- Email: [email protected]
Design of a solar-blind ultraviolet band-pass filter based on frequency domain superposition
Accepted Manuscript Design of a solar-blind ultraviolet band-pass filter based on frequency domain superposition
YiBiao Yang, YaTing Bai, XiaoDan Zhao, MingDa Zhang, HongMing Fei, ZhiHui Chen PII:
S0749-6036(18)31090-5
DOI:
10.1016/j.spmi.2018.06.062
Reference:
YSPMI 5797
To appear in:
Superlattices and Microstructures
Received Date:
23 May 2018
Accepted Date:
28 June 2018
Please cite this article as: YiBiao Yang, YaTing Bai, XiaoDan Zhao, MingDa Zhang, HongMing Fei, ZhiHui Chen, Design of a solar-blind ultraviolet band-pass filter based on frequency domain superposition, Superlattices and Microstructures (2018), doi: 10.1016/j.spmi.2018.06.062
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Design of a solar-blind ultraviolet band-pass filter based on frequency domain superposition YiBiao Yanga,b,*, YaTing Baia, XiaoDan Zhaoa, MingDa Zhanga, HongMing Feia, ZhiHui Chena,b a Department
of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China Laboratory of Advanced Transducers and Intelligent Control System, Taiyuan University of Technology, Ministry of Education, Taiyuan 030024, China *Corresponding author: [email protected] b Key
Abstract In this paper, a band-pass filter based on photonic crystals is designed by using the principle of frequency domain superposition. The influence of the heterostructure position, period numbers and incidence angles on transmission spectrums are analyzed. The filter can achieve efficient filtering in 240-280nm solar-blind ultraviolet band, with an average transmittance of 72.2%. Simultaneously, a good band-stop appears in near ultraviolet and visible region (300-700nm) and its average transmittance is below 3.4%. It provides a choice in the application of solar-blind ultraviolet detection technology. Keywords: Photonic crystal; Band-pass filter; Transfer matrix method; Solar-blind ultraviolet detection 1. Introduction Ultraviolet between 240-280nm will be absorbed by ozone layer when sunlight passes through the atmosphere. Such light, which can’t reach the surface of the earth, is named the Solar-blind ultraviolet (SBUV) [1, 2]. SBUV is widely applied in the detection of corona [3-5], tail flame from missile [6, 7], fires [8, 9] and many other area for the influence of the sunlight can almost be ignored. SBUV technology [1012] makes the most of the characteristics of the atmosphere absorbing ultraviolet radiation so that it has a good working background of small interference and less false signals. However, the signal of ultraviolet radiation source is generally weak and the ultraviolet detector is required to have high sensitivity and low noise. Therefore, it is very important to improve the filtering performance of SBUV filter. Photonic crystals (PCs) [13-16] have drawn intense attention due to their unique electromagnetic properties and potential applications. Owing to simple structure, easy preparation, and convenient tuning mode, many studies choosing one-dimensional (1D) PCs as ultraviolet filters have been reported. Wang [17] designed a multilayer structure of metal medium to realize the pass band with 260nm being the center, and the band gap from 280nm to the near infrared band. J.D. Hoyo [18] introduced the AlF3 material in the structure to enhance the reflection of Al and realized the bandpass in Lyman-Alpha band (100-130nm). Fu [19] introduced metal Al in the structure in order to design a deep cut-off feature in the visible band. Although containing the metal medium in structure can achieve a better cut-off in the visible band, it has low transmittance in the SBUV band, which leads to unobvious improvement effect on the SBUV filter. In this paper, we devise a 1D band-pass filter based on PC. By using the principle of frequency domain superposition [20, 21], we obtained the filter structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10 and realized high transmittance in SBUV band and
ACCEPTED MANUSCRIPT forbidden band in visible light band. The influences of the PCs parameters and incident angles on transmission spectrum are theoretically analyzed. 2. Structural model and computational method Our design uses Si3N4 and SiO2 to avoid the high rate of absorption in deep ultraviolet band [22]. But the ratio of the refractive index of the two materials is low, which leads to emerge a narrow band gap in the ultraviolet band. In order to broaden the scope of the band gap, we design a PC band-pass filter of a quantum well structure, which is stacked by five PCs. The structure is shown in Fig. 1.
Fig. 1. Schematic of a SBUV band-pass filter. PCs (s=1-5) represents five PCs. N , M are the period numbers of PCs (s=2-4) and PC5, respectively. aj (j=1-5) are the lattice constant of PCs (s=1-5).
