Single-step detection of toxic airborne metallic nanoparticles using Goos–Hänchen effect in photonic Bragg grating structures

A real-time photonic crystal sensor is suggested for the detection of airborne heavy metal nanoparticles (HMNPs). The sensor consists of a sandwiched sampling cell between two stacks of alternating TiO2 and Si-Ge layers, forming the core of the device. The sensor’s performance is based on monitoring changes in both the intensity and phase of a probe beam as it propagates through the core. By analyzing the fluctuations in intensity, central frequency, and full width at half maximum (FWHM) of the resonant mode within the transmittance spectrum bandgap, or by monitoring the phase changes at the angle of maximum transmittance that may result in a remarkable Goos–Hänchen (GH) shift in transmittance, the sensor can identify the pollutant nanoparticles. Tuning the thicknesses of the slabs and the number of unit cells in the photonic crystal can dynamically shift the resonant mode and bandgap edges, allowing for easy adjustment of the sensor’s responsivity. Furthermore, the optical response of the sensor can be tuned through external parameters such as the incident angle of the probe light or an externally applied electric field. Additionally, the sensor exhibits sensitivity not only to changes in the extent of the sample but also to the shape of the present HMNPs. These characteristics make the proposed configuration cost-effective, user-friendly, and suitable for HMNPs detection without the need for complex sample preparation, data analyses or additional tools/accessories.


Introduction
Production of toxic heavy metal nanoparticles (HMNPs) is unavoidably increasing along with the further industrialization of the countries. These hazardous contaminants can easily spread in air and water sources and according to the reports of the world health organization (WHO) they are known as the reason for many irreparable injurious to human health after exposure [1]. These nanoparticles can suspend in the air for long while and are insoluble in liquids thus can move to far distances via fluidic atmospheres. Thus today not only the reduction of their production is the case but also the early detection of their presence has become a concern for scientists. However, it is also worth noting that in some aspects, sensing the airborne HMNPs is much more challenging than the case of detecting nanoparticles that are dispersed in liquids. The main reason might be related to more possibility of random movements in gas atmospheres compared to the liquids in which Brownian motion (moving due to just diffusions) is more dominant [2]. As a result, during the last decades we have witnessed a lot of efforts in the design and fabrication of sensors that are capable of detecting and identifying contaminating nanoparticles inside gas samples.
For instance, colorimetric-based detection [3], Electrical Sensors (such as Capacitive-based and Corona discharge Sensors), continuous flow microfluidic devices, and electrochemical-based detection platforms have been discussed in the past few years in this regard [4,5]. One can find a comprehensive review regarding these useful methods in the most recently published article by Fanti et al [6]. There is also a lot of desire at present to integrate multiple technologies such as microfluidics, micro/nano electromechanical systems and data analysis approaches to reach fast, accurate, real-time, and low-cost Lab on-chip (LoC) platforms [6][7][8]. In the other approach, a sensor based on a nano/mico-meter-sized mechanical element with the possibility of vibration at specific frequencies has been suggested [8]. The presence of nanoparticles is detected in this sensor by measuring the changes in the frequency of the vibrating mechanical part when particles deposit on it. Although some valuable suggestions (such as benefiting electrostatic field based trappings) have been presented recently to increase the efficiency of these sensors [8] but still particle landing on the nano/micro-sized cantilever is a challenging issue and it is hard to collect enough amounts of particles in a reasonable time scale in this method to realize fast detection. Furthermore, there exist some other difficulties in using these devices, such as finding appropriate ways to clean the cantilever effectively to be used in the next measurements and the absolute need for severe data analysis approaches after recording the experimental information.
