The research and commercial development of fiber-optic sensors has grown significantly over the past 40 years. In particular, fiber Bragg gratings have become a well-researched and widely accepted tool for various environmental applications due to their outstanding advantages of high sensitivity, compact size, mechanical robustness, batch fabrication, and superior multiplexing capability.

In recent years, the tilted fiber Bragg grating (TFBG) has emerged as a new type of fiber-optic sensor, which possesses the advantages of fiber Bragg gratings and adds the ability to resonantly excite multiple cladding modes [1,2]. The TFBG device not only can realize single-point sensing of physical parameters such as temperature, strain [3], bend [4,5], and twist angle [5,6], but also opens up many possibilities for analyzing materials outside the fiber without breaking the core/cladding structure via conventional chemical etching or tapering [7,8]. The unique properties of the cladding modes make the TFBG a versatile platform for realizing light–matter interactions. The cutoff cladding mode, which lies at the transition point between the guided cladding modes and the leaky cladding modes, possesses an effective refractive index (RI) equal to that of the surrounding medium and exhibits strong evanescent fields, acting as the tentacle to probe the external environment. Utilizing the cutoff mode, the TFBG has proven to be an excellent tool for true RI sensing [9], magnetic field sensing [10], biochemical analysis [11–14], gas sensing [15,16], and battery monitoring [17,18].

Since the invention of the TFBG, significant efforts have been made to develop new strategies for enhancing sensing performance, leading to several advancements. To accurately derive the measured quantity from spectra, various demodulation methods have been proposed, including the envelope method [19], area method [20], envelope derivation method [21], and methods based on convolutional neural networks [22]. Beyond demodulation, a range of new sensing structures have been introduced and studied. By inscribing multiple consecutive TFBGs with different tilt angles in the same fiber, the spectral range can be expanded, and the RI sensing range can be enlarged [23]. The reliability of TFBG sensors for RI sensing, particularly against polarization effects, can be improved by using cascaded perpendicular TFBGs [24]. Additionally, the deposition of nanofilms such as graphene [25] or high-RI nano coatings [26] on the outer surface of TFBGs has proven effective in increasing RI sensitivity and extending the sensing range.

TFBGs have also been successfully utilized in various optical fibers beyond single-mode fibers, including multimode fibers [27], multicore fibers [28], and side-channel microstructured fibers [29], to enable diverse sensing applications. Recent studies have demonstrated that the optical spectrum and sensing performance of TFBGs can be tuned by thinning the fiber cladding [30,31], presenting new opportunities for the TFBG sensing device.

In this work, however, we propose the opposite, i.e., to artificially enlarge the cladding diameter of a standard single-mode-fiber (SMF) and demonstrate a new hybrid TFBG-capillary sensing device that shows improved sensing performance over the bare SMF TFBG. The sensing device is realized by inserting a bare TFBG inscribed in an SMF into a silica capillary and filling the air gaps with RI-matching oil. In this way, the fiber cladding and the silica capillary, whose refractive indices are identical, act as a new thick cladding, and the whole device can be regarded as a TFBG with an enlarged cladding. Our study shows that the free spectral range (FSR) of the cladding mode fringes in the spectrum tends to shrink as the outer diameter (OD) of the whole device increases. This results in an increased number of cladding modes and a denser spectrum compared to the bare TFBG. This hybrid sensing device also exhibits distinct cutoff points and similar RI sensitivity compared to bare TFBGs. With an outer cladding of 1000 μm, the detection accuracy can be improved by nearly an order of magnitude. This new sensor scheme can improve the sensing performance and reduce the cost of each sensor, and, most importantly, the outer capillary can act as a sacrificial layer to withstand harsh processing, such as high-temperature coating depositions and chemical etching.

The configuration of the proposed superfine multiresonant TFBG-capillary sensor is shown in Fig. 1, where a TFBG written in an SMF with an OD of 125 μm is inserted into a silica capillary whose inner diameter (ID) is about 126 μm, slightly larger than the OD of the optical fiber. The thin gap between the optical fiber and the capillary is filled with refractive index matching oil (Cargille Labs, USA, Series AA, RI $1.4560\pm 0.0002$) whose RI at wavelengths near 1550 nm is close to that of pure silica (1.444). Thus, the silica capillary, the RI-matching oil, and the optical fiber cladding tend to have the same RI. In this way, the whole device can be regarded as a new optical fiber device with an 8.2 μm fiber core and a thick cladding with a TFBG written in the fiber core. In a conventional TFBG, when a broadband light beam propagating as the fundamental mode in the fiber core encounters the tilted grating, a large number of cladding modes can be excited. Here, we anticipate the excitation of a significantly greater number of cladding modes in the new TFBG-capillary sensor device due to the larger effective V-number of the cladding. Furthermore, the evanescent wave of these extended cladding modes reaches beyond the outer surface of the capillary, enabling its use in various sensing applications.

