Introduction

Chemical processes can be monitored using various optical fiber-based probes in normal-incidence reflection or surface-reflection configurations1,2. A major advantage of such probes is their resistance to electromagnetic interference. In addition, quartz optical fibers exhibit low optical loss, enabling long-distance remote monitoring over several kilometers and measurements in harsh environments, such as high temperatures, high pressures, and chemically aggressive conditions. Most commercially available optical fiber probes are currently metal-based and cannot adequately withstand nitric acid, hydrofluoric acid, and other strong inorganic acids. Therefore, probes made from chemically resistant materials are in high demand.

In recent years, geometric deformation of optical fibers, such as U-shaped or tapered configurations, has been actively investigated to enhance the evanescent field at the fiber–medium interface, thereby improving sensitivity for refractive index (RI) sensing3,4,5. Other fiber-based approaches have also been reported, including U-shaped probes for temperature sensing6, drop-like probes for salivary pH sensing7, and leak-detection sensors for hydrogen8 and ammonia9. Comprehensive reviews further summarize fiber-optic chemical and biosensors10. Optical fiber-based liquid level sensors have been demonstrated using multimode interference (MMI) structures such as no-core fibers11. While these approaches can achieve high sensitivity, they often require specialized fiber processing or additional structural components, thereby increasing fabrication complexity. These strategies increase light–matter interaction by exposing the optical field to the surrounding medium. In contrast, lens-based probes rely on reflection and refraction control via optical interfaces, enabling multiple mechanisms to achieve RI sensitivity. The present study focuses on lens-based probes, offering a robust, chemically resistant alternative to conventional fiber-deformation methods. The detection sections of conventional RI probes often incorporate quartz prisms or hemispherical lenses. A hemispherical lens consists of two structural elements—a curved surface and a flat surface—which require O-rings for lens fixation and impose design constraints. In contrast, a plano-convex (PC) lens consists of three elements: a curved surface, a flat surface, and a beveled, blackened, anti-reflective (BBAR) edge12. In optical systems such as camera lenses, the BBAR regions are typically blackened to suppress stray light. The BBAR region also serves as a handling point, improving ease and stability during lens manipulation. The curvature of a PC lens can be flexibly designed to precisely position the optical fiber from the center to the vicinity of the BBAR, even when light enters from the flat side. Furthermore, because a blackened BBAR effectively eliminates stray light, the fiber can be positioned slightly beyond the BBAR region when necessary. Given these distinct advantages for probe design, PC lenses are promising alternatives to hemispherical lenses in RI measurement applications. Recent advances in lens-integrated fiber probes have demonstrated the feasibility of microstructured optics for compact, high-performance sensing13; however, the material must be appropriately selected to optimize probe performance. Quartz and sapphire are standout optical materials with superior optical and chemical properties.

Recent advances in smartphone-based sensing have enabled compact, low-cost optical detection systems by leveraging the built-in flash LED as the excitation source and the camera as the detector. Several research groups have successfully implemented fiber-optic or guided-wave structures connected to smartphones for chemical and biological measurements. Liu et al. demonstrated a surface plasmon resonance (SPR) biosensor that used the smartphone flash and camera for optical interrogation through a capillary-based fiber system14. Hossain et al. further integrated an optical fiber bundle with a smartphone camera to realize a portable spectrometer for rapid spectral analysis15. In the biomedical field, Markvart et al. developed a pulse-wave monitoring device that used a polymer optical fiber illuminated by the smartphone flash, achieving a simple fiber-optic detection scheme without external instrumentation16. A recent review by Yang et al. comprehensively summarized smartphone-integrated optical fiber biosensors, emphasizing their potential for field-deployable, point-of-care, and educational applications17.

