key: cord-1038436-1376et64
authors: Ameen, Ayman A.; ElSayed, H.; Aly, Arafa H.
title: Towards a highly efficient air purifier using annular photonic crystals in UV regimes
date: 2021-04-21
journal: RSC advances
DOI: 10.1039/d1ra00991e
sha: 5b320b763edbd0efa75773d90f69562499afd957
doc_id: 1038436
cord_uid: 1376et64

Air purifiers play a vital role in fighting the spread of airborne transmitted diseases like COVID-19, rubeola, Mycobacterium tuberculosis, and varicella-zoster, which represent a fundamental challenge. This paper introduces a new enhancement to ultraviolet (UV) air purifiers in air ventilation systems, which delivers a higher inactivation UV dose, eliminating the need for either higher exposure time or a stronger UV source. The modified transfer matrix method in the cylindrical geometry represents the main tool of our theoretical considerations. The new enhancement utilizes an annular photonic crystal (APC) for reflecting UV radiation 99%. The numerical simulation shows that the structure is stable over a wide range of operating scales that fit the extensive range of air purifiers, working at different scales. Additionally, the possibility of using APC over a wide range of UV sources is investigated.

Indoor air ventilation plays a vital role in spreading airborne transmitted illnesses like SARS-CoV-2 (COVID- 19) , rubeola, Mycobacterium tuberculosis, and varicella-zoster. [1] [2] [3] Air recirculation is an efficient way of saving buildings' energy. However, it also contributes to the transfer of pathogens by aerosol. 2, 4, 5 Air ventilation in public buildings, like public transport, schools, hospitals, restaurants and shops requires engineering controls and disease prevention. One of the most effective methods to disinfect the air from pathogens is using ultraviolet germicidal irradiation (UVGI). 6, 7 The ultraviolet radiation range (180 nm to 320 nm) can inactivate biological systems through photochemical degradation of their genetic material. The genetic material of coronaviruses like SARS-CoV-2 consists of singlestranded RNA (ssRNA), which shows a level of inactivation when exposed to UV radiation. 8 The level of inactivation of the pathogens depends on the UV dose and the pathogen. According to the FDA, the optimal UV dose should reduce the pathogens by a 3-log level or more. 9 UV radiation has been used in medial air puriers. 10 However, some pathogens such as ssRNA viruses, require a high dose of UV or longer exposure time to achieve a high inactivation level. We can use a reector to reect more UV radiation. Thus, the UV dose increases without the need for either stronger UV sources or long exposure time.

A high level of reectivity with low loss can be achieved using photonic crystals (PCs), periodic structures whose refractive indices change periodically. Due to this periodicity, a range of frequencies is forbidden to propagate in these structures; this range is called photonic band gap (PBG). 11, 12 The periodicity of PCs can be designed in one, two, or three dimensions. A complete PBG can be formed in the three-dimensional PCs only. Researchers have tested a wide variety of PC materials like dielectrics, metals as well as various materials. [13] [14] [15] Furthermore, lithographic techniques, chemical vapor deposition (CVD), 16 self-assembly, 17 and other fabrication techniques have been successfully used to build PCs. Moreover, a huge set of congurations from periodic to quasi-periodic have been studied to arrange PC materials. [18] [19] [20] [21] PCs have been demonstrated in a massive number of applications in many different areas due to their outstanding properties. In this regard, PBG with high reectivity could be very useful for laser emissions, optical communication, photovoltaic panels, and waveguides. 22, 23 By introducing a defect layer inside the periodic structure, a resonance transmittance peak appears inside the PBG. 24 A change in a particular condition like temperature can alter its electromagnetic response. Such tunability can be used as a sensor for the detection or measurement of that condition. Therefore, PCs based sensors are widely designed and fabricated for detection temperature, hydrostatic pressure, acoustic waves, and magnetic elds. [25] [26] [27] One of the classes of one-dimensional PCs is annular photonic crystals (APCs), also called cylindrical Bragg reectors or photonic circular crystals. 28, 29 APCs are periodic concentric cylindrical multilayer structures. APCs attracted attention since Kaliteevski et al. untiles the transfer matrix method in the cylindrical coordinates to describe the eclectic and magnetic elds inside coaxial layers. 30 APCs found a lot of applications in laser emission, optical communication, and optical electronics. 22, 31, 32 Moreover, researchers found that APCs have better sensing capabilities than planar PCs, which are promising with many chemical and biological applications. Here, we intend to present a new UV air purier system based on APCs for higher UV inactivation doses. Our designed structure could be suitable for indoor air ventilation systems in public places like restaurants, hospitals, etc. The paper is divided into four sections: in the next section, we discuss the main feature of our structure and the basics of our theoretical modeling. In the third section, we present the reectance spectra of our APCs in UV regimes besides the discussion of the effect of the related parameters. Finally, we have introduced our conclusion and suggestion for future applications in section four.

