1 Introduction

In the field of fiber optics, refractive index sensors have been widely investigated because of their potential applications in chemical, biological, and food industries. Such sensors have many advantages over conventional electrical sensors like faster response, immune to electromagnetic interference, lesser cost, and higher sensitivity (Urban et al. 2010; Riza et al. 2019; Jung et al. 2011; Sahota et al. 2021). Generally, fiber Bragg grating is commonly used to measure temperature, stress, pressure, refractive index, humidity, etc. (Cho et al. 1135; Dinia and Frezza 2020; Fu 2012; Guan et al. 2013; Yang et al. 2011; Sangeetha and Krishnan 2020; De-Jun et al. 2014). Various optical elements such as FBGs (fiber Bragg gratings) (Othonos et al. 2000), microfiber interferometer (Ahmed et al. 2016), multimode interference structures (Zhao et al. 2016), etc. are used to measure refractive index of different chemical solutions, etc. Amongst them FBG is preferred over other technologies because it can be used for remote distribution sensing, fast interrogation, etc. For remote distributed sensing fiber Bragg grating is suitable to measure refractive index but before specific modifications, it has larger temperature cross-sensitivity (Gu et al. 2018). FBG based refractive index sensors are admired choices, when there is a need to deal with the quality check of certain liquids or materials, for structural monitoring applications like structure bending, etc., to measure pH values of certain solutions, to check the toxicity of the different liquids in industries. A high sensitivity using ordinary FBG is not possible and some modifications are need to be done like improvision of structure, usage of different types of gratings, coatings of different materials, etc. can be used.

Modifications can be done in structures, grating type and different materials. Structures such as D- shaped (Xue et al. 2019), thinned shaped (Iadicicco et al. 2005), micro-structured FBG (Presti et al. 2020), hollow suspended core fiber (Tian et al. 2019), helical microfiber Bragg grating (Liao et al. 2019), spherical-shape structure (Gu et al. 2018), thinned cladding structure (Chen et al. 2017), etc. are used to improve the sensitivity of refractive index sensor. To make such special structures different processes like mechanical or chemical etching, tapering (Niu et al. 2018), etc. are used. After etching cladding part of sensor, sensitivity is improved as more evanescent waves are formed but with the etching of cladding mechanical strength of the sensor is also reduced which results in lower durability. Different types of gratings like uniform grating (Sangeetha and Krishnan2020), long-period grating (Frazao et al. 2001), chirped grating (Korganbayev et al. 2018), tilted grating (Zhang et al. 2019), are also widely used but amongst them long period are widely used. By using long period grating sensitivity is higher but coupling losses are also there. Coating materials like reduced graphine oxide (Singh et al. 2020), polymer (Zhang et al. 2012), titanium oxide (Tahhan et al. 2017), silicon oxide(Korposh et al. 2011), negative refractive index modification line (Chen et al. 2017), etc. have been used in refractive index sensor. Specially designed structures with different types of the grating such as hollow eccentric optical fiber(HEOF) (Guan et al. 2013), SMF- TCF-SMF (STCS) results with Mach Zehnder interferometer (Zhao et al. 2016), Mach-Zehnder fiber interferometers (Li et al. 2019) with long period fiber gratings, etc.

To improve the sensitivity etched structures are widely used. Using etching when cladding of fiber is etched such that one side of fiber looks like D in shape, higher sensitivity is achieved than that of ordinary sensor (Dong et al. 2019). With an increase in etching the sensitivity of refractive index sensor is also increased proportionally (Iadicicco et al. 2005; Chen et al. 2017). Consequently, to improve the sensitivity, in novel double D-shaped refractive index sensor, etching has been done from opposite side in D-shaped fiber resulting in 2 D-shapes in refractive index sensor. This proposed novel double D-shaped fiber, whose structure is cascaded with an FBG (fiber Bragg grating) inscribed inside the single mode fiber is used for RI sensing of glucose solution with different concentrations. By observing the shift of Bragg wavelength of structure of double D-shaped fiber, sensitivity of sensor can be obtained for the refractive index ranging from 1.33 to 1.43 approximately. For D-shaped fiber the achieved sensitivity is of 35.26 nm/RIU and for double D-shaped refractive index sensor the achieved sensitivity is of 47.37 nm/RIU. As the depth of etching is increased the sensitivity of the sensor is also increased as stronger evanescent field is experienced by cladding modes but there is decrement in the mechanical strength and durability of sensor. Also, the results of D-shaped fiber and double D-shaped fiber are compared with the existing work in terms of sensitivity of refractive index. The proposed sensor has characteristics of compact structure, simple configuration, and higher sensitivity, which provides potential applications in RI measurement.