The superfine multiresonant TFBG-capillary sensor is fabricated by inserting a bare TFBG probe into the inner hole of the silica capillary, which is prefilled with RI-matching oil. Pure silica capillaries with an ID of $\sim 126\mathrm{\mu m}$ and ODs of 381 μm, 700 μm, and 1000 μm are commercially available. Since the OD of the TFBG is only slightly smaller than the ID of the capillary, it is not easy to insert the TFBG into the capillary. Therefore, we fixed the capillary on a stationary stage and mounted the TFBG on a three-axial translation stage to enable high-precision manipulation of the TFBG. The whole process was observed in real time from two perpendicular directions by two sets of long working distance microscopes. The capillaries were infiltrated with RI-matching oil by the capillary force prior to the insertion of the TFBG probe. The RI-matching oil, which has the same RI as the fiber cladding and the silica capillary, can not only bridge the nanogap between the fiber cladding and the capillary to allow the light to pass from the fiber cladding into the capillary but also act as a lubricant to facilitate the insertion of the TFBG probe.

A typical microscopic image of a TFBG probe and a capillary that are still separated and well-aligned is shown in Fig. 2(a). The same pair of TFBG probe and capillary after insertion is shown in Fig. 2(b). Then the superfine multiresonant TFBG-capillary sensor is transferred into the microfluidic cell of an acrylic sensor chip and fixed. In our study, the TFBG-capillary sensors with different ODs are fabricated using the same method. The micrographs showing the cross sections of these devices are displayed in Fig. 2(c). The red circles mark the outer profile of the optical fiber, whose diameter is 125 μm.

The experimental setup for measuring the spectrum of the superfine multiresonant TFBG-capillary sensor and for RI sensing is shown in Fig. 3. A broadband source (BBS) with a spectrum range of 1500–1620 nm was used to provide an unpolarized input light. The polarization state of the incident light was precisely controlled by a polarizer and a polarization controller (PC). The incident light was introduced into the TFBG-capillary sensor through a circulator, and the reflected light was guided to the OSA (Yokogawa, AQ6370C). Thus, the reflection spectrum was captured and recorded by the OSA with a spectral resolution of 0.015 nm. A gold mirror deposited at the cleaved end of the fiber is used to reflect the transmitted light so that the transmission spectrum of the TFBG can be measured in reflection (facilitating the use of the device as a true “point sensor”).

First, we investigated the optical spectrum property of the superfine multiresonant TFBG-capillary device. In this study, we used a TFBG with a tilt angle of 12°. Silica capillaries with an ID of $\sim 126\mathrm{\mu m}$ and ODs of 381 μm, 700 μm, and 1000 μm were tested.

The measured reflectance spectra of the superfine multiresonant TFBG-capillary sensor with different ODs are shown in Fig. 4(a). The spectrum of the bare TFBG is also shown in the figure for comparison. All TFBG-capillary sensors and the bare TFBG were free-standing in air during the measurement. For a bare TFBG, the resonant fringes of the cladding modes can be distinguished from each other. However, for a TFBG-capillary sensor with an OD of 381 μm, the number of resonant fringes increases dramatically compared to the bare TFBG, and the depth of the fringes also shows a reduction while the shape of the lower envelope stays nearly unchanged. When the OD of the device is increased to 700 μm and further to 1000 μm, the number of resonant fringes further increases, and the depth of the fringes further decreases while the shape of the lower envelopes remains almost unchanged. To show the details of the spectra more clearly, the magnified spectra in the wavelength range of 1550–1552 nm are shown in Fig. 4(b). It is clear that as the OD of the device increases, the density of the fringes also increases, and the FSR and the depth of the fringes all decrease. We also found that the core mode resonance of the TFBG near 1610 nm remains unchanged as the OD of the superfine multiresonant TFBG-capillary sensor increases since the core mode fields do not extend further than a few micrometers away from the core diameter and do not perceive the cladding diameter change.

These experimental results were verified by simulating the transmission spectrum of the TFBG-capillary sensor. Simulations of the transmission spectra for enlarged diameter TFBGs were obtained by first calculating the vector mode fields and effective indices of the core and cladding as functions of cladding thickness and wavelength. This was achieved using a cylindrical finite-difference mode solver designed for layered structures with complex permittivity. Subsequently, transmission spectra were obtained through complex coupled-mode theory to establish mode couplings at each wavelength, with a Runge–Kutta algorithm employed to calculate the transfer function across the wavelength range. The simulation parameters for the fiber were as follows: core diameter = 8.2 μm, cladding diameter = 125 μm to 1000 μm, core refractive index = 1.4535, and cladding RI = 1.4441.

