1 Introduction

Photonics-based temperature sensors have recently gained a lot of attention, owing to their small size, immunity to electromagnetic interference, and reduced sensitivity to environmental disturbances like mechanical shocks and humidity (Chiang et al. 2020; Kim and Yu 2016). Compared to optical fiber temperature sensors (Hameed et al. 2015; Karim et al. 2023; Muñoz-Hernandez et al. 2020; Reyes-Vera et al. 2017), temperature sensors based on silicon-on-insulator (SOI) platform can realize relatively high sensitivity. In addition, SOI based sensors can profit from advanced complementary metal-oxide-semiconductor (CMOS) fabrication techniques and ease of integration with other devices for on-chip applications (Chiang et al. 2020). Many SOI based temperature sensors have been demonstrated to achieve a relatively good performance with various device configurations, such as micro-ring resonators (Kim et al. 2010a; Kim and Yu 2016) photonic crystal nanobeam cavities (Zhang et al. 2016), Mach–Zehnder Interferometer (MZI) (Guan et al. 2016; Lee 2015; Zhang et al. 2018; Ding et al. 2021), and waveguide Bragg gratings (WBGs) (Klimov et al. 2015). In this context, Kim et al. (2016) have proposed a two cascaded ring resonators SOI based temperature sensor that operates by monitoring the resonance wavelength shift. The sensor achieves a temperature sensitivity of 0.294 nm/°C by utilizing the Vernier effect (Benenson et al. 2006). However, this improvement came at the expense of limited resolution, i.e., the temperature detection limit, due to its large error on envelope peak fitting. Based on the same device architecture concept, Zhang et al. (2016) have introduced a temperature sensor based on cascaded silicon photonic crystal nanobeam cavities. In this sensor, one of the two cavities has a blue shift in its wavelength in response to decreasing temperature while the other has a red shift, with the total sensitivity of 0.163 nm/°C.

Mach–Zehnder Interferometer (MZI) is another robust structure for increasing the sensitivity of the SOI temperature sensor. Based on MZI, Ding et al. (2021) have proposed a temperature sensor without sacrificing detection range on the SOI platform using cascaded MZIs. Such a sensor achieves a temperature sensitivity of 1.753 nm/°C without introducing negative thermo-optic coefficient (TOC) materials. One of the promising materials that is utilized in temperature sensors structures, as a cladding (Chiang et al. 2020) or core (Hameed et al. 2015) material, is the nematic liquid crystal (NLC). This is due to its high TOC which results in high sensor sensitivity with simple filling process (Hameed and Obayya 2019). In, Chiang et al. (2020) have demonstrated a SOI photonic temperature sensor based on a two-mode nano-slot waveguide with NLC cladding. The measured sensitivities are equal to 0.810 nm/°C around room temperature and 1.619 nm/°C near 50 °C.

Although, having different advantages from their respective device configurations, all the previously reported SOI temperature sensors still have limited sensitivities. This is due to the high refractive index contrast in the SOI platform with strong optical confinement through the silicon (Si) core with intrinsic TOC of 1.86 × 10–4/°C (Zhang et al. 2016). In this paper, a novel design of highly sensitive temperature sensor is proposed and analyzed. The suggested structure relies on a silica/silicon (SiO2/Si) V-groove channel waveguide infiltrated with NLC as a temperature dependent material and gold (Au) as a plasmonic material. The sensing mechanism is based on the surface plasmon resonance (SPR) technique (Tathfif et al. 2021a, 2022; b). Such a technique relies on the coupling between the surface plasmon modes (SPMs) excited at the metal/dielectric interfaces and the guided core modes (Rashid et al. 2021a; b). At resonance, the effective indices of the core guided mode and SPM are equal. In such case, phase matching occurs where maximum power transfer takes place from the guided core mode to the SPM (Hassan et al. 2020, 2021). A shift in the resonance wavelength is detected when the refractive index of the NLC is changed in response to any variations in the temperature. Hence, the effective index of the fundamental mode supported by the NLC channel is changed, and thus the sensitivity can be measured. The sensing characteristics of the suggested sensor are studied using the full-vectorial finite element approach (Obayya et al. 2000, 2002). The reported sensor achieves an average temperature sensitivity of 24.5 nm/°C for a temperature range from 15 to 40 °C. The obtained wavelength sensitivity is higher than those of most similar temperature sensors based on SiO2–Si or silicon-on-insulator (SOI) technology in literature (Chiang et al. 2020; Kim et al. 2010a; Kim and Yu 2016; Klimov et al. 2015; Zhang et al. 2016; Ding et al. 2021). In addition, the suggested sensor offers an average amplitude sensitivity of 0.135 °C−1 with a figure of merit (FOM) of 0.43 °C−1. Further, the proposed structure is CMOS compatible with simple design that can be easily fabricated with high stability and inevitable fabrication errors. It is worth mentioning that, while there are many temperature sensors reported in literature to work in the visible or near infrared regimes, most of them have low temperature sensitivity (Han et al. 2021; Irfan et al. 2022; Kazanskiy et al. 2021). The proposed temperature sensor offers higher temperature sensitivity than other previously reported sensors including purely plasmonic sensors owing to the existence of the temperature dependent material i.e., NLC material in the core region. Thus, as the temperature changes, a significant change in the refractive indices (ne and no) of the NLC material occurs. Accordingly, a large variation to the optical properties of the core mode (especially its neff) results in a large shift in the resonance wavelength (λPMW) with high temperature sensitivity.

