Multimode optical fiber sensors: from conventional to machine learning-assisted

Multimode fiber (MMF) sensors have been extensively developed and utilized in various sensing applications for decades. Traditionally, the performance of MMF sensors was improved by conventional methods that focused on structural design and specialty fibers. However, in recent years, the blossom of machine learning techniques has opened up new avenues for enhancing the performance of MMF sensors. Unlike conventional methods, machine learning techniques do not require complex structures or rare specialty fibers, which reduces fabrication difficulties and lowers costs. In this review, we provide an overview of the latest developments in MMF sensors, ranging from conventional methods to those assisted by machine learning. This article begins by categorizing MMF sensors based on their sensing applications, including temperature and strain sensors, displacement sensors, refractive index sensors, curvature sensors, bio/chemical sensors, and other sensors. Their distinct sensor structures and sensing properties are thoroughly reviewed. Subsequently, the machine learning-assisted MMF sensors that have been recently reported are analyzed and categorized into two groups: learning the specklegrams and learning the spectra. The review provides a comprehensive discussion and outlook on MMF sensors, concluding that they are expected to be utilized in a wide range of applications.


Introduction
Optical systems were not at the forefront of technology development for a considerable period until the invention of the laser in the 1960s [1].This breakthrough made it possible to have a functional and practical optical system in the foreseeable future.In 1966, Kao and Hockham made a significant discovery in fiber optics by predicting that the strong attenuation of glass was not an intrinsic property but rather caused by chemical impurities in the glass composition [2].Their meticulous calculations on transmitting light over long distances through optical glass fibers predicted the possibility of producing glass with an attenuation rate of no more than 20 dB km −1 , a significant improvement from the common 1000 dB km −1 rate at that time.The first graded-index fiber, which had an attenuation rate below 100 dB km −1 , was introduced in 1969 [3].Since then, tremendous advancements have been made in this field.Merely one year later, in 1970, the first single-mode fiber (SMF) with an attenuation rate below 20 dB km −1 was developed [4].With a more profound comprehension that the loss is wavelength-dependent, the milestone of 1 dB km −1 was reached in 1976 [5].Finally, in 1979, a loss of only 0.2 dB km −1 at 1550 nm [6], which is very close to the limit of what is possible at all with fused silica, was realized.As the study of fiber optics became more exhaustive [7,8], advancements in manufacturing led to the development of various auxiliary components.The evolution of optical fibers not only revolutionized optical communications [9,10], but also paved the way for the creation of optical fiber sensors [11,12].
Over the past two decades, optical fiber sensors have experienced tremendous growth, with the technology now offering significant practical advantages over electrical sensors.This is due to their intrinsic characteristics, which include compact size, lightweight design, fast response times, immunity to electromagnetic interference, remote sensing capabilities, and resistance to corrosive and hazardous environments [13][14][15][16][17][18][19][20][21].Compared to the SMF, multimode fiber (MMF) has a much larger core and supports multiple modes.When the light is injected into an MMF, the propagation velocity of each mode is highly dependent on the incident angle.Light injected at a larger angle will travel a longer path within the fiber.As a result, different modes will travel varying distances, leading to a phenomenon known as modal dispersion.Our previous work recapped various optical fiber sensors based on multimode interference (MMI) [22].However, it is worth noting that MMF sensors are not limited to MMI-based designs.In fact, many different types of MMFs, including specialty fibers, such as microfiber [23,24], square-core fiber [25,26], and thin-core fiber [27], have been extensively developed and utilized in sensing applications.Recently, the blossom of machine learning methods, which can benefit the analysis of the MMI in MMFs, paves a new path to enhance the performance of MMF sensors and new applications like biosensors.
In this paper, we summarize an overview of the representative MMF sensors from conventional (i.e.not machine learning-assisted) to machine learning-assisted methods in the last decade.Section 2 focuses on the conventional methodbased MMF sensors and categorizes them based on their applications, such as temperature and strain sensors, displacement sensors, refractive index (RI) sensors, curvature sensors, bio/chemical sensors, and other sensors.Section 3 delves into the topic of machine learning-assisted MMF sensors, while section 4 offers insightful discussions and predictions regarding the future challenges and advancements in this field.In conclusion, this work is expected to inspire researchers to explore novel techniques for enhancing the performance of MMF sensors in the future.

Conventional methods-based multimode fiber sensors
Countless MMF sensors have been designed and widely used in various sensing applications [28][29][30][31].Traditionally, the performance of these sensors has been improved through structural design modifications [32,33].This section provides a comprehensive categorization of MMF sensors based on their sensing applications, including temperature and strain sensors, displacement sensors, RI sensors, bio/chemical sensors, and curvature sensors.Their distinct structural configurations and sensing properties are reviewed in detail.

