The development of advanced sensing technologies has become an indispensable tool for various applications, ranging from environmental monitoring to biomedical diagnostics [1–4]. Among these cutting-edge technologies, plasmonic optical fiber sensors have emerged as a promising avenue due to their ability to harness the unique optical properties of both nanoparticles (NPs) and optical fibers [5–8]. By leveraging the exceptional light-matter interactions that occur at the nanoscale, plasmonic optical fiber sensors can offer unprecedented sensitivity and selectivity, making them ideal candidates for ultrasensitive detection and real-time monitoring [9–15].

Specifically, using an optical fiber with immobilized plasmonic NPs at the core surface, each particle exhibits localized surface plasmon resonance (LSPR), intensifying the electromagnetic fields at their surfaces [16]. Besides the LSPR modes can also engage in intricate interactions with each other and even with the substrate, giving rise to interesting collective or hybrid plasmonic effects [17–19]. These depend on NP size, shape, and arrangement as well as NP-substrate and NP-NP spacing [20–24]. Since these parameters collectively determine the ultimate sensitivity to refractive index (RI) changes in the surrounding medium, understanding the interplay between these factors is crucial for tailoring the sensor response and optimizing its performance. Plasmonic coupling of densely packed NPs can be observed mainly through the LSPR shift due to neighboring NP interaction and is primarily dependent on interparticle spacing [17,25,26]. Thus, at small interparticle distances, highly intense electromagnetic fields (hot spots) are generated, which can prove beneficial for sensing applications like surface-enhanced Raman scattering (SERS) or light-matter interaction enhancement [27–29]. Interestingly, 1D or 2D NP arrays can also give rise to collective plasmonic modes that interact and propagate throughout the entire NP array showing similar behavior to the surface plasmon resonance (SPR) observed in plasmonic thin films [30,31].

Nevertheless, the considerable variability in the refractive index sensitivity (RIS) observed for NP based plasmonic optical fiber sensors may suggest another plasmonic mechanism. For example, focusing solely on studies involving Au nanospheres, whilst Mie theory predicts RIS between 30 and 80 nm per refractive index unit (RIU), the RIS values reported for Au NPs deposited on optical fibers range from 50 to 2016 nm/RIU [16,32–41]. These wide range RIS values also contrast with the low RIS values obtained experimentally from colloidal dispersions and NPs immobilized on flat glass substrates [13,36,42–44]. Despite extensive investigations, the prevailing explanations for these behaviors mainly attribute the observed sensitivities to either: (1) the formation of hot spots among NPs due to interparticle coupling; (2) the light-waveguiding mechanisms observed in insulator-metal-insulator (IMI) like structures as continuous metal films or ordered NPs arrays [35,45–47]; (3) the excitation of lossy mode resonances (LMRs) in the polyelectrolytes layer (PEL) [40,48,49]. However, it has become evident that the first explanation alone fails to account for the high sensitivities reported, as perfectly aligned and spaced dimers and trimers are only capable of presenting a maximum RIS of around 500 nm/RIU [50]. Regarding the light-waveguiding mechanisms, Otte et al. [35] proposed this mechanism considering the IMI structure composed by a metal layer of sparse Au nanoellipsoids of high aspect ratios (modeled by a homogeneous and anisotropic effective RI layer) located between a glass substrate and the external medium. Later, Spacková et al. presented similar results [51]. Regardless of the reported high RIS values, the capability to obtain the required highly effective RI layer with lower aspect-ratio NPs was not demonstrated. Also, the proposed numerical model should create an evanescent field towards the external medium (like the SPR wave obtained through plasmonic thin films). Finally, as the study was conducted on planar substrates, the optical behavior obtained on optical fiber platforms with randomly immobilized NPs is yet to be studied. Finally, regarding the LMR effect, a thick PEL is required to observe the effect of the RIS being dependent on PEL thickness when above the NPs. Nevertheless, no LMR effect is produced when a thin PEL is between the fiber and the NPs [40].