2 Design considerations and basic theory

2.1 Design considerations and fabrication methodology

The 3D, cross-sectional views of the proposed structure and the sensing system setup are depicted in Fig. 1. The reported design consists of a Silica-NLC groove with a triangular cross-section with a base width wb, and a depth/height hc. It is worth noting that the utilized anisotropic NLC material is of type E7 where the ordinary refractive index (no) and extraordinary refractive index (ne) are within the range 1.5–1.8 in the visible and near infrared spectral regions (Li et al. 2005). So, a cladding layer of SiO2, with a thickness of hd and a refractive index (n) of 1.46 (Abd-Elkader et al. 2019) (smaller than no and ne), is thermally grown on the Si substrate. Owing to its high optical quality, the SiO2 is selected as a cladding layer to the NLC material that can realize better waveguiding properties. Further, the SiO2 layer has a quite small n which prevents the leakage of the optical field toward the Si substrate.

Fig. 1
figure 1

a 3D schematic diagram and b 2D cross section of the proposed temperature sensor and (c) the schematic diagram of the proposed sensing system

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Several fabrication methods, including focused ion beam milling (Dhawan et al. 2011; Heikal et al. 2013) and electron beam lithography (Bozhevolnyi et al. 2006), can be employed to perform the reported NLC channel waveguide design. In this context, a V-groove channel waveguide filled with NLC has been fabricated on SiO2-Si substrate by d’Alessandro et al. (2006). Wet etching of n-Si substrates followed by thermal growth of a SiO2 cladding layer can be utilized to produce the V-groove. The reported design also has a top cladding of N-SF10 glass to encapsulate the NLC material. Moreover, a thin photo-alignment layer of Nylon 6 is extended on the glass plate to improve the planar, homogeneous alignment of the NLC molecules. Such a layer can yield better initial alignment for the NLC molecules along the x-axis when there is no applied electric filed (Beccherelli et al. 2005). Additionally, mechanical rubbing can be applied to the Nylon 6 layer to encourage homogenous alignment of the LC molecules in the desired direction (Hameed et al. 2017). It is worth mentioning that the very thin alignment layer can also be used on the sidewalls of the groove to achieve better alignment of the molecules. The dispersion effect of the alignment layer on the propagation characteristics can be neglected because it is much thinner than all other composing materials. Then, capillary forces can be employed to fill the NLC material in the cell product from the silicon wafer and the glass cover. In this regard, Xu et al. (2009) have reported a composite waveguide with NLC cladding based on an inverted polymer channel. For such a design, a more homogeneous alignment for the NLC molecules has been achieved. Additionally, in Xu et al. (2009), reactive ion etching, and conventional photo lithography techniques have been employed to fabricate a channel waveguide on SiO2/Si wafer. Further, a very thin layer of polyimide has been deposited to create the alignment layer (Xu et al. 2009). It is worth noting that the excitation through V-groove filled with liquid crystal waveguide has been performed experimentally and reported in d’Alessandro et al. (2006). A pigtailed polarization controller was connected to a single mode fiber (SMF), terminated with a cleaved face to couple the light to the LC optical channel waveguide (d’Alessandro et al. 2006). The measured coupling loss was about 10 dB which is acceptable in channel based optical waveguides (Zou et al. 2002). In the present work, it is believed that the same technique can be used for the excitation through the reported sensor where a tunable laser can be connected directly to the SMF (cleaved from the side connected to the V-groove LC waveguide). The NLC ordinary index (no) and extraordinary index (ne) are given by Eq. (1) as reported in (Li et al. 2005):