Temperature and strain sensors
Temperature and strain sensing is almost an everlasting topic [34][35][36][37][38]. Numerous representative MMF sensors have been reported in the last decade.A notable example is the alcohol-filled simplified hollow-core (SHC) photonic crystal fiber (PCF) sensor proposed by Shuhui Liu et al [39] This sensor operates on the anti-resonant reflecting guidance mechanism and is achieved by infiltrating alcohol into a single air hole in the air cladding of the PCF (figure 1(a)).A double Fabry-Pérot (F-P) resonator was formed by the combination of the alcohol-filled layer and silica cladding in the cross-section of a PCF.This induces leaky mode resonance at the resonant wavelengths of the double-layered F-P resonator, resulting in periodic lossy dips in the transmission spectrum that are highly sensitive to the surrounding environment.The wavelengths of the lossy dips shifted to the shorter wavelengths with increasing temperature, and a sensitivity of −0.48 nm • C −1 was obtained between room temperature and 60 • C. Further, the lossy dips exhibited linear decay against the rising water level, and a sensitivity of 1.1 dB mm −1 was achieved.
In 2014, Zhang et al [40] presented a temperature sensor consisting of a single-mode-multimode-single-mode (SMS) structure with a specifically designed and synthesized thermooptic polymer cladding (figure 1(b)).The MMF cladding was removed entirely and replaced by a 1 mm-diameter polymer cladding designed and synthesized for two characteristics, i.e. proper RI and high thermo-optic coefficient.The RI of the polymer is higher than that of the MMF core at room temperature but reduced by increasing temperature.Therefore, Figure 1.Schematic diagrams of (a) alcohol-filled SHC-PCF in an SMS structure [39], (b) SMS structure with polymer coating [40], (c) FBG in SMS structure [41], (d) two cascading LPGs [43], (e) SMF-MMF FBG [44], (f) balloon-like bent SMS structure [45], (g) all-fiber MZI with SPF-TCPCF [46]. it leads to two different mode interferences (leaky mode and guided mode) at different temperatures, enlarging the measuring range of temperature.The obtained maximum temperature sensitivities were 1.4 dB • C −1 below 61 • C −1 and 15 nm • C −1 in the range of 72 • C-75 • C.
Similarly, Song et al [41] developed a fiber sensor capable of measuring temperature and strain simultaneously using fiber Bragg gratings (FBGs) in the multimode section of an SMS structure (figure 1(c)).This innovative structure utilized the spectral properties of both the FBG and SMS to accurately measure and differentiate the temperature and strain responses of the two signals.The authors also noted that the FBG writing process was employed as an effective means to fine-tune and optimize the SMS transmission spectrum for sensing.
Besides FBG, long-period gratings (LPGs) in SMF have also been demonstrated for simultaneous temperature and strain measurement [42].In 2014, Wang et al [43] presented a hybrid fiber sensor for the simultaneous measurement of temperature and strain based on MMF and LPGs.The structure was similar to the SMS structure, where a segment of a fewmode fiber (FMF) was used as the MMF section (figure 1(d)).Two cascading LPGs were inscribed in the FMF and the output SMF sections.Simultaneous temperature and strain measurements were realized by measuring the different resonance dip shifts of these two LPGs.A temperature sensitivity of 46.4 pm • C −1 was achieved in the range of 30 • C-90 • C, while the strain sensitivity was −2.9 pm µε −1 in the range of 0-800 µε.
In 2015, Sun and Wu [44] investigated the combination of MMI and multimode FBG for simultaneous strain and bending measurement, as shown in figure 1(e).The MMF between SMF and FBG functioned as the transmitting MMF.The bending of this section distorted the MMI, leading to a redistribution of mode population that can be detected by analyzing power redistribution at various wavelengths of the multimode FBG.Additionally, bending affected the coupling efficiency of reflected modes from MMF to SMF, resulting in varying trends in the power of reflected modes.Consequently, the bending can be measured by ratiometrically detecting the power change of different reflected modes.However, as the FBG was not bent, its wavelength was not influenced by the bending and was able to be used for strain sensing.Therefore, simultaneous/discriminating strain and bending sensing were achieved by measuring the reflected power and wavelength of the proposed structure.The measured strain and bending sensitivities were 0.92 pm µε −1 and 2.1 dB mm −1 .
Mohd Noor et al [45] formed a simple low-temperature sensor utilizing MMI in a balloon-like SMS structure (figure 1(f)).As the MMF is bent with a small curvature (mimicking a balloon shape), the MMI in the MMF is passed through the cladding and excited into the acrylate coating of the MMF.Hence, the thermo-optic effects of this structure are also influenced by the acrylate coating on the MMF.The acrylate material coating of the MMF has a significant thermo-optical coefficient (TOC), which results in boosted temperature sensitivity.A maximum temperature sensitivity of −2060 pm • C −1 was obtained from the wavelength shift and −25.1 nW • C −1 from intensity change in the range of 27 • C-31 • C, respectively.Note that the temperature sensitivity and measurement range can be further improved based on the MMF bending radius, core diameter, and length.Schematic diagrams of (a) two FBGs in untapered and tapered regions of an SMF combined with an SMS structure containing an NCF [47], (b) SGMS structure [48], (c) T-SMS structure [49], (d) S-tapered MMF structure (reproduced from [50].CC BY 4.0), (e) reflective bi-core fiber structure [51], (f) MSM structure with coating [52], (g) smartphone-based chirped FBG in MMF structure (© 2021 IEEE.Reprinted, with permission, from [53]).
Naeem et al [46] experimentally demonstrated a temperature sensor based on an all-fiber Mach-Zehnder interferometer (MZI) using a selectively polymer filled (SPF) two-core photonic crystal fiber (TCPCF).Figure 1(g) shows that the TCPCF has two independent cores (Core-1 and Core-2) surrounded by air holes, and the air holes in the cladding of Core-1 are selectively infiltrated with UV-curable polymer while the remaining air holes are kept unfilled.The polymer material had a high TOC, which made the effective index of Core-1 mode sensitive to the ambient temperature change, while the other core (Core-2) was insensitive.The large mismatch in the thermo-optic property between the cores led to a significant temperature sensitivity enhancement and a sensitivity of 1.595 nm • C −1 was achieved.
In 2016, a fiber sensor based on a combination of MMI, fiber tapering, and FBGs was proposed by Oliveira et al [47] for simultaneous measurement of strain, temperature, and RI (figure 2(a)).Two FBGs were written in the same SMF: one in the untapered and the other in the tapered region.A no-core fiber (NCF) section was spliced between the SMF containing FBGs and another SMF to generate the SMS structure.As each section of the sensor (FBG1, FBG2, and the MMI) showed discriminate responses to temperature, strain, and RI, it was feasible to measure multi-parameters simultaneously.The results showed a sensitivity of −1.29 pm µε −1 , 34.82 pm • C −1 , and 116.5 nm RIU −1 (refractive index unit), respectively, for strain, temperature, and RI.This work also indicated that a simple production and combination of all the parts involved is attractive for optical fiber sensing.
A strain sensor based on a single-mode-gourd-shapedmultimode-fiber-single-mode (SGMS) fiber structure was proposed by Tian et al [48] in 2017 (figure 2(b)).To achieve the desired gourd shape, only the cladding regions at the distal ends of two MMFs were reshaped to form hemispheres.These were then spliced together using a standard commercial arc fusion splicer, creating a gourd-shaped segment that formed an F-P cavity between the two distal ends of the MMFs.This section was then sandwiched between two SMFs to complete the SGMS structure.When light is transmitted through the F-P cavity, a small portion of the transmitted light intensity escapes to the external regions, primarily consisting of highorder modes that are excited and transmitted in the MMF.Due to the gourd-shaped joint, some high-order modes become leaky modes interacting with the ambient environment.As a result, a composite interference pattern, combining the inherent MMI and F-P interference, is observed, demonstrating a significant improvement in strain sensitivity compared to the traditional SMS structure.The experimental results determined a strain sensitivity of −2.6 pm µε −1 in the range of 0-1000 µε .
Sun et al [49] introduced high-order modes interference based on a twisted SMS structure (T-SMS) for simultaneous measurement of temperature and strain, where the MMF section was heated and twisted to form a kind of periodic circular trace on the surface of the MMF (figure 2(c)).This structure can couple more power of the light into the MMF cladding, and high-order modes are excited effectively.The discrimination of temperature and strain measurement was realized by the method of spatial frequency demodulation, which means the spatial frequency spectrum was transformed by the fast Fourier transform.The obtained maximum temperature and strain sensitivities are 17.33 pm • C −1 and −7 pm µε −1 , and high measurement resolutions reached ±0.89 • C and ±2.14 µε.This work has great potential in the dual-parameter measurement of temperature and strain with high resolution.
In 2018, Tian et al [50] proposed a unique MMF sensor, an S-tapered MMF structure (figure 2(d)), based on composite interference as a high-sensitivity strain sensor.The MMF section of a conventional SMS structure was tapered into an S-shaped form using a standard fusion splicer, which introduced an extra MZI within the MMF section.Similar to [48], when the light propagates through the S-tapered region, a small portion of the light leaks out of the fiber.Combining the inherent MMI, the composite interference was established.Therefore, two interference dips were observed in the wavelength domain, which also gave the possibility for dualparameter measurement simultaneously.The maximum strain sensitivity of −103.8 pm µε −1 was achieved with a strain resolution of 0.2 µε, which is almost 33 times higher than the strain sensitivity of a conventional SMS structure.The proposed sensor can be potentially utilized in high-accuracy strain measurement scenarios.
In 2019, Lobo Ribeiro et al [51] proposed a reflective bicore fiber structure for strain, temperature, and torsion sensing (figure 2(e)).The bi-core fiber was spliced to an SMF, where the optical power transmitted through the SMF was coupled equally into the two cores and continued propagating and coupling between both cores over the bi-core fiber.The other distal end of the bi-core fiber was silver-mirror-coated, which reflected the optical power.The reflected optical power was transmitted back and partially coupled into the SMF core.The sensing mechanism was the measurand induced shift of the phase difference between the light propagating in these two cores.The sensitivities were obtained as −39.1 pm • C −1 , −1.64 pm µε −1 , and −2 pm/|degree| for temperature, strain, and torsion.The result also indicated that it was feasible to measure torsion up to an amplitude of 180 • , but it was not possible to discriminate clockwise and anti-clockwise torsions.
Opposite to the SMS structure, the multimode-singlemode-multimode (MSM) fiber structure was also utilized in sensing applications.Huang et al [52] fabricated a temperature and RI sensor based on an MSM structure coated with graphene-metal hybrid films (figure 2(f)).It was demonstrated that a gold film with a graphene-topping layer or graphene film with a gold-topping layer affected the RI sensitivity due to the changes in the plasmon resonance properties.The surface plasmon resonance (SPR) effect was enhanced by absorbing the spherical gold-silver core-shell nanoparticles (Au@Ag NPs) on the surface of the graphene-gold film.The RI sensitivity reached 1591 nm RIU −1 and 3680 nm RIU −1 when the RIs were 1.3330 and 1.4005, respectively.For temperature measurement, this surface was further modified with polydimethylsiloxane (PDMS).Therefore, a high sensitivity of 1.02 nm • C −1 was achieved with good repeatability.These high sensitivities indicated that this configuration is potentially suitable for many fields, including nano-medicine.
Portable optical fiber sensing systems are certainly one of the current improvement trends.In most cases, the usage of optical fiber sensors necessitates the presence of a light source, as well as additional devices such as an interrogator and an optical spectrum analyzer (OSA).However, it is essential to note that the need for an OSA can be avoided in specific schemes, such as edge-filtering schemes.Nowadays, smartphones, not only for communication, are capable of processing, storing, and exchanging various information and data for external applications.The LED flash, CMOS camera, and microprocessor in the smartphone can perfectly function as the light source, optical detector, and processing system in a basic optical sensing system.Several smartphone-based optical fiber sensors and spectrometers have been reported [54][55][56][57][58][59].In smartphone-based systems without external devices, such as a separate light source, MMF would be a more suitable choice, as LEDs only emit spatially incoherent light.
In 2021, Markvart et al [53] developed a smartphone-based FBG strain sensor interrogation system with a chirped FBG inscribed in a graded-index multimode fiber (GIMMF), as shown in figure 2(g).This prototype was tested with strain sensing and validated by comparing it to the use of a commercial spectrometer.A strain sensitivity of 0.401 nm mε −1 was achieved in the range of 0-2.4 mε.This work paved a new way for ultra-low-cost and portable sensing systems by combining the advanced development of optical fiber sensors and smartphones.
The sensing applications, sensor configurations, MMF types, measurement ranges, and sensitivities of the fiber sensors for temperature and strain sensing mentioned above are summarized in table 1.

