1 Introduction

Photonic crystals (PCs) are modern class of unique structures, which can amend the transmission of electromagnetic waves over a wide frequency range and therefore able to attract a great deal of research interest. Owing to their extraordinary optical properties, PC-based devices have received remarkable attention in sensing, networking and communication applications (Panda et al. 2016; 2019; Ramanujam et al. 2019). PCs integrated on SOI platform offers certain benefits like lower parasitic capacitance effect, low leakage current, high speed operation (Soref 1998; Colinge 1991; Peters 1993). SOI based photonic devices deliver unmatched optical properties due to high refractive index contrast between silicon substrate and oxide layer (Soref et al. 1991; Fischer et al. 1995). Thus, SOI structures with different types of materials, play key role in photonic integrated circuits for numerous photonics applications like interconnect, filter, sensor (Tidmarsh and Drake 1998; Yariv and Yeh 1984; Yablonovitch and Gmitter 1989; Zengerle and Leminger 1995; Tamir 1990). PCs are special structures based on periodic alternation in refractive index, in the order of wavelength of the propagating light signal. The periodic change in the dielectric function leads to considerable modification in both the transmission and reflectance spectrum. Moreover, the photonic crystal structures are blessed with a novel property, i.e. a photonic band gap (PBG), which prohibits the propagation of certain frequencies of the electromagnetic waves through the structure (Armenise et al. 2010; Nayak et al. 2016). This PBG phenomenon can be judiciously utilised for envisaging novel optical sensors for monitoring biomolecules, atmospheric gases, chemicals, temperature, and pressure (Penget et al. 2017; Panda and Pukhrambam 2020).

Among different compound materials used in the design of PCs, lithium niobate (LiNbO3) has come up as a potential material for application in nonlinear and integrated optics. LiNbO3 has been proven as a mature material for monitoring the flow of light signals in photonic devices (Arizmendi 2017; Liang et al. 2017). Owing to its high purity, LiNbO3 has become the first choice of researchers for the design of novel optoelectronic devices. In addition to this, LiNbO3 shows photorefractive, ferroelectric, electro-optic and acousto-optic properties, which enable it to find successful applications in optical and microwave frequency ranges (Geiss 2011). Also, LiNbO3 shows some exceptional photonic band gap characteristics, which make it a suitable candidate for the design of highly efficient optoelectronic devices such as optical switches, optical modulators, photochemical sensors, and photonic waveguides (Bernal et al. 2009; Prakash et al. 2019). LiNbO3 based photonic crystal structures can find extensive applications in the field of biosensing (Christoph et al. 2015; Manpreet and Chetan 2014; Buswell et al. 2008; Hugo et al. 1991; Ayyanar et al. 2018). Among different biomolecules, sucrose is one of the key elements which is basically an aqueous solution of sugar and appears as a suitable component for creation of various chemical products like glycerol, ethanol, and citric acid (Caballero 2003). Moreover, concentration of sucrose in an aqueous solution finds extensive applications in pharmaceutical measures such as preservation of protein and food. Hence, it is indispensable to accurately sense the sucrose concentration. Numerous researches have already been performed towards exploring sensing of different biomolecules by using photonic waveguides (Katz and Willner 2004; Chen et al. 2016), but there is little research on sensing sucrose concentrations, which makes the present investigation noteworthy. In Panda et al. (2016, 2018), the authors demonstrated a 1D photonic waveguide and lucidly analysed the effect of different kinds of losses that persist during transmission of light signals through the waveguide. Further, in references Amiri et al. (2019), Robinson and Dhanlaksmi (2016), Palai et al. (2018), Tang and Wang (2008) and Wang and Tang (2012), the authors have lucidly represented sensing of glucose, urea, sodium chloride, DNA, protein by using photonic structures for realising efficient photonic integrated circuits. Also, several photonics structures are proposed Xiaoxia et al. (2020), Frischeisen et al. (2008), Chow et al. (2004), Ge et al. (2013) and Dorfner et al. (2009) to sense various analytes with analysis of important sensing characteristics like sensitivity and limit of detection (LOD).

