Defected photonic crystal as propylene glycol THz sensor using parity-time symmetry | Scientific Reports

Scientific Reports volume 14, Article number: 23209 (2024) Cite this article

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Detecting unsafe levels of chemical gases and vapors is essential in improving and maintaining a healthy environment for all to enjoy. Propylene glycol is a colorless, synthetic gas commonly used in medications, fragrances, and cosmetics. It causes side effects such as headaches, lightheadedness, nausea, and fainting. So, monitoring of propylene glycol is critically vital. This study uses a defected photonic crystal as a propylene glycol THz sensor. Due to the high absorption of propylene glycol, the intensity of the resonant confined mode is very small. As a result, the performance of the designed sensor seems unsatisfactory. We will use parity-time symmetry for the first time in THz to magnify the resonant confined mode to detect propylene glycol. The effect of microcavity thickness, incident angle, and gain/loss factor will be studied. The optimized sensor recorded distinguished results compared to other studies for the detection of propylene glycol.

Many hazardous and toxic chemical gases and vapors have an important impact in a variety of fields, including national defense, manufacturing in industries, medicine, and sustainability1,2,3,4. Propylene glycol (PG) is a chemical gas present in medications, fragrances, and cosmetics. PG is a great solvent for a variety of organic chemicals. PG is utilized as a surfactant or solvent for numerous items and as an active component in enamels, brakes, varnishes, paints, antifreeze, and engine coolants. PG significantly affects human organs (e.g., kidneys, eyes, liver, and skin)5. Headaches, lightheadedness, nausea, and fainting can all be brought on by PG1,5. PG is a flammable liquid that has the potential to catch fire. So, detection of PG is extremely important.

One-dimensional photonic crystals (1DPCs) are periodic optical structures that manipulate the transmittance, absorbance, and reflectance of photons in a similar way that periodic potentials in a semiconductor crystal affect electrons6,7,8,9. 1DPCs have unique properties that make them suitable for various applications in optics and photonics. 1DPC structure consists of alternating layers of different dielectric materials with varying refractive indices (RIs) arranged in a single dimension. Due to destructive interference from the periodic structure, a photonic band gap (PBG) is created and blocks the propagation of photons through it10. When light encounters the 1DPC, constructive and destructive interference patterns are created due to the differences in refractive indices. At certain frequencies, destructive interference dominates, resulting in a PBG where light cannot propagate through the 1DPC. The ability of 1DPC to control the propagation of light through PBGs is fundamental to their functionality in devices like filters, reflectors, and sensors11,12,13,14,15,16.

Nowadays, PT symmetry in optical periodic structures has emerged as a fascinating field of study for both technology and science since the publication of a collection of studies pointed out that the concepts of PT symmetry can be explored in a rich environment in photonics and optics17,18,19. The complex RI \(\:n\left(x\right)\) in the optical media functions as complex potential \(\:V\left(x\right)\). \(\:{n}_{R}\left(x\right)\) denotes the real part of RI (RI distribution), and \(\:{n}_{I}\left(x\right)\) represents the loss and gain profiles of the medium. PT symmetry indicates that \(\:{n}_{R}\) must be an even function, and the function of gain-loss (\(\:{n}_{I}\)) must be an odd as follows: \(\:{n}_{R}\left(x\right)={n}_{R}(-x)\) and \(\:{n}_{I}\left(x\right)=-{n}_{I}(-x)\). Fortunately, all of these ingredients, loss, gain, and refractive index, are easily implemented in PCs. The confined peak will be magnified by achieving the PT symmetry conditions20.

In this study, an easy, rapid, efficient, and sensitive model of a PG sensor in the THz range using 1DPC with magnified confined resonance. Taking the absorption of the PG analyte into account makes our results very close to the experiment. The absorption of the PG analyte causes a decrease in the intensity of the confined peaks and the performance of the model. We used PT symmetry to magnify the peaks and enhance the performance to overcome this issue.