Displacement sensors
Displacement detection has garnered significant attention from researchers due to its crucial role in smart structure monitoring, particularly in infrastructure, where it is one of the most critical mechanical parameters.Additionally, there is a high demand for micro-displacement precision measurement in geological monitoring, equipment control, and microscopic techniques.Various structures featuring SMFs have found widespread use in current applications, such as an MZI [60], an FBG [61], and an LPG [62].In this section, we present several representative displacement sensors using various MMFs over the past decade to give a guideline for developing MMFbased displacement sensors.
The most common MMF-based sensor, the SMS structure, was used by Wu et al [63] for the simultaneous measurement of displacement and temperature sensing, as shown in figure 3(a).The MMF section was in contact with a circular mandrel with a diameter of 1.4 mm, which lies in the middle of the MMF section (point B).The displacement was applied by the translation stage moving from point C to C ′ so the MMF section was bent around the mandrel.The experiment demonstrated a displacement sensitivity of 5.89 pm µm −1 in the range of 0-600 µm and a temperature sensitivity of 11.6 pm In 2011, Fan et al [64] fabricated PCF coils and experimentally investigated the possibility of transverse displacement sensing (figure 3(b)).First, the birefringent characteristics of the PCF coils were studied.The PCF coils were fabricated by winding PCFs on straws and put into a Sagnac loop interferometer to obtain the birefringent properties.Measuring the birefringence value with variant fiber turns indicated that the birefringence values are almost independent of fiber turns but depend on the bending radius.According to this property, the PCF coil was utilized for transverse displacement sensing.A fabricated PCF coil with a radius of 0.61 cm was placed between two planes, which applied a transverse displacement.A very high displacement sensitivity of 90.4 nm mm −1 was achieved in the range of 0-0.25 mm.
Similarly, Su et al [65] proposed a displacement sensor employing an FMF in an SMS structure with a helix coil shape (figure 3(c)).First, the intermodal interference between the LP 01 and LP 02 modes of the FMF under bending was studied theoretically and experimentally.It was observed that the critical wavelength shifted monotonically with curvature in a large range.Furthermore, critical wavelength detecting was proven more advantageous than the peaks/dips detecting method because it can avoid overlapping with adjacent peaks and sensitivity differences between peaks/dips at different wavelengths.Therefore, a displacement sensor employing an SMF-FMF-SMF structure inserted into a helix coil was be created.The pitch of the helix coil was changed when the distance between its two ends was changed, which resulted in the curvature variation of the FMF.A maximum sensitivity of 0.172 nm mm −1 was obtained in a wide range of 0-120 mm.
In 2017, Gao et al [66] tested a capillary-covered silica hollow-core fiber (HCF) for displacement sensing based on the anti-resonant reflecting optical waveguide (figure 3(d)).To create an F-P resonator in the silica cladding, a portion of the capillary was coated with a silver film on its internal surface.Subsequently, a segment of silica HCF was inserted into this capillary.The transmission spectrum exhibited lossy dips, indicating the achievement of the leaky mode of the guided light at the resonant wavelength of the F-P resonator.By adjusting the position of the capillary, the distance between the silver film and the silica HCF was modified, thereby influencing the effective reflectivity of the F-P  [64], (c) SMF-FMF-SMF structure with a helix coil shape (© 2016 IEEE.Reprinted, with permission, from [65]), (d) silica HCF covered with capillary [66], (e) Kretschmann configuration on a GIMMF (Reprinted with permission from [67] © The Optical Society), (f) balloon-shaped bent SMS structure (Reprinted with permission from [68] © The Optical Society), (g) SPR 3D micro-displacement fiber sensor (reproduced from [69].CC BY 4.0).resonator.Consequently, the transmission power of the dips changed.Therefore, displacement sensing was realized with a sensitivity up to 0.578 dB µm −1 , and this sensor was insensitive to temperature.
Zhu et al [67] demonstrated a micro-displacement sensor based on SPR by manufacturing a Kretschmann configuration on a GIMMF, as shown in figure 3(e).An SMF was used to change the radial position of the incident beam as the displacement.In the GIMMF, the angle (α) between the light beam and fiber axis is changed by the displacement (d).As this angle is closely related to the resonance angle, the resonance wavelength of the fiber SPR shifted with the changing displacement.Then, a short section at one distal end of the GIMMF and a step-index multimode fiber (SIMMF) were polished with the same angle (β).These two polished distal ends were spliced in a reversed shape.To further enhance the SPR effect, the polished surface of the GIMMF was coated with a 50 nm-thickness gold film.This sensor achieved a maximum sensitivity of 10.32 nm µm −1 with a minimum resolution of 2 nm in a wide range of 0-25 µm.In addition, sensitivity can be further improved by enlarging the fiber polishing angle, enlarging the RI of the external medium, or enlarging the numerical aperture (NA) of the GIMMF.Therefore, this micro-displacement fiber sensor will be a good candidate for many industrial applications.
Similar to [45], Tian et al [68] used the balloon-shaped bent SMS structure for displacement sensing (figure 3(f)).As the MMF section of the SMS structure was bent, the original MMI changed, while an extra MZI was introduced within the MMF section at a certain bending radius (determined as r = 9.60 mm).Thus, a composite interference based on the changed MMI and MZI, which improved the performance of the proposed sensor significantly, was established.The axial displacement was applied to the balloon-shaped section in the range of 0-100 µm, and a maximum displacement sensitivity of 0.51 dB µm −1 was obtained at the operation wavelength of 1654.7 nm.Additionally, a good repeatability of this sensor for displacement measurement was tested by increasing and decreasing displacement.
Recently, a three-dimensional (3D) micro-displacement fiber sensor based on SPR was designed and explained for the first time by Wei et al [69], which contained displacement fiber and sensing fiber, as shown in figure 3(g).The displacement fiber (on the left side) was formed by splicing the biased two-core fiber and GIMMF with a core diameter of 100 µm, which moved along the X-axis, Y-axis, and Z-axis to generate Y: 0 to 9 µm 3.543 nm µm −1 (Z) Z: 0 to 6 µm micro-displacement.The 3D micro-displacement sensing fiber was realized by fabricating two V-groove SPR sensing areas in the Y-axis (vertical) and Z-axis (horizontal) directions on the GIMMF with a core diameter of 105 µm.The two V-grooves were perpendicular to each other, and the inclined surfaces were coated with 50 nm-thickness gold film.The sensitivity of the proposed sensor was affected by the V-groove opening angle and the SPR resonance angle of the beam incident on the V-groove slope.It was found that the smaller the V-groove opening angle, the higher the micro-displacement sensitivity.
As the feasible angle that could be fabricated by CO2 laser was from 100 • to 116 • , the V-groove angle of 100 • was selected for high sensitivity.The average sensitivities of the resonance wavelength and the resonance valley depth in the X-axis direction are 0.148 nm µm −1 and −0.0014 a.u.µm −1 , respectively, in the range of 0-240 µm.In the Y-axis and Z-axis, the resonance wavelength sensitivities directions are −3.724nm µm −1 and 3.543 nm µm −1 , while the resonance valley depth sensitivities are −0.0458a.u.µm −1 and −0.0494 a.u.µm −1 , respectively.In addition, the testing results indicated the increasing distance between the two cores resulted in higher sensitivity (both wavelength and valley depth) but reduced detection range.Therefore, the biased two-core fiber can be selected according to the practical requirements.The sensing properties, sensor structures, MMF types, measurement ranges, and sensitivities of the displacement sensors mentioned above are summarized in table 2.