2 Design and principal of double D-shaped fiber

2.1 Principle of FBG sensor

A fiber Bragg grating is a periodic deviation of refractive index in core along the length of optical fiber by exposing its core to an intense optical interface pattern in presence of ultraviolet (UV) light (Hill and Meltz 1997). Being a fiber optic sensor, a Bragg grating has all the advantages usually attributed to significances, such as low loss relative to the fiber length, immunity to electromagnetic and radio frequency interference, small size and weight, intrinsically safe operation in environments characterized by hazardous materials, high sensitivity and long-term reliability. Fiber Bragg grating technology reveals an inherent serial multiplexing capacity and an ability to provide absolute measurements without the need for referencing. This makes it the natural alternative to conventional electrical sensing technologies.

When the phase- matching condition is satisfied, the contributions of reflected light from each grating plane add constructively in the backward direction to form a back-reflected peak with a center wavelength defined by the grating parameters (Sahota et al. 2021). The reflected wavelength which is also known as Bragg wavelength can be measured using Bragg condition as expressed in Eq. 1:

$$ \lambda_{{{\text{FBG}}}} = {\text{2n}}_{{{\text{eff}}}} \Lambda $$
(1)

where, neff is the effective index and Λ is the period of grating. Shift in Bragg wavelength (ΔλFBG) can be expressed as the twice of product of change of effective refractive index (Δneff) of the surrounding of the sensor and grating period of the FBG inside the sensor as shown in Eq. 2. Therefore, Bragg wavelength shift can be expressed as in Eq. 2 (Chen et al. 2007):

$$ \Delta \lambda {\text{FBG}} = {2}\Delta {\text{neff}}\Lambda $$
(2)

Thus, FBG sensor for detection of the environmental refractive index change is based on the Bragg wavelength shift.

2.2 D-shaped fiber FBG based refractive index sensor

The structure of D-shaped fiber (DSF) as illustrated in Fig. 1, is a combination of two single mode fibers with grating inscribed in one of the SMF. In D-shaped refractive index sensor, cladding part is etched from one side. When incident light encounters D-shaped fiber with fundamental mode, from core mode a segment of light will be coupled with modes of higher order of cladding in D-shaped fiber. A similar study has been done in Dong et al. (2019), where D-shaped refractive index sensor is used to find sensitivity of glycerin solution. Refractive index sensor uses the total internal reflection (TIR) concept, where the light transmits through the fiber is frequently reflecting from interface of cladding-core in a very lossless manner (De-Jun et al. 2014). For reflecting light at angle which is near to the critical angle, a significant portion of the power (a decayed electric field) extends into the cladding or medium which surrounds the core, known as the evanescent wave, extends only to a short distance from the interface, with power dropping exponentially with distance (Liang et al. 2011). The strength of these evanescent fields is also affected by environmental refractive index variation around them. Bragg grating reflection or transmission properties have to be strongly affected to measure the change in refractive index of D-shaped fiber efficiently. Different types of evanescent fields are generated by the different modes which are propagating through the fiber, which leads to radiation of optical field outside the core of the fiber. As the high order of modes increase, the generation of corresponding evanescent field will also increase. Consequently, in evanescent areas modes of higher orders have larger optical power distribution resulting in more sensitivity of the refractive index sensor.