To the best of the authors’ knowledge, very few researches have been carried out to date regarding FDTD approach for photonic band gap exploration, particularly for the 1D photonic crystal. In order to provide some clarification of the aforementioned issue, we have simulated a 1D photonic crystal through FDTD methodology to reveal the change in the band gap characteristics with respect to different concentrations of sucrose solution. Moreover, we have chosen the FDTD technique over other existing methods such as Plane Wave Expansion (PWE) and Transfer Matrix Method (TMM), owing to its simple analysis and accurate outcomes pertaining to the band gap investigation. Aside from this, the primary reason for selecting the 1D structure is its compactness, simplicity and cost effectiveness from the design point of view, which can be fabricated using available technologies. To uncover more on the claim of sensing through band gap analysis, we have proposed LiNbO3 material in the design of various layers of the 1D PhC structure, which add novelty to this work as this is not tested in published works. Furthermore, detailed analysis of reflected light energy, transmitted light energy, diffraction loss, and shift in reflected wavelength, PBG edges and PBG width escalates the novelty of the present research. Finally, a comparative analysis in terms of sensitivity and LOD is specified to measure the sensing performance, where the superiority of the present research is clearly illustrated.

2 Proposed structure and method

Over the last two decades, researchers have experimented with different materials and studied their properties to design photonic crystal structures and suggested that the best suited materials can be hybrid compound materials owing to their notable properties. In this research, we have considered a LiNbO3 compound material for designing the proposed structure, which shows simultaneously photorefractive, ferroelectric, electro optic and acoustic optic properties. 1D PCs already have been commercialised and can be certainly fabricated with the help of widely accepted methodologies. These techniques include e-beam lithography, FIB (focused ion beam) method, sol–gel techniques, physical vapour deposition (PVD), chemical vapour deposition (CVD), molecular beam epitaxy, and spin coating methods (Chen et al. 2004; Schürmann et al. 2006; Langer et al. 1999; Huaizhong et al. 2016). The aforesaid techniques have been widely accepted by the semiconductor industries for manufacturing high quality, high performance 1D structures and also the same have been nicely executed in researches discussed in the introduction section. Out of the aforementioned techniques, choosing most apposite method is really vital pertaining to the fabrication feasibility. As of now, spin coating technique has been extensively employed in fabrication of 1D layered structures. The foremost beauty of this method is that it can be applied to a wide variety of materials as well as nanoparticles and polymer solutions. In spin coating method, initially some precursor solution is put on a plane substrate and afterwards spin method is conducted for evaporation of solvents. An annealing process is followed to congeal the thin film. The thickness of the developed thin film can be well organised by precisely governing the rotation speed. Now, coming to the fabrication steps of the proposed structure, spin coating technique can be applied to form a LiNbO3 layer on the top of the SOI structure. Afterwards, photolithography process can be used through the application of photoresist to dissolve the required portion of the layer, which forms the second layer (air). Focusing on the feasibility aspect of fabrication, spin coating method is proven to be technically simple with greater controllability and cost effective for realization of 1D photonic structures as compared to the fabrication methods for higher dimensional photonic structures (El et al. 2011; Ravi Kanth Kumar et al. 2002; Desmond et al. 2012).