The heterostructure can be expressed as (PC1)6(PC2)N(PC3)N(PC4)N(PC5)M, which is composed of five PCs. Here, N is the period numbers of PC2-4, and M is the period number of PC5. The thickness is represented as aj (j=1-5), aj = d(Si3N4)j + d(SiO2)j, where d(Si3N4)j and d(SiO2)j are two kinds of film thicknesses of PCs (s=1-5), respectively. The specific values are shown in Table 1. θ is the incidence angle. Table 1. The thickness of Si3N4 and SiO2 PC1
PC2
PC3
PC4
PC5
d(Si3N4)/nm
40.1
48.3
56.4
66.8
77.1
d(SiO2)/nm
57.4
68
78.7
92.5
106.2
In our work, Si3N4 and SiO2 are periodically arranged as high and low refractive index materials in each PC. The refractive indices of Si3N4 and SiO2 are n1 and n2, which are relatively stable in the research band and the materials almost have no absorption in the ultraviolet band, as shown in Fig. 2. Considering the influence of dispersion and absorption of Si3N4 and SiO2 on transmission spectrum, Fig. 2 is a diagram of the relation between the dispersion and absorption coefficient of the two materials with the change of wavelength.
ACCEPTED MANUSCRIPT
Fig. 2. The refractive indices and absorption coefficients of Si3N4 and SiO2.
In the calculation, the propagation characteristics of light in one-dimensional periodic dielectric materials are studied by means of transfer matrix method. The heterostructure is arranged periodically in the direction of Y-axes, and the characteristic matrix of a single layer can be expressed as:
cos i Mi i sin i i
i sin i i cos i
, (1) Here, i k0 n j d i cos i , k 0 is the wave vector c , where ω is the frequency of the incident wave and c is the speed of light in vacuum. ni and di are the refractive index and thickness if the i-th layer. i depends on the polarization of the waves. For TE
mode, i i i cos i , while for TM mode, i i i cos i . Here is the dielectric constant and is the permeability. is the incident angle. The feature matrix of a multi-layer structure can be expressed as: P m M M P 11 i 1 m21
m12 m22
, (2) At specific wavelengths and incident angles, the transmission and reflection coefficients as well as the transmittance and reflectivity of the multilayer dielectric film can be expressed as follows:
t
r
2 f (m11 m12 h ) f (m21 m22 h )
(3)
(m11 m12 f ) f (m21 m22 h ) (m11 m12 h ) f (m21 m22 h )
R r T
,
,
(4)
2
,
h 2 t . f
(5) (6)
3. Simulation results and discussions Based on the principle of superposition in frequency domain, we stack five
ACCEPTED MANUSCRIPT periodically arranged PCs. According to the transmission spectrum, the influence of position arrangements, period numbers of PCs and incidence angles are theoretically analyzed. Photonic band gap is one of the basic properties of PCs. Here we have analyzed the band gap range of PCs with lattice constants of 97.5nm, 116.3nm, 135.1nm, 159.3nm and 183.3nm, respectively. As the lattice constant becomes larger , the forbidden band moves to the long-wave side, and the forbidden band width is gradually widened , as shown in Fig. 3. It is conceived that five PCs can be stacked to form a broad forbidden band. The structure is (PC1)6(PC2)N(PC3)N(PC4)N(PC5)M.
Fig. 3. The photonic band gap of PC1-5.
On normal incidence, when N=5 and M=6, the five PCs are arranged in accordance with the size of the lattice constant, where the film thicknesses of Si3N4 and SiO2 in each PC are shown in Table 1. In Fig. 4(a), there is a high transmission spectrum in the 240-280nm and a wide band gap in the 300-700nm. The forbidden band covers the whole near ultraviolet and visible bands, which satisfies the high acquisition rate of the 240-280nm ultraviolet signal and the signal is not interfered by the visible band for SBUV detection technology.
ACCEPTED MANUSCRIPT
Fig. 4. The transmission spectrum of PC2-4 position combination.
We fixed the PCs with the minimum and maximum lattice constants on the edge and disrupted the arrangement of other PCs. Fig. 4(b)-(f) are the transmission spectrums of the combination of three PCs positions in the middle of the heterostructure. It shows that high transmission spectrum also appears in the 240280nm band, while many sharp peaks appear in the band gap in 300-700nm. It is because such disruptions of the middle PCs are equivalent to introducing defects into the whole structure. The characteristic of photonic localization causes the impure peaks in the forbidden band. Only the heterostructure (PC1)6(PC2)5(PC3)5(PC4)5(PC5)6, which arrangement is according to the size of lattice constant, accords with the standard of deep cut-off in near ultraviolet and visible band. In Fig. 4(a), under the same periodic number of PC1 and PC5, the cutoff of the band gap at short-wave side is better than that at long-wave side. To optimize the cutoff of the band gap at long-wave side, we changed the period number of PC5. The spectrums are shown in Fig. 5. With the increase of the period number M (M=6, 8, 10), the cutoff of the forbidden band near 700nm is getting better. However, the small impure peaks in the forbidden band are not affected by the change of period number. When M=10, the whole band gap is more similar to “rectangle”, which satisfies our demand for the band gap.