The suggested PG THz sensor is composed of a 1DPC using \(\:Si{O}_{2}\) (A) and \(\:Si\) (B) layers, as clear in Fig. 1. The periodic 1DPC contains a defect sample (\(\:{D}_{0}\)) layer sandwiched between two \(\:Si{O}_{2}\) layers (\(\:{D}_{1}\) and \(\:{D}_{2}\)) to prevent \(\:Si\) oxidation. The whole suggested PG THz sensor is represented as \(\:{\left(AB\right)}^{N}\left({D}_{1}{D}_{0}{D}_{2}\right){\left(AB\right)}^{N}*Si{O}_{2}\:substrate\). \(\:N=5\) is the number of \(\:Si{O}_{2}*Si\) periods. The sample microcavity (SMC) will be occupied with an aqueous solution with different concentrations of PG.

Schematic of \(\:{\left(AB\right)}^{N}\left({D}_{1}{D}_{0}{D}_{2}\right){\left(AB\right)}^{N}*Si{O}_{2}\:substrate\) structure as PG THz sensor.

In the THz region, the RI and amplitude absorption (\(\:\alpha\:\)) of PG aqueous solution with different concentrations of PG were measured over a frequency range from 0.30 THz to 2.50 THz21. By fitting the RI and amplitude absorption of aqueous solution with different concentrations of PG from 0% (water) to 100% (PG), we get the following equations as a function of frequency (\(\:f\)) from 0.5 THz to 2.5 THz:

For 0% PG, 0 mol/l (water):

For 20% PG, 2.73 mol/l:

\(\:\alpha\:=-\:7.85127{\:f}^{2}\:+\:73.2429\:f\:+\:38.009\:\:\:\:\:\left({R}^{2}=0.996\right)\) (4)

For 40% PG, 5.47 mol/l:

For 60% PG, 8.20 mol/l:

For 80% PG, 10.93 mol/l:

\(\:\alpha\:=-\:0.830281{\:f}^{2}\:+\:41.9095\:f\:+\:5.00986\:\:\left({R}^{2}=0.999\right)\) (10)

For 100% PG, 13.67 mol/l:

From these RIs and amplitude absorption relations, the complex RI of aqueous solution with different concentrations of PG from 0% (water) to 100% (PG) is calculated as follows:

where \(\:{C}_{0}\) is the vacuum’s speed of light. The RIs and thicknesses of \(\:A\) and \(\:B\) layers are 2.1, 3.4, 30 μm, and 7 μm, respectively. The thickness of the layers \(\:{D}_{1}\) and \(\:{D}_{2}\) is 2 μm.

The transmittance (T) of the TE polarized THz wave (Transverse Electric) due to the interaction with the PG sensor will be investigated with the transfer matrix method (TMM) as follows22,23,24,25,26,27:

The total matrix of the structure is:

where \(\:{A}_{11}\), \(\:{A}_{12},\)\(\:{A}_{21}\), and \(\:{A}_{22}\) are elements of the total matrix. The matrix of each layer can be represented as follows:

where \(\:{n}_{i}\) and \(\:{\theta\:}_{i}\) are the RI and incident angle.

The angles of incidence for each layer are calculated using Snell’s law as follows:

To calculate \(\:\left({a}_{A}{a}_{B}\right)\) for N periods, the Chebyshev polynomials of the second kind are used28. The transmittance coefficient is given by:

where \(\:{\varnothing\:}_{0}\) and \(\:{\varnothing\:}_{s}\) are for ambient medium and \(\:Si{O}_{2}\) substrate. The total transmittance of the \(\:{\left(AB\right)}^{N}\left({D}_{1}{D}_{0}{D}_{2}\right){\left(AB\right)}^{N}*Si{O}_{2}\:substrate\) structure is given by:

Besides, Bloch’s theorem is used to ensure the region of photonic bandgap (PBG) of the discussed THz PG sensor structure (infinite periods) as follows29:

where \(\:K\) is the z component of the Bloch wave vector.

TMM has been used to simulate filters30, sensors31,32,33,34,35, etc. Wang et al.36 experimentally and theoretically (using TMM) studied the reflectance of 1DPC as a reflector. The experiment coincided with the results using TMM. Gutierrez et al.37 fabricated and modeled a device to sense any change in chemical reaction, optical path, refractive index, temperature, and roughness while forming porous films. In 2022, Zhang et al.38 experimentally and theoretically (using TMM) designed an optical filter using PT symmetry. These numerical and experimental results recorded very good matches with accepted discrepancy because of the non-optimized design of the coupling coefficients and fabrication errors.

