To investigate the sensing performance of the 1D Fibonacci quasiperiodic PC sensors, we first explore the detection peaks in the transmission spectra of the proposed sensor for different Fibonacci generations and analytes, as shown in Fig. 2. The refractive indices of SiO2\(\left({n}_{1}\right)\) and TiO2 \(\left({n}_{2}\right)\) are possessed from the literature [43, 44]. The thicknesses of layer A (SiO2) and layer B (TiO2) are considered\({ d}_{1}=100 nm\),\({d}_{2}=90 nm\) respectively. The refractive indices \({n}_{1}\) and \({n}_{2}\) have the values 1.475 and 2.365 for the wavelength 700 nm, respectively. The thickness of the analyte layer is chosen\({ d}_{s}=1.5 \mu m\). The transmission spectra of the proposed sensors for different Fibonacci generations with the analyte layer refractive index (\({n}_{S})\) variation are shown in Fig. 2. We observe that the transmission band regions and sensing peaks change with different Fibonacci generations in the proposed sensor structures. Different Fibonacci structures conduct to localization of sensing peaks at different positions and in numbers. Here, we obtain the two sensing regions for the sensor structure of \({\left({F}_{3}\right)}^{7}S{\left({F}_{3}\right)}^{7}\) and a single sensing region for the other structures of \({\left({F}_{4}\right)}^{4}S{\left({F}_{4}\right)}^{4}\), \({\left({F}_{5}\right)}^{2}S{\left({F}_{5}\right)}^{2}\), and \({\left({F}_{6}\right)}^{1}S{\left({F}_{6}\right)}^{1}\), as can see in Figs. 2(a), 2(b), 2(c) and 2(d), respectively. The sensing peaks positions \({(\lambda }_{p})\) have variations toward higher wavelength with increasing the values of \({n}_{S}\). The separation insight of the sensing peaks position \({(\lambda }_{p})\) for different \({n}_{S}\)-values and Fibonacci generations are depicted in the insets in the corresponding figures.

For the different Fibonacci structures and analyte refractive indices, the sensing peak positions\({ (\lambda }_{p})\), sensitivity, and FOMs have variations. To look closely at such variations, we plot the graph for \({\lambda }_{p}\) with \({n}_{S}\), sensitivity, and FOMs with \(\varDelta {n}_{S}\) in Fig. 3 for the sensor structures with different Fibonacci generations. From the Figs. 3(a) to 3(d), we observe that the sensing peak positions \({\lambda }_{p}\) shift toward higher wavelength with \({n}_{S}\)-values for all the cases. The variations of \({\lambda }_{p}\) with \({n}_{s}\) are linear, but they reveal dissimilar slope transformations for different Fibonacci generations. For the sensor structure of \({\left({F}_{3}\right)}^{7}S{\left({F}_{3}\right)}^{7}\), the sensitivity and FOM for the first order and second order sensing peaks, respectively, increases and decreases with \(\varDelta {n}_{S}\), as shown in Fig. 3(e). Here, \(\varDelta {n}_{S}\) represents the difference of two respective refractive indices as the value of \({n}_{21} \left(=1.33-1.31\right),\) \({n}_{32} \left(=1.35-1.33\right),\) \({n}_{43} \left(=1.37-1.35\right),\) \({n}_{54} \left(=1.39-1.37\right),\) and\({n}_{65} \left(=1.41-1.39\right)\). Layer thicknesses are\({ d}_{1}=100 nm\),\({d}_{2}=90 nm\), and\({ d}_{s}=1.5 \mu m\). Maximum sensitivity and FOMs of the sensor with \({\left({F}_{3}\right)}^{7}S{\left({F}_{3}\right)}^{7}\) are, respectively, 465 nm/RIU and 1033.33 RIU−1 for the first order peaks and 530 nm/RIU and 963.64 RIU−1 for the second order peaks. For the other sensor structures of \({\left({F}_{4}\right)}^{4}S{\left({F}_{4}\right)}^{4}\), \({\left({F}_{5}\right)}^{2}S{\left({F}_{5}\right)}^{2}\), and \({\left({F}_{6}\right)}^{1}S{\left({F}_{6}\right)}^{1}\), the sensitivity and FOM are randomly change with \(\varDelta {n}_{S}\) as shown in Figs. 3(f), 3(g) and 3(h), respectively. The changes in the sensing peaks and sensitivity are the results of the changes in the structural arrangements for the different Fibonacci generations. The FOMs vary due to changes in the full-width half maxima (FWHM) of sensing peaks under the influence of the different Fibonacci sequences. For all cases, as shown in Fig. 3, we obtain the maximum sensitivity of 530 nm/RIU and the maximum FOM of 2983.33 RIU-1. The remarkable modification and high sensitivity and FOM values offer an approach to realize the potential refractive index sensors.