Although these smartphone-interrogated systems are promising for portable and rapid diagnostics, their performance is limited by the output power and spectral stability of the smartphone LED, as well as the camera’s pixel resolution and susceptibility to ambient light. Moreover, the optical path is generally open to the environment, making the measurement vulnerable to contamination and alignment errors. In contrast, fiber- or lens-integrated probes confine light within a well-defined guided path, providing higher optical stability, reproducibility, and compatibility with chemically aggressive conditions. Therefore, while smartphone-based sensors are well-suited for low-cost and on-site screening, the present study focuses on a quartz- and sapphire-based lens probe that complements these portable techniques by offering superior precision, robustness, and chemical resistance.

This study aims to develop a high-sensitivity optical probe that balances the chemical resistance against optical RI-sensing performance. The probe body was constructed from perfluoroalkoxy alkane (PFA), which is known for its exceptional chemical stability. The optical component was a PC lens crafted from quartz or sapphire. Both lens materials are highly transparent, durable, and resistant to harsh chemicals. This paper determines the optimal design conditions and evaluates the RIs of the optical probes in detail.

Materials and methods

Materials

The RI measurements were performed in sucrose and potassium permanganate (KMnO4) purchased from Kanto Kagaku Co., Ltd. (Japan). Sucrose was adopted as the RI standard and KMnO4 was employed in additional optical experiments. 1-Propanol was purchased from Kanto Kagaku Co., Ltd. (Japan). Light oil was obtained from a local gas station, and Japanese rice wine and liquor were purchased from local retailers in Kawasaki, Japan. A general industrial-use antifreeze solution was obtained from Showa Industries (EG Brine, Japan). Pure water was obtained via reverse osmosis, followed by ion exchange and filtration in a Simplicity UV system (Merck Millipore, USA). Plastic single-core optical fibers with a diameter of 0.97 mm (SHCN-100, Asahi Kasei Corp., Japan) were assembled with a handmade synthetic-quartz PC lens supplied by Hotta Optical Co., Ltd. (Japan) or a PC sapphire lens manufactured by Sigma Koki Co., Ltd. (Japan). The output of a tungsten-halogen lamp (SLS201L/M, Thorlabs, USA) was passed through the optical fiber and the transmitted light was analyzed in a fiber-coupled CCD spectrometer (HR-2000 + ES, Ocean Optics, USA) to obtain the transmission spectrum.

Assembly of optical fibers with a PC lens

First, we calculated the effective range of light incidence on the spherical surface. For simplicity, we set R to 1 and determined the position at which the incident angle reaches the critical angle18. Light entering from x1 is reflected at point P(x1, y1) in Fig. 1a. The corresponding angle θ2 was calculated as.

Fig. 1
figure 1

(a) Calculation of the reflection angle (θ₂) and (b) correlation between θ₂ and the distance (x) between fibers positioned on a PC lens. Horizontal red and blue dashed lines indicate the critical angles of sapphire and quartz, respectively, and the vertical black dashed line marks the lens outer diameter. (c–f) Ray-tracing simulations showing the influence of NA values (0.5 and 0.22), fiber diameter (0.5 and 1.0 mm), and inter-fiber spacing D1 (2.0 and 4.6 mm) on optical coupling inside the PC lens. (c) Fiber φ 0.97 mm, D1 = 2.0 mm; (d) Fiber φ 0.50 mm, D1 = 2.0 mm; (e) Fiber φ 0.97 mm, D1 = 4.6 mm; (f) Fiber φ 0.50 mm, D1 = 4.6 mm. Ray propagation was calculated using Snell’s law (RI = 1.456 for quartz). A larger NA produces a broader acceptance half-angle [θmax = 20.1° in quartz], causing greater divergence and leakage beyond the BBAR edge, whereas a smaller NA (θmax = 8.7°) confines the light more effectively. These results confirm that D1 and NA jointly determine the reflection efficiency and coupling stability between the input (A) and output (B) fibers.