Refractive index sensors
The RI is a parameter that has garnered significant interest owing to its potential applications in various fields, such as chemical analysis, food testing, and biomedical diagnosis [70].In other words, RI optical fiber sensors are particularly useful in these areas, as they can be employed as either chemical or biosensors [71,72].
Since MMF core-based RI sensors attracted researchers' interest [73][74][75], in 2015, Shao et al [76] proposed an RI sensor based on an FBG connected with a segment of the MMF core, as shown in figure 4(a).When the sensor is used for RI sensing, the surrounding liquid functions as the cladding of the MMF core, which makes the effective indices of the core mode and high-order modes change more strongly than the normal MMF.The output power variation of the SMS structure with surrounding RI could modulate the core mode of FBG, which transforms the surrounding RI information into the reflective power changes of the FBG core mode.Therefore, the RI sensing was realized by measuring the power changes, and an enhanced sensitivity of 193.55 dB RIU −1 was achieved in the RI range of 1.3350-1.4042RIU.
Ujihara et al [77] fabricated a tapered polymer optical fiber (POF) utilizing internal heating caused by high-power propagating light (500 mW) instead of conventional external heating, which was demonstrated to be capable of generating evanescent waves that can measure the RI of liquid from 1.333 to 1.410.The tapered POF was placed in an SMS structure as the MMF, and the RI sensitivity of this easy structure was approximately 107 dB RIU −1 .Note that the initial induced loss, which remains after the fabrication of tapers, is a critical issue that needs to be addressed.Therefore, the tapers created using this technique may better suit RI sensing with a reflectometry configuration.
As the hetero-core structure is suitable for fabricating SPR sensors, it has been widely used in many applications, such as temperature and RI sensors [52,78].However, this structure has only one sensing channel.In 2017, a dual-channel SPR RI sensor based on a hetero-core configuration was demonstrated by Liu et al [79], which cascaded a conventional and polished hetero-core structure (figure 4(b)).The polished part was a circular truncated cone shape coated with 50 nm-thickness gold film.Due to the core diameter mismatch, when the light enters the SMF, most of the light wave leaks into the cladding of the  [80]), (d) SMF-FTMN-SMF [81], (e) SMS cascaded with a balloon-like SMF [82], (f) experimental setup to detect fiber speckle patterns with D-shaped MMF (© 2020 IEEE.Reprinted, with permission, from [83]), (g) MNM with coated NCF [84], (h) MMF-tapered HCF-MMF [85].
SMF and causes total internal reflection on the surface of the SMF.The surface plasmon wave is excited as the SMF surface is coated with gold film.Subsequently, the sensing information is carried by the reflective light and coupled into the output MMF.The experiments showed that at the polishing angle of 14 • and in the RI range of 1.333-1.385,the resonance wavelength range was 754-965 nm, which could be separated from that of the conventional hetero-core structure part (600-700 nm).Thus, a dual-channel sensor was established, and the sensitivity of the two channels is 1980.77nm RIU −1 and 4057.69 nm RIU −1 , respectively.
In 2019, a corrugated surface LPG fabricated on a commercial POF using a simple mechanical die press print method was developed by Xue et al [80] for RI sensing (figure 4(c)).This method is simple, low-cost, and efficient compared to using ultraviolet exposure or a femtosecond laser to write the LPGs in POFs.The sensing principle was based on the LPGsinduced propagation losses caused by the mode coupling among guided modes as well as between guided modes and leaky modes.The mode-coupling characteristics were affected by the variation in the environmental RI, which, in the end, affected the transmitted intensity.A characterization of this sensor for different POF diameters and grating periods was presented, which indicated that an LPG on a thin POF exhibits better RI sensitivity than on the thick one.The optimal parameters were decided as the grating period of 100 µm, groove depth of 65 µm, and tilted angle of 20 • , and the corresponding sensitivity was obtained as 2815% RIU −1 with a resolution of 1.39 × 10 −4 RIU in the RI range of 1.33-1.45.
One year later, Wang et al [81] reported a structure based on a folded-tapered multimode-no-core (FTMN) fiber sandwiched between two SMFs for simultaneous RI and temperature sensing (figure 4(d)).A composite interference was established by combining the inherent MMI and the folded-tapered-MMF induced MZI, as there were two main frequency components in the Fourier frequency spectra of the FTMN fiber interferometer.This sensor achieved a maximum sensitivity of 1191.5 nm RIU −1 with a resolution of 1.68 × 10 −5 RIU in the low RI range of 1.3405-1.3497,while a temperature sensitivity of 64.8 pm • C −1 with a resolution of 0.31 • C in the range of 20 • C-90 • C. The simultaneous measurement was achieved by monitoring the wavelength shifts of two interference dips in the transmission spectrum.
Coincidently, another balloon-like hybrid fiber sensor was proposed by Hu et al [82] for simultaneous RI and temperature measurement.Compared to [45,68], where the MMF was bent as balloon-like, this structure cascades an SMS and a bending SMF, i.e. balloon-like (figure 4(e)).The sensing principle was based on the combination of two interferences: the MMI in the SMS structure and the interference in the bending SMF between the core mode and the whispering gallery mode or the cladding mode.By carefully controlling the length of the MMF section in the SMS and the bending diameter of the bending SMF, two distinguishable dips without overlap were observed in the transmission spectrum.Therefore, the simultaneous measurement of RI and temperature was achieved by tracking the wavelength shifts of the two dips, respectively.The measured RI sensitivity was 331.71 nm RIU −1 in the RI range of 1.333-1.404,while the temperature sensitivity was Besides observing wavelength shifts or power changes in the transmission spectrum of the MMF, a new method of analyzing the output speckle patterns of a D-shaped MMF structure was proposed by Mu et al [83] for RI sensing (figure 4(f)).It has been established that the number of speckles in the specklegram is directly proportional to the number of excited modes.Consequently, more excited modes in multimode fiber (MMF) boost sensitivity to changes in the surroundings.One common approach to increase the number of excited modes is to introduce asymmetry in the excitation, such as using the D-shaped fiber.It enhances the exposure of the fiber to the external medium, thereby increasing the sensitivity of light guidance within the fiber.As a result, D-shaped MMF, also known as side-polished MMF, has found numerous applications, and our previous work has provided a comprehensive review of MMI-based sensors utilizing side-polished MMFs [22].The sensor was immersed in Glycerol solutions with different concentrations, and it was found that the regular variations of the zero-mean normalized cross-correlation coefficient for each speckle pattern correspond to different RIs.A wide RI range of 1.352-1.444was tested, and a high sensitivity of 10.47 RIU −1 was obtained, with the polishing depth being 18 µm and the length being 5 cm.
Hu et al [84] presented an SPR fiber sensor based on a multimode-no-core-multimode (MNM) structure for RI sensing (figure 4(g)).The NCF section was coated with chromium and gold to improve the sensing performance.The impact of the NCF diameter and length on the RI sensitivity was investigated.As different NCF diameters were tested, when the diameters of the MMF and the NCF were mismatched, two tapering areas occurred at the splicing joints.The experiments indicated that a shorter NCF with an appropriately larger diameter than the MMF diameter was optimal to boost the sensitivity.The maximum sensitivity was 11 792 nm RIU −1 with a maximum resolution of 2.04 × 10 −5 RIU in the RI range of 1.3330-1.4102.
Recently, a similar SPR sensor based on MMF-tapered HCF-MMF structure was explored by Teng et al [85] also for RI measurement.A new method, observing the resonance wavelength difference between the MMI wavelength and the SPR peak, was exploited, as the MMI peak and SPR peak shifted in opposite directions when the RI increased.As shown in figure 4(h), after the HCF was tapered, the hollow core of the HCF collapsed in the tapered region.Further, the HCF section was coated with a 50 nm-thickness gold film to improve the SPR effect.The sensing performance of the proposed structure with different taper ratios and HCF core diameters was investigated experimentally.A sensitivity up to 7592.25 nm RIU −1 was reached with a 30 µm core diameter HCF and a taper ratio of 3.3.
A summary of the RI sensors cited above is presented in table 3, including sensing properties, sensor structures, MMF types, measurement ranges, and sensitivities.