Figure 2A, B clear the RI and amplitude absorption of aqueous solution with different concentrations of PG from 0% (water) to 100% (PG). By increasing the PG concentration, the RI and amplitude absorption decrease. Besides, the RIs of PG aqueous solutions decrease with the frequency increase, but the amplitude absorption increases with the frequency increase.

Measured and fitted (A) RI and (B) amplitude absorption of aqueous solution with different concentrations of PG from 0% (water) to 100% (PG).

By modeling a 1DPC made of layers A and B (\(\:Si{O}_{2}\) and \(\:Si\)) without defect layers \(\:\left({D}_{1}{D}_{0}{D}_{2}\right)\) using TMM and Bloch’s theorem (Fig. 3A), a photonic bandgap (PBG) extended from 1.51551 THz to 1.91286 THz as a result of the RI contrast between \(\:Si{O}_{2}\) and \(\:Si\). The position of the PBG is compatible with the following relation (for normal incidence)39:

Transmittance of discussed THz PG sensor at different concentrations of PG from 0% (water) to 100% (PG): (A) without defect, (B) with defect, and (C) peaks shift.

Accourding to Eq. (26), \(\:{f}_{PBG}\)=1.56 THz. In the case of the defect \(\:{\left(AB\right)}^{N}\left({D}_{1}{D}_{0}{D}_{2}\right){\left(AB\right)}^{N}\text{*}substrate\), the thickness of \(\:{D}_{0}\) is 12 μm. The sample cavity at the center of the defect will be occupied with an aqueous solution with different concentrations of PG from 0% (water) to 100% (PG). Due to the breaking of the periodicity with defect layers \(\:\left({D}_{1}{D}_{0}{D}_{2}\right)\), a confined peak appeared inside the PBG, as clear in Fig. 3B. In Fig. 3C, by increasing concentrations of PG from 0% (water) to 100% (pure PG), the confined peak is shifted to blue THz waves from 1.77154 THz (for water) to 1.78461 THz (for pure PG) due to the increase of RI, according to the standing wave equation39:

where m is the order. With increasing the concentrations of PG, the RI of PG (\(\:{n}_{sample}\)) decreases, the effective RI (\(\:{n}_{eff}\)) decreases, and the \(\:{f}_{R}\) increases.

The efficacy of any sensor is often measured by different parameters such as sensitivity (S), bandwidth (FWHM), figure of merit (FoM), quality factor (Q), and detection limit (DL) as follows:

Table 1 shows the different parameters, such as sensitivity (S), bandwidth (FWHM), figure of merit (FoM), Q-factor, and detection limit (DL) of the described THz sensor at different concentrations of PG. By increasing the concentrations of PG, the \(\:{f}_{R}\) increases, the intensity of confined peak increases, the FWHM decreases, the S changes between 0.6 GHz/mol/l and 1.3 GHz/mol/l, the FoM changes between 0.02 l/mol and 0.06 l/mol, the Q-factor increases from 43.42 to 83.39, and the DL changes between 0.83 mol/l to 2.23 mol/l. In general, the efficiency of the sensor needs to be enhanced. So, different geometrical will be optimized to increase the performance.

The impact of sample cavity thickness (\(\:{D}_{0}\)) on the designed sensor will be investigated as clear in Fig. 4A–C. The \(\:{f}_{R}\), FWHM, S, FoM, Q-factor, and DL of the designed sensor are tuned by changing the sample cavity thickness. By increasing the width of \(\:{D}_{0}\), the frequency of the confined peak decreases according to Eq. (27). On the other hand, the FWHM increases from 0.03 THz to 0.10 THz, the S increases from 0.03 GHz/mol/l to 3.13 GHz/mol/l with increasing the width of \(\:{D}_{0}\) from 1 μm to 20 μm. At the narrow cavity width (1–15 μm), the moving FoM is very high. The FoM at 1 μm is 0.001 l/mol, at 5 μm is 0.010 l/mol, at 9 μm is 0.021 l/mol, at 12 μm is 0.029 l/mol, and at 15 μm is 0.033 l/mol. At cavity width wider than 15 μm (20 μm), the FoM slightly decreases (0.032 l/mol). Both Q-factor and DL decrease with increasing the width of \(\:{D}_{0}\) from 1 μm to 20 μm to record the lowest value at 20 μm. As the width of \(\:{D}_{0}\) of 15 μm has the best FoM than at 20 μm, the width of \(\:{D}_{0}\) of 15 μm will be selected for the following optimization.

performance parameters of the designed sensor; (A) \(\:{f}_{R}\) and FWHM, (B) S and FoM, and (C) Q-factor and DL versus the sample cavity width.