ACCEPTED MANUSCRIPT
Fig. 5. The transmission spectrum of heterostructure (PC1)6(PC2)5(PC3)5(PC4)5(PC5)M (M=6,8,10).
As is mentioned above, the period number of PC1 is 6, and the period number M of PC5 is 10. In order to smooth the impure peaks in the band gap, we studied the period number N of the internal PC2, PC3 and PC4. The transmission spectrum of N=3-6 are shown in Fig. 6. When N=3, because the period numbers of the three PCs are too small, the cut-off of their own band edges are not high, which causes three small “forbidden bands” in the wide forbidden band of 300-700nm and high transmittance peak over 50% at 565nm. However, with the increase of the period number N, the small impure peaks in the band gap are gradually smoothed. When N=6, the impure peaks in the wide band gap almost disappeared. Only a defect peak with low transmittance near 400nm was found. Due to its position in the near ultraviolet band, it has little effect on the performance of the filter for the SBUV detection technology. Finally, we design the quantum well structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10, which can meet the high transmittance of 240-280nm in the SBUV band, and the average transmittance is 72.2%. Meanwhile, the average transmittance of 300-700nm in the near ultraviolet and visible bands is 3.4%.
Fig. 6. The transmission spectrum of structure (PC1)6(PC2)N(PC3)N(PC4)N(PC5)10 (N=3-6).
On oblique incidence, different polarization stats have a great influence on the
ACCEPTED MANUSCRIPT transmission spectrums. When the incidence angle θ is taken to be 0°, 15°, 30°, and 45°，the transmission spectrum is modulated by the two polarization modes of TE and TM, as shown in Fig. 7. The solid line in the graph represents the TM mode, and the dashed line represents the TE mode. For TM mode, with the increase of the angle, the transmission spectrum shows blue shift and the band gap width is reduced by 100nm. The average transmittance of the transmission spectrum in the 240-280nm solar-blind band rises from 72.2% to 77.7%. When the incident angle is greater than 30°, there will be more impure peaks in the wide band gap of 300-700nm. The average transmittance of the band gap increases from 3.4% up to 6.4%. For TE mode, with the increase of the incident angle, the transmission spectrum also shows blue shift and the band gap width shrinks by 60nm. The average transmittance in the 240280nm band dropped from 72.2% to 44.1%. In the band gap of 300-700nm, the impure peaks almost disappeared, and the average transmittance decreased from 3.4% to 1.1%. Although a better deep cut-off is achieved, the average transmittance in the solar-blind band becomes lower. Fig. 8 shows the transmission spectrum varies with the incident angle increases from 0° to 45° for both modes. Considering the detection of ultraviolet signals in the distance, the incident angle of signals is usually less than 30°, so the heterostructure meets the SBUV filtering requirement.
Fig. 7. The transmission spectrum of structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10 with incident angle variation in TE and TM mode. (a) θ=0°; (b) θ=15°; (c) θ=30°; (d) θ=45°.
Fig. 8. The transmission spectrum of structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10 at TM and TE mode when the incident angle is changing from 0°to 45°.
4. Conclusions
ACCEPTED MANUSCRIPT In this paper, we designed a PC SBUV filter using the principle of frequency domain superposition. High transmission of 240-280nm and wide band gap of 300700nm are obtained by adjusting the arrangement position of the PCs. The optimization of the period number M of outer PC5 makes the cut-off of the spectral line higher at long-wave side. The optimization of the period number N of inner PC2-4 eliminates the tiny impure peaks in the wide forbidden band, and the quantum well structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10 is finally obtained. For both TE and TM mode, the transmission spectrums show blue shift by the modulation of the angle. We found that small incident angle (<30o) can meet the filtering performance of the filter. This band-pass filter applied to the solar-blind ultraviolet band can achieve high transmission in 240-280nm, and deep cut-off in 300-700nm. It has some significance for the development of ultraviolet filter. Acknowledgment This work was supported by National Natural Science Foundation of China (No.61575138, No.11674239); Natural Science Foundation of Shanxi province (No.201601D202013, No.2016011048). References [1] Y. Yuan, Performance of 128x128 solar-blind AlGaN ultraviolet focal plane arrays, Proceedings of SPIE - The International Society for Optical Engineering, 7381 (2009) 73810I-73810I-73819. [2] H. Cheng, Performance characteristics of solar blind UV image intensifier tube, Proceedings of SPIE - The International Society for Optical Engineering, 7384 (2009) 73840H-73840H-73847. [3] F. Yang, J. Pan, Research on dual spectrum solar-blind ultraviolet corona detection system, in: Selected Proceedings of the Photoelectronic Technology Committee Conferences Held AugustOctober, 2015, pp. 95221S. [4] L. Jian-zhuo, W. Xue-jin, H. Jian-bo, G. Bang-hui, Q. Feng, W. Jian, F. Wei, S. Qiang, Design of three-band optical system used in corona detection, Optics & Precision Engineering, 19 (2011) 12281234. [5] W. Zhou, H. Li, X. Yi, J. Tu, J. Yu, A criterion for UV detection of AC corona inception in a rodplane air gap, IEEE Transactions on Dielectrics & Electrical Insulation, 18 (2011) 232-237. [6] S. Song, L. Lin, W. Wang, Design of Solar Blind Ultraviolet Warning Optical System, Laser & Optoelectronics Progress, 50 (2013) 102203. [7] Y. Chen, Design of solar-blind UV optical system for missile approach warning, in: Optical Design and Testing VI, 2014, pp. 92721U-92721U-92727. [8] Y.Y. Wang, G.Q. Gao, J.M. Zhang, Design of ultraviolet flame detector based on C8051F120, Transducer & Microsystem Technologies, 32 (2013) 89-92. [9] Z. Liu, Design of fire detection equipment based on ultraviolet detection technology, in: Selected Papers From Conferences of the Photoelectronic Technology Committee of the Chinese Society of Astronautics, 2015, pp. 95210S. [10] B. Wang, Y. Wang, X. Zhong, N. Ruan, Research on solar-blind UV optical imaging system, Proceedings of SPIE - The International Society for Optical Engineering, 9449 (2015) 94492L94492L-94496. [11] W. Fan, S. Kang, Y. Chen, Design of a solar-blind ultraviolet detection system, Proceedings of the Spie, 141 (2016) 101411N. [12] J. Wang, Y. Chen, Optical Design of Solar Blind Ultraviolet Signal Target Simulator, Journal of Changchun University of Science & Technology, (2017). [13] X. Zhao, Y. Yang, J. Wen, Z. Chen, M. Zhang, H. Fei, Y. Hao, Tunable dual-channel filter based on the photonic crystal with air defects, Appl Opt, 56 (2017) 5463-5469. [14] S. Sahel, R. Amri, L. Bouaziz, D. Gamra, M. Lejeune, M. Benlahsen, K. Zellama, H. Bouchriha, Optical filters using Cantor quasi-periodic one dimensional photonic crystal based on Si/SiO 2, Superlattices & Microstructures, 97 (2016) 429-438. [15] S.R. Entezar, Photonic crystal wedge as a tunable multichannel filter, Superlattices & Microstructures, 82 (2015) 33-39. [16] B. Kazempour, K. Jamshidi-Ghaleh, M. Shabzendeh, Transmittance properties of tunable filter in a 1D photonic crystal doped by an anisotropic metamaterial, Superlattices & Microstructures, (2017).
ACCEPTED MANUSCRIPT [17] T. Wang, W. Xu, H. Lu, F. Ren, D. Chen, R. Zhang, Y. Zhen, Solar-blind ultraviolet band-pass filter based on metal–dielectric multilayer structures, Chinese Physics B, 23 (2014) 404-408. [18] J.D. Hoyo, M. Quijada, Enhanced aluminum reflecting and solar-blind filter coatings for the farultraviolet, in: Society of Photo-Optical Instrumentation Engineers, 2017, pp. 3. [19] X. Fu, K. Guo, S. Xiong, J. Zhang, B. Sun, H. Jiang, Development of Wide-Band Low-Noise Filter for Solar Blind Detection System, Chinese Journal of Lasers, 44 (2017) 0603002. [20] M. Barati, A. Aghajamali, Near-infrared tunable narrow filter properties in a 1D photonic crystal containing semiconductor metamaterial photonic quantum-well defect, Physica E: Low-dimensional Systems and Nanostructures, 79 (2016) 20-25. [21] H. Guan, P. Han, Y. Li, X. Zhang, W. Zhang, Analysis and optimization of a new photonic crystal filters in near ultraviolet band, Optik - International Journal for Light and Electron Optics, 123 (2012) 1874-1878. [22] J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, R. Zhang, Design and fabrication of UV band-pass filters based on SiO 2 /Si 3 N 4 dielectric distributed bragg reflectors, Applied Surface Science, 364 (2016) 886-891.
ACCEPTED MANUSCRIPT Highlights 1. A solar-blind ultraviolet filter based on frequency domain superposition is devised. 2. The filter achieves efficient filtering (72.2%) in SBUV band. 3. There is a wide band gap in 300-700nm and the average transmittance is below 3.4%. 4. It has some significance for the development of ultraviolet filter.