Curvature sensors
Curvature is a fundamental parameter in mechanical engineering, robotics, control engineering, security monitoring, and structural engineering.As a result, researchers have increasingly focused on curvature sensing, leading to the development of several curvature fiber sensors.Our previous work provided a brief overview of MMI-based curvature fiber sensors.In this section, we aim to highlight some exemplary MMF sensors that can serve as valuable references for the development of curvature fiber sensors in the future.
In 2020, Marrujo-García et al [86] proposed and studied an in-fiber MZI based on a SMF-MMF-HCF-MMF-SMF structure for curvature sensing, as shown in figure 5(a).The sensor was attached to a steel sheet with the aid of PDMS to ensure better controlling the sensor curvature and also create a package for practical applications, e.g.structural health monitoring.When the sensor was bent, the core and cladding modes experienced different bending losses, causing their output intensity to vary and producing a variation in the contrast of the output signal.Thus, the curvature sensing could be realized using the contrast of the interferometric pattern.The impact of the length of the HCF section on the sensitivity was investigated to achieve the highest curvature sensitivity.The highest curvature sensitivity was obtained as −17.28 ± 2.30 dB m −1 in the range of 1.84-2.94m −1 when the length of HCF was 2.5 mm.Further, the best performance of the proposed sensor, i.e. a combination of good curvature sensitivity (−11.80 ± 1.30 dB m −1 ) and wide curvature range (0.95 m −1 -2.78 m −1 ), was realized using a 1 mm-long HCF.
Zhou et al [87] demonstrated a sensor based on a sevencore fiber (7-CF) for precise extrusion curvature and tensile strain sensing.As shown in figure 5(b), the 7-CF was lateral core-offset spliced to two short sections of MMF on each side and then sandwiched between two SMFs (SMF-MMF-7-CF-MMF-SMF).The eccentric locations of the seven cores result in varying propagation constants of the core modes and cladding mode, and the phase difference alters with bending or stretching.The lateral core-offset structure enhances the interference effect, leading to greater sensitivity and precision.As a result, the wavelength shift was observed to measure curvature and tensile strain accurately.The maximum curvature and strain sensitivities of 25.96 nm m −1 and 0.094 nm µε −1 were achieved, respectively.
Similar to the 7-CF structure, a high fringe visibility MZI sensor based on a four-core fiber (4-CF) was reported by Yang et al [88] Compared to the 7-CF structure, this 4-CF structure utilized two coupling sections fabricated by cascading short segments of FMF, MMF, and large core diameter MMF, instead of only MMFs (figure 5(c)).When the light propagates through the first coupling section, which functions as a beam splitter, the light is coupled into the 4-CF.The four-core and cladding modes are excited and propagating along the 4-CF.In the second coupling section, these modes interfere with each  other and couple back the output SMF.The measurement results showed that these mode couplers significantly improved the interference fringe visibility, and a maximum fringe visibility of 30 dB was obtained in the transmission spectrum, which is much higher than the MZI using only MMFs as the couplers and provided a high coupling efficiency.The maximum curvature sensitivity of 20.77 nm m −1 in the range of 0.2893-0.7916m −1 and 9.99 nm m −1 in the range of 0.7916-1.039nm m −1 was obtained, while the maximum temperature sensitivity was 61 pm Last year, a sawtooth fiber structure-based MZI was proposed by Wei et al [89] for curvature sensing and bending direction recognition (figure 5(d)), which was also possible to be used for multi-parameter sensing.The cladding of an SMF was removed at equal intervals by a CO 2 laser to fabricate the sawtooth structure, and two MMFs were spliced at both ends of this SMF to form an MSM hetero-core structure.The sawtooth part causes the SMF core deviate from the neutral plane of the optical fiber.As a result, when the fiber is concave or convex bent, the optical path of the core mode changes, resulting in curvature sensing and direction recognition.The curvature sensitivity can be improved because of the local stress in the bending sawtooth structure.The realized curvature sensitivity reached −15.16 nm m −1 and 8.32 nm m −1 at 0 • (concave direction) and 180 • (convex direction) bendings, respectively.Furthermore, this sensor experimented for torsion, and the sensitivity was −0.30 nm (rad m −1 ) −1 in the range of 0-13.96rad m −1 .The temperature and strain sensitivities were 58.90 pm • C −1 and −3.62 pm µε −1 in the range of 25 • C-130 • C and 0-800 µε, respectively.The results showed that the sensor has the potential for simultaneous measurement of temperature and other sensing quantities or strain and other parameters.It is important for applications such as the medical field, astronomical telescope, and structural engineering.
The same group also reported an SPR sensor based on a Vgroove fiber [90], where multiple continuous and equidistant V-grooves were fabricated on a SIMMF with a core diameter of 40 µm (SIMMF-40), as shown in figure 5(e).The V-grooves were used to excite the cladding mode effectively when the light reached the V-groove area.After 2 cm, another SIMMF with a core diameter of 105 µm (SIMMF-105) was spliced to the V-groove fiber.The area between the last V-groove and SIMMF-105 was rotatably coated with 50 nm-thickness gold film on the cladding to form the SPR sensor.The bending of this structure deformed the opening angles of the Vgrooves, and the excited cladding mode changed, resulting in the change of the SPR incident angle and the shift of the resonance wavelength.When this probe was concave bent, the opening angle became smaller, the resonance dip shifted to a shorter wavelength, and the sensitivity was −5.98 nm m −1 in the range of 0-13.275m −1 .For convex bending, the increased opening angle led to a red shift of the resonance dip with a sensitivity of 1.42 nm m −1 in the range of 0-20.8 m −1 .
An easy-fabricated MZI utilizing a simple combination of SIMMF and GIMMF was proposed by Yang et al [91] for curvature measurement (figure 5(f)).A section of GIMMF (50 µm core diameter) was sandwiched between two short SIMMFs (105 µm core diameter) to form an MZI, which was then spliced with an input and output SMF.The sensing characteristics of the SIMMF-GIMMF-SIMMF structure were simulated to provide a theoretical guideline for the main parameter designs of the curvature fiber sensors.It was experimentally demonstrated that this structure provides higher spectral contrast with appropriate structured parameters.The sensing performance of different GIMMF lengths was experimentally investigated, found that when the GIMMF was short enough (⩽10 mm), the intensity of the interference dips exhibited high sensitivity to the bending but was nearly insensitive to the ambient temperature.The total length of the proposed sensor could be only 3 mm with 1 mm-long GIMMF and SIMMFs, and the maximum curvature sensitivity could be up to −78.75 dB m −1 in the small range of 0-2.36 m −1 .In addition, this compact sensor can be utilized as a temperatureinsensitive curvature sensor, making it ideal for a wide range of sensing applications, including bending, vibration, acceleration, and strain.
Li et al [92] also proposed a groove-included structure for simultaneous measurement of curvature and temperature.
A section of inclined-plane-polished HCF filled with PDMS was spliced with two short sections of MMFs, which acted as a coupler to couple the light from the input SMF into the PDMS-filled air hole and the annular core of the HCF and then re-couple the two beams into the output SMF (figure 5(g)).As the PDMS and HCF cladding have different refractive indices, the propagating beams have different optical paths, which generates an MZI.When the probe was bent, the two grooves deformed the MZI structure and thus enhanced the curvature sensitivity.The temperature sensitivity was improved due to the high TOC of the PDMS polymer filled in the HCF.As the interference dips reacted differently to the temperature and curvature changes, a simultaneous measurement was realized.The experimental curvature sensitivity of −6.833 nm m −1 and temperature sensitivity of 4.278 nm • C −1 were obtained in the range of 0-45.97 m −1 and 25 • C-95 • C, respectively.Compared to the curvature sensor based on the conventional SMF-HCF-SMF structure without grooves [94], the sensitivity of the proposed configuration was improved about 99 times.
Recently, the core diameter mismatch of the MMFs for high-order cladding modes excitation was also employed by Ma et al [93] for curvature sensing.As shown in figure 5(h), a short SIMMF with a core diameter of 50 µm was spliced to a 105 µm core diameter SIMMF, which functioned as a mode splitter and coupler.A section of NCF with a diameter of 125 µm was sandwiched between these two splitters/couplers.When light propagates through this structure, the core mismatch between two SIMMFs and the NCF effectively excites the cladding modes three times, resulting in the filtration of weak cladding modes but exciting the higher-order cladding modes.This process significantly enhances the curvature sensitivity.The highest curvature sensitivity of −114.74 nm m −1 was achieved in the range of 0-0.49778 m −1 at the interference dip of 1408 nm.Additionally, this sensor was also tested for temperature and strain measurement, and the results showed that this sensor is almost insensitive to temperature and strain.
A summary of the curvature sensors cited above is presented in table 4, including sensing properties, sensor structures, MMF types, measurement ranges, and sensitivities.

