Introduction

The unusual growth of tissues inside brain or middle of spine may result development of brain tumors. Such tumors may affect the proper functioning of human brain. These brain tumors are grouped into two basic categories as primary and metastatic. Primary brain tumors are developed either from tissues of brain or their immediate surroundings. Primary brain tumors are further classified into glial or non glail and bening or malignant. On the other hand metastatic brain tumors may develop elsewhere in the human body and may infiltrate into brain through human bloodstream. The benign is least aggressive class of tumors. They may exist inside cells or adjoining regions of brain. Such tumors are generally noncancerous and are not responsible for spreading of malignancy into the other tissues. Normally malignant brain tumors contain cancer cells and are considered to be dangerous for infected persons because they spread rapidly into other parts of brain. There are more than 120 know varieties of tumors which belong to brain or nervous system of human body. The approaches pertaining to the diagnosis and treatment of these tumors are not unique. It is dependent upon the type of cells and the area of the existence of tumors inside human body. The diagnosis of brain tumor is a very complicated and challenging process due to the requirement of sophisticated medical equipments along with number of medical experts of different fields to ensure safety of the patient during the procedure. The early stage and timely detection of brain tumors is curable but the process of treatment is very costly and painful for the patient. Since brain is one of the most sophisticated as well as complex part of human organs which consists of more than a hundred billion nerves, so lot of precautions are involved while testing and treating brain tumors. Brain also provides the artificial intelligence support which controls our movement, thoughts, speech and also ensures the proper and smooth working of other parts of body. As an estimate 19 million new cancer cases along with 10 million deaths due to cancer are being reported per year across the globe. Most of these deaths are due late diagnosis of the cancer which reaches to last stage. Therefore the development of rapid, accurate, advance and cost effective mechanism for detection of malignant tumors is an essential requirement to make early stage and timely detection of tumors possible. In order to save the life of patient suffering from cancer the early stage and timely detection of tumor is the most necessary requirements1,2.

Presently available photonic bio-sensing technologies are amongst those which could address the challenges involved in the earlier stage and timely detection of malignancy in human body. In traditional bio-sensing techniques, bio-sensing devise has to be inserted inside the sample which is in the form of liquid called analyte on the other hand in photonic bio-sensing technology cavity region of the device has infiltrated by fluid sample under investigation3,4,5. Moreover such devices have several advantages like accuracy in results, cost effectiveness, rapid and fast processing of samples under investigation. Basically any biosensor based on photonic biosensing technology is consisted of five elementary parts. The first part is the fluid sample under investigation. It is known as analyte. The second part of the device is used for sensing the analyte under consideration. This part is identified as a bio-receptor. The information from bio-receptor is being sent to third part of the biosensor which is known as transducer. The working of transducer is to produce measurable signals. These measureable signals are being fetched in to the fourth part of biosensor which consists of an electronic circuit to produce digital signals. Finally the combination of hardware and software is used for display of results as an outcome of investigations6,7,8.

Photonic crystals (PhCs) are one of the most essential and integral part of photonic bio-sensing technology as discussed above9,10,11. Actually PCs are the multilayer thin film structures of periodically varying refractive index of the constituent materials. Depending upon the periodic modulation of refractive index of layers they can be classified into one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D). PhCs have tremendous ability of controlling the propagation of electromagnetic waves (EMWS) passing through them due to the formation of photonic band gap (PBG). The remarkable PBG properties make them suitable to be used in designing the light driven modern photonic devices. The devices like optically driven photonic switches, reconfigurable photonic biosensors, PhCs based waveguides and filters are some examples of light driven modern devices which are playing a prominent role in the field of photonic engineering and technology12,13. Nowadays involvement of PhCs in the designing of biosensors for investigating various kinds of biomedical fluids has become new hot topic of research due to their simple design and easier fabrication14,15,16. For example high performance ultra-sensitive biosensor capable of detecting cancers cells proposed by Arafa et al.17 and Nouman et al. suggested a 1D PhC based biosensing design for rapid detection of brain lesions with ultra-high sensitivity of value 3080.80 nm/ RIU18.