Fig. 1
figure 1

Schematic diagram of D-shaped fiber

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Both core and cladding mode will propagate in the D-shaped fiber and this region will act as a channel for light and matter interaction. Modes of cladding will interfere with core modes because of different modal phases and in lead out SMF they get interfere resulting in making an interferometer for all fiber modals. A relatively stronger evanescent field is formed outside the D-shaped fiber because of the etched region. As the RI sensor is etched partially from the cladding part, a stronger evanescent field is experienced by cladding modes in D-shaped fiber outside the cladding of sensor. When there is a deviation in the concentration of glucose, the RI of sensor will also change which results in shift of Bragg’s wavelength traveling through D- shaped fiber.

2.3 Double D-shaped fiber FBG based refractive index sensor

To improve the sensitivity, more cladding part of the sensor is needed to be etched. Therefore, cladding of the D-shaped FBG sensor etched from the opposite side of etched section of D-shaped fiber, which results in structure of double D-shaped FBG sensor as shown in Fig. 2. At the interference of double D-shaped fiber and its external environment, the generated electric field is higher than that of DSF, as a wider area is etched in double D-shaped. The strength of these evanescent fields is more affected by environmental refractive index variation for the double D-shaped fiber. Consequently, in evanescent areas modes of higher order have larger optical power distribution resulting in more sensitivity of the refractive index sensor. When incident light encounters double D-shaped fiber from core mode a segment of light coupled with modes of higher order of cladding in double D-shaped fiber. Both core and cladding mode will propagate through the double D-shaped fiber and this region will act as a light and matter interaction channel. More no of modes of cladding will interfere with core modes because of different modal phases and in lead out SMF they get interfere resulting in the making of the interferometer for all fiber modal. When there is a deviation in concentration of glucose solution with refractive index ranging from 1.33 to 1.43, RI of sensor will also deviate and this results in a shift in reflected Bragg wavelength of transmission spectrum traveling through double D-shaped fiber.

Fig. 2
figure 2

Schematic diagram of double D-shaped fiber

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3 Results and discussion

The designing and simulation of double D-shaped fiber based refractive index sensor is carried out on gratingMOD tool of optical software R-Soft CAD. Using gratingMOD, the refractive index sensitivity of D-shaped and double D-shaped refractive index sensor are measured for glucose solution. Coupled mode theory is used to calculate the reflection spectrum. Here, coupled mode theory is used in the software to describe the coupling of the co or counter propagating fundamental and cladding modes. Using parameters as shown in Table 1, a structure with core diameter of 13.5 μm and cladding diameter of 139 μm is used in designing of D-shaped and double D-shaped fiber as shown in Fig. 3. Here, grating type is volume index with structure type as fiber and grating period is of 0.5. Background refractive index is considered as refractive index of glucose solution which is required to be sensed. Delta for core is 0.028 and for cladding is 0.02, when concentration of glucose solution is considered as 50%. Depth of etching for D-shaped groove is of 30 µm from each side. Free space wavelength considered RI sensor is of 1.45 µm. Fiber Bragg grating is inscribed in fiber from length (l) 0–1000 μm in Z-direction

Table 1 Comparison of D-shaped fiber, proposed work and Dong et al. 2019
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Fig. 3
figure 3

Refractive index distribution of double D-shaped fiber

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For increased concentration of glucose in solution within a range of 0% - 50% in water, RI changed from 1.33 to 1.43. When the concentration of glucose in water is 0%, corresponding refractive index is 1.33 and with the increased glucose concentration in water i.e. upto 10%, its refractive index is also increase to 1.35. Similarly, for refractive index 1.43 the concentration of glucose in water is reached to 50%. When cladding part is etched, sensitivity of the sensor increases with the increase of depth of etching in cladding. The ratio of difference between the shift in wavelengths of glucose solution at 0% concentration and 50% concentration to the difference of corresponding refractive index will result in sensitivity of DSF sensor. For refractive index of glucose solution ranging between 1.33 and 1.43 approximately, the obtained sensitivity is 35.26 nm/RIU. All the shifted wavelengths are represented in the Fig.4.