The proposed SOI based 1D photonic crystal structure is shown in the Fig. 1, which consists of three layers, out of which the outer layers are designed with a LiNbO3 compound material and the inner layer is taken as air. The thicknesses of the outer layer and inner layer are taken as d1 = 650 nm and d2 = 350 nm, respectively, whereas their permittivity is considered as ε1 = 5.303 and ε2 = 1 respectively. The photonic structure is considered to be created by e-beam lithography on a silicon substrate of 1 mm thickness. Additionally, infiltration technique is used to put aqueous solution of different sucrose concentrations in the middle layer. Based on the variation in refractive index, different sucrose concentrations can be sensed with enhanced sensitivity by observing the reflected wavelength shift according to the experimental setup shown in the Fig. 2. Light having wavelength of 390 nm is emitted from a laser source and incident on the proposed structure. At his wavelength, the proposed structure shows higher refractive index contrast between the adjacent layers, which yields more band gap. Light from the laser source can be focused and collected from the waveguide through a microscope objective lens for maximising the coupling efficiency. The light signals which fall within the band gap get reflected and others get transmitted through the structure. The directions of incident, reflected and transmitted light are shown with arrows in Fig. 1. Further, the aqueous solution is infiltrated in the second layer (i.e. air) and the reflected light energy is measured with a power meter. The principal reason for choosing the above thicknesses of different layers of the photonic structure is that maximum band gap is attained only at this thickness values, whereas for other values of thickness, band gap gradually decreases. Aside this, optimising the proposed structure with this thicknesses, diffraction loss is mitigated, which smoothen the passage of light in the waveguide. Also, at the aforementioned structure parameters, the suggested structure shows linear variation of sensing parameters and hence behaves as a suitable sensor for sensing different sucrose concentrations in an aqueous solution.

Fig. 1
figure 1

Crossectional view of the proposed SOI based 1D PhC structure

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Fig. 2
figure 2

Proposed experimental setup of sucrose sensor using 1D photonic structure

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3 Computational methodology

A 1D photonic sensor has been envisaged in this article to sense sucrose concentration in an aqueous solution through a band gap analysis, where the band gap is computed through dispersion relation by manipulating an FDTD method. Although various methods are available to address the band gap characteristics of photonic structures, the FDTD technique is a simple and efficient analysis method for assessing the band gap properties in photonic structures (Sukhoivanov and Guryev 2009). The FDTD computational technique lies on discretization of Maxwell’s equations. Beside this, the FDTD method is quiet efficient to permit complete exploration of electromagnetic waves over an arbitrary time by discretizing Maxwell’s equations, such that one can collect any required data from the wave. In addition to this, the FDTD method shows great potential to solve the electromagnetics simulations even for large problem dimensions. FDTD employs a time domain method, so a broad frequency range can be covered during simulations, which leads to easy treatment of nonlinear material properties.

The propagation of EM waves through the proposed 1D photonic crystal structure are governed by Maxwell equations, which can be expressed as:

$$ \nabla \times \vec{E} = - \mu \frac{{\partial \vec{H}}}{\partial t} $$
(1)
$$ \nabla \times \vec{H} = \varepsilon \frac{{\partial \vec{E}}}{\partial t} + \vec{J} $$
(2)

The above equations are employed as the backbone for calculation of different electric field and magnetic field components that persist in the proposed structure. By using Eqs. (1) and (2), the band structure for magnetic field components can be realised by solving Helmholtz’s equation, which can be expressed as,

$$ \frac{\partial }{\partial x}\frac{1}{\varepsilon \left( x \right)}\frac{\partial }{\partial x}H\left( x \right) + \frac{{w^{2} }}{{c^{2} }}H\left( x \right) = 0 $$
(3)

where, H represents magnetic field component, c is the light speed, w denotes the Eigen frequency, \( \varepsilon \)(x) is the periodic dielectric function. Certain boundary conditions are applied for calculation of magnetic field component H(x) with respect to different wave vectors. These boundary conditions are periodic in nature and referred as Bloch boundary conditions, which can expresses as below (Chhoker and Bajaj 2015),

$$ H\left( {x + a,y + b,z + c} \right) = H\left( {x,y,z} \right).e^{{ - i.k_{x} .a - j.k_{y} .b - k.k_{z} .c}} $$
(4)

where, a, b and c are dimension of unit cell along the x, y and z axis respectively, \( k_{x} \), \( k_{y} \) and \( k_{z} \), and represent the wave vectors along the corresponding axis. As per the present research, we have considered 1D PhC structure, which has periodicity variation along x axis only, so Eq. (4) reduces to

$$ H\left( {x + a} \right) = H\left( x \right).e^{{ - i.k_{x} .a}} $$
(5)

Thus, by considering Bloch periodic boundary conditions, it will be feasible to analyse Eigen states with respect to wave vector, which leads to computation of band structure (Sukhoivanov and Guryev 2009).