Recently the development in the field of material engineering has provided us an opportunity to use of nanocomposite materials in the fabrication of photonic devices. Actually nanocomposite materials are those materials in which metal or dielectric nanoparticles are embedded into host materials. This inclusion of nanoparticles into host material results the relatively larger value of refractive index19 of the host material in contrast to the conventional dielectrics or metals. Such nanocomposite materials have found novel applications like fabrication of high quality optical lenses and microscope with high resolution capabilities. The size of the nanoparticle embedded into host material like metal, superconductor, dielectric and semiconductor may vary between 1 and 100 nm depending upon the requirement pertaining to the application20. The insertion of nanoparticles into host material reduces the absorption depending upon the volume fraction and radius of spherical nanoparticles. Moreover the technological development in the field of nanosciences attracts the attention of researchers to design and develop photonic biosensors made up of nanocomposite materials21. For example Pandey et al. presented how to use ZnO–TiO2 nanocomposite power pellets for morphological and relative humidity sensing applications22. Zhou et al., suggested a novel way of detecting breast cancer cells by using graphene oxide based nanocomposite23 materials.

From past few years researchers have given their attention for designing of photonic structures made up of dielectrics, semiconductors, metamaterials as well as metals24,25,26,27 of tremendous biosensing applications. Moreover application of superconductors (SCs) as a constituent material in the development of 1D PhCs has explored new possibility of making externally tunable photonic devices. The optical properties of such devices can easily be controlled by changing the temperature of ambient medium because refractive index of the superconductor depends upon London penetration depth which in turn depends upon temperature of surrounding environment. The break in periodicity of the constituent material layers of 1D PhCs by introducing a defect layer of SC results the existence of resonant mode of high transmission inside PBG of the defective PhCs. The position, intensity and full width half maximum (FWHM) of such resonant modes can easily be tuned with the help of changing the temperature of SC material externally28. This temperature dependent external tuning of resonant mode inside PBG has inspired the material scientists to develop the verity of nanocomposite materials with superconducting host. For example Ramanujam et al. suggested biosensing applications of 1D defective PhC in which defect layer of air is encapsulated between SiO2 embedded nanocomposite layers of Yttrium barium copper oxide29. Recently Malek et al. suggested 1 D defective PhC composed of nanocomposite superconducting material for detection of cancerous brain tumors30. Fatma et al. studied the identification of gamma-ray radiation using a 1D DPhC made up of polymer doped porous silicon photonic structures. They have infiltrated the pours of porous silicon 1D DPhC with crystal violet and carbon fuchsine. The periodicity of the structure has been broken by adding defect layer of poly-vinyl alcohol polymer at the middle of the structure31. Ayman et al. also investigated a pressure sensing hetero-structured ternary photonic crystal whose silicon dioxide and porous silicon layers have embedded quantum dots for amplify the sensitivity of the structure32. A novel approach for detecting tumor markers by using PhC doped with AlEgen has been suggested by Zhijun et al. They have used the method of infiltrating luminogens with aggregation-induced emission (AIEgens) for achieving higher sensitivity33. Diptimayee et al. suggested how sensing capabilities of PhC resonating structure with exponentially graded refractive index profile can be enhanced34. Zaky et al. suggested how 1D DPhCs can be utilized as an effective pressure sensor by using the mechanism of parity-time symmetry for monitoring the different kind of pressure variations of the gases emitted from the ground35.

