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A critically coupled resonator (CCR) is a thin-film structure that can absorb nearly all of the incident electromagnetic radiation, leading to null scattering. In order to effectively achieve and control the critical coupling (CC) phenomena, we replace the polymer absorbing layer by a graphene-based multi-film structure. FDFD (finite difference frequency domain) method is used to solve the Maxwell equation, and the graphene's surface conductivity is calculated by using the Kubo formula. Our results demonstrate that the CC phenomenon is realized at the near-infrared frequency and the frequency of absorption peak can be engineered by the Fermi energy of the graphene sheets. With increasing Fermi energy the absorption peak moves to the longer wavelength side. The effective permittivity of a multi-film structure has a strong dependence on the thickness of the dielectric and the layer number of the grapheme sheets in the multi-film structure. It is found that the central frequency of the absorption peak shifts towards longer wavelength side with increasing layer number of the graphene sheets M and the thickness of dielectric d1. Moreover, we also demonstrate that the absorption efficiency is affected by the electron-phonon relaxation time and the incident angle. It is clear that the central frequency of the absorption peak has a slight shift and the absorption is changed with the relaxing time and incident angle. The results offer the theoretical basis to the design of graphene-based critical coupling devices and optical detectors.
[1] Novoselov K S, Geim A K, Morozov S V 2004 Science 306 666
[2] Bao Q L, Kian P L 2012 ACS Nano 6 3677
[3] Wu H Q 2013 Chin. Phys. B 22 098106
[4] Grigorenko A N, Polini M, Novoselov K S 2012 Nat. Photonics 6 749
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[19] Zhou L, Wei Y, Huang Z X, Wu X L 2015 Acta Phys. Sin. 64 018101 (in Chinese) [周丽, 魏源, 黄志祥, 吴先良 2015 64 018101]
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[21] Gusynin V P, Sharapov S G, Carbotte J P 2007 J. Phys. : Condens. Matter 19 026222
[22] E. H. Hwang, S. Adam, S. Das Sarma 2007 Phys. Rev. Lett. 98 186806
[23] Wang H, Huang Z X, Wu X L, Ren X G 2011 Chin. Phys. B 20 114701
[24] Lu S L, Wu X L, Ren X G, Mei Y S, Shen J, Huang Z X 2012 Acta Phys. Sin. 61 194701 (in Chinese) [鲁思龙, 吴先良, 任信钢, 梅诣偲, 沈晶, 黄志祥 2012 61 194701]
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[1] Novoselov K S, Geim A K, Morozov S V 2004 Science 306 666
[2] Bao Q L, Kian P L 2012 ACS Nano 6 3677
[3] Wu H Q 2013 Chin. Phys. B 22 098106
[4] Grigorenko A N, Polini M, Novoselov K S 2012 Nat. Photonics 6 749
[5] Liu M 2011 Nature 474 64
[6] Vakil A, Engheta N 2011 Science 332 1291
[7] Koppens F H L, Chang D E, García de Abajo F J 2011 Nano. Lett. 11 3370
[8] Thongrattanasiri S, Koppens F H L, García de Abajo F J 2012 Phys. Rev. Lett. 108 047401
[9] Ferreira A, Peres N M R, Ribeiro R M, Stauber T 2012 Phys. Rev. B 85 115438
[10] Nikitin A Y, Guinea F, Martin-Moreno L 2012 Appl. Phys. Lett. 101 151119
[11] Nefedov I S, Valaginnopoulos C A, Melnikov L A 2013 J. Opt. 15 114003
[12] Iorsh I V, Mukhin I S, Shadrivov I V, Belov P A, Kivshar Y S 2013 Phys. Rev. B 87 075416
[13] Othman M A K, Guclu C, Capolino F 2013 Opt. Express 21 7614
[14] Sreekanth K V, De Luca A, Strangi G 2013 Appl. Phys. Lett. 103 023107
[15] Zhang T, Chen L, Li X 2013 Opt. Express 21 20888
[16] Tischler J R, Bradley M S, Bulovi V 2006 Opt. Lett. 32 2045
[17] Tischler J R 2007 Org. Electron. 8 94
[18] Reddy K N, Gopal A V, Gupta S D 2013 Opt. Lett. 38 2517
[19] Zhou L, Wei Y, Huang Z X, Wu X L 2015 Acta Phys. Sin. 64 018101 (in Chinese) [周丽, 魏源, 黄志祥, 吴先良 2015 64 018101]
[20] Hanson G W 2008 J. Appl. Phys. 103 064302
[21] Gusynin V P, Sharapov S G, Carbotte J P 2007 J. Phys. : Condens. Matter 19 026222
[22] E. H. Hwang, S. Adam, S. Das Sarma 2007 Phys. Rev. Lett. 98 186806
[23] Wang H, Huang Z X, Wu X L, Ren X G 2011 Chin. Phys. B 20 114701
[24] Lu S L, Wu X L, Ren X G, Mei Y S, Shen J, Huang Z X 2012 Acta Phys. Sin. 61 194701 (in Chinese) [鲁思龙, 吴先良, 任信钢, 梅诣偲, 沈晶, 黄志祥 2012 61 194701]
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