The rejected frequency range, i.e. band gap is further utilised to compute energy associated with the reflected light. In the above mentioned band gap analysis, the dielectric permittivity (\( \varepsilon \)) of LiNbO3 is calculated using the expression (Zelmon et al. 1997),

$$ \varepsilon = 1 + \frac{{2.6734 \times \lambda^{2} }}{{\lambda^{2} - 0.01764}} + \frac{{1.2290 \times \lambda^{2} }}{{\lambda^{2} - 0.05914}} + \frac{{12.614 \times \lambda^{2} }}{{\lambda^{2} - 474.60}} $$
(6)

The reflected light energy (\( E_{r} \)) can be obtained by utilising the following expression (Nayak et al. 2016),

$$ E_{r} = \frac{h \times c}{{\lambda_{up} - \lambda_{lo} }} $$
(7)

where, \( \lambda_{up} \) and \( \lambda_{lo} \) denote the upper wavelength bound and lower wavelength bound of the attained band gap respectively, h represents the plank’s constant and c is the speed of light.

After computation of reflected intensity from the obtained band gap, the diffraction loss (Panda et al. 2016) can be expressed as

$$ D_{loss} = 1 - sin^{2} \left( {\frac{\pi dn}{\lambda }} \right) $$
(8)

where d represents the thickness of the proposed waveguide, n denotes refractive index and λ is the reflected wavelength, which lies within the band gap.

The transmitted energy through the proposed structure can be obtained by using the following expression (Swain et al. 2020),

$$ E_{T} = \left( {E_{I} - E_{r} } \right)e^{{ - \left( {\alpha t + \beta d} \right)}} $$
(9)

where \( E_{T} \) represents the transmitted energy, \( E_{I} \) denotes the incident light energy corresponding to the wavelength 390 nm, \( E_{r} \) is the reflected light energy. Further, the factor \( e^{{ - \left( {\alpha t + \beta d} \right)}} \) is the total absorption factor, which includes absorption due to both material (\( e^{ - \alpha t} ) \) and analytes (\( e^{ - \beta d} \)), where \( \alpha \) is the attenuation coefficient of LiNbO3, t is the thickness of the LiNbO3 grating. The factor \( e^{ - \beta d} \) can be expressed in simplified form as \( e^{ - \varepsilon cd} \), where \( \varepsilon \) is the extinction coefficient of sucrose, c and d denote the sucrose concentration and thickness of the middle layer of the proposed structure respectively. As the value of \( e^{ - \beta d} \) is very small as compared to \( e^{ - \alpha t} , \) so absorption factor due to the analytes is neglected in the calculations.

Furthermore, we computed the sensitivity (S) parameter to appraise the performance of the proposed sensor, which is given as (Shaban et al. 2017):

$$ S = \frac{{\Delta \lambda_{S} }}{\Delta n} $$
(10)

Here, \( \Delta \lambda_{S} \) represents the shift in resonance wavelength and \( \Delta n \) is the change in refractive index associated with different sucrose concentrations.

To judge the sensor performance and to compare it to the performance of other sensor techniques, it is useful to derive the limit of detection (LOD). This parameter is noteworthy because it is defined as the lowest quantity or concentration of a compound that can be reliably detected with a given analytical method. For the numerical computation of LOD, we utilised the losses incurred in the proposed structure like diffraction loss. Thus here the LOD indicates the quantity of analytes which can be distinguished with above 99% reliability, and can be represented as (Romain et al. 2015):

$$ LOD = \frac{3 \in }{S} $$
(11)

where \( \in \) represents the standard deviation of error of diffraction loss and S denotes the sensitivity of the sensor. The LOD result and the comparison with other sensing methods are given in Table 2 and are discussed in Sect. 4.