YiBiao Yang, YaTing Bai, XiaoDan Zhao, MingDa Zhang, HongMing Fei, ZhiHui Chen PII:
S0749-6036(18)31090-5
DOI:
10.1016/j.spmi.2018.06.062
Reference:
YSPMI 5797
To appear in:
Superlattices and Microstructures
Received Date:
23 May 2018
Accepted Date:
28 June 2018
Please cite this article as: YiBiao Yang, YaTing Bai, XiaoDan Zhao, MingDa Zhang, HongMing Fei, ZhiHui Chen, Design of a solar-blind ultraviolet band-pass filter based on frequency domain superposition, Superlattices and Microstructures (2018), doi: 10.1016/j.spmi.2018.06.062
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Design of a solar-blind ultraviolet band-pass filter based on frequency domain superposition YiBiao Yanga,b,*, YaTing Baia, XiaoDan Zhaoa, MingDa Zhanga, HongMing Feia, ZhiHui Chena,b a Department
of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China Laboratory of Advanced Transducers and Intelligent Control System, Taiyuan University of Technology, Ministry of Education, Taiyuan 030024, China *Corresponding author: [email protected] b Key
Abstract In this paper, a band-pass filter based on photonic crystals is designed by using the principle of frequency domain superposition. The influence of the heterostructure position, period numbers and incidence angles on transmission spectrums are analyzed. The filter can achieve efficient filtering in 240-280nm solar-blind ultraviolet band, with an average transmittance of 72.2%. Simultaneously, a good band-stop appears in near ultraviolet and visible region (300-700nm) and its average transmittance is below 3.4%. It provides a choice in the application of solar-blind ultraviolet detection technology. Keywords: Photonic crystal; Band-pass filter; Transfer matrix method; Solar-blind ultraviolet detection 1. Introduction Ultraviolet between 240-280nm will be absorbed by ozone layer when sunlight passes through the atmosphere. Such light, which can’t reach the surface of the earth, is named the Solar-blind ultraviolet (SBUV) [1, 2]. SBUV is widely applied in the detection of corona [3-5], tail flame from missile [6, 7], fires [8, 9] and many other area for the influence of the sunlight can almost be ignored. SBUV technology [1012] makes the most of the characteristics of the atmosphere absorbing ultraviolet radiation so that it has a good working background of small interference and less false signals. However, the signal of ultraviolet radiation source is generally weak and the ultraviolet detector is required to have high sensitivity and low noise. Therefore, it is very important to improve the filtering performance of SBUV filter. Photonic crystals (PCs) [13-16] have drawn intense attention due to their unique electromagnetic properties and potential applications. Owing to simple structure, easy preparation, and convenient tuning mode, many studies choosing one-dimensional (1D) PCs as ultraviolet filters have been reported. Wang [17] designed a multilayer structure of metal medium to realize the pass band with 260nm being the center, and the band gap from 280nm to the near infrared band. J.D. Hoyo [18] introduced the AlF3 material in the structure to enhance the reflection of Al and realized the bandpass in Lyman-Alpha band (100-130nm). Fu [19] introduced metal Al in the structure in order to design a deep cut-off feature in the visible band. Although containing the metal medium in structure can achieve a better cut-off in the visible band, it has low transmittance in the SBUV band, which leads to unobvious improvement effect on the SBUV filter. In this paper, we devise a 1D band-pass filter based on PC. By using the principle of frequency domain superposition [20, 21], we obtained the filter structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10 and realized high transmittance in SBUV band and
ACCEPTED MANUSCRIPT forbidden band in visible light band. The influences of the PCs parameters and incident angles on transmission spectrum are theoretically analyzed. 2. Structural model and computational method Our design uses Si3N4 and SiO2 to avoid the high rate of absorption in deep ultraviolet band [22]. But the ratio of the refractive index of the two materials is low, which leads to emerge a narrow band gap in the ultraviolet band. In order to broaden the scope of the band gap, we design a PC band-pass filter of a quantum well structure, which is stacked by five PCs. The structure is shown in Fig. 1.
Fig. 1. Schematic of a SBUV band-pass filter. PCs (s=1-5) represents five PCs. N , M are the period numbers of PCs (s=2-4) and PC5, respectively. aj (j=1-5) are the lattice constant of PCs (s=1-5).
