Abstract

Artificial control of the thermal radiation is of growing importance to fundamental science and technological applications, ranging from waste heat recovery to thermophotovoltaics. Nanophotonics has been proven to be an efficient approach to manipulate the radiation. In comparison with structures utilizing planar subwavelength scale lithography, in this paper, we propose a cascaded all-dielectric multilayer structure to selectively manipulate the thermal radiation characteristics in long-wavelength infrared (LWIR). The broadband emissivity in non-atmospheric windows (6.3-7.5 µm) can reach 0.95 and the average absorption rate is below 3% in atmospheric windows (8-14 µm). The multilayer structure is insensitive to the polarization of the incident waves and maintains a good rectangular absorptivity curve even with large oblique incidence angle at 45 degrees. The outstanding properties of the nanostructures promise various applications in infrared sensing and thermal imaging.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (6)

X. Zhao, C. Chen, A. Li, G. Duan, and X. Zhang, “Implementing infrared metamaterial perfect absorbers using dispersive dielectric spacers,” Opt. Express 27(2), 1727–1739 (2019).
[Crossref]

A. Li, X. Zhao, G. Duan, S. Anderson, and X. Zhang, “Diatom Frustule-Inspired Metamaterial Absorbers: The Effect of Hierarchical Pattern Arrays,” Adv. Funct. Mater. 29(22), 1809029 (2019).
[Crossref]

X. Zhao, Y. Wang, J. Schalch, G. Duan, K. Cremin, J. Zhang, C. Chen, R. D. Averitt, and X. Zhang, “Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers,” ACS Photonics 6(4), 830–837 (2019).
[Crossref]

D. Dong, Y. Liu, Y. Fei, Y. Fan, J. Li, Y. Feng, and Y. Fu, “Designing a nearly perfect infrared absorber in monolayer black phosphorus,” Appl. Opt. 58(14), 3862–3869 (2019).
[Crossref]

J. Silva, H. Kala, D. K. Triphathi, and K. K. M. B. D. Silva, “Large Area Silicon-Air-Silicon DBRs for Infrared Filter Applications,” J. Lightwave Technol. 37(3), 769–779 (2019).
[Crossref]

R. Sarzala, L. Piskorski, T. Czyszanowski, and M. Dems, “Influence of Various Bottom DBR Designs on the Thermal Properties of Blue Semiconductor-Metal Subwavelength-Grating VCSELs,” Materials 12(19), 3235 (2019).
[Crossref]

2018 (7)

A. Cardin, K. Fan, and W. Padilla, “Role of loss in all-dielectric metasurfaces,” Opt. Express 26(13), 17669–17679 (2018).
[Crossref]

L. Zhao, H. Liu, Z. He, and S. Dong, “All-metal frequency-selective absorber/emitter for laser stealth and infrared stealth,” Appl. Opt. 57(8), 1757–1764 (2018).
[Crossref]

L. Peng, D. Q. Liu, H. F. Cheng, S. Zhou, and M. Zu, “A Multilayer Film Based Selective Thermal Emitter for Infrared Stealth Technology,” Adv. Opt. Mater. 6(23), 1801006 (2018).
[Crossref]

X. Wang, Y. Liang, L. Wu, J. Guo, X. Dai, and Y. Xiang, “Multi-channel perfect absorber based on a one-dimensional topological photonic crystal heterostructure with graphene,” Opt. Lett. 43(17), 4256–4259 (2018).
[Crossref]

Y. Huang, M. Pu, Z. Zhao, X. Li, X. Ma, and X. Luo, “Broadband metamaterial as an “invisible” radiative cooling coat,” Opt. Commun. 407, 204–207 (2018).
[Crossref]

Y. Li, X. Bai, T. Yang, H. Luo, and C. W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9(1), 273 (2018).
[Crossref]

R. Hu, S. Zhou, Y. Li, D. Y. Lei, X. Luo, and C. W. Qiu, “Illusion Thermotics,” Adv. Mater. 30(22), 1707237 (2018).
[Crossref]

2017 (6)

