Plus Shaped Single Grating based Optical Fiber Structure for Water Sensing Application


 Fiber grating sensors demonstrate great potential especially for the refractive index based sensing. However, a meticulous effort is still required to improve the sensitivity of fiber grating sensors towards water sensing. In this work, for the first time we have numerically investigated a plus shaped single grating within the core of optical fiber for water sensing applicaions. The primary objective of incoroporating the plus shaped grating within the core is to increase the sensitivity in comparison to existing grating sensors while increasing the analytes quantity. The testing of designed grating sensor model is done within the refractive index range from 1.33 to 1.39 with a remarkable wavelength shift of 65 nm. The analysis of proposed model of grating sensor is accomplished by using finite difference time domain (FDTD) method under the contour of perfect matched layer (PML) as boundary conditions at the interface of core and grating. The attained results depicts the significant sensitivity of the proposed fiber grating sensor for water sample sensing.


I. Introduction
THE concentration of water pollutants is extensively studied for various applications in the area of oceanography, clinical testing, food testing, and quality monitoring of water resources [1][2][3]. In traditional techniques, water pollutant detection techniques, the detection of presence of ion concentration in water was done on the basis of conductivity which is highly sensitivity to electromagnetic interference. As a result such techniques were not able to ful ll the demand of high precision and sensitivity which are desirable from competent water sample sensor [4]. The optical ber based sensors are of great interest because of their wide application domains, immune to electromagnetic interference, easiest miniaturization and remote control [5] [6]. The expectation of new technological solutions is proportionally increasing with the growing demand of optical ber based sensors and biosensors. The optical bers were included in sensing applications to increase the sensitivity of sensor systmes [7].
Various optical ber based models were utilized for the salinity sensing, that increases due to the presence of ions in water samples. Some notable attempts are ber based interferometers [8][9][10][11][12]. tapered bers [13,14], photonic crystal bers (PCF's) [15,16], surface plasmon resonance (SPR) sensors [17,18], micro ber [4,19] and ber grating sensors [20][21][22][23]. However, the interferometeric probes were less sensitive when immersed into the targeted samples. The tapered ber sensor structures sustains higher sensitivity with precise calibration. PCF and SPR sensors exhibit higher sensitivity with higher costs and complicated fabrication procedures. The micro ber based sensors also exhibits higher sensitivity for external environment with precise adjustment of loop diameter to attain high reproducibility. Concurrently, the optical ber grating have been extensively used for the numerous applications such as mode converters [24], wavelength selective devices [25], dispersion compensators [26], pulse compressors [27], and in sensing applications [28][29][30][31][32]. The ber grating is designed by periodically modulating the core refractive index of optical ber structure. On the basis of grating periods, the grating structures were classi ed into two categories: rst, where the grating period is less than one micron and termed as Fiber Bragg Gratings (FBG) [33]. In another kind, the gratings period of hundreds of microns is used and termed as long period grating (LPG) structures [34]. In FBG's, the fundamental mode of core gets coupled with its counterpropagating mode and optical signal not penetrates into cladding due to which the detection of external refractive index (RI) becomes impossible. Whereas, LPG in turn makes the coupling of fundamental core mode with cladding modes feasible that results into set of resonances in the transmission spectrum [28]. Therefore, the LPG's based sensors have been used for RI sensing [35], chemical sensing [36], and monitoring of variation in thin overlay lms with high accuracy [37]. Moreover, these sensors receives attraction in biological sensing applications such as bacteria [38,39], viruses [40], proteins [41], and nucleic acids [42]. Therefore, the overwhelming development of ber grating based sensors leads to the development of different kind and geometry of gratings to achieve better sensitivity and accuracy. For instance, a V-shaped LPG based bending vector sensor has been proposed with effective dip in wavelength shift and higher sensitivity [30]. In an another approach, a Dshaped FBG based RI sensor has been proposed by side polishing the core layer after cleaving the half clad [31]. The main motivation behind the creation of different strucutres of grating is to improve the eld distribution and to attain effective modulation that can produce better and precise results for RI sensing.
Therefore, in this work, for the rst time we have numerically design and examined a plus shaped grating in optical ber structure for the monitoring of ionic pollutants in water samples. Several studies have been reported for the RI based detection of ionic pollutants in water samples. For instance, a micro ber based Sagnac loop has been used for the detection of presence of chloride ions in water samples [4]. In another work, a corrugated ber grating has been used for the detection of Lead ions in water samples. The RI of water samples containing ionic pollutants is ranges from 1.33-1.39 [43]. Therefore, in this work, we have analyzed the proposed sensor geometry under the RI ranges from 1.33 to 1.39, and as a result the wavelength shift of 65 nm was achieved while considering the perfect matched layers (PML) as boundary conditions at the interface of grating and core. The inclusion of plus shaped grating also increases the contact surface of sensor structure with analytes, that results into higher sensitivity. The analysis of designed structure of sensor model was carried out by using ninte difference time domain (FDTD) method. The paper comprises ve sections: the introductory part of the work paper is covered in Section I. Section II and III, present the designing of proposed sensor model and corresponding results, respectively. A comparative analysis of proposed model is discussed in Section IV. The conclusion and future aspects of the work is discussed in Section V.