The influence of angle of incidence (\(\:\theta\:\)) on the designed sensor will be studied as clear in Fig. 5A–C. The \(\:{f}_{R}\), FWHM, S, FoM, Q-factor, and DL of the designed sensor are varied by moving the \(\:\theta\:\). By increasing \(\:\theta\:\), the frequency of the confinedpeak increases according to Brag Snell’s law40. On the other hand, the FWHM vibrates from 0.049 THz to 0.065 THz, the S increases from 1.81 GHz/mol/l to 2.96 GHz/mol/l, the FoM vibrates from 0.03 l/mol to 0.05 l/mol, with increasing the θ from 0 degrees to 67 degrees. Both Q-factor and DL decrease with increasing the θ from 0 degrees to 67 degrees. At higher angles than 67 degree, the confined peak diapeared. The θ of 67 degrees in principle, will be selected for the following optimization.

performance parameters of the designed sensor; (A) \(\:{f}_{R}\) and FWHM, (B) S and FoM, and (C) Q-factor and DL versus the angle of incidence.

Figure 6 clears the variation of transmittance of discussed THz PG sensor for different concentrations of PG at \(\:{D}_{0}\) of 15 μm and θ of 67. in spite of the confinedpeak shift is enhanced after the optimization comparing with Fig. 3C, the FWHM and intensity of peak should be enhanced. To solve this issue, the confinedpeaks need to be magnified using the well known parity-time (PT) symmetric 1DPC (PT-1DPC)41,42,43,44.

Transmittance of discussed THz PG sensor for different concentrations of PG from 0% (water) to 100% (PG) at \(\:{D}_{0}\) of 15 μm and θ of 67 degrees.

By doping the \(\:Si{O}_{2}\) layer with quantum dots, the gain and loss layer can be prepared20,45. The gain layer will be externally pumped with an optical pump46. The gain layer will be excited by the optical pump, and a certain frequency of photons will be absorbed by the quantum dots. Quantum dots re-emit these photons with the same frequency of propagated distinct peak by stimulated emission. The coupling between distinct peaks and re-emitted frequencies causes the magnification process. The complex RI of gain and loss layers are \(\:{n}_{gain}={n}_{R}-0.01\:Q\) and \(\:{n}_{loss}={n}_{R}+0.01\:Q\), where \(\:Q\) is the gain/loss factor. Figure 7 clears the schematic of PG sensor after taking the PT conditions into account.

Schematic of \(\:{\left(AB\right)}^{N}\left({D}_{1}{D}_{0}{D}_{2}\right){\left(AB\right)}^{N}*Si{O}_{2}\:substrate\) structure as PG THz sensor after PT symmetry modifications.

Using PT symmetry conditions in this study affects the position of the bandgap due to the change in the complex refractive index, as clear in supplementary data. Now, the transmittance of discussed THz PG sensor for 0% concentration of PG is checked. The structure recorded low transmittance again at \(\:Q=1\). So, the transmittance is investigated at different Q. As clear in Table 2, the transmittance gradually increases with increasing the value of Q from 0 to 12.4. Then, the transmittance decreases. As clear in Fig. 8A, the transmittance of the discussed THz PG sensor has the highest value of \(\:3.8\times\:{10}^{6}\) % at Q of 12.4. Figure 8B clears the variation of transmittance of discussed THz PG sensor for different concentrations of PG at \(\:{D}_{0}\) of 15 μm and θ of 67 after achieving the PT symmetry conditions. The magnification (transmittance) of the confined peak at 0% PG concentration has the highest value (\(\:3.8\times\:{10}^{6}\) %). By increasing the PG concentration from 20 to 40%, 60%, 80% and 100%, the transmittance of the confined peak changed from 1185 to 858%, 670%, 569%, to 468%. Due to the drop in transmittance with increasing PG concentration, the FWHM increases. From results in Fig. 8B, it can be concluded that the investigated structure is very suitable for the detection of low concentrations close to 0% than higher concentrations. Table 3 ensures that the described sensor has high sensitivity compared to others. As fast as the pulse lasts, the optical response of the proposed sensor happens instantly47 which is in order of several nanoseconds48.