The evolution of the spectrum with increasing cladding diameter is shown in Fig. 4(c) (limited to a wavelength range of 1551–1556 nm because these simulations are very time-consuming). The simulated spectrum shows that the FSR and the depth of the fringes decrease as the OD of the device increases, consistent with the experimental results presented in Fig. 4(b). The simulated FSRs at a wavelength around 1551 nm for capillaries with outer diameters of 125 μm, 381 μm, 700 μm, and 1000 μm were calculated to be 1.301 nm, 0.474 nm, 0.265 nm, and 0.179 nm, respectively. The experimentally measured corresponding values in Fig. 4(b) are 1.260 nm, 0.492 nm, 0.252 nm, and 0.164 nm, respectively, showing good agreement. We then plotted the FSR of the experimental and simulation results as a function of the OD in Fig. 4(d) to facilitate a more intuitive comparison. This comparison demonstrates that the experimental results are in good agreement with the simulation results. With these results, we can obtain the value of the OD for any desired FSR.

The cutoff point of the TFBG is a unique feature that can be exploited for sensing applications. In theory, the cutoff point satisfies the criteria that the effective RI (ERI) of a given cladding mode is equal to the surrounding RI (SRI). Since the TFBG supports numerous cladding modes with different ERIs, the cutoff point can serve as an indicator to quantify the SRI. Such a refractometer is superior to the other fiber-optic or prism refractometers in that it measures the true value of the RI since the ERI of the cutoff point is always equal to the SRI [22]. However, a limitation of this measurement strategy is that the resonance wavelengths of the cladding modes are a series of discrete points, and the sensor is “blind” between the mode resonances, thus reducing the detection accuracy.

According to our results in the previous section, the superfine multiresonant TFBG-capillary device supports many more cladding modes than the bare TFBG, with a diameter of 125 μm and a much denser spectrum of mode resonances. In this respect, the superfine multiresonant TFBG-capillary sensor should provide a solution to the long-standing SRI discretization problem.

Then, we evaluated the RI sensing performance of the proposed sensor. Two superfine multiresonant TFBG-capillary sensors with ODs of 381 μm and 1000 μm were investigated, and a bare TFBG with an OD of 125 μm was also tested for comparison. We first studied the spectral response of the three devices by testing liquids with RIs ranging from 1.3334 to 1.4050 (measured with a digital refractometer at the wavelength of 589.3 nm) with large intervals. The purpose of the study is to investigate the RI sensitivity of the superfine multiresonant TFBG-capillary sensor. The recorded spectra of the two TFBG-capillary sensors and the bare TFBG are shown in Fig. 5(a). The two superfine multiresonant TFBG-capillary sensors show a similar tendency to the bare TFBG with increasing SRI. As expected, the cutoff points tend to red shift with increasing SRI. We have extracted the positions of the cutoff points for all three devices and plotted them as a function of SRI in Fig. 5(b). It is clear that the TFBG-capillary sensors with different ODs exhibit the same sensitivity in the RI range of 1.3334–1.4050. And all three devices show high linearity. From these results, we can conclude that the behavior of the cutoff mode is independent of the OD of the TFBG. In fact, this can be explained by the phase-matching equation, $${\lambda }_{\mathrm{cl}}=[n_{\mathrm{eff}}^{\mathrm{co}}({\lambda }_{\mathrm{cl}})+n_{\mathrm{eff}}^{\mathrm{cl}}({\lambda }_{\mathrm{cl}})]\mathrm{\Lambda },$$(1)where ${\lambda }_{\mathrm{cl}}$ and $\mathrm{\Lambda }$ are the wavelength of the cladding mode and the projection of the grating period along the fiber axis, respectively. $n_{\mathrm{eff}}^{\mathrm{co}}({\lambda }_{\mathrm{cl}})$ and $n_{\mathrm{eff}}^{\mathrm{cl}}({\lambda }_{\mathrm{cl}})$ are the ERIs of the core mode and the cladding mode at the wavelengths of ${\lambda }_{\mathrm{cl}}$. For the cutoff cladding mode, we have the cutoff wavelength ${\lambda }_{\mathrm{cutoff}}={\lambda }_{\mathrm{cl}}$ and the SRI $n_{\mathrm{sr}}({\lambda }_{\mathrm{cl}})=n_{\mathrm{eff}}^{\mathrm{cl}}({\lambda }_{\mathrm{cl}})$. By substituting these two equations into Eq. (1), we can get $${\lambda }_{\mathrm{cutoff}}=[n_{\mathrm{eff}}^{\mathrm{co}}({\lambda }_{\mathrm{cl}})+n_{\mathrm{sr}}({\lambda }_{\mathrm{cl}})]\mathrm{\Lambda }.$$(2)