$${n}_{o,e}={A}_{o,e}+\frac{{B}_{o,e}}{{\lambda }^{2}}+\frac{{C}_{o,e}}{{\lambda }^{4}}$$
(1)

where λ is the free space wavelength of the excitation light, Ao = 1.4994, Bo = 0.0070 μm2, Co = 0.0004 μm4, Ae = 1.6933, Be = 0.0078 μm2, and Ce = 0.0028 μm4, at the room temperature (T) of 25 °C. It is noteworthy that no and ne are temperature dependent within the temperature range from 15 to 55 °C according to the study reported by Li et al. (2005). The relative permittivity tensor, εr of the E7 NLC material (Li et al. 2005) is taken as:

$${\varepsilon }_{r}=\left[\begin{array}{ccc}{n}_{o}^{2}{\mathit{sin}}^{2}\varphi +{n}_{e}^{2}{\mathit{cos}}^{2}\varphi & \left({n}_{e}^{2}-{n}_{o}^{2}\right)sin\varphi cos\varphi & 0\\ \left({n}_{e}^{2}-{n}_{o}^{2}\right)sin\varphi cos\varphi & {n}_{e}^{2}{\mathit{sin}}^{2}\varphi +{n}_{o}^{2}{\mathit{cos}}^{2}\varphi & 0\\ 0& 0& {n}_{o}^{2}\end{array}\right],$$
(2)

where φ is the rotation angle of the director of the NLC as may be seen in the inset of Fig. 1.

Figure 2 shows the wavelength dependent no and ne of the NLC material at different ambient temperatures according to Eq. (1) (Li et al. 2005) from λ = 1–2.5 μm. It may be seen from Fig. 2a that the differences between the no curves corresponding to different temperatures are relatively small, especially for short wavelengths. On the other hand, these differences become larger for long wavelengths. Meanwhile, the differences between the ne curves at different temperatures are relatively large over the whole wavelength range, Fig. 2b. Therefore, the operation of the suggested sensor depends on the variation of ne to attain the highest temperature sensitivity.

Fig. 2
figure 2

Wavelength dependent NLC refractive indices; a no and b ne at different ambient temperatures according to Eq. (1) (Li et al. 2005)

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It is worthy to note that under the effect of a strong applied electric field limit, the NLC molecules can have an in-plane alignment (Haakestad et al. 2005; Wei et al. 2009). Moreover, the direction of the electric field and consequently the rotation angle (φ) of the NLC director can be tuned by using two electrodes with an effective driving voltage of 50 Vrms (Wei et al. 2009). The electrodes can be integrated with SOI or SiO2/Si waveguides as proposed in Maune et al. (2003). Maune et al. (2003) have presented electrically tuned SOI based ring resonators by using the NLCs as the waveguide side and top cladding material. Additionally, the orientation of the NLC molecules can be controlled by photolithographically defining the electrodes all around the ring resonator. Thus, the cladding refractive index and, hence, the resonant wavelengths of the ring resonator can be controlled (Maune et al. 2003). Therefore, it is believed that the fabrication of the suggested sensor structure and integration with other photonic components can be successfully achieved.

In order to excite the SPR wave, a gold (Au) layer of thickness hAu and a width of wb is deposited on the glass layer. The dielectric constant of Au is calculated via the Drude Lorentz model in Hameed and Obayya (2019), Eq. (3).

$${\varepsilon }_{Au}={\varepsilon }_{\infty }-\frac{{\omega }_{P}^{2}}{\omega \left(\omega +i{\omega }_{\tau }\right)}$$
(3)

where \(\omega\) is the angular frequency of the guided wave, \({\omega }_{\tau }\) is the damping frequency, \({\omega }_{{\text{P}}}\) is the plasma frequency, and \({\varepsilon }_{\infty }=9.75\) is the high frequency dielectric constant. Here, \({\omega }_{\tau }=1.45 \times {10}^{14} {\text{rad}}/{\text{s}}\), \({\omega }_{{\text{P}}}=1.36 \times {10}^{16} {\text{rad}}/{\text{s}}.\) Figure 3 investigates the frequency dependence of the real and imaginary parts of the dielectric constant of Au according to Eq. (3) (Hameed and Obayya 2019).