Transmittance of discussed THz PG sensor (A) for 0% concentration of PG at different gain/loss factor (Q), (B) for Q of 12.4 at different PG concentrations.

In this study, magnified confined peak of defective PC using PT symmetry as a PG sensor in the THz region has been discussed. The optimized sensor recorded a sensitivity of 62.6 GH/RIU. The confined peak is strongly magnified at lower concentrations (\(\:3.8\times\:{10}^{6}\) % at 0% concentration) than at higher concentrations. So, the investigated structure is very suitable for the detection of low concentrations close to 0% with high sensitivity compared to others. Finally, PT symmetry can be considered as an excellent solution for high absorption of analytes.

Requests for materials or code should be addressed to Zaky A. Zaky.

Adamyan, Z. et al. Nanocomposite sensors of propylene glycol, dimethylformamide and formaldehyde vapors. J. Sens. Sens. Syst. 7, 31–41. https://doi.org/10.5194/jsss-7-31-2018 (2018).

Article ADS Google Scholar

Zaky, Z. A., Al-Dossari, M., Hendy, A. S., Badawy, W. M. & Aly, A. H. Periodic open and closed resonators as a biosensor using two computational methods. Sci. Rep. 14, 11943. https://doi.org/10.1038/s41598-024-61987-3 (2024).

Article ADS CAS PubMed PubMed Central Google Scholar

Zaky, Z. A., Al-Dossari, M., Sharma, A., Hendy, A. S. & Aly, A. H. Theoretical optimisation of a novel gas sensor using periodically closed resonators. Sci. Rep. 14, 2462. https://doi.org/10.1038/s41598-024-52851-5 (2024).

Article ADS CAS PubMed PubMed Central Google Scholar

Zaky, Z. A., Mohaseb, M. & Aly, A. H. Detection of hazardous greenhouse gases and chemicals with topological edge state using periodically arranged cross-sections. Phys. Scr. 98, 065002. https://doi.org/10.1088/1402-4896/accedc (2023).

Article ADS CAS Google Scholar

Robertson, O. et al. Tests for the chronic toxicity of propylexe glycol and triethylene glycol on monkeys and rats by vapor inhalation and oral administration. J. Pharmacol. Exp. Ther. 91, 52–76 (1947).

CAS PubMed Google Scholar

Han, P. & Wang, H. Extension of omnidirectional reflection range in one-dimensional photonic crystals with a staggered structure. J. Opt. Soc. Am. B 20, 1996–2001. https://doi.org/10.1364/JOSAB.20.001996 (2003).

Article ADS CAS Google Scholar

Zaky, Z. A. et al. Theoretical optimization of Tamm Plasmon Polariton structure for pressure sensing applications. Opt. Quant. Electron. 55, 738. https://doi.org/10.1007/s11082-023-05023-0 (2023).

Article CAS Google Scholar

Hojo, H. & Mase, A. Dispersion relation of electromagnetic waves in one-dimensional plasma photonic crystals. J. Plasma Fusion Res. 80, 89–90. https://doi.org/10.1585/jspf.80.89 (2004).

Article ADS CAS Google Scholar

Wu, F., Liu, T., Chen, M. & Xiao, S. Photonic bandgap engineering in hybrid one-dimensional photonic crystals containing all-dielectric elliptical metamaterials. Opt. Express 30, 33911–33925. https://doi.org/10.1364/OE.469368 (2022).

Article ADS CAS PubMed Google Scholar

Al-Dossari, M., Zaky, Z. A., Awasthi, S. K., Amer, H. A. & Aly, A. H. Detection of glucose concentrations in urine based on coupling of Tamm–Fano resonance in photonic crystals. Opt. Quant. Electron. 55, 484. https://doi.org/10.1007/s11082-023-04621-2 (2023).

Article CAS Google Scholar

Zaky, Z. A. et al. Theoretical analysis of porous silicon one-dimensional photonic crystal doped with magnetized cold plasma for hazardous gases sensing applications. Opt. Quant. Electron. 55, 584. https://doi.org/10.1007/s11082-023-04907-5 (2023).

Article CAS Google Scholar

Abohassan, K. M., Ashour, H. S. & Abadla, M. M. Tunable wide bandstop and narrow bandpass filters based on one-dimensional ternary photonic crystals comprising defects of silver nanoparticles in water. J. Phys. Chem. Solids 161, 110484. https://doi.org/10.1016/j.jpcs.2021.110484 (2022).