In this section, we introduce a brief description of our structure and the theoretical considerations that govern the interaction with the incident UV radiation. As shown in Fig. 1 , the proposed APCs is designed from periodic concentric cylindrical multilayers over a hollow-core with a radius r 0 .

Each unit cell of the periodic part (L) is designed from a bilayer with refractive indices n 1 and n 2 corresponding to thickness d 1 and d 2 , respectively. The distance from the center to the end of a specied layer i is denoted as r i and can be described as:

where, N is the periodicity number. The structure's primary purpose is to increase the UV dose by reecting more UV radiation to achieve a higher pathogen deactivating rate. The design consisted of a UV source in its central tube where the untreated air enters from one side, as shown in Fig. 2 . The incoming air is exposed to UV radiation with an almost complete reection on the central tube walls due to the APC. Thus, we can achieve a higher UV dose without the need for a more powerful UV source. In order to analyze the optical characteristics of APCs, the electric and magnetic elds at the interfaces of APCs are studied using the transfer matrix method (TMM) in cylindrical coordinates. 30 For cylindrical Bragg wave, TE and TM are the two possible polarization modes. The non-zero electromagnetic elds TE mode, are E z , H f and H r . The electric eld E z can be described by the following wave equation:

The solution of E z can be obtained by using the separation of variables method as the following:

where, m, J m and Y m are the azimuthal number, Bessel function, and Numann function, respectively. The wavenumber of the propagating electromagnetic wave inside material with permittivity 3 and permeability m is k ¼ u ffiffiffiffiffi m3 p : The relation between E z and H f can be given by

part of the magnetic eld H f can be obtained by substituting of E z in the previous equation as the following:

which is the intrinsic admittance of the material. The electric and magnetic elds in a single layer with a refractive index n j and interfaces at r jÀ1 and r j can be represented by the following matrix:

where, the elements of the matrix M j are described in the following form: The electric and magnetic felids at the interfaces of the APC structure is expressed as

where the matrix M is the result of the product of the APC's single matrix layers and acquired as

The reectance coefficient of the APC could be investigated as a function of the matrix elements as:

In the above equation, M 11 , M 12 , M 21 and M 22 , are the elements of the matrix M. The admittances of the core layer p 0 and the nal medium p f is given by

; where j takes the value 0 and f. The parameter C ml is obtained from the following expression:

where, H Hankel function and their derivatives, respectively. The equations for TM-mode can be acquired by replacing every i, 3 by Ài, m respectively, and vice versa. Finally, the reectance from APC can be obtained by,