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$$\:{\theta\:}_{2}{=90^\circ\:-\theta\:}_{1}$$
(1)

where

$$\:{\theta\:}_{1}={\text{tan}}^{-1}\frac{\sqrt{{R}^{2}-{x}^{2}}}{x}$$
(2)

and

$$\:{x}^{2}+{y}^{2}={R}^{2}$$
(3)

Next, the results were adjusted by varying the lens’s radius of curvature (Fig. 1b). In the quartz lens, total internal reflection occurs when θ2 exceeds the critical angle (43.3°), which corresponds to x = 2.51 in Fig. 1b19. In the sapphire lens, the critical angle for internal reflection of 587-nm light is reduced to 34.5° (in air at 22 °C), corresponding to x = 2.0219. Interestingly, the x-value at the critical angle for quartz nearly coincides with the outer diameter of the lens. For safety reasons, the BBAR thickness was set to 1.5 mm. The lens specifications based on these design considerations are summarized in Fig. 2.

Fig. 2
figure 2

Schematic of the measurement setup and specifications of the plano-convex (PC) lenses used in this study. The diagram shows the optical and electrical configuration comprising the LED driver, photodiode, amplifier, and microcontroller unit (MCU). The photograph shows the homemade sensor chip composed of two plastic optical fibers and a PC quartz lens sealed with a PFA holder to prevent liquid ingress. A 0.5 mm-thick polyvinyl chloride (PVC) sheet was placed between the bottom of the beaker (or resin tray) and the lens. The PVC sheet was black or white depending on the experimental conditions, and the lens-to-reflector distance (D2) was set to 0.5–3.5 mm. The inset table lists the geometrical parameters of the PC lenses (diameter = 5.0 mm, edge thickness = 1.6 mm, radius of curvature = 3.68 mm for quartz and 3.63 mm for sapphire).

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Two optical fibers were placed in parallel with a specific separation on the flat surface of the lens (Fig. 1c–f). When the fibers were closely spaced, as illustrated in Fig. 1c, the numerical aperture (NA) of the fiber and Snell’s law20 imposed an acute reflection angle at the inner surface of the lens, increasing light leakage outside the lens and reducing the amount of light reaching the output fiber. In contrast, an appropriate inter-fiber distance ensured that the reflected rays approached the critical angle, thereby improving coupling efficiency, as shown in Fig. 1e. We hypothesized that maintaining an appropriate inter-fiber distance would ensure efficient light coupling between the fibers, as similarly discussed in geometrical optimization studies21.

In addition to the geometrical parameters, the NA strongly governs the angular spread of rays entering the lens. A larger NA produces a broader acceptance cone and greater divergence inside the lens, whereas a smaller NA confines the rays within narrower limits. To clarify these effects, geometrical ray-tracing simulations were carried out using computer-aided design (CAD) software to visualize light propagation through the PC lens by varying the NA (0.5 and 0.22), fiber diameter (0.5 and 1.0 mm), and inter-fiber distance D1 (2.0 and 4.6 mm). Ray propagation was calculated according to Snell’s law using the refractive index of quartz (RI = 1.456). The simulated results (Fig. 1c–f) show that both D1 and NA jointly determine the reflection efficiency and optical coupling between the input (A) and output (B) fibers. Most of the rays reflected at the inner surface of the synthetic-quartz lens remained above the critical angle, indicating efficient transmission to the output fiber.

Furthermore, the proportion of reflected rays incident on the upper flat surface that entered the output fiber was quantitatively assessed. The emission efficiency, defined as the ratio of the light incident length on the fiber core to the total illuminated length on the flat surface, was 33% for NA = 0.5 and 0% for NA = 0.22 in Figs. 1c and 12% and 0% in Figs. 1d and 81% and 62% in Fig. 1e; and 100% and 98% in Fig. 1f, respectively. Because the optical power is proportional to the core area, fibers with diameters of 0.97 mm and 0.5 mm differ by approximately fourfold in total light intensity, explaining the higher overall brightness observed in Fig. 1c and e.