Article CAS Google Scholar

Zaky, Z. A., Al-Dossari, M., Hendy, A. S., Zayed, M. & Aly, A. H. Gamma radiation detector using Cantor quasi-periodic photonic crystal based on porous silicon doped with polymer. Int. J. Mod. Phys. B. https://doi.org/10.1142/S0217979224504095 (2024).

Suthar, B. & Bhargava, A. Biosensor Application of One-Dimensional Photonic Crystal for Malaria Diagnosis, Plasmonics 16 59–63. https://doi.org/10.1007/s11468-020-01259-8 (2021).

Awasthi, S. Multichannel tunable polarizing filter properties of one-dimensional ternary photonic crystal containing single-negative materials. Indian J. Phys.. https://doi.org/10.1007/s12648-020-01939-5 (2021).

Zaky, Z. A., Al-Dossari, M., Hendy, A. S. & Aly, A. H. Studying the impact of interface roughness on a layered photonic crystal as a sensor. Phys. Scr. 98, 105527. https://doi.org/10.1088/1402-4896/acfa4a (2023).

Article ADS CAS Google Scholar

Guo, A. et al. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902. https://doi.org/10.1103/PhysRevLett.103.093902 (2009).

Article ADS CAS PubMed Google Scholar

Rüter, C. E. et al. Observation of parity–time symmetry in optics. Nat. Phys. 6, 192–195. https://doi.org/10.1038/nphys1515 (2010).

Article CAS Google Scholar

Ramezani, H., Kottos, T., El-Ganainy, R. & Christodoulides, D. N. Unidirectional nonlinear PT-symmetric optical structures. Phys. Rev. A 82, 043803. https://doi.org/10.1103/PhysRevA.82.043803 (2010).

Article ADS CAS Google Scholar

Zaky, Z. A., Alamri, S., Zhaketov, V. & Aly, A. H. Refractive index sensor with magnified resonant signal. Sci. Rep. 12, 13777. https://doi.org/10.1038/s41598-022-17676-0 (2022).

Article ADS CAS PubMed PubMed Central Google Scholar

Musina, G. R. et al. Optimal hyperosmotic agents for tissue immersion optical clearing in terahertz biophotonics. J. Biophotonics 13, e202000297. https://doi.org/10.1002/jbio.202000297 (2020).

Article CAS PubMed Google Scholar

Yeh, P. Optical Waves in Layered Media (Wiley New York, 1988).

Zaky, Z. A., Mohaseb, M., Hendy, A. S. & Aly, A. H. Design of phononic crystal using open resonators as harmful gases sensor. Sci. Rep. 13, 9346. https://doi.org/10.1038/s41598-023-36216-y (2023).

Article ADS CAS PubMed PubMed Central Google Scholar

Zaky, Z. A. et al. Photonic crystal with magnified resonant peak for biosensing applications. Phys. Scr. 98, 055108. https://doi.org/10.1088/1402-4896/accbf1 (2023).

Article ADS CAS Google Scholar

Zaky, Z. A., Alamri, S., Zohny, E. I. & Aly, A. H. Simulation study of gas sensor using periodic phononic crystal tubes to detect hazardous greenhouse gases. Sci. Rep. 12, 21553. https://doi.org/10.1038/s41598-022-26079-0 (2022).

Article ADS CAS PubMed PubMed Central Google Scholar

Tammam, M. T. et al. Defected Photonic Crystal Array Using Porous GaN as Malaria Sensor, presented at the IOP Conference Series: Materials Science and Engineering. https://doi.org/10.1088/1757-899X/1171/1/012005 (2021).

Zaky, Z. A., Panda, A., Pukhrambam, P. D. & Aly, A. H. The impact of magnetized cold plasma and its various properties in sensing applications. Sci. Rep. 12, 3754. https://doi.org/10.1038/s41598-022-07461-4 (2022).

Article ADS CAS PubMed PubMed Central Google Scholar

Zeng, C., Luo, C., Hao, L. & Xie, Y. The research on magnetic tunable characteristics of photonic crystal defect localized modes with a defect layer of nanoparticle. Chin. Opt. Lett. 12, S11602. https://doi.org/10.3788/COL201412.S11602 (2014).