The numerical modeling of sensors based on optical fibers coated with plasmonic NPs from the aforementioned authors can also provide great insights into the underlying physical mechanisms. These range from simpler studies based on Mie scattering for plasmonic NPs in solution to NPs affected by retardation effects on their polarizability due to the presence of a substrate, interparticle coupling effects by changing their mean distance, or even approaches using an effective medium approximation provided by Maxwell Garnett theory [52–54]. The latter is of special relevance in the simulations of immobilized NPs over waveguiding structures, such as optical fibers, as interesting coupling phenomena can arise from the interaction with guided light [55,56].

Herein, we carry out theoretical and experimental investigations into the phenomena (LSPR and/or SPR) that determine the sensitivity of randomly assembled Au nanoparticle optical fibers to changes in refractive index. Thus, we deeply analyze the effect of the NP size and NP surface coverage in the optical response of the fiber to determine the optimal conditions for enhanced RIS. Besides, experimental results are compared to numerical outcomes from discretization of many interacting NPs or by treating them as a homogeneous plasmonic layer. Finally, the efficacy of the plasmonic sensing configuration will be validated for the purpose of biological sensing, specifically for the detection of thrombin protein (THR). This protein is a serine protease which regulates hemostasis and blood coagulation. Thus, fast and precise measurements can help to assess individual needs and mitigate possible clinical conditions. In this study, THR binding aptamers will be used as they assure the best measurement specificity [57–61].

The sensor configuration is based on an optical fiber sensor tip, which includes a decladded section with immobilized gold NPs (Fig. 1). Additionally, a silver film is deposited onto the end facet of the fiber, forming a mirror. This design allows for interaction between the evanescent field and Au NPs while enabling real-time monitoring of the Au NP deposition on the decladded section.

The bulk behavior of assembled Au NPs on the optical fiber was investigated using an effective index medium approximation (EMA), such as the gradient effective medium approximation (GEMA) proposed by Czajkowski et al. [62]. In this scenario, instead of discretizing a large number of NPs (computationally intensive), the system is approximated by a homogeneous layer of a given RI [52]. This approximation provides a more accurate model compared to the widely used Maxwell Garnett (MG) or Bruggeman models, which are extensively employed for accurately describing the behavior of plasmonic NPs [52,63]. This enhanced accuracy is attributed to the fact that the NPs are not simply described by a single homogeneous layer but involve multiple layers. Besides, this method allows geometrical anisotropies to be taken into account and the overall improvement of geometry accuracy by creating a gradient-like layer stack. Figure 2A shows the simulation model using a transfer-matrix method (TMM) formalism with a light cone incident from the fiber core, corresponding to the multimodal behavior on a paraxial approximation and a detection layer in the same layer. The effective index of each layer for this GEMA method can be calculated as follows. First, a layer stack with a partial density (${\mathit{f}}_{\text{partial}}$) equivalent to the discretized section along the NP height is given by Eq. (1): $$f_{\text{partial}}=\frac{6hL(1+L)R-3h^2{L}^2-2(2+3L)R^2}{2R^2{L}^3},$$(1)where $R$ is the NP radius, $L$ is the number of discretized layers, and $h$ is the layer height. The effective layer density ($f_{\mathrm{layer}}$) is then obtained by multiplying the calculated $f_{\text{partial}}$ by the total NP density ($f_{\mathrm{NP}}$). Finally, the effective index of each layer ${\epsilon }_{\mathrm{eff}}^i$ is calculated as follows using a modified MG theory for accounting for both NP anisotropy and size [63]: $${\epsilon }_{\mathrm{eff}}^i={\epsilon }_m\frac{{\epsilon }_m+(L_i(1-f_{\mathrm{layer}})+f_{\mathrm{layer}})({\epsilon }_{\mathrm{NP}}-{\epsilon }_m)+({\epsilon }_m-{\epsilon }_{\mathrm{NP}})(1-f_{\mathrm{layer}})\mathrm{\Delta }}{{\epsilon }_m+L_i(1-f_{\mathrm{layer}})({\epsilon }_{\mathrm{NP}}-{\epsilon }_m)+({\epsilon }_m-{\epsilon }_{\mathrm{NP}})(1-f_{\mathrm{layer}})\mathrm{\Delta }},$$(2)where ${\epsilon }_m$ and ${\epsilon }_{\mathrm{NP}}$ are the permittivity of the surrounding medium and NP, respectively. $\mathrm{\Delta }=x^2+2/3i{x}^2$, where $x$ is a size parameter given by $x=\pi R\sqrt{{\epsilon }_m}/\lambda$. Finally, ${\mathit{L}}_i$ is the geometrical factor for the ellipsoidal NP, which is 1/3 for Au nanospheres.