Measurement setup

Figure 2 shows the measurement setup for the designed sensor system, using a step-index optical fiber with a 970-µm-diameter polymethylmethacrylate (PMMA) core. One end of the optical fiber was connected to a single-wavelength light-emitting diode (LED: 660 nm, Alpha-One Electronics Ltd., Japan) as the light source; the other end was connected to a silicon photodiode (S1787-08, Hamamatsu Photonics K. K., Japan).

The LED light source was powered by a hand-made power supply (Toyoko Kagaku Co. Ltd., Japan), and pulsed signals were obtained through a hand-made amplifier (Toyoko Kagaku Co. Ltd., Japan) that amplifies the original gain by up to 20 times. Prior to measurement, the light quantity and gain were adjusted with a power meter (Graytechnos Co. Ltd., Japan). The pulsed signals were converted to analog voltages on the circuit board, and the light intensity was adjusted from 0 to 5 V. The obtained data were recorded using NR-500 and NR-TH08 data loggers (Keyence Co. Ltd., Japan). The RIs of the sample solutions were measured using a refractometer (PAL-RI, ATAGO Co. Ltd., Japan). The absorption spectra were measured with a spectrometer (HR2000 + ES, Ocean Optics, USA) equipped with a built-in CCD and a halogen lamp SLS201 (Thorlabs Inc., USA) as the light source. The sample volume in the absorption measurements was 2 mL, sufficient for wetting the entire lens surface. The geometrical modeling and ray-tracing simulations were conducted using CAD software (CADSUPER 2023, Marble Co., Ltd., Japan).

Results and discussion

Influence of inter-fiber distance on light intensity

Figure 3a presents three examples with different distances (here denoted D1) between the centers of the two fibers. The voltage measurements clearly differed between water (RI = 1.333) and the 60% sucrose solution (RI = 1.442) and the light intensity reaching the detector obviously depended on D1 (Fig. 3b). Interestingly, at D1 = 4.6 mm, the light intensity reaching the detector increased, even though the calculated fiber–lens contact area decreased by 23% compared with D1 = 2 mm. When D1 was less than 4 mm and the fiber contact area remained within the lens, the light intensity in air did not change significantly. In contrast, as D1 approached the outer diameter of the lens, the light intensity continuously increased until D1 reached the edge of the lens. When D1 increased from 4.0 mm to 5.0 mm, the light intensity increased by a factor of approximately 2.5. The simulation results shown in Fig. 1c–f are consistent with these experimental observations. When D1 is small, the wider divergence produced by NA = 0.5 causes a portion of the rays to escape beyond the BBAR region, reducing the collected intensity. As D1 increases, the reflected rays approach the critical angle, enhancing coupling efficiency, particularly for lower-NA fibers (NA = 0.22) whose angular spread is narrower. These results support the interpretation that both D1 and NA govern the effective reflection and transmission paths inside the PC lens.

Fig. 3
figure 3

(a) Examples of optical probes with different distances between the fiber centers and (b) influence of inter-fiber distance on light intensity. The left and right y-axes indicate the intensity in air (orange line plot) and the corresponding intensity changes between measurements in water and 60% sucrose solution (blue bar graph), respectively.

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The response variations shown in Fig. 3b strongly depend on whether the internal reflection angle (θ₂) within the lens approaches the critical angle. As illustrated in Fig. 1a and b, light emitted from the input fiber enters the flat surface of the lens and is reflected at the curved surface. As the incident angle x approaches the periphery, the reflection angle θ₂ increases and approaches the critical angle (43° for quartz), where total internal reflection is more likely. When the fiber-to-fiber distance (D1) is small (e.g., 2–3 mm), the reflection angle is sufficiently below the critical angle, leading to some light leaking out of the lens and reducing the coupling efficiency to the output fiber. In contrast, when D1 increases to 4.0–4.6 mm, the reflection angle approaches the critical angle, minimizing internal reflection loss and sharply increasing the detected light intensity. This behavior is the primary cause of the intensity enhancement observed in Fig. 3b.