The heterostructure can be expressed as (PC1)6(PC2)N(PC3)N(PC4)N(PC5)M, which is composed of five PCs. Here, N is the period numbers of PC2-4, and M is the period number of PC5. The thickness is represented as aj (j=1-5), aj = d(Si3N4)j + d(SiO2)j, where d(Si3N4)j and d(SiO2)j are two kinds of film thicknesses of PCs (s=1-5), respectively. The specific values are shown in Table 1. θ is the incidence angle. Table 1. The thickness of Si3N4 and SiO2 PC1
PC2
PC3
PC4
PC5
d(Si3N4)/nm
40.1
48.3
56.4
66.8
77.1
d(SiO2)/nm
57.4
68
78.7
92.5
106.2
In our work, Si3N4 and SiO2 are periodically arranged as high and low refractive index materials in each PC. The refractive indices of Si3N4 and SiO2 are n1 and n2, which are relatively stable in the research band and the materials almost have no absorption in the ultraviolet band, as shown in Fig. 2. Considering the influence of dispersion and absorption of Si3N4 and SiO2 on transmission spectrum, Fig. 2 is a diagram of the relation between the dispersion and absorption coefficient of the two materials with the change of wavelength.
ACCEPTED MANUSCRIPT
Fig. 2. The refractive indices and absorption coefficients of Si3N4 and SiO2.
In the calculation, the propagation characteristics of light in one-dimensional periodic dielectric materials are studied by means of transfer matrix method. The heterostructure is arranged periodically in the direction of Y-axes, and the characteristic matrix of a single layer can be expressed as:
cos i Mi i sin i i
i sin i i cos i
, (1) Here, i k0 n j d i cos i , k 0 is the wave vector c , where ω is the frequency of the incident wave and c is the speed of light in vacuum. ni and di are the refractive index and thickness if the i-th layer. i depends on the polarization of the waves. For TE
mode, i i i cos i , while for TM mode, i i i cos i . Here is the dielectric constant and is the permeability. is the incident angle. The feature matrix of a multi-layer structure can be expressed as: P m M M P 11 i 1 m21
m12 m22
, (2) At specific wavelengths and incident angles, the transmission and reflection coefficients as well as the transmittance and reflectivity of the multilayer dielectric film can be expressed as follows:
t
r
2 f (m11 m12 h ) f (m21 m22 h )
(3)
(m11 m12 f ) f (m21 m22 h ) (m11 m12 h ) f (m21 m22 h )
R r T
,
,
(4)
2
,
h 2 t . f
(5) (6)
3. Simulation results and discussions Based on the principle of superposition in frequency domain, we stack five
ACCEPTED MANUSCRIPT periodically arranged PCs. According to the transmission spectrum, the influence of position arrangements, period numbers of PCs and incidence angles are theoretically analyzed. Photonic band gap is one of the basic properties of PCs. Here we have analyzed the band gap range of PCs with lattice constants of 97.5nm, 116.3nm, 135.1nm, 159.3nm and 183.3nm, respectively. As the lattice constant becomes larger , the forbidden band moves to the long-wave side, and the forbidden band width is gradually widened , as shown in Fig. 3. It is conceived that five PCs can be stacked to form a broad forbidden band. The structure is (PC1)6(PC2)N(PC3)N(PC4)N(PC5)M.
Fig. 3. The photonic band gap of PC1-5.
On normal incidence, when N=5 and M=6, the five PCs are arranged in accordance with the size of the lattice constant, where the film thicknesses of Si3N4 and SiO2 in each PC are shown in Table 1. In Fig. 4(a), there is a high transmission spectrum in the 240-280nm and a wide band gap in the 300-700nm. The forbidden band covers the whole near ultraviolet and visible bands, which satisfies the high acquisition rate of the 240-280nm ultraviolet signal and the signal is not interfered by the visible band for SBUV detection technology.
ACCEPTED MANUSCRIPT
Fig. 4. The transmission spectrum of PC2-4 position combination.
We fixed the PCs with the minimum and maximum lattice constants on the edge and disrupted the arrangement of other PCs. Fig. 4(b)-(f) are the transmission spectrums of the combination of three PCs positions in the middle of the heterostructure. It shows that high transmission spectrum also appears in the 240280nm band, while many sharp peaks appear in the band gap in 300-700nm. It is because such disruptions of the middle PCs are equivalent to introducing defects into the whole structure. The characteristic of photonic localization causes the impure peaks in the forbidden band. Only the heterostructure (PC1)6(PC2)5(PC3)5(PC4)5(PC5)6, which arrangement is according to the size of lattice constant, accords with the standard of deep cut-off in near ultraviolet and visible band. In Fig. 4(a), under the same periodic number of PC1 and PC5, the cutoff of the band gap at short-wave side is better than that at long-wave side. To optimize the cutoff of the band gap at long-wave side, we changed the period number of PC5. The spectrums are shown in Fig. 5. With the increase of the period number M (M=6, 8, 10), the cutoff of the forbidden band near 700nm is getting better. However, the small impure peaks in the forbidden band are not affected by the change of period number. When M=10, the whole band gap is more similar to “rectangle”, which satisfies our demand for the band gap.