The above mentioned piece of tremendous research work motivated us to contribute in the field of biomedical engineering by proposing a simple 1D defective photonic crystal (DPhC) based biosensor for detection of various malignant tissues of human brain because the early stage detection of malignant brain tissues is the one of essential requirement for prevention of the rapid growth of cancerous cells in human body. The proposed structure is capable of identifying the malignant tissues of human brain if any, by detecting the minute change in refractive index of sample containing brain tissues of various parts of human brain. The refractive index of sample containing different brain tissues varies due to change in the size of the tissues as well as their concentration. In the present work we have considered the variation of refractive index from 1.3333 to 1.4591. Apart from the detecting the malignancy in human brain our sensing design could also investigate other samples as well whose refractive index varies from 1.3333 to 1.4591. Thus our design can be considered as a refractive index sensor which can comfortably sense the refractive index variations from 1.3333 to 1.4591. The present research work deals with 1D DPhC whose air cavity is surrounded by SiO2 embedded nanocomposite high temperature superconductor buffer layers. To the best of our knowledge 1D DPhC composed of SiO2 nanocomposite buffer layers has been rarely used for investigating malignancy in human brain tissues.

Biosensor design

The proposed biosensing design (AB)NCDC(AB)N is capable of sensing and detecting the malignancy in brain tissues. Here A and B are representing alternate layers of materials Si and air of two binary 1D PhCs (AB)N. The alphabet N has been used to represent the period number of each 1D PhC. The air cavity region D of the proposed structure has been surrounded either side by two buffer layers C of nanocomposite superconducting material26,27. The modified cavity region consisting of three layers of two materials is sandwiched between two identical 1D binary PhCs (AB)N to form the proposed photonic biosensing design (AB)NCDC(AB)N as depicted in Fig. 1. The lumber puncher procedure is applied to extract cerebrospinal fluid (CSF) samples containing different brain tissues with the help of long needle passes through human skull. After extraction the CSF sample is inserted into the air cavity region D of the proposed biosensor for examination as per the details shown in Fig. 1. Presently available thin film deposition technologies depending upon the material used in the design may be utilized to fabricate the proposed biosensing structure like spin coating, doctor-blade, dip coating approaches etc.

Figure 1
figure 1

The schematics of proposed 1D photonic biosensor in which cavity region has been created by sandwiching pair of nanocomposite superconducting buffer layers either side of cavity region.

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Modeling and simulation

The refractive index (RI) and thickness of material layers A and B of 1D PhC (AB)N used in the proposed design (AB)NCDC(AB)N are being represented by n1, n2 and d1, d2 respectively. The refractive index and thickness of pair of SiO2 embedded nanocomposite superconductor material YBa2Cu3O7 are denoted by n3 and d3 respectively. The thickness of air cavity region D is d4. The various CSF samples under investigation will be poured into the cavity region one by one. The sum of the thicknesses of layers A and B is represented by dd = d1 + d2.

The refractive index of high temperature superconductor YBa2Cu3O7 is described with the help of the two-fluid model as28,29,30

$${n}_{sc}=\sqrt{1-\frac{{c}^{2}}{{\omega }^{2}{{\lambda }_{L}}^{2}}}$$
(1)

where c, ω and λL are representing speed of incident EMWs in free space, angular frequency of the incident EMWs and the temperature-dependent London penetration depth high temperature superconducting material YBa2Cu3O7, respectively. The expression of temperature-dependent London penetration depth is given as21

$${\lambda }_{L}\left(T\right)=\frac{{\lambda }_{o}}{\sqrt{1-{\left(\frac{T}{{T}_{c}}\right)}^{2}}}$$
(2)

here \({\lambda }_{o}\) is the London penetration depth at T = 0 K and Tc is the critical temperature of the superconducting material.

The effective permittivity (εeff) of SiO2 embedded nanocomposite superconducting material is defined with the help of Maxwell–Garnett formula as18,26

$${\varepsilon }_{eff}= \frac{{\varepsilon }_{m} (2 \eta {\varepsilon }_{sc}-2 \eta {\varepsilon }_{m}+ {\varepsilon }_{sc}+ 2 {\varepsilon }_{sc})}{(2 {\varepsilon }_{m} +{\varepsilon }_{sc}+ \eta {\varepsilon }_{m}- \eta {\varepsilon }_{sc})}$$
(3)

where \({\varepsilon }_{m}\) is the permittivity of the dielectric material SiO2, \({\varepsilon }_{sc}\)(\(= n_{sc}^{2}\)) is the permittivity of high temperature superconductor material YBa2Cu3O7 and \(\eta\) is representing the volume fraction of SiO2 material embedded into YBa2Cu3O7. The symbol nsc is representing refractive index of YBa2Cu3O7.