K. Q. Le, Q. M. Ngo, and T. K. Nguyen, “Nanostructured Metal–Insulator–Metal Metamaterials for Refractive Index Biosensing Applications: Design, Fabrication, and Characterization,” IEEE J. Sel. Top. Quantum Electron. 23(2), 388–393 (2017).
[Crossref]

K. Q. Le, J. Bai, Q. M. Ngo, and P.-Y. Chen, “Fabrication and Numerical Characterization of Infrared Metamaterial Absorbers for Refractometric Biosensors,” J. Electron. Mater. 46(1), 668–676 (2017).
[Crossref]

H. Yu, Z. Zhao, Q. Qian, J. Xu, P. Gou, Y. Zou, J. Cao, L. Yang, J. Qian, and Z. An, “Metamaterial perfect absorbers with solid and inverse periodic cross structures for optoelectronic applications,” Opt. Express 25(7), 8288–8295 (2017).
[Crossref]

L. Cai, A. Y. Song, P. Wu, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref]

C. Lili, A. Y. Song, W. Peilin, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

2016 (1)

2015 (2)

L. Zhu, A. P. Raman, and S. Fan, “Radiative cooling of solar absorbers using a visibly transparent photonic crystal thermal blackbody,” Proc. Natl. Acad. Sci. U. S. A. 112(40), 12282–12287 (2015).
[Crossref]

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. L. Thong, and C. Qiu, “Invisible Sensors: Simultaneous Sensing and Camouflaging in Multiphysical Fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref]

2014 (2)

T. Han, X. Bai, J. T. Thong, B. Li, and C. W. Qiu, “Full control and manipulation of heat signatures: cloaking, camouflage and thermal metamaterials,” Adv. Mater. 26(11), 1731–1734 (2014).
[Crossref]

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref]

2013 (2)

2012 (1)

J. Fan, X. Liu, J. K. Furdyna, and Y. H. Zhang, “ZnTe/GaSb distributed Bragg reflectors grown on GaSb for mid-wave infrared optoelectronic applications,” Appl. Phys. Lett. 101(12), 121909 (2012).
[Crossref]

2010 (2)

X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010).
[Crossref]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

2005 (1)

G. F. H. Hogstrom and C. G. Ribbing, “Realization of selective low emittance in both thermal atmospheric windows,” Opt. Eng. 44(2), 026001 (2005).
[Crossref]

1978 (1)

J. J. Moré, “The Levenberg-Marquardt algorithm: implementation and theory,” Lect. Notes Math. 630, 105–116 (1978).
[Crossref]

An, Z.

Anderson, S.

A. Li, X. Zhao, G. Duan, S. Anderson, and X. Zhang, “Diatom Frustule-Inspired Metamaterial Absorbers: The Effect of Hierarchical Pattern Arrays,” Adv. Funct. Mater. 29(22), 1809029 (2019).
[Crossref]

Anoma, M. A.

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref]

Averitt, R. D.

X. Zhao, Y. Wang, J. Schalch, G. Duan, K. Cremin, J. Zhang, C. Chen, R. D. Averitt, and X. Zhang, “Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers,” ACS Photonics 6(4), 830–837 (2019).
[Crossref]

Bai, J.

K. Q. Le, J. Bai, Q. M. Ngo, and P.-Y. Chen, “Fabrication and Numerical Characterization of Infrared Metamaterial Absorbers for Refractometric Biosensors,” J. Electron. Mater. 46(1), 668–676 (2017).
[Crossref]

Bai, X.

Y. Li, X. Bai, T. Yang, H. Luo, and C. W. Qiu, “Structured thermal surface for radiative camouflage,” Nat. Commun. 9(1), 273 (2018).
[Crossref]

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. L. Thong, and C. Qiu, “Invisible Sensors: Simultaneous Sensing and Camouflaging in Multiphysical Fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref]

T. Han, X. Bai, J. T. Thong, B. Li, and C. W. Qiu, “Full control and manipulation of heat signatures: cloaking, camouflage and thermal metamaterials,” Adv. Mater. 26(11), 1731–1734 (2014).
[Crossref]

Cai, L.