Article ADS Google Scholar

Xiang, Y., Dai, X., Wen, S. & Fan, D. Enlargement of zero averaged refractive index gaps in the photonic heterostructures containing negative-index materials, Phys. Rev. E 76, 056604. https://doi.org/10.1103/PhysRevE.76.056604 (2007).

Zaky, Z. A. & Aly, A. H. Novel smart window using photonic crystal for energy saving. Sci. Rep. 12, 10104. https://doi.org/10.1038/s41598-022-14196-9 (2022).

Article ADS CAS PubMed PubMed Central Google Scholar

Zaky, Z. A., Singh, M. R. & Aly, A. H. Tamm resonance excited by different metals and graphene. Photonics Nanostruct. Fundam. Appl. 49, 100995. https://doi.org/10.1016/j.photonics.2022.100995 (2022).

Article Google Scholar

Zaky, Z. A., Amer, H. A., Suthar, B. & Aly, A. H. Gas sensing applications using magnetized cold plasma multilayers. Opt. Quant. Electron. 54, 217. https://doi.org/10.1007/s11082-022-03594-y (2022).

Article CAS Google Scholar

Zaky, Z. A., Al-Dossari, M., Zohny, E. I. & Aly, A. H. Refractive index sensor using fibonacci sequence of gyroidal graphene and porous silicon based on Tamm Plasmon Polariton. Opt. Quant. Electron. 55, 6. https://doi.org/10.1007/s11082-022-04262-x (2023).

Article CAS Google Scholar

Zaky, Z. A., Hanafy, H., Panda, A., Pukhrambam, P. D. & Aly, A. H. Design and analysis of gas sensor using tailorable fano resonance by coupling between tamm and defected mode resonance. Plasmonics 17, 2103–2111. https://doi.org/10.1007/s11468-022-01699-4 (2022).

Zaky, Z. A., Al-Dossari, M., Matar, Z. & Aly, A. H. Effect of geometrical and physical properties of cantor structure for gas sensing applications. Synth. Met. 291, 117167. https://doi.org/10.1016/j.synthmet.2022.117167 (2022).

Article CAS Google Scholar

Wang, Z. et al. 1D partially oxidized porous silicon photonic crystal reflector for mid-infrared application. J. Phys. D 40, 4482. https://doi.org/10.1088/0022-3727/40/15/016 (2007).

Article ADS CAS Google Scholar

Ramirez-Gutierrez, C. F., Martinez-Hernandez, H. D., Lujan-Cabrera, I. A. & Rodriguez-García, M. E. Design, fabrication, and optical characterization of one-dimensional photonic crystals based on porous silicon assisted by in-situ photoacoustics. Sci. Rep. 9, 1–15. https://doi.org/10.1038/s41598-019-51200-1 (2019).

Zhang, B. et al. Bandwidth tunable optical bandpass filter based on parity-time symmetry. Micromachines 13, 89. https://doi.org/10.3390/mi13010089 (2022).

Lova, P., Manfredi, G. & Comoretto, D. Advances in functional solution processed planar 1D photonic crystals. Adv. Opt. Mater. 6, 1800730. https://doi.org/10.1002/adom.201800730 (2018).

Article CAS Google Scholar

Zaky, Z. A., Sharma, A., Alamri, S. & Aly, A. H. Theoretical evaluation of the refractive index sensing capability using the coupling of Tamm–Fano resonance in one-dimensional photonic crystals. Appl. Nanosci. 11, 2261–2270. https://doi.org/10.1007/s13204-021-01965-7 (2021).

Article ADS CAS Google Scholar

Ameen, A. A., Al-Dossari, M., Zaky, Z. A. & Aly, A. H. Studying the effect of quantum dots and parity-time symmetry on the magnification of topological edge state peak as a pressure sensor. Synth. Met. 292, 117233. https://doi.org/10.1016/j.synthmet.2022.117233 (2023).

Article CAS Google Scholar

Barvestani, J. & Mohammadpour, A. The effect of the centric graphene layer on the exceptional points of parity-time symmetric photonic crystals. Opt. Quant. Electron. 56, 880. https://doi.org/10.1007/s11082-024-06754-4 (2024).