ACCEPTED MANUSCRIPT
Fig. 5. The transmission spectrum of heterostructure (PC1)6(PC2)5(PC3)5(PC4)5(PC5)M (M=6,8,10).
As is mentioned above, the period number of PC1 is 6, and the period number M of PC5 is 10. In order to smooth the impure peaks in the band gap, we studied the period number N of the internal PC2, PC3 and PC4. The transmission spectrum of N=3-6 are shown in Fig. 6. When N=3, because the period numbers of the three PCs are too small, the cut-off of their own band edges are not high, which causes three small “forbidden bands” in the wide forbidden band of 300-700nm and high transmittance peak over 50% at 565nm. However, with the increase of the period number N, the small impure peaks in the band gap are gradually smoothed. When N=6, the impure peaks in the wide band gap almost disappeared. Only a defect peak with low transmittance near 400nm was found. Due to its position in the near ultraviolet band, it has little effect on the performance of the filter for the SBUV detection technology. Finally, we design the quantum well structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10, which can meet the high transmittance of 240-280nm in the SBUV band, and the average transmittance is 72.2%. Meanwhile, the average transmittance of 300-700nm in the near ultraviolet and visible bands is 3.4%.
Fig. 6. The transmission spectrum of structure (PC1)6(PC2)N(PC3)N(PC4)N(PC5)10 (N=3-6).
On oblique incidence, different polarization stats have a great influence on the
ACCEPTED MANUSCRIPT transmission spectrums. When the incidence angle θ is taken to be 0°, 15°, 30°, and 45°，the transmission spectrum is modulated by the two polarization modes of TE and TM, as shown in Fig. 7. The solid line in the graph represents the TM mode, and the dashed line represents the TE mode. For TM mode, with the increase of the angle, the transmission spectrum shows blue shift and the band gap width is reduced by 100nm. The average transmittance of the transmission spectrum in the 240-280nm solar-blind band rises from 72.2% to 77.7%. When the incident angle is greater than 30°, there will be more impure peaks in the wide band gap of 300-700nm. The average transmittance of the band gap increases from 3.4% up to 6.4%. For TE mode, with the increase of the incident angle, the transmission spectrum also shows blue shift and the band gap width shrinks by 60nm. The average transmittance in the 240280nm band dropped from 72.2% to 44.1%. In the band gap of 300-700nm, the impure peaks almost disappeared, and the average transmittance decreased from 3.4% to 1.1%. Although a better deep cut-off is achieved, the average transmittance in the solar-blind band becomes lower. Fig. 8 shows the transmission spectrum varies with the incident angle increases from 0° to 45° for both modes. Considering the detection of ultraviolet signals in the distance, the incident angle of signals is usually less than 30°, so the heterostructure meets the SBUV filtering requirement.
Fig. 7. The transmission spectrum of structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10 with incident angle variation in TE and TM mode. (a) θ=0°; (b) θ=15°; (c) θ=30°; (d) θ=45°.
Fig. 8. The transmission spectrum of structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10 at TM and TE mode when the incident angle is changing from 0°to 45°.
4. Conclusions
ACCEPTED MANUSCRIPT In this paper, we designed a PC SBUV filter using the principle of frequency domain superposition. High transmission of 240-280nm and wide band gap of 300700nm are obtained by adjusting the arrangement position of the PCs. The optimization of the period number M of outer PC5 makes the cut-off of the spectral line higher at long-wave side. The optimization of the period number N of inner PC2-4 eliminates the tiny impure peaks in the wide forbidden band, and the quantum well structure (PC1)6(PC2)6(PC3)6(PC4)6(PC5)10 is finally obtained. For both TE and TM mode, the transmission spectrums show blue shift by the modulation of the angle. We found that small incident angle (<30o) can meet the filtering performance of the filter. This band-pass filter applied to the solar-blind ultraviolet band can achieve high transmission in 240-280nm, and deep cut-off in 300-700nm. It has some significance for the development of ultraviolet filter. Acknowledgment This work was supported by National Natural Science Foundation of China (No.61575138, No.11674239); Natural Science Foundation of Shanxi province (No.201601D202013, No.2016011048). References [1] Y. Yuan, Performance of 128x128 solar-blind AlGaN ultraviolet focal plane arrays, Proceedings of SPIE - The International Society for Optical Engineering, 7381 (2009) 73810I-73810I-73819. [2] H. Cheng, Performance characteristics of solar blind UV image intensifier tube, Proceedings of SPIE - The International Society for Optical Engineering, 7384 (2009) 73840H-73840H-73847. [3] F. Yang, J. Pan, Research on dual spectrum solar-blind ultraviolet corona detection system, in: Selected Proceedings of the Photoelectronic Technology Committee Conferences Held AugustOctober, 2015, pp. 95221S. [4] L. Jian-zhuo, W. Xue-jin, H. Jian-bo, G. Bang-hui, Q. Feng, W. Jian, F. Wei, S. Qiang, Design of three-band optical system used in corona detection, Optics & Precision Engineering, 19 (2011) 12281234. [5] W. Zhou, H. Li, X. Yi, J. Tu, J. Yu, A criterion for UV detection of AC corona inception in a rodplane air gap, IEEE Transactions on Dielectrics & Electrical Insulation, 18 (2011) 232-237. [6] S. Song, L. Lin, W. Wang, Design of Solar Blind Ultraviolet Warning Optical System, Laser & Optoelectronics Progress, 50 (2013) 102203. [7] Y. Chen, Design of solar-blind UV optical system for missile approach warning, in: Optical Design and Testing VI, 2014, pp. 92721U-92721U-92727. [8] Y.Y. Wang, G.Q. Gao, J.M. Zhang, Design of ultraviolet flame detector based on C8051F120, Transducer & Microsystem Technologies, 32 (2013) 89-92. [9] Z. Liu, Design of fire detection equipment based on ultraviolet detection technology, in: Selected Papers From Conferences of the Photoelectronic Technology Committee of the Chinese Society of Astronautics, 2015, pp. 95210S. [10] B. Wang, Y. Wang, X. Zhong, N. Ruan, Research on solar-blind UV optical imaging system, Proceedings of SPIE - The International Society for Optical Engineering, 9449 (2015) 94492L94492L-94496. [11] W. Fan, S. Kang, Y. Chen, Design of a solar-blind ultraviolet detection system, Proceedings of the Spie, 141 (2016) 101411N. [12] J. Wang, Y. Chen, Optical Design of Solar Blind Ultraviolet Signal Target Simulator, Journal of Changchun University of Science & Technology, (2017). [13] X. Zhao, Y. Yang, J. Wen, Z. Chen, M. Zhang, H. Fei, Y. Hao, Tunable dual-channel filter based on the photonic crystal with air defects, Appl Opt, 56 (2017) 5463-5469. [14] S. Sahel, R. Amri, L. Bouaziz, D. Gamra, M. Lejeune, M. Benlahsen, K. Zellama, H. Bouchriha, Optical filters using Cantor quasi-periodic one dimensional photonic crystal based on Si/SiO 2, Superlattices & Microstructures, 97 (2016) 429-438. [15] S.R. Entezar, Photonic crystal wedge as a tunable multichannel filter, Superlattices & Microstructures, 82 (2015) 33-39. [16] B. Kazempour, K. Jamshidi-Ghaleh, M. Shabzendeh, Transmittance properties of tunable filter in a 1D photonic crystal doped by an anisotropic metamaterial, Superlattices & Microstructures, (2017).
ACCEPTED MANUSCRIPT [17] T. Wang, W. Xu, H. Lu, F. Ren, D. Chen, R. Zhang, Y. Zhen, Solar-blind ultraviolet band-pass filter based on metal–dielectric multilayer structures, Chinese Physics B, 23 (2014) 404-408. [18] J.D. Hoyo, M. Quijada, Enhanced aluminum reflecting and solar-blind filter coatings for the farultraviolet, in: Society of Photo-Optical Instrumentation Engineers, 2017, pp. 3. [19] X. Fu, K. Guo, S. Xiong, J. Zhang, B. Sun, H. Jiang, Development of Wide-Band Low-Noise Filter for Solar Blind Detection System, Chinese Journal of Lasers, 44 (2017) 0603002. [20] M. Barati, A. Aghajamali, Near-infrared tunable narrow filter properties in a 1D photonic crystal containing semiconductor metamaterial photonic quantum-well defect, Physica E: Low-dimensional Systems and Nanostructures, 79 (2016) 20-25. [21] H. Guan, P. Han, Y. Li, X. Zhang, W. Zhang, Analysis and optimization of a new photonic crystal filters in near ultraviolet band, Optik - International Journal for Light and Electron Optics, 123 (2012) 1874-1878. [22] J. Dai, W. Gao, B. Liu, X. Cao, T. Tao, Z. Xie, H. Zhao, D. Chen, H. Ping, R. Zhang, Design and fabrication of UV band-pass filters based on SiO 2 /Si 3 N 4 dielectric distributed bragg reflectors, Applied Surface Science, 364 (2016) 886-891.
ACCEPTED MANUSCRIPT Highlights 1. A solar-blind ultraviolet filter based on frequency domain superposition is devised. 2. The filter achieves efficient filtering (72.2%) in SBUV band. 3. There is a wide band gap in 300-700nm and the average transmittance is below 3.4%. 4. It has some significance for the development of ultraviolet filter.