Since both the ERI of the core mode $n_{\mathrm{eff}}^{\mathrm{co}}({\lambda }_{\mathrm{cl}})$ and the RI of the surrounding medium $n_{\mathrm{sr}}({\lambda }_{\mathrm{cl}})$ are independent of the OD of the cladding, it is reasonable that the position of the cutoff point is independent of the OD of the capillary.

How is the detection accuracy improved if the sensitivity remains unchanged and the resonances are slightly weaker with the superfine multiresonant TFBG-capillary sensor? The improvement lies in the smaller spacing of the resonances. We evaluated the performance of the TFBG-capillary sensor with an OD of 1000 μm and compared it to that of a bare TFBG to assess its SRI measurement accuracy. A series of liquid samples with refractive indices ranging from 1.35710 to 1.36144 in small increments was used in the study. The spectral responses of the bare TFBG and the TFBG-capillary sensor are shown in Figs. 6(a) and 6(b), respectively. We measured the SRI using the wavelength of the cutoff resonance dip. These cutoff dips were identified by locating the resonance dip with a significantly reduced amplitude. The results indicate that for SRI increments as small as $\sim 0.0005$, the bare TFBG cannot distinguish between samples with an SRI change smaller than approximately 0.002. The cutoff point shows a step-like behavior during SRI small increments, as illustrated in Fig. 6(c), consistent with previous research [32]. The bare TFBG’s detection accuracy is limited to 0.002 due to the wide spacing between adjacent cladding modes in the spectrum. In contrast, the superfine multiresonant TFBG-capillary sensor with a 1000 μm OD features a spacing of about 0.164 nm. This allows it to discriminate between the RIs of these liquid samples with high resolution and good linearity, as demonstrated in Figs. 6(b) and 6(d).

It should be noted that for this demonstration, we selected the RI range of 1.35710–1.36144. In practice, the superfine multiresonant TFBG-capillary sensor is applicable within the RI range of 1.333–1.40, as illustrated in Fig. 5. The resolution can be further enhanced by increasing the device’s OD. However, there is a limit to this improvement. As the OD increases, the depth of the cladding mode’s fringe decreases, making it more challenging to identify the cutoff mode. Therefore, a balance must be struck between resolution and signal-to-noise ratio. Additionally, advanced demodulation methods, such as the derivation method or those based on convolutional neural networks, could aid in identifying the cutoff resonance dip.

Compared with conventional TFBG sensors, the superfine multiresonant TFBG-capillary sensor offers a much denser comb-like spectrum, resulting in enhanced spectral resolution for the cutoff cladding mode. It is worth noting that the spectral density can also be increased by inscribing multiple gratings within a single section of optical fiber [33,34]. However, compared to these sensors, the resonance dip density in the TFBG-capillary sensor can be more easily adjusted by using silica capillaries with varying outer diameters. Additionally, the resonance dips in the spectra of the TFBG-capillary sensor are more neatly aligned compared to those of a multigrating sensor. Additionally, it provides a replaceable sacrificial interface for surface chemical functionalization and biochemical analysis. For instance, functional two-dimensional material sensing layers, typically deposited on a substrate via plasma-enhanced chemical vapor deposition (PECVD) at high temperatures (200°C–1000°C), cannot be applied directly to bare TFBG sensors. However, this can be achieved on the outer surface of silica capillaries, provided the deposition occurs before insertion of the TFBG.

In summary, we have proposed and demonstrated a superfine multiresonant TFBG-capillary sensing device, which is constructed by inserting a TFBG probe into a silica capillary filled with an RI-matching oil. We systematically investigated its spectral characteristics and sensing performance using the cutoff cladding modes. Our research indicates that the inclusion of a capillary causes the TFBG spectrum to become denser, as the larger cladding outer diameter supports more cladding modes. Both the spacing between adjacent fringes and the fringe depth decrease with an increasing capillary OD. This enlarged OD results in the TFBG-capillary sensor exhibiting improved spectral resolution for RI sensing using the cutoff mode. The hybrid sensing device holds significant promise for high-performance biochemical analysis. Our proposed sensing scheme is flexible in configuration, providing new material options and sensing strategies for the development of novel fiber sensing devices.