To examine the effect arising on the variations of sensing peaks due to the different Fibonacci generations periodicity (p), we have depicted the transmission spectra for the sensor structures of \({\left({F}_{3}\right)}^{p}S{\left({F}_{3}\right)}^{p}\), \({\left({F}_{4}\right)}^{p}S{\left({F}_{4}\right)}^{p}\), \({\left({F}_{5}\right)}^{p}S{\left({F}_{5}\right)}^{p}\), and \({\left({F}_{6}\right)}^{p}S{\left({F}_{6}\right)}^{p}\) with different values of the periodicity (p) in Fig. 4. We observe that the sensing peak positions are the same for all the cases with different periodicities, but their FWHM and intensity change with periodicity. The changes in the FWHM and intensity show the diverse behavior for the different Fibonacci generations. It is the result of the different layer numbers and their staking under different Fibonacci generations. The intensity of the sensing peaks decreases to a minimum with the periodicity as proceed to the higher-order Fibonacci generations. The FWHMs are also become narrower with increasing the periodicity. The remarkable variations in the intensity and FWHM of the sensing peaks induce the optimized periodicity for different generations.

To optimize the thicknesses constituted layers in the sensor structures, we have demonstrated the transmission spectra for the layers thickness \({d}_{s}\), \({d}_{1}\), and \({d}_{2}\) in Figs. (5), (6) and (7), respectively, with sensor structures of the 3rd, 4th and 5th Fibonacci generations. As per the above results, we have preferred the periodicity (p) 7, 4, and 2 for the 3rd, 4th, and 5th Fibonacci generations, respectively. In Fig. 5, we have shown the transmission spectra and the transformation of sensing peaks for the variation of sample layer thicknesses \({d}_{s}\) from 1 µm to 2 µm with different values of \({n}_{S}\), and \({d}_{1}=100 nm\) and \({d}_{2}=90 nm\). The separations and position of the sensing peaks show the noticeable changes with increasing the value of \({d}_{s}\) for all cases. We observe that the FWHMs of the sensing peaks also change with \({d}_{s}\). The Fibonacci sequence generations also show the considerable effect on the separations, positions, and FWHMs of the sensing peaks, as depicted in Figs. 5(a), 5(b), and 5(c) for the sensor structures of \({\left({F}_{3}\right)}^{7}S{\left({F}_{3}\right)}^{7}\), \({\left({F}_{4}\right)}^{4}S{\left({F}_{4}\right)}^{4}\), and \({\left({F}_{5}\right)}^{2}S{\left({F}_{5}\right)}^{2}\), respectively. With the variation in the values of \({d}_{s}\), the sensitivity and FOMs change due to the transformation in the separation and FWHM of the sensing peaks for different Fibonacci generations.

A similar investigation has also been carried out to reveal the impact of layer thicknesses \({d}_{1}\) and \({d}_{2}\) on the sensing performance, and demonstrated in Figs. (6) and (7), respectively. We have considered the layer thickness \({d}_{1}\)varies from 80 nm to 160 nm, and other layer thickness fixed as \({d}_{2}=90 nm\) and \({d}_{s}=1.5 \mu m\) for Fig. (6) and chosen the layer thickness \({d}_{2}\) from 60 nm to 140 nm with the fixed values of \({d}_{1}=100 nm\) and \({d}_{s}=1.5 \mu m\) for Fig. 7. It can be seen that the transmittance band and sensing peaks shift toward higher wavelength with increasing the values of \({d}_{1}\) and \({d}_{2}\) for all cases of \({n}_{S}\). The changes in the transmission spectra and sensing peak performances under the influence of the Fibonacci generation can be viewed in sections (a), (b), and (c) of Figs. (6) and (7), respectively. One can see that the separation, position, and FWHM of the sensing peaks depend on the sample layer thickness, constituted PC layer thickness with different Fibonacci generation. Thus, a substantial quantity of the sample is required for getting considerable sensitivity. These results induce consideration of the appropriate structural parameters with the different Fibonacci sequences for efficient sensing performance.