In parallel with other methods, alternative platforms which seem to be far from most of the abovementioned limitations are the optical sensors. The variety of these techniques is very large but the most important ones are based on fluorescence or luminescence spectroscopy, dynamic/static scatterometry, surfaceenhanced Raman spectroscopy (SERS), laser heating of the atmosphere under study and tracking the changes of the optical features, plasmonic imaging, and optical fiber-based sensing [9][10][11]. Although each of these valuable approaches has its own advantages and has been able to increase hope in the possibility of HMNP detection, they have also some challenges to be implemented in practice. Necessities of many optical elements, high production costs, challenges in measurement steps, and demanding extra data analysis (signal/image processing) to extract the final result are some of the difficulties for most of the above-mentioned optical sensors. Thus still researchers are looking to find novel approaches in this regard besides improving the previously suggested techniques. The aim is to not only get rid of such problems but also to be able to detect as low concentrations of HMNPs as possible, in a fast, real-time, cost-effective, and simple way without the need for any extra biomarkers.
Optical detectors based on photonic crystals (PCs) are the other kind of platforms for sensing applications that have been widely suggested in the past decade [12][13][14]. These crystals have been well matured not only from the existing intellectual curiosity concerning the electromagnetic wave's behavior in complicated mediums but also from finding wide practical applications [15,16]. It is well proven that the performance of the sensors based on PCs in most cases is as simple as using a single probe beam and evaluating regulations in its features which must be in connection with the characteristics of the sample filled in the cell(s) embedded in the sensor. Thus it is worth making further efforts to develop gas sensors based on these crystals.
Taking into consideration of these facts, a gas sensor with a simple structure based on a one-dimensional PC is suggested in this article for classifying HMNPs suspended in the air without the need for any extra marker(s), complicated data processing, and difficult sample preparations. In most cases, just detuning in the intensity of the probe beam is traced to relate particle recognition to the observed changes. However, here in the suggested approach, further attention is paid to the phase changes of the transmitting probe beam besides its intensity alterations. This might be another advantage as it is well proven that the phase of light, changes far more rapidly as a function of any change in environmental parameters compared to the variations that take place in its intensity [17]. In fact, phase features of light are representative properties of it and many important phenomena might be related to the light phase characteristics [12]. Thus sensors based on phase tracings can have improved performance compared to the common sensors that are based on just detecting the intensity alterations.
Goos-Hänchen shift (GHs) is considered in our study for evaluation of the probe light phase changes due to the presence of any HMNP in the air sample. This shift which in fact describes the parallel lateral deviation of the actual reflected/transmitted beam at an interface compared to the one predicted by geometrical optics has been suggested before in many applications including new generations of optical switches and sensors [13,14]. However, although the prediction and theoretical explanation of GHs dates back to several decades ago, but still large efforts are made to find appropriate materials and structures that for which, GHs take place on a measurable scale. Otherwise, it will not be possible to benefit GHs in any sensing applications in practice. Different strategies have been followed in this regard to meet the urgent need. Using hybrid structures has been suggested extensively to increase GHs in photonic elements [18,19]. In these methods, two-dimensional or thin semiconductor materials such as graphene and TMDCs are integrated into the structure to make the transfer of free electrons between layers easy or make it possible to use surface plasmon polaritons (SPP) excitation to increase GHs amount [18,19]. Also, it has been shown that this effect might be signified remarkably by using negative index metamaterials [20], weak absorptive media, symmetrical optical waveguides with metal-cladding [21,22], and multilayer structures made of alternating unit-cells such as photonic crystals (PCs) [23,24]. In between, it seems that PC-based structures might be more useful in this regard due to their unique features and simplicity. For instance in other cases when internal parameters and the structure are fixed, it would be very difficult (if not impossible) to apply passive/active regulations in its features and thus to tune GHs. However, it has been well shown in the last years that optical features and the response of PCs, even with finalized structure (if designed appropriately) could be easily tuned [25,26]. Then it seems more practical to benefit from an appropriate tunable PC structure for phase sensing applications. Furthermore, as is discussed thoroughly in the result section, the suggested platform presents acceptable GHs in wavelength range near to visible light interval which also might be considered as a remarkable point.