Bio/chemical sensors
Bio/chemical sensing has been the central research topic for a few decades.Due to the well-known advantages of optical fiber sensors, such as electromagnetic immunity, biocompatibility, portability, and fast response, various fiber-optic bio/chemical sensors have been developed, especially in the last several years [95][96][97].To realize bio/chemical sensing, biocompatible coating and nanoparticles (NPs) immobilization on the sensing surface of the probe are essential to improve the performance of the sensors.In the following, several representative sensor configurations, materials, and NPs are presented and discussed.
In 2015, Mishra and Gupta [98] fabricated and characterized an SPR pH sensor utilizing an unclad MMF core coated with silver (Ag), ITO (In 2 O 3 :SnO 2 ), aluminum (Al), and smart hydrogel layers (in this sequence), as shown in figure 6(a).When the pH of the fluid surrounding the hydrogel layer changed, the hydrogel layer swelled and shrinked, leading to its RI changes.By observing the wavelength shifts caused by RI changes, the pH measurement of the fluid was achieved.
The ITO layer was used to increase the sensitivity, while the aluminum layer was used for accuracy enhancement.The experimental results showed that this sensor exhibited high sensitivity at low and high pH values but not at the middle pH values.The thickness of the ITO and aluminum layers were optimized as 40 nm and 10 nm, respectively.The obtained maximum sensitivity was around 19.5 nm pH −1 .In 2018, an optofluidic label-free MZI-based biosensor using a twin-core hollow optical fiber (TC-HOF) was proposed and experimentally demonstrated by Yang et al [99] for the streptavidin-biotin binding sensing (figure 6(b)).The TC-HOF had a central hole, two embedded cores, and two micro holes (inlet and outlet) for injecting liquids.The central hole acted as a microfluidic channel where the liquids flowed.One core was suspended on the inner surface of the central hole serving as sensing arm, while at a sufficient distance, the other core was embedded in the silica cladding as reference arm.Thus, an integrated all-fiber MZI was formed.The entire outer surface of the suspended core was chemically modified with streptavidin to capture the biotin molecules by the streptavidinbiotin binding when the fluid flowed in the central hole, resulting in RI changes around the sensing arm, and subsequently, the spectral shifts in the transmission spectra.The MZI was tested with a high RI sensitivity of 2577 nm RIU −1 , and combined with this RI sensitivity, a net biotin detection sensitivity of 16.9 nm (mg ml −1 ) −1 for the biotin concentration in the range of 0.01-0.1 mg ml −1 .The streptavidin-biotin binding facilitated label-free sensing, making it an excellent option for monitoring the real-time and in situ biochemical binding of biotin with a range of biomolecules, including cells, antigens, antibodies, and DNA.
The Vernier effect has been successfully employed in optical fiber sensors for a variety of applications in the last few years, e.g.temperature sensing [100], axial strain and magnetic field sensing [101], gas RI sensing [102], gas pressure sensing [103], and airflow sensing [104].Here, we reviewed a representative sensor reported by Li et al [105] using the Vernier effect with a cascaded F-P interferometer for hydrogen sensing.As depicted in figure 6(c), the sensor consists of a section of large mode area fiber (LMAF) and a section of HCF, coated with Pt-loaded WO 3 /SiO 2 powder.This coating increases the local temperature of the sensor head when it comes into contact with a hydrogen atmosphere.The solid core and air have a RI mismatch, resulting in Fresnel reflection at the air-glass interface.Thus, three mirrors were formed in the light path.A small portion of the light was reflected at these mirrors, and the reflected spectrum superimposed at the SMF.Meanwhile, the majority of the light continued to propagate through the HCF and the LMAF.As a result, two cascaded F-P cavities were formed.By utilizing the vernier effect and selecting appropriate cavity lengths, the sensitivity was significantly enhanced.This was achieved by making the free spectral range of one cavity close, but not equal, to the other.Experimental results demonstrated a hydrogen sensitivity of −1.04 nm/% within the range of 0%-2.4%.
In 2020, the speckle patterns generated by the MMI in the MMFs used for monitoring vital bio-signs, including  [98] with permission from the Royal Society of Chemistry), (b) the optofluidic TC-HOF-based MZI for detecting streptavidin-biotin binding [99], (c) the cascaded F-P interferometer hydrogen sensor [105], (d) the fabric-integrated MMF sensing system for measuring heart rate, respiration rate, and pulse wave velocity (reproduced from [106].CC BY 4.0), (e) the silver thin film-based fiber sensor decorated with CTAB-functionalized ZnO/CNT nanocomposite for the detection of catechol (reproduced with permission from [107]), (f) the etched reflective SMF-7-CF structure using CuO-NFs, AuNPs, and GO for cancer cells detection (reproduced with permission from [108]), (g) the cholesterol sensor using AuNPs and ZnO-NPs immobilized MPM/SPS probe [109], (h) the AgNPs and GO immobilized tapered SMS structure for detecting L-cysteine [110], (i) the 2D material-assisted LSPR-based sensor using MCF for creatinine detection (reproduced from [111].CC BY 4.0).respiratory rate, heart rate, and pulse wave velocity, were reported by Bennett et al [106] with a simple fabric-integrated MMF sensor.The sensing system consisted of a laser, a SIMMF, a single digital defocused camera, and a computer (figure 6(d)).The sensing principle relied on tracking the point-wise intensity variations of the speckle patterns radiating from the MMI in the deformed MMF caused by heart palpitations/respiratory expansions.The experimental results indicated that the algorithm for speckle pattern processing, i.e. the sum of the absolute value of the first-time derivative of the speckle pattern pixels' gray intensities between consecutive frame images, provided the highest sensitivity and SNR.Meanwhile, it also allowed the simultaneous detection of heartbeats and respiratory rates and the evaluation of the heartbeat variation related to arrhythmia.Besides, monitoring pulse wave velocity also allowed for estimating the systolic blood pressure.This simple MMF sensor embedded in the fabric could be potentially developed in 'smart clothes' for continuous monitoring of vital bio-signs.
Pathak and Gupta [107] developed and demonstrated an SPR-based fiber-optic catechol sensor.Figure 6(e) shows the sensor configuration, where an unclad MMF core with a diameter of 600 µm was coated with a silver film and a cetyltrimethylammonium-bromide (CTAB)-functionalized zinc oxide/carbon nanotube (ZnO/CNT) nanocomposite over the silver film.The CTAB-functionalized ZnO/CNT nanocomposite acted as sensing layer, and due to its high RI, it could also enhance the sensitivity of the SPR sensor.According to the CTAB concentration and the pH of catechol samples, the proposed sensor had two different operational regimes.In the high pH range, the maximum sensitivity of 5.46 nm µM −1 was obtained at pH 9.5 with a 4 mM CTAB concentration, while the 0.8 mM CTAB concentration showed the highest sensitivity of 3.44 nm µM −1 at pH 7.0.Besides, the probe was tested to prove a reproducible and stable performance in the catechol concentration range of 0-100 µM.
The excellent performance of the proposed sensor governs the practical usability for the quantitative determination of catechol in the fields such as environmental monitoring, food industry, and biological applications.Cancer cell detection has been a very important topic attracting the considerate attention of many researchers.A label-free and ultra-sensitive sensor based on a reflective SMF-7-CF structure was proposed by Singh et al [108] for detecting cancerous cells, as shown in figure 6(f).The sensing principle relied on the modulation of internal coupling coefficients between the cores of the 7-CF, and thus, it was etched to increase the evanescent wave and coupling of modes.Further, the etched part helped increase the supermodes, which interacted with various nanomaterials and produced localized surface plasmon resonance (LSPR) phenomenon.Additionally, the probe was immobilized with different nanomaterials: optimized 10 nm gold nanoparticles (AuNPs) for increasing the sensitivity by LSPR, graphene oxide (GO) and copper oxide nanoflowers (CuO-NFs) for increasing the surface area and adsorption capability, and 2-deoxy-D-glucose (2-DG) over nanomaterials for specific binding cancer cells.Various cancerous cell lines (HepG2, Hepa 1-6, MCF-7, and A549) and normal cell lines (NCF and LO2) were detected, and the performance of the sensor indicated an ultra-sensitivity for HepG2, Hepa 1-6, MCF-7, A549, NCF, and LO2 cell lines with a limit of detection of 3, 2, 2, 2, 10, 4 cells ml −1 , respectively, in the linear range of 1 × 10 2 -1 × 10 6 cells ml −1 .
Another LSPR phenomenon-based sensor was reported by Agrawal et al [109] for cholesterol (Cho) sensing using a photosensitive fiber (PSF).Two structures, i.e.MMF-PSF-MMF and SMF-PSF-SMF (figure 6(g)), immobilized of AuNPs and afterward coated with ZnO-NPs were compared and showed that the MMF-PSF-MMF exhibited an excellent performance on Cho sensing.A wide detectable range of 0.1-10 mM was achieved using biocompatible AuNPs with multiple surface functionalities.A remarkable sensitivity of 0.6898 nm mM −1 was obtained with a limit of detection (LoD) of 0.6161 mM.Then, the authors proposed another similar sensor based on silver nanoparticles (AgNPs) and GO immobilized tapered SMS structure for detecting L-Cysteine [110], as shown in figure 6(h).This structure combined tapering and heterocore structures to enhance the sensitivity, where the MMFs improved the measurement range due to the larger diameter, and the tapering converted a part of the guided light into an evanescent wave to interact with the surrounding medium.This probe was demonstrated with significantly improved performance in various parameters: LoD (63.25 µm), sensitivity (7.0 nm mM −1 ), correlation coefficient (99.04%), and linearity range (10 nM-1 mM).These two sensors showed great potential for label-free detection and real-time medical diagnosis in medical applications in the near future.
Recently, Li et al [111] proposed a two-dimensional (2D) material-assisted LSPR-based sensor using a multicore fiber (MCF) for creatinine detection in the human body.As shown in figure 6(i), the probe consists of a cascaded MCF and MMF sandwiched between two SMFs.The sensing region, i.e. the MCF and MMF sections, was etched to generate strong evanescent waves, further enhancing the LSPR phenomenon of AuNPs.This region was also immobilized with GO and MoS 2 -NPs for increasing the biocompatibility, while the creatininase enzyme layer was for specifical binding of the creatinine.Therefore, the detection of the creatinine concentration in the sample solution was achieved.The proposed sensor exhibited a sensitivity of 0.0025 nm µM −1 , a standard deviation of 0.107, and an LoD of 128.4 µM over a linear detection range of 0-2000 µM.It also indicated the capability of measuring creatinine concentrations comparable to those found in patients with severe uremia, which could enable early detection and treatment.
The sensing applications, sensing mechanisms, MMF types, measurement ranges, and sensitivities of the bio/chemical sensors noted above are summarized in table 5.

Other sensors
In addition to the MMF sensors mentioned earlier, there are numerous other types of MMF sensors that cannot be exhaustively covered in detail.However, we can provide a few examples of widely utilized MMF sensors to illustrate the boundless applicability of MMF sensors.These include magnetic field sensing [112][113][114][115][116], distributed acoustic sensing [117], fluidic flow measurement [118], steel corrosion monitoring [119], relative humidity (RH) sensing [120][121][122], gas pressure sensing [103,123,124], and volatile organic compound (VOC) gas detection [125,126].Table 6 provides a summary of the key parameters for the sensors discussed.More in-depth information, including sensor configurations and sensing principles, can be found in corresponding references.

Machine learning-assisted multimode fiber sensors
Due to the mode-mixing and modal dispersion in the MMF, the waves propagating in the MMF are scrambled, and the outputs at the distal end of an MMF are seemingly random patterns known as speckles.This effect cannot be avoided.Despite this, light transmission in the MMF remains deterministic.The prospect of deterministic light propagating through MMFs has been proven to be useful for different applications [127,128], and various specklegram sensors have been reported [129].Machine learning methods have been booming in the last few years due to the development of computation power.The MMF-based applications benefit significantly from the blossom of machine learning, such as MMF imaging [130][131][132][133][134], as it is an advanced tool to progress and analyze complex images and patterns.Since the speckles are easily affected by changes in the light propagation and surrounding environment, the ambient changes can be measured by quantifying the speckle distortion.Therefore, the power of machine learning processing complex speckles has great potential to broaden the possible sensing applications and improve the sensing performance.Recently, different machine learning-assisted MMF-based sensors have been reported, which is the new trend for developing MMF-based sensors.Here, we classify them into two categories.The major one is to utilize machine learning to learn the specklegrams, where a large number of collected specklegrams are fed to the neural network for training, validation, and testing.The other is to learn the experimental data, e.g. the transmission spectra, to enhance the sensing sensitivity or enlarge the measurement range.