Fig. 3
figure 3

Real and imaginary parts of the dielectric constant for Au as functions of angular frequency according to Eq. (3) (Hameed and Obayya 2019)

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2.2 Theory of operation

The operation of the suggested temperature sensor depends on the electromagnetic coupling between the fundamental mode supported by the NLC core region and one of the surface plasmon modes (SPMs) constructed on the surface of the Au strip deposited on the top of the glass layer. This coupling occurs when these two modes are in phase matching i.e., both have the same effective index (neff). This coupling occurs at a certain wavelength that is called resonance wavelength or phase matching wavelength (λPMW). This phenomenon is called surface plasmon resonance (SPR) and it is one of the main mechanisms utilized in sensing applications. According to the temperature dependence of no and ne, changing temperature of the NLC material would affect the neff of the fundamental core mode (confined in the NLC core) and accordingly shifts the λPMW to larger/shorter values. Regarding the temperature dependence of the refractive indices of SiO2 (n_SiO2) and Nylon 6 material especially in the studied wavelength range (i.e., λ = 1.4–2 μm), it is worth noting that n_SiO2 is approximately constant. In this regard, an experimental study has been conducted in Tan and Arndt (2000) and the results revealed that variation of n_SiO2 with temperature in the range (15–45 °C) is very small. In addition, the refractive index of Nylon 6 is nearly constant under temperature variations within the studied range (15–45 °C) in our study according to previous experiments conducted by d’Alessandro et al. (2006, 2021), El-Nicklawy et al. (2010). As it can be seen from Fig. 2, no is less sensitive to temperature variations than ne (Li et al. 2005). Thus, the operation of the proposed sensor depends on ne (Li et al. 2005). At φ = 90°, the director of the NLC material is normal to Ex and is parallel to Ey, so εr takes the diagonal form of [no2, ne2, no2] which can be verified via Eq. (2). Thus, as the operation depends on the variation of ne due to temperature variation, only the TM core mode (affected by ne) is considered in this study. To enhance the coupling strength between the TM core mode and SPM, the glass layer made of N-SF10 glass with a refractive index that is very close to ne and can be calculated using Eq. (4) as reported in Schott (2011). This would enhance the leakage from the NLC core to the upper glass cladding layer which enables strong interaction between the core light and the Au film. Hence, the coupling becomes stronger which enhances the sensing operation of the proposed sensor (Schott 2011).

$${n}^{2}-1= \frac{1.62153902{\lambda }^{2}}{{\lambda }^{2}-0.0122241457}+\frac{0.256287842{\lambda }^{2}}{{\lambda }^{2}-0.0595736775}+\frac{1.64447552{\lambda }^{2}}{{\lambda }^{2}-147.46893}$$
(4)

In order to measure the performance of the reported sensor, both the wavelength and amplitude sensitivities are considered. Wavelength sensitivity denoted as Sλ can be calculated according to Eq. (5) as in (Rifat et al. 2015).

$${S}_{\lambda }=\frac{\Delta {\lambda }_{PMW}}{\Delta T} (nm/^\circ{\rm C} )$$
(5)

where ΔλPMW and ΔT are the change in the phase matching wavelength and the variation of the NLC temperature, respectively. In addition, the amplitude sensitivity (SA) is another important parameter in measuring the performance of SPR based sensors. SA is defined by Eq. (6) as (Hameed et al. 2015).

$${S}_{A}=-\frac{1}{\alpha \left(\lambda ,T\right)}\frac{\delta \alpha \left(\lambda ,T\right)}{\Delta T} {(\mathrm{^\circ{\rm C} }}^{-1})$$
(6)

where \(\alpha \left(\lambda ,T\right)\) is the confinement loss of the studied core mode at a temperature T and \(\frac{\delta \alpha (\lambda ,T)}{\Delta T}\) is the difference between the values of α in the two loss peaks under study divided by the change in temperature (\(\Delta T\)). In this study, the modal confinement loss (α) is determined from the imaginary part of the mode effective index as follows (Crutchfield et al. 2004):

$$\mathrm{\alpha }({\text{dB}}/\mathrm{\mu m})= \frac{20\times {10}^{-4}}{{\text{ln}}(10)}\times \frac{2\uppi }{\uplambda }\times {\text{imaginary}}({{\text{n}}}_{{\text{eff}}})$$
(7)