The transfer matrix formulation has been used to study the propagation of EMWs from air into the proposed 1D DPhC (AB)NCDC(AB)N at an angle of incident θ0 as describe below36,37,38

$$M_{j} = \left( {\begin{array}{ll} {\cos \gamma _{j} } \hfill & \quad { - \frac{i}{{p_{j} }}\sin \gamma _{j} } \hfill \\ { - ip_{j} \sin \gamma _{j} } \hfill & \quad {\cos \gamma _{j} } \hfill \\ \end{array} } \right)$$
(4)

here the alphabet j has been used to represent transfer matrix of any layer j of the design. The value of pj in j-th layer is \(p_{j} = z_{0} n_{j} \cos \theta_{j}\) and \(p_{j} = \frac{{\cos \theta_{j} }}{{z_{0} n_{j} }}\) for s and p polarized EMWs respectively. Here \(\gamma_{j} = \frac{2\pi }{{\lambda_{0} }}n_{j} d_{j} \cos \theta_{j}\). The notations dj, nj and θj are representing thickness, refractive index and ray angle of EMW inside j-th layer of the structure. The z0 and λ0 are used for representing free space impedance and free space wavelength respectively. In order to get total transfer matrix of whole structure we have extended the above formulation as

$$\begin{aligned} M_{T} & = \left( {X_{A} X_{B} } \right)^{N} X_{C} X_{D} X_{C} \left( {X_{A} X_{B} } \right)^{N} \\ & = \left( {\begin{array}{*{20}l} {M_{{11}} } \hfill & {M_{{12}} } \hfill \\ {M_{{21}} } \hfill & {M_{{22}} } \hfill \\ \end{array} } \right) \\ \end{aligned}$$
(5)

The elements of total transfer matrix MT are represented by M11, M12, M21 and M22. The expression of transmission coefficient t of whole structure is given by

$$t = \frac{{2\eta_{0} }}{{(M_{11} + M_{12} \eta_{S} )\eta_{0} + (M_{21} + M_{22} \eta_{S} )}}$$
(6)

In Eq. (6) η0 and ηS have been used to represent an incident and exit media of the design. For s polarized EM wave \(\eta_{0} = z_{0} n_{0} \cos \theta_{0} ,\) and \(\eta_{S} = z_{0} n_{S} \cos \theta_{S}\) whereas for p polarized EM wave \(\eta_{0} = \frac{{\cos \theta_{0} }}{{z_{0} n_{0} }}\) and \(\eta_{S} = \frac{{\cos \theta_{S} }}{{z_{0} n_{S} }}.\)

The transmittance (T) of the whole 1D DPhC (AB)NCDC(AB)N is given by36,37,38

$$T = \frac{{\eta_{S} }}{{\eta_{0} }}\left| t \right|^{2}$$
(7)

Results and discussions

In the present piece of research work we have studied the interaction between incident EMWs with the proposed biosensor composed of 1D DPhC. The transfer matrix method (TMM) and MATLAB software both have been used to carry out the simulations of entire research work. The refractive index and thickness of Si layer A is set to be n1 = 3.3 and d1 = 0.35 μm respectively. On the other hand the refractive index and thickness of air layer B has been chosen as n2 = 1and d2 = 0.275 μm respectively. The thickness d3 of both nanocomposite buffer layers is set to be 0.09 μm whose wavelength dependent dielectric constant has been obtained by using Eqs. (1)–(3). The thickness of cavity region has been chosen as d4 = dd, where dd = d1 + d2 is length of the period of 1D PhC (AB)N. The period number of both the 1D PhCs has been fixed to N = 2 to make our design as small as possible. The numeric value of London penetration depth (λ0) of high temperature superconductor (HTS) YBa2Cu3O7 at temperature 0 K has been taken to be 200 nm. The critical temperature of nanocomposite material layers has been set to 92 K. In this study we have fixed the ambient temperature (T) and volume fraction (η) of nanocomposite layers as 92 K and 0.2 respectively. The permittivity of dielectric material embedded into SiO2 has been taken to be 2.1025. We have considered air in place of substrate. In order to investigate the biosensing capabilities of proposed design we have plotted transmission spectra of the design with the help of Eqs. (4)–(7) and MATLAB software. All the simulations of the proposed design have chosen carried out at normal incidence i.e. θ = 0° in order to overcome the difficulties associated with oblique incidence. The results of proposed biosensing photonic structure can be obtained by connecting both the ends of proposed structure with single mode fiber (SMF). The use of SMF limits the wave vector criterion associated with the design during measurements. The white light source is connected to the one end of fiber which is joined with input end of the design. The other end of the fiber connected with output terminal of the proposed design is joined with optical spectrum analyzer (OSA) which projects the output results into monitor via computer.