Learning the specklegrams
In 2020, Sun et al [135] developed a fiber optic system based on MMI for directional position sensing with machine learning, which established an image recognition program to find the hidden correlations between the interference patterns and fiber deformations.The specklegrams were not directly used in this work, but the multi-ring patterns also generated by the MMI were employed.Figure 7 shows that the system collects images automatically from different positions with relatively large distances along four axes for directional sensing while positioning studies from a fixed distance with small steps along a given direction to test the spatial resolution.The collected images were trained, validated, and tested by a convolutional neural network (CNN), i.e. 18-layer residual networks (ResNet-18), having relatively higher accuracy and fewer computational operations.The results showed that an accuracy of over 97% was achieved with the ResNet-18 model to recognize interference patterns from four different directions, each with ten classes, with an 800 µm spatial resolution, using merely 320 images for each class.Additionally, the system achieved over 60% accuracy in recognizing the position with a resolution of 5 µm when using a larger dataset of up to 1000 images.
Different from the utilization of multi-ring patterns, Liu et al [136] introduced an adopted visual geometry group network (VGG-Net) to learn the MMF specklegrams for bending recognition (figure 8).Different bendings were applied to the MMF section, and the corresponding specklegrams were recorded by a camera to create the datasets for training, validation, and testing.The trained VGG-Net could classify the specific bending status with average accuracies of 92.8% and 96.6% for MMFs with core diameters of 105 µm and 200 µm, respectively.This study presented the potential of one single MMF being independently used as a bending sensor, which is commonly required in applications such as structure monitoring and robotic arms.Based on this study, the authors developed a curvature sensor by optimizing the sensor and neural network in 2022 [137].The well-trained network could predict the curvature from any speckle gram within the trained curvature range.The results indicated that the model trained by specklegrams corresponding to 20 curvatures could successfully predict the curvatures corresponding to the MMF specklegrams under 57 curvatures.A good curvature sensing capability in the curvature range of 1.55-6.93m −1 was achieved, where the prediction error is within an error range of ±0.3 m −1 for 94.7% of the specklegrams.Due to the irrelevant information in the specklegrams, it was complex to train the network.To simplify the process, the authors employed a method to reduce redundant information, namely texture feature extraction [138].The uniform local binary pattern algorithm was used to extract texture feature vectors from all specklegrams, which were then utilized as datasets for the CNN.The results showed that the one-dimensional (1D) CNN, trained by the texture features of the specklegrams from an MMF with a core diameter of 50 µm, exhibited high prediction accuracy in the same curvature range of 1.55-6.93m −1 as their previous work.The proposed method assisted with 1D CNN could recognize 41 curvatures with an accuracy of 100% for curvature recognition.For curvature sensing, the prediction error was within a range of ±0.1 m −1 for 91.4% of the samples in the test set.The proposed method made a significant improvement and demonstrated the potential to be used in complex bending applications.
According to the relevant studies on bending sensors, in 2021, Lu et al [139] proposed a multi-point bending based on a sensitized plastic fiber with deep learning (figure 9(a)).Three sensitized areas, i.e. the polished areas, were fabricated on top of the plastic fiber.As different bending-sensitive areas of the sensitized fiber caused the output speckle changes, the  specklegrams were collected when the sensitized areas were bent independently and simultaneously.The CNN was trained and tested with collected datasets to discriminate the output specklegrams and analyze the bending angles in different sensing areas.The results showed accuracy rates of 99.2%, 96.1%, and 93.5% for bending intervals of 15 • , 10 • , and 5 • , respectively.Yang et al [140] later enhanced a multi-point bending sensor that could identify both the bending state and bending positions simultaneously, as shown in figure 9(b).They optimized the sensing system and utilized ResNet-18, another CNN, to successfully determine five bending positions.The proposed bending recognition scheme was highly effective and robust, achieving a prediction accuracy of 99.13% and a prediction speed of 4.75 ms per frame.Besides the 1D bending sensor mentioned before, a 3D multi-point deformation sensor was illustrated using machine learning-based specklegrams classification [141], as shown in figure 9(c).As CNN is commonly used for a large-size dataset, for a small-size dataset   [142]), (b) picture of a series of fluid channels etched radially through the SMF using focused ion beam milling (reproduced from [144].CC BY 4.0). in this experiment, a simple neural network, i.e. the k-nearest neighbor (KNN) algorithm, was used.The KNN only requires tuning one hyperparameter (the value of k), and it was easy to implement for different applications.Compared to CNN, a similar classification accuracy of close to 100% was achieved.The proposed scheme provided a low-cost setup with a high degree of freedom for 3D deformation sensing and also has the potential to be developed for 3D shape sensing.
Machine learning promotes the development of specific sensors, e.g. a 2D tactile sensor based on the combination of MMI and deep learning was reported [142].A winding MMF was embedded inside a soft elastic silicone substrate, as shown in figure 10(a), and the output specklegrams were recorded when the probe was touched.A ten-layer ResNet was adapted for training, validation, and testing.It demonstrated that, even with only a few hundred images, the achieved accuracy was over 95% for touch position at an XY resolution of at least 0.5 mm × 0.5 mm.Additionally, force sensing in the Z direction was tested using the probe, and a resolution of 3 g was reached with an accuracy of close to 100%.This work opened up new application directions and potentially fulfilled the need in many fields, such as biotechnology.
Liang et al [143] investigated an open cavity F-P sensor as a pressure sensor by demodulating the random speckle patterns, which were considered the carrier of the F-P transmission spectrum.The trained CNN successfully extracted the spectral features from the speckle patterns, showcasing its ability to accurately distinguish the F-P spectral differences between neighboring orders.This precision is achieved due to the high sensitivity of the speckles.By resolving the fringe order ambiguity problem, the measurement range significantly improved, as it now only relies on the calibration range.The experiments exhibited a pressure resolution of 0.001 MPa.Besides, by replacing the camera with a quadrant detector, a high-speed measurement was achieved, which indicated a new way to balance high resolution, large dynamic range, high-speed measurement, and low cost by optimizing the setup.
Lately, an RI sensor based on learning the specklegrams was demonstrated [144].Instead of a single MMF, an MSM structure was used, and a series of fluid channels were etched radially through the SMF using focused ion beam milling, as shown in figure 10(b).The fluid channels enhanced the interaction between the fluid and the light propagating through the fiber, further improving the sensitivity.A neural network, ResNet-18, was employed to learn the mapping between the RI of the fluid and the specklegrams at the output distal end.It was demonstrated that the proposed sensing scheme exhibited a recognition accuracy of 99.68% with a speed of 4.5 ms per frame in the RI range of 1.3326-1.3679.Additionally, a long-term stability test was operated, which showed the sensing accuracy of the system was consistently over 95% for 24 h.

Learning the spectra
Despite the machine learning-assisted specklegram-based schemes, machine learning can also learn and analyze the measured spectra of the sensor to enhance the sensing performance.
It is well known that undesired ambient perturbations limit the applications of MMF sensing and imaging, as the changes in the propagation characteristics lead to low image quality and poor sensing performance.However, it is challenging to discriminate the influences from the complex MMI in the MMF.In 2021, Nguyen et al [145] revealed the feasibility of MMF for specific measurements, even under strong noise from other perturbations, assisted by deep neural networks (DNNs), as shown in figure 11(a).This concept was exemplified through temperature measurement using a sapphire crystal optical fiber (SOF).The SOF was implemented into an SMS structure, and random environmental noise was introduced to the SOF to obtain a multitude of intricate transmission spectra at the distal end of the output SMF.These spectra included information on the measured parameter and the accompanying noise, i.e. temperatures and noise.Additionally, a DNN, the multilayer perceptron (MLP) architecture, was trained using datasets that comprised the spectral information and the corresponding temperature labels.The experimental results showed that the well-trained MLP could predict the temperature value from a complex MMF transmission spectrum (noise applied) with an accuracy close to 100%.This work indicated that, in principle, thanks to the power of deep learning, it is feasible to use any type of MMF for any measurand under any environmental noise.
A curvature sensor based on the MMI was reported by Zhu et al [146] with the assistance of machine learning for spectra analysis.The fiber consisted of an easy-fabricated SMF-NCF-HCF-SMF structure, and the high-order modes excited in the NCF contributed significantly to the curvature sensitivity enhancement.By tracking the spectral dip in the transmission spectrum, an enhanced curvature sensitivity of 16.34 dB m −1 was obtained in a restricted measurement range of 0.55-1.45m −1 , compared to conventional SMF-HCF-SMF structure.The experiments demonstrated that the measurement range was limited due to the signal demodulation approach, i.e. spectral dip tracking method, as the probe still exhibited non-linear and non-monotonic responses in a broad curvature range.On account of machine learning, the oneto-one mapping between the measured raw spectrum and the curvature on the sensor was realized to broaden the measurement range.The measurement range was successfully expanded to 0.55-3.87m −1 using a single-layer artificial neural network.
While various non-invasive biosensors have been developed, the integration of machine learning undoubtedly offers an additional possibility for the creation and advancement of these biosensors.Pal et al [147] proposed a machine learning-empowered MMF-based non-invasive sensing system for blood glucose monitoring.An unclad MMF was used to create an evanescent wave to achieve direct interaction of the light with the subject's finger.The leaky mode can penetrate the skin barrier and detect the blood plasma glucose and iron-containing protein.Meanwhile, another MMF (with jacket and cladding) was placed next to the unclad MMF as a reference.The output speckle patterns varied with the bloodstream affected by blood glucose.When no magnetic field was applied, the variation was negligible for both fibers.With the applied alternating current-generated magnetic field affecting the skin, the MMF (with jacket and cladding) showed a negligible blood glucose sensing effect, while the leaky modes of the unclad MMF changed polarization under Faraday's effect and reflected from the iron-containing hemoglobin affected by the magnetic field.The recorded speckle patterns were converted into amplitude changes over time in glucose levels, which were further preprocessed by removing the noise and inferring data at applied magnetic field frequency.Utilizing the machine learning algorithm, i.e. the Naïve Bayes classification algorithm, blood glucose levels could be classified.This system allowed the implementation of an automatic and real-time blood glucose monitoring.
In analyzing the transmission spectra of MMI-based sensors, the traditional approach involved tracking spectral dips (or peaks) to determine shifts.However, this method becomes challenging when dealing with complex spectra, such as overlapped or unstable spectra.Tracking the wavelength shift or power changes at a single wavelength becomes impractical.In such cases, using the whole transmission spectrum for accuracy sensing is more suitable.In 2022, Kanon Toda et al [148] employed machine learning to characterize MMI in multi-core POF for temperature sensing.Two multi-core POFs were tested, namely MB-350 and MB-1000, which have 3500 and 13 000 cores, respectively.As the multi-core POF was initially designed for image transmission, the experiments showed that the wavelength shifts of the spectral peaks/dips nor the critical wavelength was observed or identified (figure 11(b)).Therefore, a neural network was used to learn the whole transmission spectra, where the input was spectral data points with corresponding wavelengths and power values, and the output was the target temperature value.The sensing characteristics of the multi-core POF were demonstrated for high-accuracy temperature sensing with a minimal error of 0.3 • C by utilizing machine learning methods.This work indicated the extension of potential applications with specialty POFs.