We have demonstrated all the above results for the analyte refractive index range from 1.31 to 1.41 because the refractive indices for most bio-fluids such as hemoglobin, glucose in the blood, blood plasma, cancer cells, etc., possess in this range [23, 26, 27, 30–33]. Therefore, the introduced Fibonacci quasiperiodic PC sensor can be employed for bio-sensing. To explore the utility of the proposed sensor as a bio-sensor, we reveal here the characteristics of the sensor for blood plasma and cancers cell sensing applications. We have picked the refractive indices for the different concentrated blood plasma from Ref. [23, 27, 45]. Figure 8 shows the transmission spectra with the variations of sample layer for different concentrations of blood plasma in the sensor with different Fibonacci generations. The sensing peaks shift toward the higher wavelength with increasing the blood plasma concentrations for all cases. It is the result of the change in the blood sample refractive index with different plasma concentrations. It can also be seen that the separation, position, and FWHM of the sensing peaks for different concentrations change with tuning the sample layer thickness and Fibonacci generations in the sensor structures.

To look closely at the variations of sensing peaks for different plasma concentrations, sample thickness, and Fibonacci generations, we have revealed the sensing peak \({\lambda }_{p}\) shifting with the blood plasma concentrations in panel (i) of Fig. 9. The changes in the position of \({\lambda }_{p}\) with the concentrations \({C}_{BP}\) are linear for all the cases, but they illustrate slightly dissimilar slope transformations for different layer thicknesses and Fibonacci generations. To examine the sensing performance of the senor for blood plasma, we have calculated the sensitivity and FOM for different concentrations contrast \(\varDelta {C}_{BP}\) by taking the blood plasma concentration of 10 g/L as a reference and shown in the panels (ii) and (iii) of Fig. 9, respectively. Here, \(\varDelta {C}_{BP}\) represents the concentrations contrast for the blood plasma concentration of 10 g/L as a reference, and the values of different concentrations contrast are \({C}_{21} \left(={C}_{20g/L}-{C}_{10g/L}\right),\) \({C}_{31} \left(={C}_{30g/L}-{C}_{10g/L}\right),\) \({C}_{41} \left(={C}_{40g/L}-{C}_{10g/L}\right),\) and \({C}_{51} \left(={C}_{50g/L}-{C}_{10g/L}\right)\). Layer thicknesses are\({ d}_{1}=100 nm\),\({d}_{2}=90 nm\), and\({ d}_{s}=1 \mu m, 1.5 \mu m, 2.0 \mu m\). The maximum sensitivity and FOM are 553.55 nm/RIU and 2214.21 RIU−1 for the sensor structures \({\left({F}_{3}\right)}^{7}S{\left({F}_{3}\right)}^{7}\), 499.5 nm/RIU and 1791.97 RIU−1 for the sensor \({\left({F}_{4}\right)}^{4}S{\left({F}_{4}\right)}^{4}\), 502.05 nm/RIU and 377.62 RIU−1 for the structure \({\left({F}_{5}\right)}^{2}S{\left({F}_{5}\right)}^{2}\), respectively. It can be seen in the figure that the sensitivity and FOM have remarkable variations with the concentrations contrast, sample layer thickness, and Fibonacci generation, but the FOM reveals a drastic variation concerning the change in the Fibonacci generations for the sensor structures. As per the results, we observe the efficient higher sensitivity with maximum value 553.55 nm/RIU and FOMs with maximum value 2214.21 RIU−1 for the blood plasma compared to the previously reported results in Refs. [23, 30, 45]. The diversity in the sensing performance of the proposed sensors in terms of sensing peak separations, high sensitivity, and FOM induce to utilize as a highly efficient and tunable sensor for the blood plasma detections.