Interestingly, increasing the Au density on the effective layer, a wavelength red-shift can be observed in both the real and imaginary components of their effective index (see Appendix B, Fig. 8). Finally, by varying the same NP density, a steep increase in the effective index profile on the NP region as can be observed in Fig. 2B for a 50 nm Au NP.

The deposition of Au NPs with sizes 20, 50, and 90 nm was carried out via electrostatic interactions employing the layer-by-layer (LbL) approach [25]. Thus, citrate-stabilized Au NPs of 50 nm with negative charge were uniformly deposited via immersion on the positively charged optical fiber (see experimental part for further details). Figure 3A shows the kinetics of 50 nm Au NP deposition, and Fig. 3C shows the SEM images of the Au NPs uniformly deposited at different immersion times, as indicated. The initial stages of Au NP immobilization (Fig. 3A) clearly show a single band increasing in intensity at 550 nm, corresponding to the LSPR band of individual Au NPs. However, as the NP density on the fiber surface ($f_{\mathrm{NP}}$) increases, interparticle coupling effects start causing an LSPR red-shift (Fig. 3B). After 15 min, a second band appears at longer wavelengths due to collective plasmonic effects with a faster growth rate than the LSPR band [see scanning electron microscope (SEM) images in Fig. 3C]. At a later stage, around 30 min, it is visible that the LSPR band ceased growing and red-shifting, while the other continued to grow and red-shift at a higher rate and without significant band widening (Figs. 3A and 3B). This finding establishes that the rightmost band does not arise from interparticle coupling, but rather from an alternative collective plasmonic mechanism mainly reliant on particle density.

Further verification of the physical driving mechanisms underlying both peaks was achieved through two numerical methods: a scattering-matrix method and GEMA model with the TMM algorithm. The first method was used for the calculation of the electromagnetic fields of the Au NPs deposited on the fiber. In the model, hundreds of 50 nm Au NPs were discretized and randomly distributed on top of a glass layer (total area of $1{\mathrm{\mu m}}^2$) and immersed in a constant dielectric medium ($n=1.333$). The total number of NPs was varied according to the desired NP density. Then, light-particle interaction was accomplished from the evanescent field coming through the glass layer. As shown in Fig. 3D, a total particle population density augmentation from 2% to 20% caused an intensity increase accompanied by 20 nm red-shift. Such behavior can be undoubtedly attributed to increased interparticle coupling. On the other hand, simulations involving the GEMA model with the TMM algorithm were conducted with a 50 nm total stack layer height and subdivided into 20 layers. The effective layer’s parameters were also calculated for different NP densities. The results indicate accordance with the experimental findings, showing a strong correlation between larger red-shifts and increased NP density (Fig. 3E). Furthermore, the density-induced increase in wavelength shift exhibits greater prominence in this plasmonic mode compared to modified LSPR resulting from interparticle coupling (Fig. 3F), aligning with experimental observations. This plasmonic phenomenon is likely linked to SPR excitation obtained in plasmonic thin-film devices, and the increase in NP density serves the purpose of modulating the meta-layer effective RI. Such an approximation is valid due to the much smaller size when compared to the light wavelength. The linking to SPR phenomena is also indicated by the GEMA structure response under $\mathrm{p}$- or $\mathrm{s}$-polarizations (see Appendix B, Fig. 9). Under s-polarization an increase of $f_{\mathrm{NP}}$ results in the intensity increase of the LSPR band without a significant wavelength shift towards longer wavelengths, whereas under $\mathrm{p}$-polarized light, the structure shows a strong shift to longer wavelengths. The sum of both polarizations shows a similar response as observed experimentally.