Ii. Designing Of Plus Shaped Single Grating
The design of plus shaped single grating structure in the core was implemented by analyszing the one single vertical slot of grating as presented in Fig. 1. The vertical single slot grating was modelled under the contour of perfect matched layer (PML) as boundary conditions at all the interfaces. The modelling of single vertical slot grating based sensor model was done in 12 µm long single mode optical ber structure. A grating of 1 µm was created at the center of ber structure. Moreover, in the model an appropriate ratio of core and cladwas considered in such a way that analysis was carried out at the core lateral width of 1.125 µm. The RI of substrate was optimized equal to the RI of cladding of optical ber. The propagation of optical signal through the core is guided by obeying the well established coupled mode theory [44,45]. The variation of effective refractive index in the ber core due to the presence of grating can be modelled as [44]; where, h 0 is the wavenumber at resonant wavelength on which design is modelled, n 0 is the the refractive index of unmodi ed core, σ, þ and Φ are the slowly varying functions of factor h 0 z. For the gratings, if we consider factor þ to be very smaller than 1 i.e. þ≪1, then the detuning factor can be describe mathematically as; Where, ω is the frequency, and the sum of electric elds of forward and backward propagating modes is written as; The coupled mode theory can be used for deriving the elds for forward and backward propagating modes. This theory is applicable for the monochromatic frequency or continuous wave (CW) source especially for linear propagation, whereas, for the pulsed input signal, it can be validated by separately considering each spectral component over the spectrum of incident pulse signal [46]. The optimized parameters of theoretical analysis can be carried forward for the fabrication of sensor model. Whereas, in rst appearance, the design of plus shaped cavity seems to be di cult in terms of fabrication, but can be easily done by using following approach: A focused ion beam (FIB) technique can be taken into consideration to fabricate the plus shaped cavity. By employing the sputtering technique to take out the ber molecules with accelerated ions, holes or cavities in micro-scale. The micro-trenches developed by FIB technique on micro and taper bers have proven to be feasible [47,48]. In larger dimension bers, FIB has been also used to mill side-accessed holes in air silica structured bers [49]. The FIB-fabricated grating structures have shown potential for the application of temperature and refractive index (RI) sensors [50]. The fundamental element for creating the plus shaped cavity in ber with aspect ratio is that the cavity should be deep enough to interact with the propagating elds and its width should be 1 micron. The investigation of FIB process on silicon has been already proven to successful [51]. However, in contrast, it is still challenging to attain a high aspect ratio cavity or hole in bulk silicon substrate [52]. The aspect ratio can be increased for gas assisted FIB technique and also feasible for optical bers [52]. To, fabricate the desired plus shaped cavity, initially the plastic jacket of ber can be manually removed.
Then, ber will be kept under scanning electron microscope while covering it with the conducting tape. Thereafter, the pattern of plus shaped cavity can be drawn over the conducting tape. Initially, the etching can be done with the depth ratio of 10 microns to maintain the ber strength. The etching process can be continued till the desired cavity attained. The fabrication of desired plus shaped cavity under FIB can be done by using Gallium ion dual beam accelerating at 30 keV. The drawn can be set to 50 nA with beam spot size of 300 nm [53]. The RI distribution of the model of single vertical slot grating based sensor model is presented in Fig. 2. From the RI distribution pro le, one can easily observe the presence of vertical slot lled with RI in the tune of 1.33 similar to real water samples. Thereafter, the results of single vertical grating has been taken into consideration and plus shaped grating based sensor is modelled as shown in Fig. 3. The plus shaped grating was modelled by including the lateral slot of length and width of 1.6 µm and 1 µm, respectively, with the single vertical slot having width of 1 µm in the propagating direction.