Discussion and prospection
Research conducted in the past decade has demonstrated the exceptional performance of MMF sensors in various sensing applications.Numerous MMF sensors have been developed and studied, and in this review, we have selected representative sensors reported in the last ten years to showcase their classic and innovative configurations, which offer limitless possibilities for applications.
However, despite the progress made in optical sensing, several challenges still need to be addressed to achieve higher sensitivity and accuracy.Nonlinearity, cross-sensitivity, and measurement range are among the main limitations to sensing capability.Tracking wavelength shifts and power changes in response to measurement changes can be nonlinear or linear only within limited ranges.Cross-sensitivity can also lead to unwanted measurement errors, which can reduce the reliability of the measured sensitivity.For example, temperatureinduced cross-sensitivity has to be considered in most cases because of the inherent thermo-optic and thermo-expansion effects in the MMFs [149,150].Furthermore, the implementation of MMF sensors is often limited by the measurement range, which can be restricted by fiber properties or sensor structures.For instance, POFs are typically only capable of measuring temperatures up to 80 • C due to their plastic composition.However, POFs outperform silica optical fibers in strain sensing, as silica fibers are typically limited to a strain range of 4000 µε in most reported sensors.To enhance measurement sensitivity and accuracy, it is crucial to identify, control, or calibrate nonlinearity and cross-sensitivity.One way to achieve a boosted sensitivity is by selecting sensors with an appropriate measurement range for specific applications.For instance, etched and tapered structures are suitable for RI sensing, but they exhibit low endurance and can only be used in applications with moderate strain.However, relying solely on this approach is insufficient to expand the measurement range.Therefore, it is essential to overcome these limits by exploring different methods for developing MMF sensors.
The conventional methods for enhancing the performance of MMF sensors can be classified into three categories: new structure, new specialty fibers, and new compensation methods.The sensors reviewed in section 2 are selected to showcase these three approaches, which include unique structures like balloon-like structures [45,68,82], S-tapered structures [50], Kretschmann structures [67], and sawtooth structures [89]; notable specialty fibers such as HCF [66,85], SPF-TCPCF [46], 7-CF [87], and 4-CF [88]; and compensation methods, e.g. using FBG or LPG [41,43,44,47,76] to discriminate the cross-sensitivity and thin-film coating [67,79,[83][84][85]90] to improve the sensing performance.Despite the challenges involved in using unique structures or new specialty fibers, such as the complex fabrication process and the need for an in-depth understanding of fiber properties, further research is still demanded.For instance, exploring the potential of these new specialty fibers in different sensing scenarios can help us identify their potential for specific applications.Moreover, incorporating creative structures in the sensors often leads to improved performance, such as increased sensitivity or an extensive measurement range.Still, it is crucial to ensure that the fabrication of unique structures is both feasible and repeatable.In order to enhance measurement sensitivity and accuracy, addressing the cross-sensitivity of the sensors becomes vital.This can be achieved by developing innovative compensation techniques, such as applying specialized coatings to the sensors or processing the measured data with different methods.
Machine learning methods have experienced remarkable advancements in recent years, leading to numerous benefits in various fields.Among these areas, MMF imaging, specifically single MMF-based endoscopic imaging, has greatly thrived due to the progress in machine learning.The robustness of machine learning in addressing the nonlinearity in MMF has unlocked fresh avenues for researchers to incorporate machine learning in MMF sensors.Consequently, machine learning techniques are primarily employed to learn the output speckles or spectra of the sensors.Speckles are highly sensitive to ambient changes, particularly deformation, making them ideal for developing curvature sensors, as demonstrated in previous works [139][140][141].With the advancements in machine learning, we anticipate more learning-assisted MMF sensors.Although the current MMF-based endoscopic imaging employs machine learning techniques to reconstruct images, it is crucial to measure the body temperature of patients during surgeries.Therefore, simultaneous imaging and sensing of MMF hold great promise in the medical field.Furthermore, the development of a portable real-time monitoring system with machine learning-assisted sensors is a potential avenue for exploration.For example, if machine learning methods are implemented in smartphones, it could lead to the creation of a smartphonebased learning-assisted MMF sensor.Such a device would be an ideal portable sensor for daily bio-sign monitoring.

Conclusion
This article provides an overview of the advancements in MMF sensors over the past decade.Initially, the review covers representative sensors developed by conventional methods, such as temperature and strain sensors, displacement sensors, RI sensors, curvature sensors, and bio/chemical sensors.Various specialty fibers are employed as the MMF in the studies presented.Furthermore, the selected sensors exhibit significant potential for designing MMF sensors with distinctive structures, diverse coating materials, and integration with other techniques such as FBG and LPG.Next, machine learning-assisted MMF sensing systems are introduced and categorized into two types, i.e. learning the speckle patterns and learning the spectra.The neural networks learn the mapping relation between perturbations and speckle patterns, which is an ideal tool for overcoming nonlinearity.Additionally, it is demonstrated that the measurement range is solely dependent on the calibration range, allowing machine learning to expand the dynamic measurement capabilities effectively.It is widely acknowledged that tracking spectral peaks or dips generated by MMI is not feasible when the spectra are too noisy and complicated.However, machine learning can learn the entire spectra, overcoming these issues and providing more accurate measurement results.Finally, this review article includes a discussion and prospects on MMF sensors.We believe that it will serve as a valuable guide for the future development of MMF sensors, utilizing conventional or machine learning methods.MMF sensors are expected to have broad applications, particularly in the bio/medical field.

Figure 6 .
Figure 6.Schematic diagrams of (a) the SPR pH sensor utilizing an unclad MMF core coated with Ag, ITO, Al, and hydrogel layer (reproduced from[98] with permission from the Royal Society of Chemistry), (b) the optofluidic TC-HOF-based MZI for detecting streptavidin-biotin binding[99], (c) the cascaded F-P interferometer hydrogen sensor[105], (d) the fabric-integrated MMF sensing system for measuring heart rate, respiration rate, and pulse wave velocity (reproduced from[106].CC BY 4.0), (e) the silver thin film-based fiber sensor decorated with CTAB-functionalized ZnO/CNT nanocomposite for the detection of catechol (reproduced with permission from[107]), (f) the etched reflective SMF-7-CF structure using CuO-NFs, AuNPs, and GO for cancer cells detection (reproduced with permission from[108]), (g) the cholesterol sensor using AuNPs and ZnO-NPs immobilized MPM/SPS probe[109], (h) the AgNPs and GO immobilized tapered SMS structure for detecting L-cysteine[110], (i) the 2D material-assisted LSPR-based sensor using MCF for creatinine detection (reproduced from[111].CC BY 4.0).

Figure 7 .
Figure 7. Schematic diagrams of (a) the sensing system, (b) the stage movement pattern for directional sensing, (c) the stage movement pattern for the fine spatial resolution.Adapted with permission from [135] © The Optical Society.

Figure 8 .
Figure 8. Schematic diagrams of (a) the sensing system, (b) the detailed structure of the CNN.Reproduced with permission from [136].

Figure 10 .
Figure 10.(a) Schematic diagrams of the soft tactile sensor with one winding MMF embedded inside (reproduced with permission from [142]), (b) picture of a series of fluid channels etched radially through the SMF using focused ion beam milling (reproduced from [144].CC BY 4.0).

Figure 11 .
Figure 11.(a) Schematic diagrams of specific measurement under strong noise using MMF and DNN and the recorded various spectra with their corresponding measurand labels are used to train the DNN (reproduced from [145].CC BY 4.0), (b) examples of the transmission spectra at different temperatures for two multi-core POFs used for training the neural network (reproduced from [148].© IOP Publishing Ltd.All rights reserved).

Table 1 .
Summary of MMF sensors for temperature and strain sensing.

Table 2 .
Summary of MMF sensors for displacement sensing.

Table 3 .
Summary of MMF sensors for refractive index sensing.

Table 4 .
Summary of MMF sensors for curvature sensing.

Table 5 .
Summary of MMF sensors for bio/chemical sensing sensing.

Table 6 .
Summary of other MMF sensors.