Now, we have carried out our analysis on the detection of cancer cells. We have considered the sample size and refractive index of the cancer cells according to the previously reported results [20, 23, 26, 31, 33, 45]. Figure 10 shows the transmission spectra of the sensor structures of (a) \({\left({F}_{3}\right)}^{7}S{\left({F}_{3}\right)}^{7}\), (b) \({\left({F}_{4}\right)}^{4}S{\left({F}_{4}\right)}^{4}\), (c) \({\left({F}_{5}\right)}^{2}S{\left({F}_{5}\right)}^{2}\) for the different cancer cells with the sample layer thicknesses. Here, layer thicknesses are also considered as\({ d}_{1}=100 nm\),\({d}_{2}=90 nm\), and\({ d}_{s}=1 \mu m\), \(1.5 \mu m\), \(2.0 \mu m\). The sensing peaks shift toward the higher wavelength for all cases with the incorporation of the cancer cell. The changes in the peak position are the result of the change in the refractive index for different cancer cells. We can see that the separation, position, and FWHM of the sensing peaks for different cancer cells change with tuning the sample layer thickness and Fibonacci generations in the sensor structures. Here, we have considered the normal cell with refractive index 1.35 and different cancer cells of Jurkat, Hela, PC12, MDA-MB-231, and MCF-7 with refractive indices 1.39, 1.392, 1.395, 1.399, and 1.401, respectively. To take a close look at the variations of the sensing peaks for different cancer cells with respect to the normal cell, we have zoom out the sensing peaks and depicted them in the insets of the respective figures.

The variations in the sensing peaks \({\lambda }_{p}\)correspond to the various cancer cells, and sensitivity and FOM for the different cancer cells with the normal cell as a reference are shown in Fig. 11. We also reveal here that the position of sensing peaks shifts toward the higher wavelength with tuning the refractive index \({n}_{C}\)from the normal cell to cancel cells for all the cases. The slops of the \({\lambda }_{p}\)vs. \({n}_{C}\)are almost linear for all the cases, but the separations in the sensing peaks for different cancer cells have different values for the sample layer thickness and Fibonacci generations. To look into the sensing performance, we have calculated the sensitivity and FOMs for different cancer cells with the normal cell as a reference, and this transformation is represented as \(\varDelta {n}_{CN}\) \((={n}_{\text{c}\text{a}\text{n}\text{c}\text{e}\text{r} \text{c}\text{e}\text{l}\text{l}}-{n}_{\text{n}\text{o}\text{r}\text{m}\text{a}\text{l} \text{c}\text{e}\text{l}\text{l}}\)). The changes in \(\varDelta {n}_{CN}\) for the cancer cell of Jurkat, Hela, PC12, MDA-MB-231, and MCF-7 are 0.04, 0.042, 0.045, 0.049, and 0.0501, respectively. The variations in the sensitivity and FOMs with \(\varDelta {n}_{CN}\) are shown in panels (ii) and (iii) of Fig. 11 for the sensor structures of (a) \({\left({F}_{3}\right)}^{7}S{\left({F}_{3}\right)}^{7}\), (b) \({\left({F}_{4}\right)}^{4}S{\left({F}_{4}\right)}^{4}\), (c) \({\left({F}_{5}\right)}^{2}S{\left({F}_{5}\right)}^{2}\), respectively. The maximum sensitivity and FOMs are 552.5 nm/RIU and 2210 RIU−1 for the sensor structures of \({\left({F}_{3}\right)}^{7}S{\left({F}_{3}\right)}^{7}\), 486.25 nm/RIU and 2986.93 RIU− 1 for the sensor of \({\left({F}_{4}\right)}^{4}S{\left({F}_{4}\right)}^{4}\), and 491.25 nm/RIU and 393.48 RIU− 1 for the structure \({\left({F}_{5}\right)}^{2}S{\left({F}_{5}\right)}^{2}\), respectively. We can see in the figures that the sensitivity and FOMs have considerable changes with the cancer cells verity, sample layer thickness, and Fibonacci generation. However, the FOM has a drastic variation for the change in the Fibonacci generations for the sensor structures. We obtain the sufficient higher sensitivity with maximum value 552.5 nm/RIU and FOMs with maximum value 2986.93 RIU− 1 for the corresponding cancer cells compared to the previously reported results in Refs. [20, 26, 31, 33, 45]. The calculated sensitivity and FOMs describe the potential of the Fibonacci quasiperiodic PC sensor as a highly efficient and tunable sensor for cancer cells detections.