Iii. Results And Discussion
The theoretical analysis and formulation was followed stepwise to achieve the precise results. The investigation of plus shaped grating based sensor model was followed by the analysis of models of linear ber core and single vertical slot grating. Initially, ber structure was studied in detail to optimize A. Linear ber core structure The analysis of linear ber core structure was done in terms of signal transmission, distribution of mode pro le, phase distribution in direetion of propagation and power con nement as shwon in Fig. 4. The transmission of optical signal through the core is presented in Fig. 4 (a), from where it can be observed that at operating wavelength the maximum power is con ned within the core. The distribution of propagating mode pro le also shown in Fig. 4 (b), from where it was conceived that the mode distribution is uniform throughout the core. The mode distribution pro le also depicts the con nement of optical power in the center of core along the propagation axis. The phase distribution of the propagating eld is exactly matched with the mode distribution pro le of eld, as provided in Fig. 4(c). The graphical representation of optical eld con nement within the core of ber is presented in Fig. 4 (d). It can be easily concluded from this gure that maximum power is con ned within the center part of core along the axis of propagation, which is about 0.9 a.u.

B. Single vertical slot grating
The analysis of single vertical slot grating structure was followed by the results of linear ber core model. A 1-µm wide vertical grating was created at the center of linear ber core. Thereafter, for analyzing the water samples, RI of vertical grating was set to 1.33 which is equivalent to the water RI.
The performance of designed structure was gauged in terms of transmission of optical signal, mode and phase distribution and power con nement in core region as revealed in Fig. 5. The propagation of optical elds through the single vertical slot grating incorporated ber is presented in Fig. 5 (a). It can be infer from the gure that a part of power was absorbed at the created grating slot and hence power at output is low in comparison of linear optical ber core structure which was discussed in previous section. Instead of absorption, a part of power is also decaying into substrate region which is considered as outer environment in proposed work as shown in Fig. 5 (b). The power leaked into external environment is not going to recombine with the eld propagating inside the core and grating structures. The phase distribution of the elds can be seen from Fig. 5 (c). This gure gives a clear understanding of the nature of variation in phase of signal propagating through the created grating. The loss in power at output can be comprehend from Fig. 5 (d), which clearly reveals that the power at the output port of designed sensor structure is low in comparison of linear optical ber structure (as depicted in Fig. 4(d).
Afterwards, the analysis of designed sensor structure was done by varying the width of slot from 0.5 nm to 1 µm, and results were obtained in terms of output intensity with respect to slot width as shown in Fig. 6. The analysis was carried out to examine the slot width for the modelling of plus shaped cavity sensor model. The output results illustrates that on narrowing the slot width below 1 µm, the output power pro le is also degrading. The power at output port for the slot width less than 100 nm is presented in inset of Fig. 6. For the slot width less than 100 nm, the power at output port almost degraded by 25 %. This loss in power at output port on narrowing down the width of grating slot below 100 nm is because of the decaying of eld in outer environment with poor con nement in core. Therefore, it can be concluded that for proposed geometry of sensor higher sensitivity can be attained at the slot widths higher than 100 nm. The results indicates that the output power pro le was sharply increases for the slot width greater than 400 nm and goes till 850 nm. Afterwards, the output power linearly increased for the slot width higher than 850 nm and almost get saturated after 1 µm. The maximum output power was attained at the slot width of 1 µm, which has been used to examine the sensing ability of plus shaped cavity. The pictorial representation of power con nement in the core at the slot width of 10 nm is presented in Fig. 7, tbat is around 75 % of the input power.

C. Plus shaped grating structure
The results of single vertical slot grating structure as discussed in previous section were taken into consideration to analyze plus shaped grating structure. The plus shaped grating model was introduced by including a lateral slot of length and width of 1.6 µm and 1 µm, respectively, as shown in Fig. 3. Inspection of designed plus shaped grating structure was done by analyzing eld propagation and con nement of optical eld in the core as provided in Fig. 8. The optical eld propagation presented in Fig. 8 (a) is plotted for the slot widths of 1 µm, which deduce that almost 25 % of power is excreted into external environment. The graphical representation of optical power con nement within the core is depicted in Fig. 8 (b). From where the degree of optical power con nement within the core is studied under variation of the slot width from 0.5 nm to 1 µm. This result illustrate that maximum power is con ned within the core when slot width set equals to 1 µm. Then, structure was investigated further under deviation of slot widths with power at output port, and obtained results are presented in Fig. 9.
The trend shown in Fig. 9 states that on increasing the slot widths to higher values the transmitted power at output port is also increasing proportionally. However, similar to single slot vertical grating there was no such remarkable variation in output power for narrower widths of plus grating slots ranging from 0.5 to 100 nm. The output power pro le for narrower slot widths is also shown in inset of Fig. 9. The maximum output power was obtained for the slot width of 1 µm while keeping xed length. Thereafter, the sensing ability of plus shaped grating model was gauged by varying the RI from 1.33 to 1.39. The analysis of proposed plus shaped grating was done in presence of RI of water ranging from 1.33 to 1.39, which covers all the ionic pollutants. The presence of ionic pollutants in water leads to the increase in its refractive index, which is vulnerable for aquatic lives. Also, it degrades the quality of drinking water that becomes a key issue in developing countries. The analysis of sensor was initiated at the wavelength of 1550 nm for the RI of 1.33. The shift in wavelength with respect to RI is presetnd in Fig. 10. From the results, it can be comprehended that on increase in RI leads to red shift in waveglength and total shift was about 65 nm for the tested range of RI. The attained results also states that the sensitivity of designed plus shaped grating structure is 1083 nm/RIU with the autocorrelation function of 99.69 %.