The refractive index of various kinds of normal and abnormal brain cells are the most important parameters for investigating the biophotonic sensing capabilities of the proposed design. Such structures can be used in various kinds of biomedical applications for designing of biosensors to get economical, efficient and fast results. This research is focused towards the biosensing application of 1D DPhC for differentiating between various kind of normal and malignant brain lesions. Actually brain lesions are particular type of brain tumors which describe localized regions of the damaged brain tissues. The unaccepted growth of these tissues may cause deadly or malignant brain tumors which may affect the life of patient. The sample containing these lesions is collected by injecting thin and long needle through the brain or spinal cord of affected person with the help of lumbar puncture or spinal tap procedure respectively. This sample contains of colorless fluid around the human brain and spinal cord which ensure the needful supplies to the organs of human brain and spinal cord and extract the waste from those places. This fluid is known as Cerebrospinal fluid (CSF). The sample containing CSF becomes an essential requirement if the person has symptoms of autoimmune diseases, inflammation in spinal cord and/or brain tissues or leukemia due to severe kind of viral or bacterial infections in CSF as per the advice of medical practitioner. The CSF fluid of refractive index 1.3333 has been taken as an internal reference in contrast to the refractive index of pure distill-water solution of value 1.333 as an external reference in order to initiate the findings.

The degree of malignancy may be determined by the refractive index of various kinds of brain lesions present in the sample and is proportional to the refractive index of samples of various brain lesions. The threshold value of refractive index of brain lesions which helps in determining malignancy is 1.395 i.e. the brain lesion samples of refractive index less than this threshold value are non-malignant otherwise the sample is said to be malignant. Table 1 below gives the refractive index of various normal and damaged brain tissues which have been investigated in this research work. The variation in the RI of various brain tissues is due to the change in the value of protein level inside different brain tissues. The protein level in cancerous cells is very high which results large RI values17,18

Table 1 Different kinds of normal and damaged brain tissues along with their refractive indices30.
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First we pour fluid samples containing different brain tissues as per the information given in Table 1, into cavity region of proposed 1D DPhC (AB)2CDC(AB)2 to carryout investigations for identifying the malignancy of sample. All the investigations pertaining to the work are being done in infrared region of electromagnetic spectrum ranging from 3.5 to 3.8 µm. The transmission spectra as presented in Fig. 2 shows 10 closely spaced different resonant peaks corresponding to fluid samples containing different brain lesions as mentioned in Table 1 inside PBG of 1D DPhC (AB)2CDC(AB)2 which extends from 3.55 to 3.85 µm under normal incidence. The existence of the large PBG of width 0.30 µm is due to the high refractive index contrast between silicon and air layers of the proposed photonic structure. As the fluid sample under examination changes from CSF to Lymphoma (as per Table 1) one by one, the resonant peak inside PBG starts to move towards higher wavelength side as evident from Fig. 2. The shifting of resonant peaks inside PBG is observed with respect to the position of resonant peak corresponding to CSF sample. This shifting of resonant peaks inside PBG is in accordance with formulation of standing wave inside laser cavity as mentioned in Eq. (8). Actually the change in the refractive index of cavity region is due to presence of different lesions into the samples. This variation in the refractive index may alter the resonant condition governing the standing wave formulation inside cavity region. This alteration is responsible for the shifting of resonant peak towards higher wavelength side inside PBG in order to fix the optical path difference inside cavity region.

$$\Delta = m\lambda = n_{eff} G$$
(8)

here notations Δ, m, λ, G and neff have been used to represent optical path difference between standing waves inside cavity region, an integer, resonant wavelength inside cavity, effective refractive index of 1D DPhC (AB)2CDC(AB)2 and geometrical path difference respectively.