A deeper insight into the nature of the plasmonic phenomena can be achieved through the calculation of the dispersion curves for the sensor configuration, as dispersion curves are visual representations of how the material RI changes with the light wavelength. As shown in Fig. 4A, the light dispersion curves on the NP meta-layer obtained as a function of $f_{\mathrm{NP}}$ evidence strong light dispersion as typically observed on SPR. Also, the dispersion curves cross the fiber light cone at successively longer wavelengths with increased $f_{\mathrm{NP}}$, which agrees with the observed wavelength red-shifts during the particle’s immobilization (Fig. 3A). The field distribution can also provide useful insights into the underlying mechanism behind the observed optical response. The existence of an SPR phenomenon is further backed by the electric field spatial distribution (Fig. 4B). This field shows the typical sinusoidal intensity profile inside the fiber, accompanied by a strong field enhancement in the metal/external interface and an exponential decay towards the external medium. Thus, no light waveguiding mechanism was observed, which should be characterized by a strong field locality in the center of the meta-layer. Moreover, this field profile is also highly dependent on $f_{\mathrm{NP}}$ since the field enhancement increases with $f_{\mathrm{NP}}$. The larger field on the outside region also increases the band dependency on the surrounding RI, a feature highly desirable for optimizing plasmonic sensor construction.

When studying the effect of the NP size, we found that the dispersion curves of the plasmonic meta-layer were dependent on its dimensions (consequently on the NP diameter), intersecting the fiber light cone at successively longer wavelengths for larger NPs (Fig. 4C). Finally, the NP size increase is also related to stronger fields on the surrounding medium (Fig. 4D). Therefore, higher NP densities and sizes should promote higher sensitivities, as numerically observed (Fig. 4E).

Next, we experimentally investigated the effect of $f_{\mathrm{NP}}$ on the RI sensitivity of the optical fiber. Therefore, optical fibers with immobilized 51 nm Au NPs at $f_{\mathrm{NP}}$ ranging from 18% to 22% were analyzed by immersing them in solvents with different RIs. The plot of the wavelength as a function of solvent RI shows a nonlinear behavior (Fig. 5A). The curves also indicated a higher RIS for larger $f_{\mathrm{NP}}$. Indeed, if we estimate the RIS in the vicinity of 1.34, values from 310 to 580 nm/RIU are obtained. Finally, larger values from 1698 to 3354 nm/RIU are obtained in the RI range near 1.41.

Interestingly, the nonlinear behavior on RIS regardless of $f_{\mathrm{NP}}$ is typical of SPR as previously reported [9,64–67]. It is simply due to the phase-matching conditions that need to occur and are dependent on a complex relation between the plasmonic material and external medium permittivity, as given by [68]$$k_{\mathrm{SP}}=\frac{2\pi }{\lambda }\sqrt{\frac{{\epsilon }_{\mathrm{metal}}{\epsilon }_{\mathrm{medium}}}{{\epsilon }_{\mathrm{metal}}+{\epsilon }_{\mathrm{medium}}}},$$(3)where $k_{\mathrm{SP}}$ is the light wavevector, $\lambda$ is the light wavelength, and ${\epsilon }_{\mathrm{metal}}$ and ${\epsilon }_{\mathrm{medium}}$ are the metal and the external medium permittivity, respectively.