The manuscript is organized in three parts in the following. First, the structure of the proposed sensor is described and the algorithms used in theoretical modeling are explained in detail. Then, the optical features of the sensor and the tunability of its performance using internal and external parameters are discussed comprehensively and the physical phenomena playing a role in the results are explained. Finally in summary the advantages of the suggested platform and its potential to be used in practice for HMNP detection are concluded.

Configuration of the sensing platform
The central core and involved parts of the suggested sensor are illustrated in the schematic diagram of figure 1. Sampling cell which is filled/emptied through appropriate channels is sandwiched between two similar stacks each of which is made of alternating layers of TiO 2 /Si-Ge slabs.
I.e. the heterostructure is considered as (TiO 2 /Si-Ge) N sampling-cell (TiO 2 /Si-Ge) N , where N is the repetition number of the unit cells stacked along the z-axis. It is worth noting that the successful deposition of TiO 2 layers on Si-Ge slabs has been already realized in experiments [27]. Thus it is very clear how simple the suggested structure is and there exists almost no serious challenge to fabricate it in practice. Interfaces of the layers are considered parallel to the x-y plane, and the z-axis is assumed to be normal to the surface of the layers of the structure. The surrounding atmosphere is air, and the light incident angle is measured with respect to the z-axis.

Theoretical modelling
Solving Maxwell Equations by taking into consideration of appropriate boundary conditions is the standard approach to study a light wave transmittance in a dielectric film. As a result, the electric field component of the electromagnetic wave propagating in the z-direction might satisfy the equation E(x,z) = E(x) exp(ikz), where E(x), k, and x are the amplitude of the electric field, propagation constant and the direction that is parallel to the slab surface respectively. Also, Bloch theory is considered as the most suitable theoretical methodology to evaluate the propagation of an electromagnetic wave through a multilayer structure. According to this theory and for the crystal made of N periods of alternating A and B layers: (AB) N and when the light incident angle is θ, the dispersion relation is [28]: Where, b is the z-component of the Bloch wave vector. It is clear that for real values of , b the Bloch wave can propagate through the crystal, and for complex values there must be a band gap in which the wave propagation is forbidden.
is the z-component of the wave vector in a specific layer of i (i = A or B). Furthermore, for TE polarization, we have: k 1 sin ( ) e m q e m ¢ = and for TM polarization: k 1 sin .
In order to extract the optical features of multilayer structures (such as PCs) in detail, an approach called as transfer matrix method (TMM) has been suggested extensively [28,29]. In this method which is based on Maxwell theory, many important physical phenomena such as multiple reflections from interfaces and the polarization state of the incident wave are considered in a simplified way and that is why more attention has been paid to it compared to the other complicated algorithms. Accordingly, two dynamic and propagation matrices are associated with each layer of a stack in this method and its transfer matrix is extracted as [29]: Actually, the matrix connects the tangential components of the electric and magnetic fields of the incident light at two sides of a slab. Using this matrix and taking into consideration of the related parameters of each layer, variations of the wave amplitude in passing a layer are determined. Here in this matrix p i is equal to / k iz 0 w m for TE and to k zl l 0 w e e for TM polarizations. Arranging an appropriate matrix for each layer of the crystal, the total structure may be considered by multiplying the matrices of all the involved layers. Thus for the ideal crystal made of N periods of A/B layers, the total transfer matrix is: Similarly, for the suggested structure, we can consider the total matrix as follows: Where the sampling cell is filled by a mixture of air and the suspended HMNPs. It is also proven that the existence of metallic nanoparticles inside a dielectric host results in significant changes in both its linear and nonlinear optical responses [30,31]. Then it seems that not only the volume fraction but also the shape and type of the suspended nanoparticles in the sampling cell might affect the optical features of the suggested PC and its performance in sensing.