L. Cai, A. Y. Song, P. Wu, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

Cao, J.

Cardin, A.

Catrysse, P. B.

C. Lili, A. Y. Song, W. Peilin, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

L. Cai, A. Y. Song, P. Wu, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

Chen, B. R.

Chen, C.

X. Zhao, C. Chen, A. Li, G. Duan, and X. Zhang, “Implementing infrared metamaterial perfect absorbers using dispersive dielectric spacers,” Opt. Express 27(2), 1727–1739 (2019).
[Crossref]

X. Zhao, Y. Wang, J. Schalch, G. Duan, K. Cremin, J. Zhang, C. Chen, R. D. Averitt, and X. Zhang, “Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers,” ACS Photonics 6(4), 830–837 (2019).
[Crossref]

Chen, J.

C. Lili, A. Y. Song, W. Peilin, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

L. Cai, A. Y. Song, P. Wu, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

Chen, P.-Y.

K. Q. Le, J. Bai, Q. M. Ngo, and P.-Y. Chen, “Fabrication and Numerical Characterization of Infrared Metamaterial Absorbers for Refractometric Biosensors,” J. Electron. Mater. 46(1), 668–676 (2017).
[Crossref]

Chen, Y.

Cheng, H. F.

L. Peng, D. Q. Liu, H. F. Cheng, S. Zhou, and M. Zu, “A Multilayer Film Based Selective Thermal Emitter for Infrared Stealth Technology,” Adv. Opt. Mater. 6(23), 1801006 (2018).
[Crossref]

Cremin, K.

X. Zhao, Y. Wang, J. Schalch, G. Duan, K. Cremin, J. Zhang, C. Chen, R. D. Averitt, and X. Zhang, “Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers,” ACS Photonics 6(4), 830–837 (2019).
[Crossref]

Cui, Y.

C. Lili, A. Y. Song, W. Peilin, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

L. Cai, A. Y. Song, P. Wu, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

Czyszanowski, T.

R. Sarzala, L. Piskorski, T. Czyszanowski, and M. Dems, “Influence of Various Bottom DBR Designs on the Thermal Properties of Blue Semiconductor-Metal Subwavelength-Grating VCSELs,” Materials 12(19), 3235 (2019).
[Crossref]

D’Orazio, A.

Dai, J.

Dai, X.

David, S. N.

Y. Zhai, Y. Ma, S. N. David, D. Zhao, R. Lou, G. Tan, R. Yang, and X. Yin, “Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling,” Science 355(6329), 1062–1066 (2017).
[Crossref]

de Ceglia, D.

Dems, M.

R. Sarzala, L. Piskorski, T. Czyszanowski, and M. Dems, “Influence of Various Bottom DBR Designs on the Thermal Properties of Blue Semiconductor-Metal Subwavelength-Grating VCSELs,” Materials 12(19), 3235 (2019).
[Crossref]

Dong, D.

Dong, S.

Duan, G.

X. Zhao, C. Chen, A. Li, G. Duan, and X. Zhang, “Implementing infrared metamaterial perfect absorbers using dispersive dielectric spacers,” Opt. Express 27(2), 1727–1739 (2019).
[Crossref]

X. Zhao, Y. Wang, J. Schalch, G. Duan, K. Cremin, J. Zhang, C. Chen, R. D. Averitt, and X. Zhang, “Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers,” ACS Photonics 6(4), 830–837 (2019).
[Crossref]

A. Li, X. Zhao, G. Duan, S. Anderson, and X. Zhang, “Diatom Frustule-Inspired Metamaterial Absorbers: The Effect of Hierarchical Pattern Arrays,” Adv. Funct. Mater. 29(22), 1809029 (2019).
[Crossref]

Fan, J.

J. Fan, X. Liu, J. K. Furdyna, and Y. H. Zhang, “ZnTe/GaSb distributed Bragg reflectors grown on GaSb for mid-wave infrared optoelectronic applications,” Appl. Phys. Lett. 101(12), 121909 (2012).
[Crossref]

Fan, K.