In addition, the refractive index (RI) of the surrounding medium influences the critical angle and thereby the response curve. For water (RI = 1.333) and 60 wt% sucrose solutions (RI = 1.38–1.44), the critical angle is smaller than that in air, resulting in higher reflection efficiency under identical D1 conditions. In particular, when 4.2 ≦ D1 ≦ 4.6 mm, the difference between water and sucrose solutions became more pronounced because, as shown in Fig. 1c and d, stronger optical coupling with the output fiber increased the total transmitted light intensity. When D1 ≧ 4.8 mm, the coupling becomes even stronger; however, the reflection angle becomes larger, reducing light leakage to the outside. Moreover, additional scattering losses at the beveled and blackened anti-reflective (BBAR) edge further diminish the intensity difference between water and sucrose solutions.

Thus, the observed increase in light intensity in air and the difference in responses between water and sucrose solutions in Fig. 3b can be consistently explained by three factors:

  1. (1)

    the approach of the reflection angle toward the critical angle as D1 increases,

  2. (2)

    scattering losses at the lens periphery (BBAR region), and.

  3. (3)

    variation in the critical angle due to the refractive index of the surrounding medium.

These interpretations are consistent with the ray-tracing simulations shown in Fig. 1c–f, confirming that D1 and the numerical aperture (NA) jointly determine the reflection and coupling efficiency within the PC lens.

To evaluate the influence of temperature on sensor performance, additional experiments were conducted, as summarized in the Supplementary Information (Figure S1). All subsequent experiments were carried out at 25 ± 1 °C. Furthermore, after assembly, each sensor’s optical output was measured in pure water, and only those units with readings within ± 6 σ of the batch mean were used for further testing.

Comparison of the quartz and Sapphire lenses

Panels A and B of Fig. 4 clarify the differences in the optical properties of quartz and sapphire lenses. In each image, the left lens is composed of quartz, and the right lens is made of sapphire with a C(0001) orientation. When viewed from the convex surface (Fig. 4a), the sapphire lens distorted the background grid pattern more substantially than the quartz lens, indicating a higher RI and a greater degree of light bending. Similarly, when viewed from the flat surface (Fig. 4b), distortion and optical aberrations were more pronounced through the sapphire lens than through the quartz lens, which exhibits relatively uniform refraction.

Fig. 4
figure 4

Comparison of observations through the (a) curved surfaces and (b) flat surfaces of the quartz (A) and sapphire (B) lenses; (c) effect of lens material on light refraction.

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Figure 4c compares images of the assembled probes with the quartz and sapphire lenses under illumination with 660-nm LED light. Light refracted from the lens, direct light leakage from the fiber through the PFA, and light reflected or refracted within the PFA are clearly distinguishable. The lenses were fixed in transparent PFA cases (holders), and the optical fiber was positioned to extend beyond the flat surface of the lens. Consequently, light spread inside the PFA was also observed. The quartz lens exhibited brighter refracted light and a smaller refraction angle than the sapphire lens.

Under the same conditions as the quartz lens, a sapphire lens was used for comparison. The hemispherical top of the lens was immersed in sucrose aqueous solutions with various RIs, and the intensities of the reflected light were recorded. The distance (D2) between the top of the lens and a black PVC sheet placed on the floor was set to 0.5 mm (as configured for the quartz lens in Fig. 2), then increased to 1.5 mm, 2.5 mm, and 3.5 mm. If the probe is used for monitoring liquid leaks from outdoor equipment, a narrow gap can easily trap debris and dust carried by rainwater. To avoid this problem, the gap should be configured as wide as possible. However, an excessively wide gap may evade proper contact with the lens surface. Accordingly, the gap width in the experiment ranged from 0.5 mm to 3.5 mm. Figure 5 plots the received light intensities of RI and D2 in probes using the quartz lens and sapphire lens materials. Each result is plotted as an average of 10 measurements.