Figure 2
figure 2

The transmittance spectra of 1D DPhC(AB)2CDC(AB)2 when cavity is loaded with ten different brain tissues in accordance with Table 1 and the thickness of cavity layer has been fixed to d4 = 0.625 µm.

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The validation of the proposed design as an efficient biosensor capable of detecting minute refractive index change is being done with the help of sensitivity calculation as per the formula given in Eq. (9). The sensitivity is one of the most popular parameters for evaluating the performance of the any biosensor as defined below in Eq. (9)18,26,27,28,29

$$S = \frac{\delta \lambda }{{\delta n}}$$
(9)

here δλ is the change in the position of central wavelength of resonant mode inside PBG due to corresponding change in refractive index (δn) of the samples under consideration. The CSF sample has been used as a reference to calculate S of the proposed structure when the cavity is loaded with different samples containing brain tissues seperately in accordance with Table 1. The numeric values of resonant wavelength (λd) and senstivity (S) of the proposed design loaded with various samples seperately corresponding to cavity thickness d4 = dd are being given in Table 2 below.

Table 2 The performance evaluation table showing refractive index (RIU), resonant wavelength (λd) and senstivity (S) of the proposed design when the cavity of thickness dd is loaded with different samples containing brain tissues.
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It has been observed from data of Table 2 that if cavity of the structure is loaded with different fluid samples containing brain tissues from CSF to lymphoma seperately, the senstivity of the proposed biosensor starts increasing from 0.13924 to 0.34260 µm/RIU corresponding to wall of solid brain and lymphoma tissues respectively. Thus the proposed structure possesses maximum senstivity value of 0.34260 µm/RIU corresponding to sample containing wall of solid brain tissues with cavity thickness d4 = 0.625 µm under normal incidence.

The effect of increasing the thickness of cavity layer on the performance

In this section, we have studied the effect of changing the thickness of cavity region on the performance of the proposed 1D DPhC (AB)2CDC(AB)2under normal incidence. For this purpose the transmission spectra of proposed structure corresponding to different values of cavity layer thicknesses (d4) as 3dd, 7dd, 11dd and 15dd are being plotted in Fig. 3a–d, respectively. In this study we have fixed the values of θ0 = 0°, η = 0.2 and T = 4.5 K. Figure 3 shows that as thickness of cavity region increases from 3 to 15dd the central wavelength of resonant modes associated with the samples containing different brain tissues shifted to lower wavelength side.

Figure 3
figure 3figure 3

The transmittance spectra of 1D DPhC(AB)2CDC(AB)2 when cavity is loaded with ten different brain tissues in accordance with Table 1 under normal incidence. The thickness of cavity layer has been fixed to (a) d4 = 3dd, (b) d4 = 7dd, (c) d4 = 11dd and (d) d4 = 15dd.