Iv. Comparative Analysis
A co mparative study of proposed work with relevant reported water sensing models is presented in Table 1. This study is done in terms of obtained autocorrelation coe cient and sensitivity. A FBG based sensor was developed for the detection of water level [46]. The development of sensor structure was done by using converntional FBG, whereas, in our work, we have introduced a novel plus shaped grating to sense the water samples. In an another work, a normal optical ber based sensor structure was implemented for water quality monitoring with ne autocorrelation coe cient but there was no discussion about the sensitivity of sensor [47]. A corrugated ber grating structure was developed for the detection of lead ions in water samples. Although, the work was fruitful but the autocorrelation coe cient and sensitivity of the sensor was not reported [48]. A portable optical ber structure has been used for the detection of E-Coli in water samples. The sensor implementation was done with the autocorrelation function of 0.95 [54]. An optical ber based Mach-Zehnder interferometer (MZI) has been reported for the monitoring of water level. The reported sensor is capable of monitoring the water level with the autocorrelation function and sensitivity of 0.99 and 1868.42 pm/nm/RIU, respectively [55]. In an another work, a D-shaped FBG was deployed for the detection of liquid samples including water [38]. The work highlighted a unique novel D-shaped FBG sensor structure, but autocorrelation coe cient and sensitivity of sensor was not addressed. A linear optical ber cable based sensor structure was also reported for the detection of water level. The sensor structure was capable of sensing the detecting the level with autocorrelation function and sensitivity of 0.9616 and 329.22 nm/RIU, respectively [56]. In present work, a novel plus shaped grating structure is precisely designed numerically and investigated for the monitoring of water samples containing ionic pollutants. A wide range of RI (1.33-1.39) is considered in present work that includes numerous ionic pollutants contaminating the drinking water. For the proposed sensor model, the attained autocorrelation coe cient and sensitivity are 0.9969 and 1083 nm/RIU, respectively.

V. Conclusion
In this work, a novel design of a plus shaped grating structure has been proposed along with its theoretical analysis. The sensing capability of designed structure was judged by testing the range of RI from 1.33-1.39 which covers almost all the ionic pollutants responsible for contaminating the water resources. The detailed analysis of designed grating structure was carried out stepwise. Initially, linear ber core structure was discussed and its charateristics were determined in terms of transmission of optical signals, mode and phase distribution pro le and con nement of optical power within the core of ber structure. Secondly, single vertical slot grating was introduced and relevant charcteristics were determined. Finally lateral grating slot was incorporated in the structure to form a plus shaped grating which is studied for its performance as water sample sensor. Simulation of the proposed structure was implemented by using nite difference time domain (FDTD) technique based software tool at 1550 nm.
Wavelength shifting on introduction of external environment in plus shaped grating structure indicates that the designed sensor structure is having high sensitivity towards water samples which is about 1083 nm/RIU with the autocorrelation function coe cient of 99. 69 %. The possible reason behing this high sensitivity can be explained as follows: 1) contact surface of sensor strucuture with analytes increases due to incorporation of plus shaped graing, 2) Another salient advantage of this structure is non requirement of creating too many gratings due to enhancement of analyte content within single plus shaped grating structure. Therefore, the innovative structure of plus shaped grating could be a point of attraction for the development of optical ber based biosensors especially for the monitoring of water samples and biological molecules.

Con ict of Interest
We all the authors declare that there is no con ict of interest.

Funding
There is no funding for the proposed work.
Author's contribution The idea was given by rst author and he also drafted the le. The result analysis was done by second and third author. The fourth author updated the draft le of manuscript.

Availibility of data and material
There is no supportive data and material available with the manuscript.

Code availability
There is no code available with the manuscript.

Ethics approval
There was no such need of ethics approval to comprise the proposed work.

Consent to participate and publication
We all the authors take all the responbiliteis of publication of manuscript.
Vii. References