Another important parameter is the full width at half maximum (FWHM) of the confinement loss curve. Unfortunately, in some cases, the increase in sensitivity is accompanied by a wide FWHM leading to a trade-off between them. Therefore, a figure of merit (FOM) parameter is assumed to evaluate the sensor performance. In this work, FOM is defined as the ratio between the wavelength sensitivity and the FWHM as depicted in Eq. (8). So, larger FOM means better sensitivity and detection limit (Qin et al. 2013).

$${\text{FOM}}=\frac{{{\text{S}}}_{\lambda }}{{\text{FWHM}}}{(\mathrm{^\circ{\rm C} }}^{-1})$$
(8)

3 Results and discussion

Full-vectorial finite element method (FVFEM) via COMSOL Multiphysics software package (https://www.comsol.com) is employed to analyze the sensing characteristics of the proposed temperature sensor. In this study, two-dimensional FEM model is used with scattering boundary conditions, minimum mesh element size of 3.9 × 10–3 μm and large degrees of freedom of 83,599 to ensure accurate results. First, the supported modes by the suggested NLC channel waveguide on silicon are studied and analyzed in detail. In this investigation, the fundamental y-polarized supported by the NLC core, and the SPMs constructed on the Au surface are considered. The selected modes are analyzed in terms of the real part of neff (Real (neff)) and the confinement loss (α). It is worth mentioning that the structural parameters hc, hd, hn, hg, hAu, and wb (Fig. 1) are initially fixed to 5 μm, 2 μm, 50 nm, 1 μm, 50 nm, and 5 μm, respectively. The initial geometry is inspired from previously similar reported SOI devices for the fabrication feasibility (d’Alessandro et al. 2006; d’Alessandro and Asquini 2021; Hameed et al. 2017) while a separate parametric study will be performed to improve the sensor performance. Figure 4 shows the wavelength dependent effective indices and the confinement losses of the y-polarized core mode and the corresponding SPM, respectively. Generally, the effective indices of the y-polarized core mode and SPM decrease with increasing the wavelength as may be seen in Fig. 4. In addition, the two effective indices of the two modes are identical at λ = 1.69 μm indicating the phase matching condition where maximum power transfer from the core mode to the SPM occurs. Therefore, a maximum loss peak is observed in the loss spectrum of the y-polarized core mode exactly at λ = 1.69 μm (phase matching wavelength; λPMW), Fig. 4. The insets of Fig. 4 represent the field plots of both y-polarized core mode and SPM at different wavelengths. It may be seen from insets (a), (b), and (e) in Fig. 4 that the two modes have different profiles at wavelengths away from the coupling point i.e., away from λPMW. On the other hand, at λPMW = 1.69 μm, both modes approximately have the same field profile (insets (c) and (d), Fig. 4) leading to maximum power transfer from the core mode to the SPM. In the proposed structure, exploiting the temperature dependence of no and ne, λPMW shifts to a longer or a shorter value then, the sensor sensitivity Sλ can be obtained according to Eq. (4).

Fig. 4
figure 4

Wavelength dependent \({{\varvec{n}}}_{{\varvec{e}}{\varvec{f}}{\varvec{f}}}\) of the y-polarized core mode (blue), SPM (red), and the confinement losses of the y-polarized core mode (black). The structural parameters hc, hd, hn, hg, hAu, and wb are initially fixed to 5 μm, 2 μm, 50 nm, 1 μm, 50 nm, and 5 μm, respectively