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Moreover it has been also observed that the increase in the thickness of cavity layer also reduces the full width half maximum (FWHM) of each resonant mode inside PBG of proposed biosensor. The increase in the thickness of cavity layer from 3 to 7dd results significant improvement in the intensity of resonant peaks as evident from Fig. 3a,b, respectively. Further increase in the thickness reduces the intensity of transmission of resonant tunneling peaks inside PBG. There is one more interesting observation that the increase in the thickness of cavity layers from 7dd to 15dd in steps of 4dd results increase in the intensity of transmission of defect modes corresponding to samples containing gray matter and white matter respectively as evident in Fig. 3b–d. The intensity of resonant peaks corresponding to these two samples is reached to maximum corresponding to d4 = 15dd. The increase in the thickness of cavity layer increases the geometrical path of the ray of light inside cavity region which improves the interaction between light and fluid samples containing various brain tissues. This interaction results the variation in intensity of resonant peaks inside PBG of 1D DPhC (AB)2CDC(AB)2. The sensitivity of the structure corresponding to fluid sample containing lymphoma brain tissues reaches to S = 0.65898 μm/RIU, when the thickness of the cavity layer is increased from dd to 3dd. Further increase in the thickness of cavity layer results corresponding increase in sensitivity of the proposed design. It is reached to maximum of 1.42607 μm/RIU at d4 = 15dd when the cavity is loaded with sample having lymphoma tissues. Thus in order to design the photonic biosensors composed of 1D DPhCs, the appropriate thickness of cavity region can be one of the designing parameters to achieve optimum sensitivity value and hence performance. The sensitivity and central wavelength of resonant peak of the proposed design corresponding to different cavity layer thicknesses are being summarized in Tables 3 and 4 along with their pictorial representation in three dimensional bar graph as shown in Fig. 4 below, when cavity is loaded one by one separately with various types of brain tissue samples as per the data of Table 1.

Table 3 The performance evaluation table showing resonant wavelength (λd) and senstivity (S) of the proposed design corresponding to different cavity layers of thicknesses dd, 3dd, 5dd and 7dd when cavity is loaded with ten different samples containing brain tissues.
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Table 4 The performance evaluation table showing resonant wavelength (λd) and senstivity (S) of the proposed design corresponding to different cavity thicknesses 9dd, 11dd, 13dd and 15dd when cavity is loaded with ten different samples containing brain tissues.
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Figure 4
figure 4

The 3D bar graph showing the sensitivity of the proposed 1D DPhC(AB)2CDC(AB)2 when cavity is loaded with ten different brain tissues in accordance with Table 1 at normal incidence corresponding to cavity layer thickness d4 which varies from dd to 15dd in steps of 2dd.

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Figure 4 shows that the sensitivity of the proposed design under the influence of various samples of different brain tissues with respect to non-malignant sample containing CSF brain tissue. Figure 4 also shows that the increase in the thickness of cavity region also improves the sensitivity of the design due to improvement in the interaction between light and samples inside the cavity region. Besides this the sensitivity of the structure becomes stagnant if we further increase the thickness of cavity region. In this work we have focused our attention to improve the sensitivity of the structure by increasing the thickness of cavity region. On the same time we have also ensured the minimum size of the structure by limiting the period number of the 1D PhC (AB)N to 2 which are fabricated either side of the cavity region containing buffer layers.

The effect of increasing the volume fraction of nanocomposite SC buffer layers on the performance

Next efforts have been made to study the effect of change in volume fraction η of nanocomposite superconducting buffer layers on the performance of the proposed 1D DPhC (AB)2CDC(AB)2 with cavity of thickness d4 = 15dd at θ = 0°. For this purpose the values of η have been changed from 0.2 to 0.8 in steps of 0.2. The transmittance of the proposed design corresponding to η = 0.4, 0.6 and 0.8 have been plotted in Fig. 5a–c respectively. Actually we wish to further increase the sensitivity of the design by changing η after optimizing thickness of cavity region as discussed in “The effect of increasing the thickness of cavity layer on the performance” Figure 5a below shows that the increase of η from 0.2 to 0.4 results the movement of resonant peaks inside PBG towards higher wavelength side in comparison to the previous results. Moreover this increase also improves FWHM of resonant peaks inside PBG corresponding to all samples. Additionally this change also results the gradual decrease in intensity of resonant peaks as we move lower side to higher side of PBG. This decrease in intensity is due to increase in refractive index of various brain tissue samples as described in Table 1. Further increase in the value of η from 0.4 to 0.8 in steps of 0.2 also decreases the intensity of the each resonant peaks corresponding to fluid samples containing wall of solid brain to lymphoma brain tissues in addition to the change in their central position and FWHM both.