It is also necessary to assume that the nanoparticles with permittivity of Ɛ 2 and susceptibility of χ 2 are randomly distributed in air and have occupied volume fraction f of the host. However, for simplicity, we can consider that all particles have the same shape with a depolarization factor of L z along the z-direction which is, of course, a geometry-dependent quantity [32]. I.e. For instance, L z = 1/3, 0 and ∞ indicate spherical, needle-like, and plate-like particles respectively. In the case of nonlinear materials, the relation between the electric field and displacement vector is given by: c denotes the 3rd order nonlinear susceptibility of the nanoparticle and E 0 refers to the applied external static field to the sampling cell. As the local field cannot be calculated exactly for the nonlinear components, then it is standard to use mean-field approximation to estimate the permittivity of the nonlinear components by: Here E 0 2 | | á ñ is the spatial average of the local field squared over the nonlinear particle. Thus the effective (fielddependent) permittivity of the sampling cell could be calculated via [32,33]: The indices 1&2 refer to air and nanoparticle respectively and the parameters are defined as [34]: These equations clearly show that the effective permittivity of the sampling cell can be tuned by controlling the externally applied electric field of E 0 . Then it might be utilized as a tool to adjust the sensor response whenever is needed. By using these equations and implementing an algorithm in MATLAB, the reflection, and transmission of the structure could be calculated by [35]:

Results and discussions
Results illustrated in figure 2(a) clearly show that even when the sampling-cell is filled with pure air, there exists a resonant defect mode in the transmittance spectrum of the suggested structure. This is normal, as the insertion of the sampling cell inside the PC has disturbed its symmetry and thus the generation of defect resonant mode inside the bandgap is sensible. However, it is shown that when the air is polluted by HMNPs of Pb, not only the central wavelength of the mode is changed but also its intensity and full width at half maximum (FWHM) are altered. This clearly reflects that the structure could be implemented in sensing applications via tracing transmittance features of a probe beam. But it is necessary to determine whether the sensor can separate different species of HMNPs or not. Panel (b) in figure 2 shows its possibility so that as the pollutant is changed, the resonant mode at the bandgap of the normalized transmittance spectrum is changed as well. Then these central wavelengths of different resonant modes might be considered as fingerprints to identify each of the HMNPs suspended in the air. The four selected materials of Fe, Hg, Pb, and Al are known as the most important and toxic heavy metal pollutants at current environmental challenges. Therefore the ability to recognize them shows the potential of the proposed sensor to solve real problems. Finally, it should be clarified that if all the pollutants are present in the air sample at the same time, but their concentration is different from each other, how the sensor will be able to detect all of them. Result presented in figure 2(c) illustrates the response of the sensor for that case. I.e. the sampling cell has been filled by air polluted with all the four HMNPs of Pb, Fe, Hg, and Al and their concentration (which could be described by f parameter) are different from each other. As is clear, although the intensities of the resonant modes related to each pollutant are different but they are well separated and it is possible to classify them simply.

Dependence on the structural parameters of the sensor
In the following, the dependence of the optical features of the suggested sensor on its structural parameters is evaluated by paying attention to just one of the selected HMNPs (the treatment for other nanoparticles is similar). Figure 3(a) represents that the normalized transmittance of the suggested PC depends on the number of the unit-cells (N) in the crystal structure seriously. Increasing the value of N, result in not only a remarkable redshift in the central wavelength of the resonant mode but also alters its width (FWHM) significantly. So that by increasing the number of the unit cells of the structure, the resonant mode inside the transmittance spectrum gets narrower. Results also reveal the dependence of the transmittance of the suggested structure on the size of its building layers. However, the dependence on the thickness of the layers A and B is more remarkable in proportion to the role of the thickness of the sampling-cell. So that when the thickness of the layers A and B are changed from 290-310 nm and 100-130 nm respectively, the central wavelength of the defect mode is shifted ∼ 17 nm and ∼ 35 nm in these cases. But increasing the thickness of the sampling-cell from 100-130 nm results in just a 6.1 nm shift in the wavelength of the mode. These behaviors might be justified by paying attention to the changes in the light phase (j = k l d l cosθ) by changing the thickness of an involved layer in the crystal or changing the number of unit cells. Increasing size of the layers or the number of the unit cells results in an increased effective optical path in the sensor. As a result, the phase match being necessary to achieve constructive resonant modes will take place in longer wavelengths. Furthermore, it is worth noting that an increase in the size/number of the layers might result in further absorption of the probe light beam. Thus an optimized condition must be selected to trade off energy absorptions as well.