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The next study is performed by assuming that the NLC temperature varies between 15 and 40 °C with a step of 5 °C and tracking λPMW in each case. Then, the temperature sensitivity of the proposed sensor is obtained according to the shift in λPMW. Figure 5a depicts the confinement loss spectra of the y-polarized core mode at different temperatures while Fig. 5b shows a bar chart of the calculated Sλ at each temperature range. It may be seen from Fig. 5a that increasing the NLC temperature generally increases the λPMW with slight variations in the loss peak values. This is due to the fact that ne decreases with temperature throughout the studied wavelength range. As a general trend, the calculated Sλ increases by increasing the temperature as depicted in Fig. 3b. For example, Sλ of 15–20 °C range is 18 nm/°C while it increases to 34 nm/°C in the 35–40 °C temperature range, Fig. 5. It is important to mention that Sλ of the suggested temperature sensor is better than those achieved by similar devices in the literature (Chiang et al. 2020; Kim et al. 2010a; Kim and Yu 2016; Klimov et al. 2015; Zhang et al. 2016; Ding et al. 2021). The amplitude sensitivity SA, and FOM of the proposed sensor are also calculated using Eqs. (6) and (8), respectively to prove the good sensing performance. Based on the analysis and the obtained results, it is worth noting that Sλ, SA and FOM are not fixed at each temperature range i.e., they’re different in 15–20 °C than 20–25 °C etc. Therefore, average instead of exact values of Sλ, SA and FOM are considered throughout the whole studied temperature range (15–40 °C) in the subsequent studies. The calculated average Sλ, average SA, and average FOM of the suggested sensor are of 24.8 nm/°C, 0.126 °C−1, and 0.365 °C−1, respectively.

Fig. 5
figure 5

a Loss spectra of the y-polarized core mode at different temperatures from 15 to 40 °C, and b the wavelength sensitivity corresponds to each studied temperature range. The structural parameters hc, hd, hn, hg, hAu, and wb are initially fixed to 5 μm, 2 μm, 50 nm, 1 μm, 50 nm, and 5 μm, respectively

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To maximize the wavelength and amplitude sensitivities of the proposed temperature sensor, a comprehensive optimization study on the structural parameters is performed. The NLC channel depth (hc), Fig. 1, is expected to have a huge effect on the core mode characteristics and control the sensing operation. In this study, the structural parameters hd, hn, hg, hAu, and wb are fixed to 2 μm, 50 nm, 1 μm, 50 nm, and 5 μm, respectively while hc is varied between 3 different values of 4 μm, 5 μm, and 6 μm. Figure 6a depicts the variation of the resonance wavelength with the temperature at different values of hc. In addition, Fig. 6b and c show the dependence of Sλ, FOM, and SA on hc, respectively. It may be seen from Fig. 6a that generally λr increases with the increase in temperature. However, increasing hc shifts λr to shorter wavelengths. Increasing hc would increase the NLC core region where the fundamental y-polarized is well-confined with a large neff. Thus, phase matching between the core mode and the SPM occurs at shorter wavelengths. In addition, Sλ decreases by increasing hc as may be seen in Fig. 6b, while the FOM increases by increasing hc. As may be seen in Fig. 6c, SA slightly increases by increasing hc. It is revealed from this study that there is a tradeoff between the FOM, Sλ, and SA. So, hc is fixed to 5 μm to keep the average values of Sλ and SA quite large 24.8 nm/°C, and 0.126 °C−1, respectively with a FOM of 0.365 °C−1.

Fig. 6
figure 6

a Temperature dependent λr at different studied hc values, b the average Sλ and FOM in terms of hc, and c the average SA versus hc. The structural parameters hd, hn, hg, hAu, and wb are initially fixed to 2 μm, 50 nm, 1 μm, 50 nm, and 5 μm, respectively while hc is varied between 4 and 6 μm

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The next structural parameter to be tuned is the width of the Au strip (wb) deposited above the glass layer as may be seen in Fig. 1. It is worth noting that wb is initially fixed to a value that is the same as the triangular NLC core width i.e., 5 μm. Now, wb is varied to larger and smaller values to show its effect on the mode coupling characteristics and the sensor performance. In this investigation, hd, hn, hg, hAu, and hc are fixed to 2 μm, 50 nm, 1 μm, 50 nm, and 5 μm. The temperature dependent resonance wavelength at different studied values of wb is depicted in Fig. 7a. It is revealed from this figure that λr generally increases with temperature (the same behavior shown in Fig. 6a). In addition, increasing wb shifts λr to longer wavelengths. Increasing wb increases the Au surface area which increases the SPM area with reduced neff for the SPM. On the other hand, increasing wb has approximately no effect on the fundamental NLC core mode. Therefore, the core mode would have the same neff as the SPM at longer wavelengths. The opposite performance is expected while decreasing wb as revealed by the blue curve in Fig. 7b. Figure 7b and c show the variation of Sλ, FOM, and SA with wb, respectively. It may be seen from Fig. 7b that Sλ increases by increasing wb, however FOM decreases by increasing wb. Further, SA has a slight decreasing behavior by increasing wb as reveled from Fig. 7c. Thus, there is a tradeoff between the FOM, Sλ, and SA while changing wb. Accordingly, wb is fixed to 5 μm to keep the average values of Sλ and SA quite large 24.8 nm/°C, and 0.126, respectively with a FOM of 0.365 °C−1.