Fig. 4
figure 4

Grating spectral response of DSF for RI ranging from 1.33 to 1.43

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As double D-shaped fiber has stronger evanescent field outside area of the cladding which results in stronger interference influenced by the SRI (surrounding RI) than D-shaped fiber. The core of double D-shaped fiber is exposed more than that of D-shaped fiber and is bordered by silica cladding consequently it is higher in sensitivity to refractive index of surrounding external environment. Figure 5 represents the power spectrum response for reflection using double D-shaped FBG based refractive index sensor.

Fig. 5
figure 5

Grating spectral response of DDSF for RI ranging from 1.33 to 1.43

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When the concentration of glucose is increased i.e. from 1.33 to 1.43 approximately, a blue shift in wavelength is observed in for both D-shaped fiber and double D-shaped fiber. When the concentration of glucose in solution is increased approximately 10% in water, RI changed from 1.33 to 1.35 and a shift of wavelength for double D- shaped fiber is achieved. In similar way, when the concentration of glucose is increased upto 50% Bragg’s wavelength is shifted further. The approximate refractive index of glucose solution with the corresponding increase in concentration of glucose in water is shown in Fig 6.

Fig. 6
figure 6

Refractive index verses glucose solution with varying concentration

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This shift results in sensitivity of 47.37 nm/RIU for refractive index ranging from 1.33 to 1.43 for different concentration of glucose solution using double D-shaped refractive index sensor. At the interface of external environment and double D-shaped fiber, a more evanescent waves (decaying electric field) were generated than D-shaped fiber because of more exposure of the core after etching. For surrounding

RI of 1.33, guided mode is confined to core region resulting in weak evanescent field. But as the SRI is increased by increasing in concentration of glucose solution guide mode is less confined to core and results in strong evanescent field and more efficient interaction with surrounding medium. Consequently, light spectrum travelling through the double D-shaped fiber imposes higher shift in Bragg’s wavelength for SRI 1.43 than DSF for same surrounding refractive index. A comparison of both type of D-shaped based refractive index sensor is shown in Fig.7. In Fig. 8, the shift in wavelength for different values of refractive index with different concentrations of glucose solution is represented. From Fig. 8, it is also evident that the shift in D-shaped fiber is lesser as compared to the shift in double D-shaped fiber. For smaller value of the refractive index there is smaller increment in the wavelength shift, while for the higher values, there is more shift of wavelength for double D-shaped fiber.

Fig. 7
figure 7

Sensitivity curve for D-shaped and double D-shaped fiber

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Fig. 8
figure 8

Shift of wavelength of D-shaped and double D-shaped fiber versus the refractive index

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The comparison of sensitivity of proposed double D-shaped FBG based refractive index sensor and D-shaped FBG based sensor with existing work has been done. The achieved sensitivity for D-shaped fiber is 35.26 nm/RIU and for DDSF is 47.37 nm/RIU for 1.33 to 1.43 range of refractive index for glucose solution. Whereas, in previous work achieved sensitivity is − 31.79 nm/RIU for glycerin solution for refractive index ranging between 1.330 and 1.428. The sensitivity of D-shaped fiber is lower than that of double D-shaped, which clearly shows that with the increase in depth of etching sensitivity of refractive index sensor will also increase.

4 Conclusion

Design of a D-shaped fiber and double D-shaped fiber has been proposed for sensing the glucose solution with refractive index ranging from 1.33 to 1.43. The etched section of D-shaped fiber and double D-shaped fiber is used for sensing refractive index. Because of the etched cladding, the resulting interference is affected by the surrounding refractive index, and become more sensitive to the external refractive index. Sensitivity of 35.26 nm/RIU and 47.37 nm/RIU is achieved for both D-shaped fiber and double D-shaped fiber RI sensors respectively. Such a sensors are compact and small in structure, therefore, can be used for refractive index sensing in medical and bio-medical applications.