4 Results and discussions

To realise the sucrose sensor, initially a simulation is carried out by employing the FDTD computational technique towards investigating dispersion relation of the proposed waveguide structure. The dispersion relation indicates the variation of frequency with respect to wave vector, which can be altered by controlling different parameters such as refractive index of the material, number of grating layers, and width and thickness of the photonic waveguide. From a simulation point of view, the thickness of the outer layers (LiNbO3) is taken to be 650 nm and thickness of the inner layer (air) is chosen to be 350 nm, whereas the width is taken as 100 nm. The refractive index for different concentrations of sucrose in the aqueous solution is acquired from Yunus (1988) and is listed in Table 1.

Table 1 Refractive index information for different sucrose concentration
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Referring to the different data listed in Table 1, simulations are carried out by deploying FDTD technique for analysis of dispersion relation between frequency and wave vector with reference to all the listed sucrose concentrations, which range from 10 g/100 ml to 70 g/100 ml. Simulation outcomes only for the low and high sucrose concentrations of 10 g/100 ml and 70 g/100 ml are depicted in this manuscript as the Figs. 3 and 4 respectively.

Fig. 3
figure 3

Dispersion relation of frequency with wave vector for 10 g/100 ml sucrose concentration

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Fig. 4
figure 4

Dispersion relation of frequency with wave vector for 70 g/100 ml sucrose concentration

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In Figs. 3 and 4, frequency in Hz is plotted in the y-axis whereas wave vector k in m−1 is shown in the x-axis. The frequency gap is highlighted with green colour in the figures, which signifies the prohibited frequency range/band gap in the proposed photonic structure. From the highlighted frequency gap, the corresponding wavelength of upper and lower edge of the PBG is computed, and also the band gap width is calculated, which are indicated in the aforementioned figures.

Figure 5 represents the variation of wavelength associated with the upper edge and lower edge of the PBG, which are shown along the primary vertical axis and secondary vertical axis (reverse order), respectively. It is observed that wavelength of the upper edge varies from 2910.60 to 3059.10 nm whereas wavelength of the lower edge varies from 3893.40 to 3944.63 nm, with respect to different sucrose concentrations. This significant linear shift in the aforementioned PBG edge can be taken as a sensing parameter for the proposed sucrose sensor.

Fig. 5
figure 5

Variation in wavelength of the PBG edge

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Further, we investigated the shift in the PBG width with reference to various sucrose concentrations, which is shown in Fig. 6. From this figure it can be seen that the width of the PBG decrease from 982.8 to 885.53 nm with respect to an increase in sucrose concentration from 10 g/100 ml to 70 g/100 ml. Interestingly, the variation in PBG width is nicely fitted with a linear trend line (R2 = 0.9907), which ensures accurate sensing of sucrose concentrations.

Fig. 6
figure 6

Variation of PBG width with respect to sucrose concentrations

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In addition to this, the shifts in the central reflected wavelengths with respect to different sucrose concentrations are thoroughly studied and are presented in Fig. 7. It can be seen that the central reflected wavelength is shifted towards higher wavelength, i.e. from 3402 nm to 3501.86 nm, for increases in the sucrose concentrations. In addition to this, the above variations follow a highly linear trend with R2 = 0.9979. This significant shift in the central reflected wavelength appears to be a key parameter to evaluate the performance of the sensor.