Fig. 7
figure 7

a Temperature dependent λr at different studied wb values, b the average Sλ and FOM in terms of wb, and c the average SA versus wb. The structural parameters hc, hd, hn, hg, and hAu are initially fixed to 5 μm, 2 μm, 50 nm, 1 μm, and 50 nm, respectively while wb is varied between 4 and 6 μm

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The thickness of Au strip (hAu) is also studied to show its effect on the mode coupling characteristics and the sensor performance. Initially, hAu is set to 50 nm and it is increased to 60 and 70 nm to tune the sensor performance in terms of Sλ, FOM, and SA. It is worth mentioning that hd, hn, and hg are fixed to 2 μm, 50 nm, 1 μm while hc and wb are set to their optimized values of 5 μm. The temperature dependent resonance wavelength at different studied values of hAu is depicted in Fig. 8a. It is revealed from this figure that λr generally increases with increasing temperature. However, increasing hAu shifts λr to shorter wavelengths. Increasing hAu slightly increases the Au lateral areas and the SPM area. Thus, the neff of the SPM would be quite larger while that of the fundamental NLC core mode is nearly constant with the variation in hAu. Therefore, the core mode would have the same neff as the SPM at quite shorter wavelengths as revealed by Fig. 8a. The opposite performance is expected while decreasing hAu while, it is kept greater than 50 nm to keep the fabrication feasibility of the proposed structure. In addition, Fig. 8b and c show the variation of Sλ, FOM, and SA with hAu, respectively. It may be seen from Fig. 8b that Sλ slightly decreases by increasing hAu, however FOM increases by increasing hAu. Further, SA has a slight increasing behavior by increasing hAu as revealed from Fig. 8c. Due to the tradeoff between the FOM, Sλ, and SA while changing hAu, it is fixed to 60 nm to keep the average values of Sλ and SA quite large 24.5 nm/°C, and 0.135 °C−1, respectively with a FOM of 0.43 °C−1.

Fig. 8
figure 8

a Temperature dependent λr at different studied hAu values, b the average Sλ and FOM in terms of hAu, and c the average SA versus hAu. The structural parameters hc, hd, hn, hg, and wb are initially fixed to 5 μm, 2 μm, 50 nm, 1 μm, 50 nm, and 5 μm, respectively while hAu is varied between 50 and 70 nm

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To prove the fabrication feasibility of the suggested temperature sensor, the tolerances of the structural parameters, ± 5% of their optimum values, are investigated as shown in Table 1. It can be observed from this table that the proposed sensor has a large fabrication tolerance in terms of its wavelength sensitivity, which ensures its robustness to the fabrication errors.

Table 1 Fabrication tolerance study of the different geometrical parameters within ± 5% and its effect on the sensor wavelength sensitivity compared to that obtained using the optimized parameters
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A summarized comparison between the suggested temperature sensor and those reported in literature is presented in Table 2. Such comparison is introduced in terms of the design, basic platform utilized, the temperature sensing range, wavelength sensitivity, and type of work (theoretical or experimental). The simplicity in design with very high wavelength sensitivity are the most important features of the proposed temperature sensor. It achieves a wavelength sensitivity better than that offered in Chiang et al. (2020), Hameed et al. (2015), Karim et al. (2023), Kim et al. (2010a), Kim and Yu (2016), Klimov et al. (2015), Muñoz-Hernandez et al. (2020), Zhang et al. (2016), Ding et al. (2021).

Table 2 Comparison between the proposed temperature sensor and those previously reported in literature
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4 Conclusion

A simple design of a highly sensitive SPR temperature sensor based on SiO2/Si V-groove waveguide with NLC is proposed and investigated. The proposed design is based on temperature dependent NLC material. A comprehensive simulation study based on FVFEM is performed to numerically analyze and optimize the suggested structure for optimal performance. For a wide temperature range from 15 to 40 °C, the reported sensor shows a high average temperature sensitivity of 24.5 nm/°C. Additionally, the introduced sensor offers an average amplitude sensitivity of 0.135 °C−1 with a FOM of 0.43 °C−1. Further, the proposed structure is CMOS compatible with high robustness to fabrication errors.