Fig. 5
figure 5

Comparison of quartz and sapphire lenses. (a) Effect of RI on light intensity in samples with different distances D2 between the lens surface and PVC plate: (A) 0.5 mm, (B) 1.5 mm, (C) 2.5 mm, and (D) 3.5 mm. (b) Effect of D2 on light intensity in solutions with different RIs: (A) RI = 1.333 (pure water), (B) RI = 1.382 (sucrose aqueous solution), and (C) RI = 1.407 (sucrose aqueous solution). The left axis represents the intensity of the quartz-lens set (☐), and the right axis represents the intensity of the sapphire-lens set (〇). Error bars indicate the range between the maximum and minimum values observed in the measurements, reflecting the variability in the data.

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For the same distance (D2) between the lens surface and the PVC plate, the light intensity of sapphire exceeded that of quartz by approximately two orders of magnitude, although the light intensities of both lenses trended similarly downward with increasing RI (Fig. 5a). However, the quartz data point near RI = 1.38 is slightly below the fitted line.

Panels A to C of Fig. 5b plot the light intensities of the quartz and sapphire samples as functions of D2. This rearrangement highlights the distinct behaviors of quartz and sapphire. Increasing D2 in the quartz-lens sample increased the received light intensity. In contrast, the sapphire sample exhibited high intensities at 0.5 mm and 2.5 mm, and lower intensities at 1.5 mm and 3.5 mm.

Because the refractive indices of quartz (RI = 1.456) and sapphire (RI = 1.765) are higher than that of air, the effective acceptance angle at the fiber–lens interface becomes narrower (Fig. 1c-f).

For instance, when NA = 0.5, the half acceptance angle decreases from approximately 30° in air to 20° in quartz and 16° in sapphire. Consequently, light entering the sapphire lens is more strongly confined within the lens medium, which may partially account for the higher apparent sensitivity but also the nonlinear intensity variations observed in Fig. 5. This indicates that the refractive index of the lens material and the fiber NA jointly influence the effective coupling geometry and optical efficiency of the probe.

These non‑linear intensity variations—absent in quartz—are most plausibly attributed to polarization‑dependent beam displacement caused by the birefringence of sapphire22. Gartman et al.23 reported that in uniaxial crystals such as sapphire, even minute changes in incidence angle or polarization state can induce phase retardation between the ordinary and extraordinary rays, resulting in focal shifts. In our study, the fiber-to-fiber distance (D1) was 4.6 mm. The light traveled along the path “fiber → lens → reflector → lens → fiber,” giving an effective optical path length of approximately 7.6 mm. Under such conditions, phase differences become non-negligible. Moreover, as the RI of the surrounding liquid increases, the response curve transitions from a downward slope to a near plateau, suggesting that the birefringence effect diminishes as the index contrast between the liquid and sapphire decreases. Taken together, phase retardation arising from axis‑dependent birefringence in sapphire, compounded by RI mismatch at the sapphire–liquid interface, likely underlies the observed D2‑dependent non‑linear intensity variations.

To investigate the RI response to relative light intensity, the initial intensity (in pure water: RI = 1.333) was set to 100, and the rate of change in the intensity–RI plot was calculated. Based on the results in Fig. 5, D2 was set to 2.5 mm for quartz and 0.5 mm for sapphire. The comparative results are plotted in Fig. 6a. The intensity–RI plot of the sapphire sample was linear across the measurement range, with an R² value of 0.999, whereas that of quartz was linear from water up to RI = 1.39 (R2 = 0.994), beyond which the intensity dropped to zero. Extrapolation suggests that sapphire intersects the x-axis at RI = 1.737, close to the RI of sapphire (1.765); that is, the results for sapphire approximate the theoretical value19. Each data point represents the average of three measurements obtained from a single sensor. Although error bars are not shown, the repeated measurements exhibited consistent trends, confirming the reproducibility of the data.