Dependence to the characteristics of the pollutants
According to the results presented in figure 3, thickness amounts of respectively 300 nm, 115 nm, and 120 nm for layers A, B, and the sampling cell, and the number of periods of 3 are selected as the values to be considered in the following studies. More than the importance of the structural features of the sensor and the size of the sampling-cell in performance of the sensor, it will be too much of a simplification not to consider the characteristics of the nanoparticles in the modeling of the sensor. In other words, a well designed sensor must not only detect the presence of a particle but also should be sensitive to the shape specifications and volumetric amount of the pollutant nanoparticles in a sample. The potential of the sensor in detecting these features is shown in figure 4. So that when the fraction of the nanoparticles increases in the volume of the sampling cell, the resonant peak shifts to longer wavelengths. Also, the width of the mode is dependent on the volume fraction of nanoparticles. It is clear that at little amounts of the pollutant, narrower width of the mode is observed such that FWHM is as 0.47, 0.50, 0.53, and 0.58 nm, respectively for f = 0.02, 0.03, 0.4, and 0.5. These results sound sensible as increasing the pollutant quantity in the sampling cell, the number of multi-scatterings will increase and thus the effective optical path will grow remarkably together with the realization of strong electromagnetic wave confinement inside the sampling cell. Thus as discussed in the previous section, the required phasematching condition takes place in longer wavelengths.
As is clear in figure 4(b) a small alteration in the geometry of the nanoparticles (which might be traced by the depolarization factor of L z along the z-direction) results in a serious change in the optical features of the sensor. Increasing the value of the L z parameter which means getting more closer to plate-like particles, results in the reduction of its FWHM amount, as by increasing the L z value from 0.01 to 0.04 by steps of 0.01, FWHM is reduced to 0.57, 0.49, 0.47 and 0.46 nm, respectively. This dependence might also be benefitted in extracting further information on the characteristics of the HMNP pollutants. In other words, when a specific HMNP pollutant is the case, the central wavelength, intensity value, and FWHM amount of the resonant mode might be considered as markers for getting more structural information about the existing nanoparticles such as their shape.

Tunability of the sensor response
Simple tunability in performance is undoubtedly a great advantage for any sensor to be used in practice. Results illustrated in figure 5 show that all important characteristics of the resonant mode (intensity, FWHM, and central wavelength) are dependent on externally controllable parameters of probe light incident angle and applied electric field to the sampling cell. This tunability is important because it will be possible to reach an optimal mode of resonant (which can be identified and analyzed more easily) by changing the angle of light incidence or by controlling the internal electric field by adjusting the externally applied voltage to the sampling cell.
This issue becomes more important especially when the gas is contaminated by several pollutants and it is important to identify all the species in the sample by obtaining well-separated, sharp, and intense peaks. It is clear from figure 5(a) that even a small change in the incident angle can significantly affect the resonant mode. But the dependence on the local electric field (in the case of Pb) is not so much and increasing the field from 100-350 kV m −1 can cause just a blueshift of 13.7 nm in central wavelength ( figure 5(b)). To further explain the importance of the applied external field in tuning the response of the sensor, we consider the case in which two pollutants of Pb and Hg are present in the sample cell at the same time and the applied electric field is 100 Kv m −1 . As is presented in figure 5(c), the related resonant modes are separated from each other by 1.1 nm in this situation. However, if the applied field is increased by three times (up to 300 Kv m −1 ), the separation between the related peaks will increase significantly. Thus, detection of the different pollutants and their classification will be possible more easily.