Notably, despite the larger particle size (D = 87 nm) and lower particle density in comparison to the smaller NPs, significantly higher RI sensitivities were achieved (Fig. 5B). The analysis of smaller NPs (21 nm) presented in Fig. 5C revealed the smallest RIS enhancement, in line with the numerical results of Fig. 4E. The observed RIS for an $f_{\mathrm{NP}}$ of 16% is nearly ten times smaller than that observed with only an $f_{\mathrm{NP}}$ of 9% for the 87 nm NP-coated fiber, highlighting the relevance of the NP size for this effect. Moreover, by tracing a vertical line at a constant $f_{\mathrm{NP}}$, e.g., 20%, in Fig. 4E, it can be seen that a linear increase in the NP diameter results in a nonlinear RIS enhancement. This aspect is highlighted in Appendix B (Fig. 10), where the RI sensitivity is analyzed. Thus, for a given $f_{\mathrm{NP}}$, the NP size is the most determinant factor impacting the observed $\mathrm{\Delta }\mathrm{RIS}$ between $f_{\mathrm{NP}}$ values of 10% and 20% at different NP diameters. Also, representative SEM images of the different Au NP sizes and densities are shown in Fig. 5D, thus evidencing a uniform NP deposition. The analysis of the RIS for the different samples (solid lines in Fig. 5C) unveils a strong correlation between the NP diameter and the initial red-shift and RI sensitivity. Moreover, the GEMA based simulations (dashed lines in Fig. 5C) are in good agreement with the experimental results.

Another interesting effect can be observed by experimentally changing the surrounding medium from water ($n=1.333$) to air ($n=1.000$), causing the SPR band to disappear and the reappearance of the LSPR band (Fig. 6A). The same effect can be observed in the calculated dispersion curves when the RI changes from 1.333 to 1.000 (Fig. 6B). The most important aspect lies with the absence of any intersection between the fiber light cone and the meta-layer dispersion curve, showing that with a surrounding medium with $n=1.000$, it is impossible to excite the SPR. Additional experiments were performed on planar substrates featuring immobilized Au NPs of different sizes, employing the same immobilization process and conditions as used with the optical fibers. As shown in Fig. 6C, the wavelength shift exhibits a linear relationship with the solvent RI being the estimated RIS of 68 nm/RIU. These findings unequivocally indicate that the excitation of the SPR under perpendicular incident illumination is not possible.

Impelled by the enhanced RIS observed on denser and larger NP ensembles, the potential of Au NP immobilized optical fiber for biosensing applications was investigated. To validate its performance, the detection of thrombin protein (THR) was chosen as the model system. Since THR plays an important role in the blood coagulation cascade and homeostasis, its typical values found in a healthy adult human depend on numerous factors. However, the traditional metric to quantify the THR level kinetics is the time to achieve a 2 nM ($1\mathrm{nM}=1\mathrm{nmol}/\mathrm{L}$) level, usually referred to as the “clot time,” which is often reached in less than 5 min [69]. The typical maximum THR concentration in a healthy individual is about 100 nM. Therefore, a test range with THR concentrations from 0.01 to 100 nM was performed.