Fig. 6
figure 6

(a) Comparison of change rates of RI responses of the lenses. The initial intensity (in pure water) is set to 100%. Quartz lens (■, D2 = 2.5 mm) and sapphire lens (●, D2 = 0.5 mm). (b) Scatter plot showing the relationship between the refractive index (RI) of different liquids and the sensor’s output voltage. Each data point corresponds to a specific solvent listed in Supplementary Table S1. A quartz plano-convex (PC) lens was used with a lens-to-reflector distance (D2) of 0.5 mm. The measurements were performed using a polytetrafluoroethylene (PTFE) beaker, which served as both a sample container and a mechanical support for the resin-embedded probe structure.

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Previous RI sensors have typically achieved either high sensitivity or a wide dynamic range, but rarely both. Fiber laser-based sensors, such as those reported by Wang et al., exhibit ultra-high sensitivity (approximately − 274 dB/RIU) but operate over a narrow RI range (1.300–1.335)24. Similarly, Saimon et al. achieved − 293 dB/RIU but only within the high-RI regime (1.450–1.531)25. On the other hand, POF-based sensors (e.g., Teng et al.26 extended the range up to RI = 1.45 with simpler setups but showed lower sensitivity (800–937%/RIU, approximately 9.0–9.7 dB/RIU) over a similar RI range. Although POF sensors generally exhibit lower sensitivity and may not be the most appropriate benchmark, they are included here because they target similar liquid-sensing applications. Similarly, an MMI-based no-core fiber sensor for liquid-level monitoring11 showed attenuation changes of 5–13 dB between water and ethylene glycol, indicating detectable RI-dependent responses, although not normalized in dB/RIU. Interestingly, our PC lens-based probe provides both advantages, consistent with other studies exploring high-RI lens materials for immersed optical fiber sensors27: the quartz lens offers − 272 dB/RIU sensitivity, while the sapphire lens delivers excellent linearity (R² = 0.999) across RI = 1.33–1.45. This dual performance is achieved using only an LED and photodiode, without the need for lasers or interferometry, thereby demonstrating a unique balance between sensitivity and range.

Figure 6b presents the measurement results, and the corresponding solvents and their RIs are listed in Table S1 in the Supplementary Information. The response was highly linear from pure water (RI = 1.333) through 1-propanol (98%, RI = 1.376), covering six concentration points. Within this range, the sensor exhibited an R² of 0.991, consistent with the trend observed in Fig. 6a. Beyond RI = 1.40, the output plateaued as the sample RI approached that of quartz, limiting the measurable range. To extend linearity toward higher-RI liquids such as light oil (RI = 1.458), a sapphire lens would be required. These results demonstrate the sensor’s potential to detect and differentiate various liquids with moderate to high RIs.

Investigation as a spectroscopic probe

As described above, the probes delivered a sufficient RI response. However, the measurements of a PC lens-based probe for spectroscopic analysis must reflect the absorption spectrum of the target solution. In addition, the response at a specific wavelength must adhere to Beer–Lambert’s law. To investigate these aspects of the proposed probes, black-and-white sheets were used as background plates beneath the lenses, and an aqueous potassium permanganate solution was used as the test sample.

Figure 7 shows the dependencies of spectral shape on sheet color and lens material, where the dip around 700 nm is attributed to absorption by the PMMA core in the optical fiber. On the white sheets (Fig. 7a and c), quartz exhibited a greater intensity change relative to the intensity of pure water than sapphire. The intensity-change profile of the quartz probe closely resembled that of potassium permanganate, suggesting that quartz, which allows more light to escape and reflect back from the white sheet than sapphire, is more suitable for obtaining spectroscopic spectra. However, neither quartz nor sapphire captured the characteristic dual peaks of potassium permanganate at 550 nm and 570 nm28. On the black sheet (Fig. 7b and d), the light intensities of both materials exhibited minimal changes. The intensity of the light returning to the quartz was reduced to approximately one-tenth of its original value. In contrast, the intensity of the light returning to the sapphire was reduced by 10% compared to that on the white sheet, indicating that sapphire is comparatively insensitive to sheet color.