These results can be interpreted as follows: when the electric field is changed, then the effective refractive index of the sample cell medium is changed (and thus the effective optical path length changes as a result). This causes in a change in the Bragg interference condition, which is in fact the origin of the photonic band gap and defect mode formation. On the other hand, increasing the probe light incident angle changes its phase by j = k l d l cosθ. Thus a blue shift in wavelength with increasing the angle is necessary for reaching appropriate phase matching condition.

Monitoring phase changes for sensing application
As it was discussed in the introduction, a worthy optical detector should be sensitive to changes of not only the probe light intensity but also to its phase characteristics which can respond to any alteration in the sensing medium much faster. In this regard and due to the importance of the issue, the dependence of the GHs in transmittance and reflectance to the structural and external parameters are discussed in detail.   However, a completely different behavior is observed in the case of the transmittance of the probe beam. So a remarkable negative GH shift takes place by adjusting the incident angle. Results illustrate that by tuning the size of the involved layers in the structure of the PC, it is possible to regulate the incident angle in which maximum negative GHs are observed. The sign of the GH shift refers to the direction of the shift and as the sign is the same for all cases then the direction of the shift will be the same. It is also clear that the maximum GH shift amount as well as the FWHM of the resonant deep is not so much dependent on the thickness of the layers.
Artmann tried to explain the generation of the GHs through stationary phase approach by considering a light beam as sum of a few plane waves of to some extent different wave vectors [37]. These components undergo different phase changes in transmitting/reflecting from an interface. Thus a lateral shift that is observed between the original beam and the final transmitted/reflected beam results from the way these components sum up together.
There exists another interpretation in which the realization of GH shift is related to the existence of hypothetical surfaces that the probe beam transmits/reflects from, instead of the real one [38]. Higher or lower placement of this plane compared to the location of the actual surface is considered as the determining factor of the displacement direction. The other important point is the realization of phase discontinuity between the incident beam and the reflected/transmitted ones from these layers.
Here for the sake of more explicit discussion and determination of the physics behind the above-mentioned results, the dependence of the absolute values of the reflection/transmittance coefficients to the incident angle and also the alterations of the relative phases with changing the angle are explored. These dependencies are plotted in figure 7 for 3 different sizes of layer A. Similar behavior is observed when the size of layer A is fixed and the thicknesses of the other layers (layer B or sample cell) are changed. As is very clear, there is no significant relation between the way the reflectance coefficient changes with the probe beam incident angle and the dependence of the relative phase on it. However, with a close look at the behaviour of the transmittance and the relative phase changes by tuning the incident angle, it is seen that an abrupt phase change takes place exactly at the same angle in which resonance is observed at the transmittance spectrum. As the resonance is more than 90% then it is accompanied by a very steep slope in the phase of the transmitted beam. Comparing the written details inside figure 7 and the data in the related panel of figure 6(b), it is clear that the resonance conditions are exactly the same in all of them and for any size of layer A. It is important to acknowledge that utilizing equations (10), (11) is a standard approach for extracting the GHs of the reflected/transmitted beams form multi-layer structures and has been already widely employed in various studies [36,39]. Additionally, since the lateral shift is obtained through the derivative of the phase of these coefficients with respect to the incidence angle, calculating GHs for abrupt jumps with infinite slopes would yield meaningless results. However, as zoom on the resonance areas in phase patterns which are illustrated in panels figures 7(e)-(g) show, although the resonance angles exhibit notably steep changes, but their slope remain finite. Hence, calculating GHs using equation (11) is sensible. Furthermore, it is worth noting that equal lateral shifts for reflected and transmitted probe beams are observed just for the lossless symmetric structures [36,39]. Then as the suggested structure includes a sampling cell in its middle that destroys the symmetry and also its contents might make the PC further absorptive, then the observed serious difference between shifts in transmittance and reflectance makes sense. Furthermore, it is worth emphasizing that the results presented in the previous sections strongly demonstrate the potential of the proposed sensor in detecting HMNP pollutants. Nonetheless, the substantial GHs observed in the transmittance spectrum could also be considered as an additional option to be utilized in the planned sensing application.