Fan, S.

C. Lili, A. Y. Song, W. Peilin, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

L. Cai, A. Y. Song, P. Wu, P. C. Hsu, Y. Peng, J. Chen, C. Liu, P. B. Catrysse, Y. Liu, A. Yang, C. Zhou, C. Zhou, S. Fan, and Y. Cui, “Warming up human body by nanoporous metallized polyethylene textile,” Nat. Commun. 8(1), 496 (2017).
[Crossref]

L. Zhu, A. P. Raman, and S. Fan, “Radiative cooling of solar absorbers using a visibly transparent photonic crystal thermal blackbody,” Proc. Natl. Acad. Sci. U. S. A. 112(40), 12282–12287 (2015).
[Crossref]

A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli, and S. Fan, “Passive radiative cooling below ambient air temperature under direct sunlight,” Nature 515(7528), 540–544 (2014).
[Crossref]

Fan, Y.

Fei, Y.

Feng, Y.

Fu, S. M.

Fu, Y.

Furdyna, J. K.

J. Fan, X. Liu, J. K. Furdyna, and Y. H. Zhang, “ZnTe/GaSb distributed Bragg reflectors grown on GaSb for mid-wave infrared optoelectronic applications,” Appl. Phys. Lett. 101(12), 121909 (2012).
[Crossref]

Gao, D.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. L. Thong, and C. Qiu, “Invisible Sensors: Simultaneous Sensing and Camouflaging in Multiphysical Fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref]

Giessen, H.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

Gou, P.

Grande, M.

Guo, J.

Han, T.

T. Han, X. Bai, J. T. Thong, B. Li, and C. W. Qiu, “Full control and manipulation of heat signatures: cloaking, camouflage and thermal metamaterials,” Adv. Mater. 26(11), 1731–1734 (2014).
[Crossref]

He, Z.

Hentschel, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010).
[Crossref]

Hogstrom, G. F. H.

G. F. H. Hogstrom and C. G. Ribbing, “Realization of selective low emittance in both thermal atmospheric windows,” Opt. Eng. 44(2), 026001 (2005).
[Crossref]

Hsu, P. C.

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A. Li, X. Zhao, G. Duan, S. Anderson, and X. Zhang, “Diatom Frustule-Inspired Metamaterial Absorbers: The Effect of Hierarchical Pattern Arrays,” Adv. Funct. Mater. 29(22), 1809029 (2019).
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R. Hu, S. Zhou, Y. Li, D. Y. Lei, X. Luo, and C. W. Qiu, “Illusion Thermotics,” Adv. Mater. 30(22), 1707237 (2018).
[Crossref]

L. Peng, D. Q. Liu, H. F. Cheng, S. Zhou, and M. Zu, “A Multilayer Film Based Selective Thermal Emitter for Infrared Stealth Technology,” Adv. Opt. Mater. 6(23), 1801006 (2018).
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L. Zhu, A. P. Raman, and S. Fan, “Radiative cooling of solar absorbers using a visibly transparent photonic crystal thermal blackbody,” Proc. Natl. Acad. Sci. U. S. A. 112(40), 12282–12287 (2015).
[Crossref]

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Zu, M.

L. Peng, D. Q. Liu, H. F. Cheng, S. Zhou, and M. Zu, “A Multilayer Film Based Selective Thermal Emitter for Infrared Stealth Technology,” Adv. Opt. Mater. 6(23), 1801006 (2018).
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ACS Photonics (1)

X. Zhao, Y. Wang, J. Schalch, G. Duan, K. Cremin, J. Zhang, C. Chen, R. D. Averitt, and X. Zhang, “Optically Modulated Ultra-Broadband All-Silicon Metamaterial Terahertz Absorbers,” ACS Photonics 6(4), 830–837 (2019).
[Crossref]

Adv. Funct. Mater. (1)