Fig. 7
figure 7

Comparison of spectral characteristics of the quartz lens with D2 = 2.5 mm (upper) and sapphire lens with D2 = 0.5 mm (lower) on a white (left) and black (right) sheet. Blue line: pure water; orange line: 10 mM KMnO4 aqueous solution; green line: intensity change. Integration time: (a) 600 ms, (b) 6000 ms, and (c, d) 200 ms.

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In our optical configuration, increasing the fiber spacing D1 effectively lengthens the optical path length (L in the Beer–Lambert law), thereby enhancing RI responsiveness. However, it also increases the overlap of stray and internally reflected beams at the lens surfaces. Moreover, the resulting longer and more complex round‑trip path degrades the signal‑to‑noise ratio, causing closely spaced absorption bands to be obscured by noise or baseline drift, and ultimately reducing the apparent spectral resolution. For these combined reasons, resolving the characteristic twin peaks of KMnO₄ becomes increasingly complex as D1 increases. In comparison, Fig. 8a shows the result obtained under the same conditions as in Fig. 7a but with D1 set to 2.5 mm, where the two characteristic KMnO₄ peaks are clearly observable. This confirms that the limitation arises from the optical configuration of the probe, rather than from the spectrometer’s nominal resolution.

Fig. 8
figure 8

(a) Measured light intensity using a quartz plano-convex (PC) lens for a 10 mM KMnO4 aqueous solution, with D1 = 2.5 mm and D2 = 2.5. A white background sheet was used beneath the sample to enhance back-reflection. (b) Relation between light intensity and potassium permanganate concentration. Lens material: quartz; sheet color: white; sample: KMnO4 aqueous solutions, with D1 = 4.6 mm and D2 = 2.5. Integration time: 600 ms. Error bars indicate the range between the maximum and minimum values observed in the measurements.

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Figure 8b shows the concentration dependence of the 550-nm light intensity of the quartz lens combined with a white sheet. Investigating the relationship between light intensity and concentration, the intensity variations were small at both low and high concentrations, although the overall linearity was high (R2 = 0.964). At low concentrations, the intensity was dominated by strong reflections from the white sheet, whereas at high concentrations, internal reflections within the lens became relatively stronger. The response of this combination may follow the Lambert–Beer law, suggesting the feasibility of using this setup as a spectroscopic probe.

Conclusion

In summary, we developed chemically robust, metal-free optical fiber probes incorporating plano-convex (PC) lenses for refractive index (RI) sensing. The probes demonstrated high sensitivity and linearity, enabled by optimizing two key geometrical parameters: the fiber-to-fiber distance (D1) and lens-to-reflector distance (D2). We identified three key findings: (1) increasing D1 brings the reflection angle closer to the critical angle, enhancing light collection; (2) the intensity difference between water and sucrose remained stable across a broad D1 range (4.2–4.6 mm), offering design tolerance; and (3) D2 significantly influenced light intensity and angular spread, affecting measurement precision.

In addition to these geometrical parameters, the numerical aperture (NA) of the fiber plays a crucial role in determining the angular confinement and optical coupling efficiency within the PC lens. Optimization of NA in conjunction with the lens curvature and material selection could further improve both sensitivity and linearity of the refractive-index response, providing a useful design parameter for future high-performance optical probes.

Quartz lenses achieved strong linearity (R² = 0.994) in RI = 1.33–1.39, while sapphire lenses delivered ~ 20× higher sensitivity with excellent linearity (R² = 0.999), despite birefringence effects. These results highlight the potential of PC-lens-based probes as practical, high-performance RI sensors suitable for deployment in chemically aggressive or remote environments. Future studies will explore temperature dependence, sapphire-specific D1 behavior, and applications in real-time liquid monitoring systems.