Fig. 7
figure 7

Variation in the central reflected wavelength with respect to sucrose concentrations

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Afterwards, we analysed the sensor performance by investigating the sensitivity parameter using Eq. (10). Sensitivity is computed for different concentrations of sucrose with respect to pure water. Figure 8 shows the variation in sensitivity in nm/RIU along the vertical axis whereas sucrose concentration in gm/100 ml is taken along the horizontal axis. A nonlinear variation in sensitivity is witnessed particularly for the case of 20 g/100 ml and 60 g/100 ml sucrose concentrations, which is due to relatively small change in wavelength shift (\( \Delta \lambda_{S} \)). Also, it has been found that a maximum sensitivity of 1016.35 nm/RIU is obtained for the proposed sensor, which proves its efficiency. Thereafter, we calculated the limit of detection of the proposed sensor with the help of Eq. (11), and we obtained a very low LOD of 2.28 × 10−4 RIU, which indicate that the proposed 1D PhC structure can minutely sense small changes in concentration of sucrose in aqueous solution. We have also compared different performance characteristics of the sensor with other researches available in the literature, which are stated in Table 2. From Table 2 it can be seen that the proposed sensor exhibits superb sensing characteristics in terms of sensitivity and LOD, with these parameters being comparable or slightly superior to other sensing techniques. However, other features of the proposed sensor (such as compactness, fabrication simplicity, and inexpensive manufacturing) make the present sensor configuration a very noteworthy contender.

Fig. 8
figure 8

Variation of sensitivity with respect to sucrose concentrations

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Table 2 Comparative analysis of sensor performance
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Later, we calculated the variation in reflected light energy and transmitted light energy in the proposed structure through numerical formulations as explained in the Sect. 3, and the results are shown in Fig. 9. The primary vertical axis represents the shift in reflected light energy (\( E_{r} \)) with respect to different sucrose concentrations, where it is perceived that \( E_{r} \) decreases from 0.3649 to 0.3545 eV as the sucrose concentration varies from 10 g/100 ml to 70 g/100 ml. Similarly, the secondary vertical axis shows the variation in transmitted light energy (\( E_{T} \)), where a shift from 1.1443 to 1.1485 eV is marked in for different sucrose concentrations. Beside this, it also has been asserted that variation of both \( E_{r} \) and \( E_{T} \) follow the linear trend line with correlation coefficients of R2 = 0.9970 and R2 = 0.9973 respectively, which deduce precise sensing of sucrose concentration by the proposed LiNb03 based 1D photonic crystal structure.

Fig. 9
figure 9

Variation of reflected light energy and transmitted light energy with respect to sucrose concentrations

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Finally, investigation on diffraction loss is carried out and it is found that there exist a definite amount of diffraction loss in the photonic crystal during propagation of a light signal, which is graphically shown in the Fig. 10. From this figure, we concluded that diffraction loss increases almost linearly from 0.152 to 0.69 Arbi.Unit with an increase in sucrose concentration.

Fig. 10
figure 10

Variation of diffraction loss with respect to sucrose concentrations

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5 Conclusions

The present research exhibits a simple yet efficient LiNb03 based 1D PhC structure for accurate sensing of different sucrose concentrations in an aqueous solution. The physics behind this research is bandgap analysis by employing an FDTD methodology with respect to various sucrose concentrations in the range 10 g/100 ml to 70 g/100 ml. Structure parameters like thickness of the PCs, refractive index of the material and height of the structure play vital roles to accomplish accurate sensing of sucrose concentrations. Sensing characteristics are realised through shift in reflected wavelength, PBG edges and PBG width with reference to variation in sucrose concentration. Furthermore, diffraction loss, reflected light energy and transmitted light energy in the proposed structure are examined, and a notable change is observed in the aforesaid parameters for different sucrose concentrations. Again, it has been divulged that variations of the aforementioned parameters nicely follow a linear trend line, which claims the proposed structure as a suitable candidate for accurate sensing of sucrose concentration in the aqueous solution. Finally, we compared sensitivity and LOD of the present research with reported researches in the literature and concluded that the proposed sensor outperforms other methods in terms of above mentioned sensing parameters.