In this section, we present the modeling results of the reectance of the designed APCs, which enhances the UVGI of the pathogens in air ventilation systems. The transfer matrix method in cylindrical coordinates, discussed in the previous section, is used to perform our calculations. We have considered that the air core is specied with n 0 ¼ 1 and UV source is situated in the center of the proposed structure. The unit cell of APCs is consisted of Al 2 O 3 and SiO 2 with periodicity number N ¼ 20. The initial thicknesses of Al 2 O 3 and SiO 2 cylindrical layers are d 1 ¼ 35 nm and d 2 ¼ 40 nm, respectively. The unpuried air pass through the inner core with an initial radius r 0 ¼ 0.5 m. We assume that the outer tube is made of Al 2 O 3 with refractive index n f . The refractive indices of the selected material are taken as a function of the frequency from the following ref. 33 and 34. Firstly, we investigate the reectance of the proposed APC for TE mode at azimuthal mode number m ¼ 0 as shown in Fig. 3 . The reectance spectrum reveals the appearance of a PBG in the wavelengths of interest with width 26.6 nm due to Bragg scattering. The center of the PBG is located at 257 nm which is chosen carefully by adjusting the structure parameters. The position and width of the PBG making it perfect for reecting most UVC spectrum emission of low-pressure mercury vapor lamps as they widely used in UVGI devices. 7 The average reection intensity of the PBG around 93%, which relatively high compared to other UV reector devices. Although the average reection of PBG is 93%, wherein the intensity around the center of the PBG reaches 99%. Moreover, the large value of core radius could be of interest and more realistic from the fabrication and manufacturing point of view. Hereinaer, we have demonstrated the effect of the inner core radius on the reectance of the proposed APCs, as shown in Fig. 4 . Here, APC parameters are taken as same as the initial values with d 1 ¼ 35 nm, d 2 ¼ 40 nm, N ¼ 40, and m ¼ 0. The effect of changing the inner core radius r 0 is almost noticeable at minimum values as 10 À7 m and it is not observable as the radius changes from 10 À4 m to 1 m as shown in Fig. 4(a) . At r 0 ¼ 10 À7 m, the position of the PBG is slightly shied to longer wavelengths with increasing of the inner core. In contrast, the position of the PBG almost remains xed with altering the inner core radius at larger values of the inner core radius from 10 À4 m up to 1 m. Moreover, the average intensity of the PBG is almost invariant with changing the inner core radius at radii greater than 10 À4 m as listed in Table 1 . Whilst, the average intensity of the PBG is slightly decreasing with reducing the inner core radius as 10 À7 m, the width of the PBG is slightly increasing as the inner core radius decreases. The average intensity is calculated by a normalized sum over all intensities from the le edge to the right edge of the PBG. The edges are considered at 50% of the maximum value in the PBG. Fig. 4(b) shows the reectance of the proposed structure at different inner core radii. The reectance shis slightly towards longer wavelengths as the inner core radius gets from 10 À7 m to 10 À6 m. As the inner core radius get values lager than 10 À6 m, the effect of changing the inner core radius became less visible on both the shape and the intensity of the reectance. Then, the position and the average intensity of the PBG are studied in Fig. 4(c) and (d). When the inner core radius ¼ 10 À7 m, the PBG appears between 243.79 nm and 270.33 nm with an average density of about 93.65%. As the inner core radius reaches 10 À6 m, the width of the PBG turns out to be 26.605 nm with an average intensity of 93.69%. The width of the PBG receives 26.61 nm with an average intensity of approximately 93.7% as the inner core radius reaches 10 À4 nm. As the inner core radius increases from 10 À4 m to 10 m, the PBG's width, and average intensity are stabilized at 26.6 nm and 93.7%, respectively. Furthermore, the position of the PBG becomes xed around 243.9 nm and 270.5 nm for the le and the right edges, respectively. The above results reveal that the effect of the inner core radius is almost insignicant for values above 10 À6 m, which opens the way towards a great number of applications with different size scale. For example, the ventilation tube could have any size from a few centimeters up to few meters without affecting the performance. This feature is crucial not only in the ventilation systems but also in other UVGI applications. Now, the inuence of the periodicity number on the reectance of the proposed APCs is examined in Fig. 5 . As the periodicity number increases, the reectance becomes more apparent, and sharper PBG is investigated, as seen in Fig. 5(a) . At N ¼ 10, the edges of the PBG are smooth and cover a larger area with a width of 32.8 nm, and its average intensity ¼ 77%. As the periodicity number increases, the PBG becomes sharper with a larger average intensity as 93.6% for periodicity number N ¼ 20, and it reaches 97% at N ¼ 30. Thus, the average intensity drops signicantly as the periodicity number decreases. On the other hand, the width is decreased as the periodicity number reduced. As the periodicity number N increases, the le edge of the PBG l L slightly shis to longer wavelengths while the right edge l R shis to shorter wavelengths but the center of the PBG l 0 almost xed as claried in Table 2 . Then, for a deep description of the role of the periodicity, we have plotted in Fig. 5(b) a color map to clarify this role as N varies from 1 to 60. The PBG is hardly observable below N ¼ 3 with average intensity below 40%. As the periodicity number increases, the PBG gets sharper with larger average intensity as it gets 93% at N ¼ 20 and reaches 98% at N ¼ 40. Also, the number of secondary peaks alongside the PBG increases with increasing the periodicity number. The position of the center of PBG is almost xed at 257 nm with a difference around one nm as the periodicity number changes. The PBG edges' wavelengths shi towards the center with increasing the periodicity number, as shown in Fig. 5(c) . Thus, as the periodicity number increases, the width of the PBG decreases, while the PBG average intensity increases, as shown in Fig. 5 (d). At N ¼ 8, the PBG has 68% average density and 35.9 nm width, while its average intensity at N ¼ 15 reaches 88% with 28.8 nm width. As N ¼ 25, the PBG's average intensity reaches 96% with a width of 25.2 nm, and its width gets 23.6 with an average intensity of 98% at N ¼ 35. Finally, we have investigated the effect of the lattice constant on the reectivity of our designed structure. In particular, the thicknesses of the constituent materials (Al 2 O 3 and SiO 2 ) are obtained based on the quarter-wave stack condition. The unit cell thickness or the lattice constant is determined as