Article ADS CAS Google Scholar

Zaky, Z. A., Al-Dossari, M., Sharma, A. & Aly, A. H. Effective pressure sensor using the parity-time symmetric photonic crystal. Phys. Scr. 98, 035522. https://doi.org/10.1088/1402-4896/acbcae (2023).

Article ADS Google Scholar

Christodoulides, D. & Yang, J. Parity-Time Symmetry and Its Applications Vol 280 (Springer, 2018).

Fang, Y., Zhang, Y. & Wang, J. J. Resonance-dependent extraordinary reflection and transmission in PC-symmetric layered structure. Opt. Commun. 407, 255–261. https://doi.org/10.1016/j.optcom.2017.09.049 (2018).

Article ADS CAS Google Scholar

Klimov, V. et al. Optical gain and stimulated emission in nanocrystal quantum dots. Science 290, 314–317. https://doi.org/10.1126/science.290.5490.314 (2000).

Ma, G., Shen, J., Zhang, Z., Hua, Z. & Tang, S. H. Ultrafast all-optical switching in one-dimensional photonic crystal with two defects. Opt. Express 14, 858–865. https://doi.org/10.1364/OPEX.14.000858 (2006).

Article ADS CAS PubMed Google Scholar

Tsurumachi, N. et al. Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures. Jpn. J. Appl. Phys. 38, 6302. https://doi.org/10.1143/JJAP.38.6302 (1999).

Article ADS CAS Google Scholar

Ge, X. & He, S. Experimental realization of an open cavity. Sci. Rep. 4, 1–5. https://doi.org/10.1038/srep05965 (2014).

Article CAS Google Scholar

Andueza, Á., Pérez-Conde, J. & Sevilla, J. Differential refractive index sensor based on photonic molecules and defect cavities. Opt. Express 24, 18807–18816. https://doi.org/10.1364/OE.24.018807 (2016).

Article ADS CAS PubMed Google Scholar

Panghal, A. et al. Terahertz chemical sensor based on the plasmonic hexagonal microstructured holes array in aluminum. In 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) 1–2. https://doi.org/10.1109/IRMMW-THz.2019.8874063 (2019).

Sun, B., Yu, Y. & Yang, W. Enhanced toroidal localized spoof surface plasmons in homolateral double-split ring resonators. Opt. Express 28, 16605–16615. https://doi.org/10.1364/OE.395068 (2020).

Article ADS PubMed Google Scholar

Aly, A. H. et al. Photonic crystal enhanced by metamaterial for measuring electric permittivity in GHz range. Photonics 8, 416. https://doi.org/10.3390/photonics8100416 (2021).

Qin, P. et al. Angle-insensitive toroidal metasurface for high-efficiency sensing. IEEE Trans. Microwave Theory Tech. 69, 1511–1517. https://doi.org/10.1109/TMTT.2020.3027016 (2020).

Article ADS Google Scholar

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The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large Groups Project under grant number RGP. 2/46/45.

Physics Department, Faculty of Science, TH-PPM Group, Beni-Suef University, Beni Suef, 62514, Egypt

Zaky A. Zaky & Arafa H. Aly

Academy of Scientific Research and Technology (ASRT), Cairo, Egypt

Zaky A. Zaky

Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russia

Zaky A. Zaky & V. D. Zhaketov

Department of Physics, Faculty of Science, King Khalid University, Abha, 62529, Saudi Arabia

M. Al-Dossari

Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, Russia

V. D. Zhaketov

Department of Technical Sciences, Western Caspian University, Baku, 1001, Azerbaijan

Arafa H. Aly

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Z.A. Zaky invented the original idea of the study, implemented the computer code, performed the numerical simulations, analyzed the data, wrote and revised the main manuscript text, and was the team leader. M Al-Dossari analyzed the data and discussed the results. V. D. Zhaketov analyzed the data and discussed the results. A. H. Aly analyzed the data and discussed the results. Finally, all Authors developed the final manuscript.

Correspondence to Zaky A. Zaky.

The authors declare no competing interests.

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Zaky, Z.A., Al-Dossari, M., Zhaketov, V.D. et al. Defected photonic crystal as propylene glycol THz sensor using parity-time symmetry. Sci Rep 14, 23209 (2024). https://doi.org/10.1038/s41598-024-73477-7

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Received: 11 July 2024

Accepted: 17 September 2024

Published: 05 October 2024

DOI: https://doi.org/10.1038/s41598-024-73477-7

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