator based all-fiber RI sensor featuring controllable sensitivity and compact size can be widely used for chemical and biological detections. The proposed scheme of generating Vernier effect also offers a universal idea to increase measurement sensitivity for optical fiber sensing structures with comb spectrum.

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

We propose that the sensitivity can be effectively improved by spatial-frequency doubling of the sensing signal before the signal processing assisted Vernier-effect demodulation via a single fiber interferometer, which has been proven to have the same effect as physically increasing the optical path difference (OPD) in an interferometer but keeps the sensor small in size and does not introduce any additional crosstalk and cost. In the proposed scheme, only one fiber interferometer is used for sensing. The sensing spectra are squared to double their spatial frequencies, and then, an artificial reference spectrum (ARS) is extracted from one of the squared spectra and multiplied by each squared spectrum to form the Vernier effect. To validate the principle, a widely used Sagnac interferometer (SI) with a conventional polarization-maintaining fiber (PMF) of only 10 cm in length is designed for temperature sensing. Significantly, by simply doubling the spatial frequency of the sensing signal, the magnification of Vernier effect is improved from 4.96 to 74.82, resulting in an ultrahigh sensitivity of 117.17 nm/°C.

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.

Sensing at small dimensions in biological and medical environments requires miniaturized sensors with high sensitivity and measurement resolution. In this work a small optical fiber probe was developed to apply the Vernier effect, allowing for enhanced temperature sensing. Such effect is an effective way of magnifying the sensitivity of a sensor or measurement system in order to reach higher resolutions. The device is a multimode silica Fabry-Perot interferometer structured at the edge of a tapered multimode fiber by focused ion beam milling. The Vernier effect is generated from the interference between different modes in the Fabry-Perot interferometer. The sensor was characterized in temperature, achieving a sensitivity of -654 pm/&deg;C in a temperature range from 30&deg;C to 120&deg;C. The Vernier effect provided a temperature sensitivity over 60-fold higher than the sensitivity of a normal silica Fabry-Perot interferometer without the effect. The temperature resolution obtained was 0.14&deg;C, however this value was limited by the resolution of the OSA and can be improved further to less than 0.015&deg;C.

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.

Programmable integrated photonics has emerged as a powerful platform for implementing diverse optical functions on a single chip through software-driven reconfiguration. At the core of these processors, photonic waveguide meshes enable flexible light routing and manipulation. However, recirculating waveguide meshes are fundamentally limited by the fixed dimensions of their unit cells, constraining their spectral and temporal resolution. These limitations hinder broadband signal processing and high-precision delay-line applications. Here, we introduce the concept of non-uniform programmable waveguide meshes by incorporating defect cells into an otherwise uniform hexagonal architecture. These defect cells preserve an external hexagonal perimeter for seamless integration while embedding smaller internal subcells that modify the spectral response via the Vernier effect. By coupling cells with different optical path lengths, we achieve a free spectral range multiplication of up to tenfold, reaching 133 GHz—surpassing the capabilities of conventional silicon ring resonators. Additionally, we demonstrate a dramatic reduction in sampling times from 75 ps to 7.5 ps, enabling ultra-fast optical signal processing and high-precision delay tuning. This approach unlocks new degrees of freedom in programmable photonic circuits, offering enhanced spectral and temporal tunability. Beyond broadband signal processing, it paves the way for advanced applications in topological photonics, quantum information processing, and high-speed optical computing.