The PBG is drastically shied towards longer wavelengths as increasing the unit cell constant, as observed in Fig. 6 (a). At L 0 ¼ 61 nm, the center of the PBG appears at 214.1 nm, and the width of the gap is equivalent to 21.3 nm with 94% average intensity. As the unit cell constant increases to 70 nm, the PBG center is slightly shied to 241.6 nm. However, the width of the PBG increased to 24.7 nm with a small decrease in the average intensity to 93.7%. The center of the PBG becomes at 272.8 nm with 28.4 nm width when the unit cell constant reaches L 0 ¼ 80 nm. Then, the unit cell effect on the APC's reectance has been examined smoothly from L 0 ¼ 60 nm up to L 0 ¼ 90 nm as shown in Fig. 6(b) . The position of the PBG shis linearly to longer wavelengths, and the unit cell constant L 0 is linearly tted to the center wavelength of the PBG l 0 according to l 0 ¼ 3.101L 0 + 24.67 with the sum of error squares equals 0.02446. 

In this paper, we introduce a new enhancement for air puriers in air ventilation systems using APCs. The numerical simulation reveals that the PBG width around 26 nm with average reection intensity of 93% and 99% reection in the center of the PBG. The PBG position is optimized at the maximum emission of mercury vapor lamps, which is widely used in UVGI devices. The effect of inner core radius is not signicant for values larger than 10 À6 m up to 10 m which opens the road towards a wide range of working scales. The effect of periodicity number on reection is crucial as the PBG width decreases while the average intensity increases as the periodicity number increases. The impact of the unit cell constant has been examined for various values. The PBG shis towards longer wavelengths as increasing the unit cell constant. Thus, the APC can adjust for a variety of UV sources.

There are no conicts to declare. 

Infection prevention and control of epidemic-and pandemic-prone acute respiratory infections in health care, 1.Guideline I.World Health Organization, ISBN 978 92 4150713 4, Subject headings are available from WHO institutional repository © World Health Organization

American Society of Heating, Refrigerating and Air-Conditioning Engineers

Handbook of optical materials

CRC Handbook of Laser Science & Technology: Optical Materials, Part

The authors thank the Academy of Scientic Research & Technology (ASRT), Egypt for supporting the current work through; Science up Program; Project ID: 7859.