According to these results, just the lateral GH shift in the transmittance is studied at the next step in order to evaluate the dependence of the shift on the characteristics of the pollutant and its volumetric amount. Figure 8 shows that similar to the previous results, the peak in transmittance amount takes place at the same incident angle where a resonance is observed for the related phase. This can consequently result in a remarkable GH shift at the same angle in the transmitted probe beam. Although the transmittance peak amounts are dependent on the fraction of the nanoparticles suspended in the air sample and their depolarization factor (which reflects the shape characteristics), the maximum resonance amounts in related phases are not so different for different conditions.
Thus the GH shift amounts are almost the same for different values of L z and f parameters. However, the resonant angle is changed by changing these parameters so that when f increases, the maximum GH shift is realized at higher angles, and vice versa, as the value of the L z increases, the resonance angle decreases as is shown in figure 8. These dependencies might be used effectively as markers for the detection of the characteristics of pollutants.
Finally, the lateral shift of the transmitted beam is studied for different bias conditions. Results in figure 9 show that by adjusting the electric field, it is possible to regulate the angle where the resonances in transmittance spectrum and the related phase are realized. As a result, the angle for maximum GH shift amount could be tuned by changing the value of E 0 . Furthermore, it is also clear that as the amount and form of the resonance in phase are independent of the field extent, then the GH shift amounts are also the same for different values of E 0 and just the resonant angles are changed.
These results also show how effective is phase-dependent sensing in comparison to intensity-dependent one. For instance as is shown in figure 5(b), in some field values, the amount of the transmittance intensity might be so low that their detection could be difficult in practice. However, the phase changes and as well the GH shift amounts are not so limited and they are remarkable in any case. Thus it is guaranteed to diagnose the changes in any condition.
Finally, it is worth noting that in consistent with the previous valuable researches reported in recent years [40][41][42], the conducted study once again confirms the remarkable potential of the sensors based on onedimensional photonic crystals in gas detection applications. However, considering its straightforward construction, easily tunable response, sensitivity to the shape of the nano-pollutants, and favorable phase behavior, the suggested structure can be regarded as a more suitable choice for identifying HMNP mixture in air.

Conclusion
All optical photonic crystal-based sensor was suggested for airborne HMNP pollutants detection. It was proved that a composite including two stacks made of alternating TiO 2 and Si-Ge layers can be considered as an appropriate substrate to sandwich a sampling cell in between and form the core of the sensor. Performance of the sensor is based on monitoring the changes in features (both intensity and phase) of a probe beam propagating through the core. I.e. identification of the pollutant nanoparticles is possible by either checking the fluctuations in intensity, central frequency, or FWHM of the resonant mode inside the transmittance spectrum bandgap or via monitoring the abrupt phase changes across the angle at which maximum transmittance takes place and thus remarkable delta function like Goos-Hänchen (GH) shift is generated in the related spectrum.
It was also proved that the optical response of the suggested sensor is in close connection with not only the structural characteristics of the crystal but also is tunable via externally controllable parameters such as probe light incident angle or externally applied electric field. In more detail, both the resonant mode and the bandgap edges shift dynamically by changing the thicknesses of the slabs, the involved number of the unit cells in PC, or these externally tunable factors. Thus it is possible to adjust its responsivity easily to find optimum conditions in each measurement. Furthermore, the sensor can well distinguish not only any change in the sample extent but also its response is sensible to the shape of the HMNPs in the sample. These might be considered unique and important advantages for the suggested sensor. Therefore, it seems that the proposed configuration has a suitable potential to be used in this important application due to its being cost-effective, simplicity in use, single-step working mechanism, no need for additional tools/accessories, or avoiding any complexity of sample preparations.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.