A. Li, X. Zhao, G. Duan, S. Anderson, and X. Zhang, “Diatom Frustule-Inspired Metamaterial Absorbers: The Effect of Hierarchical Pattern Arrays,” Adv. Funct. Mater. 29(22), 1809029 (2019).
[Crossref]

Adv. Mater. (3)

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. L. Thong, and C. Qiu, “Invisible Sensors: Simultaneous Sensing and Camouflaging in Multiphysical Fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref]

T. Han, X. Bai, J. T. Thong, B. Li, and C. W. Qiu, “Full control and manipulation of heat signatures: cloaking, camouflage and thermal metamaterials,” Adv. Mater. 26(11), 1731–1734 (2014).
[Crossref]

R. Hu, S. Zhou, Y. Li, D. Y. Lei, X. Luo, and C. W. Qiu, “Illusion Thermotics,” Adv. Mater. 30(22), 1707237 (2018).
[Crossref]

Adv. Opt. Mater. (1)

L. Peng, D. Q. Liu, H. F. Cheng, S. Zhou, and M. Zu, “A Multilayer Film Based Selective Thermal Emitter for Infrared Stealth Technology,” Adv. Opt. Mater. 6(23), 1801006 (2018).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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Figures (4)

Fig. 1.
Fig. 1. Schematic of frequency-selective absorber. (a) Selective transmission part which consists of alternately placed Ge and ZnSe has high transmission in 5-8 µm and high reflectance in 8-14 µm. (b) Absorption part constructed of PbS and ZnSe layers that can absorb most of electromagnetic waves in 5-14 µm. (c) Frequency-selective absorber is optimized by the combination of two parts. (d) Diagram of a multilayer dielectric film with plane wave excitation. dj and nj represents the thickness and index of each layer, respectively. ${\theta _0}$ is the incident angle and ${\theta _{k + 1}}$ is the angle of emergence (e) Real(n) and imaginary(k) part of refractive index of PbS in LWIR. PbS owns high index around 4 in LWIR and exhibits loss among 6-10µm and 12-14 µm.
Fig. 2.
Fig. 2. (a) Simulated and calculated transmission (T), reflection (R) and absorption (A) spectra of Struct. 1 versus normal incidence with x-polarization. The normalized electric field profile distributions of Struct. 1 at (b) 5µm, (c) 7µm and (d) 9µm. The structure is marked with red line.
Fig. 3.
Fig. 3. (a) Simulated and calculated transmission (T), reflection (R) and absorption (A) spectra of Struct. 2 versus normal incidence of x-polarization waves. The normalized electric field profile distributions of the Struct. 2 at wavelengths (b) 5µm, (c) 7µm, (d) 9µm and (e)11µm. The structure is marked with red line. For wavelength of 5µm, 7µm and 9µm, the intensity of transmitted electric field is very weak because of the strong reflection in 5µm and 9µm, and high absorption in 7µm. At wavelength of 11µm, most of the electromagnetic waves are transmitted through the structure.
Fig. 4.
Fig. 4. Diagram of oblique incidence with electric field of (a) x-polarization and (d) y-polarization. Simulated absorption spectra versus incident angle for x polarization of (b) Struct. 1 and (c) Struct. 2. Simulated absorption spectra versus incident angle for y-polarization of (e) Struct. 1 and (f) Struct. 2. The two structures, for both polarizations, maintain a good rectangular absorptivity curve even with large oblique incidence angle at 45 degrees.

Tables (1)

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Table 1. The material and thickness of each layer in the all-dielectric multilayer structures.

Equations (6)

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[ B C ] = { j = 1 K [ cos δ j i η j sin δ j i η j sin δ j cos δ j ] } [ 1 η K + 1 ]
δ j = 2 π λ n j d j cos θ j
η j = { n j / cos θ j ( p p o l a r i z a t i o n ) n j cos θ j ( s p o l a r i z a t i o n )
R = ( η 0 B C η 0 B + C ) ( η 0 B C η 0 B + C )
T = 4 η 0 η K + 1 ( η 0 B + C ) ( ( η 0 B + C ) )
M 2 = i = 1 n ( A i A i ¯ Δ A i ) 2

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