Figure 5
figure 5

The transmittance spectra of 1D DPhC(AB)2CDC(AB)2 when cavity of thickness 15dd is loaded with ten different samples containing brain tissues in accordance with Table 1 at normal incidence. The volume fraction of nanocomposite pair of buffer layers fabricated either side of cavity layer is fixed to (a) η = 0.4, (b) η = 0.6 and (c) η = 0.8.

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The visualization of the numeric data of Table 5 is being presented in Fig. 6. It depicts 3D bar graph showing sensitivity of the proposed design corresponding to three different values of volume fraction of nanocomposite superconducting buffer layers when cavity is loaded with various fluid samples containing different brain tissues as per the information given in Table 5. Figure 6 also shows that the increases in η from 0.4 to 0.8 in steps of 0.2 also increases the sensitivity of the design loaded with each sample of different brain tissues. The sensitivity attains to maximum of 2.80434 µm/RIU with η = 0.8 corresponding to multi sclerosis brain tissue sample as evident in Table 5. At fixed value of η the sensitivity is almost same for all samples under investigation as evident in Fig. 6.

Table 5 The performance evaluation table showing resonant wavelength (λd) and senstivity (S) of the proposed design with d4 = 15dd and θ = 0° corresponding to nanocomposite SC buffer layers of different values of volume fraction (η) as 0.4, 0.6 and 0.8 when cavity is loaded with ten different samles containing brain tissues.
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Figure 6
figure 6

The 3D bar graph showing the sensitivity of the proposed 1D DPhC(AB)2CDC(AB)2 when cavity is loaded with ten different brain tissues in accordance with Table 1 at d4 = 15dd and θ0 = 0° corresponding to different values of volume fraction of nanocomposite SC buffer layers as 0.4, 0.6 and 0.8.

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The sensitivity of the proposed 1D DPhC (AB)2CDC(AB)2 can be further increased to maximum by increasing the volume fraction of nanocomposite superconducting buffer layers of the cavity apart from the optimizing the thickness of cavity region. In this study we have explored the idea to improve the sensitivity of design by optimizing the two internal parameters associated with the cavity as d4 and η instead of optimizing the external parameters of the structure as temperature of superconducting nanocomposite layer as well as angle of incidence.

Finally, we have compared the performance of the proposed work with the similar kind of biosesning work based on photonic and plasmonic structutres for establishing the superiority of our work. Table 6 highlights the major features which are important for comparing the performance of any biosesning designs based on photonic structures at large. The comparison shows that the sensitivity of our design reacheses to maximum of 2804.34 nm/RIU (2.80434 µm/RIU) when the structure is loaded with sample containing multi sclerosis brain tissues as seen from Table 5.

Table 6 Comparison between the performance of proposed design with other biosensing designs of similar nature.
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Conclusion

The aim of the proposed work is to design an efficient and sensitive 1D photonic biosensor capable of detecting malignancy in different samples of brain tissues. The cavity of proposed the 1D DPhC (AB)2CDC(AB)2 is composed of pair of nanocomposite SC buffer layers fabricated either side of air cavity region to improve the interaction of light and fluid sample under investigation. The TMM and MATLAB software both have been used to carry out the simulation pertaining to the work. The performance of the proposed design has been evaluated in terms of sensitivity of the proposed design loaded with various brain tissue samples. The sensitivity of the proposed design has been improved by increasing the thickness of cavity layer in addition to volume fraction of nanocomposite SC buffer layers. We have obtained the optimized values of cavity layer thickness as well as volume fraction of nanocomposite superconducting buffer layers as 15dd and 0.8 respectively to get maximum sensitivity from the design. The sensitivity of the proposed design loaded with lymphoma sample of cavity layer thickness 15dd is 1.42607 μm/RIU. This value of the sensitivity can easily be reached to S = 2.66136 μm/RIU by changing η from 0.4 to 0.8 when the cavity is loaded with multi sclerosis brain tissue samples. The findings of this study are very useful for designing various biosensing structures which have significant and decisive role in the field of biomedical applications.