Initially, two fibers were coated with 70 nm Au NPs ($f_{\mathrm{NP}}$ 7% and 14%). The RISs of both fibers were measured to be of 544 and 1301 nm/RIU (measured at an external RI around 1.340) for $f_{\mathrm{NP}}$ of 7% and 14%, respectively. At a higher surrounding RI, around 1.39, their RIS increased considerably, reaching 1110 and 2385 for $f_{\mathrm{NP}}$ of 7% and 14%, respectively (see Figs. 7A and 7B). For the thrombin detection, the Au NP immobilized optical fibers were first functionalized with a poly-L-lysine (PLL) layer and after that with thrombin binding aptamers (TBAs), resulting in a red-shift of the main band due to the increased RI around the NPs (Fig. 7C). The fiber sensors were first sequentially exposed to increasing concentrations of THR (30 min of incubation time, see experimental section for further details). The optical properties were recorded at the final stage of each incubation step on the Tris buffer solution, which was also used as the washing solution. As shown in Fig. 7D, a red-shift was observed with higher concentrations of THR, although more pronounced for the higher NP density sensor. The experimental data followed a sigmoid-shaped profile and were fitted using the Hill model since it has been demonstrated as the best model for the aptamer–thrombin interaction [70]: $$y={\lambda }_{\max }\frac{x^n}{k^n+x^n},$$(4)where $x$ and $y$ are the THR concentration and sensor response, respectively. ${\lambda }_{\max }$ is the maximum wavelength shift [71]. Note that the Hill equation returns $k$ as a metric of binding, and $n$, the Hill coefficient. $k$ represents the concentration of protein at half-maximal binding, and $n$ reports on cooperativity. The best fit to the experimental data with Eq. (4) yielded the curve in Fig. 6B and the following values for the parameters: $k=2.42\pm 0.10\mathrm{nM}$ and $59.59\pm 754.0\mathrm{nM}$, and $n=0.94\pm 0.14$ and $0.33\pm 0.01$ for the 7% and 14% concentration configurations, respectively. The value of $k$ is essentially undetermined in both cases due to the relatively high detection range of the sensor, at least four orders of magnitude. Interestingly, the uncertainty for the 14% concentration configuration suggests a higher detection range. On the other hand, $n$ values smaller than 1 indicate the occurrence of a negatively cooperative binding, which is an expected behavior since the probability of binding reduces as the surface covering increases. The estimated limit of detection (LOD) determined as the concentration of antigen that generates 10% of the signal of the control samples (EC10) is 0.07 and 3.47 nM for the 7% and 14% concentration configurations, respectively. The LOD is displayed explicitly by a star marker in Fig. 7D. The near 50-fold decrease in the obtained LOD underlines the significance of the NP density increase, and an LOD well below the 2 nM level of the “clot time” ensures great resolution to THR efficient detection. These results are better than comparative studies with plasmonic optical fiber-based sensors that show LOD between 0.54 and 100 nM [57–59,61].

Finally, to evaluate cross-sensitivity, the sensor was incubated with human transferrin (HTR) protein (140 nM). The analysis of the optical response did not reveal a wavelength red-shift (Fig. 7E) indicating negligible HTR binding.

In summary, we have theoretically demonstrated that randomly immobilized Au NP-coated optical fibers can support SPR. Moreover, we established a clear distinction between the LSPR and SPR supported by these plasmonic optical fibers. Through the comparison of experimental results with numerical simulations, we elucidated the complex interplay between LSPR and coupled SPR effects in the plasmonic optical fibers. Thus, larger $f_{\mathrm{NP}}$ and NP sizes favor the SPR effect over LSPR. This behavior is not restricted to Au NPs and can be expanded to any plasmonic NPs, regardless of the shape and nature, randomly immobilized on an optical fiber.

Furthermore, studying the effect of Au NP size and surface coverage enabled us to identify the optimal conditions for achieving enhanced RIS and therefore sensing capabilities. Notably, we observed improved sensitivities for optical fiber modified with larger NP size and higher $f_{\mathrm{NP}}$, primarily attributed to the dominating influence of the SPR effect. The experimental RIS of Au NP-based optical fibers with $f_{\mathrm{NP}}$ of 15% varied from 135 to 6998 nm/RIU (RI region around 1.39) for an Au NP diameter from 20 to 90 nm. Similarly, 90 nm Au NP-based optical fibers showed RIS from 1297 to 6998 nm/RIU (RI region around 1.39) for $f_{\mathrm{NP}}$ between 9% and 14%. These findings offer valuable insights into the design and optimization of plasmonic optical fiber sensing platforms.

Finally, we demonstrated the practical utility of the Au NP-coated optical fibers by detecting THR. Using a 70 nm Au NP-based optical fiber with an $f_{\mathrm{NP}}$ of 14%, we achieved a remarkably low LOD of 0.07 nM. This value represents a remarkable improvement compared to those reported in the literature for plasmonic optical fiber-based sensors.

The knowledge gained from this study propels the progress of plasmonic optical fiber sensing, thereby expanding its potential applications across various fields, from biomedical diagnostics to environmental monitoring, and chemical analysis.