Open Access
Add to BibSonomyAbstract
The metal film perforated with a micro-nano cone air hole (CAH) can serve as an optical device having asymmetric transmission. In this paper, we numerically investigate the metal film perforated with periodic arrays of cone air holes (PACAH) and find that the metal PACAH can also implement asymmetric optical transmission. In the short wave band of visible light, Al PACAH shows the most obvious effect of asymmetric optical transmission. And in the middle-long wave band, Ag PACAH shows the effect best. When RL (the radius of large end of hole) = 600 nm, RS (the radius of small end of hole) = 150 nm, t (the film thickness) = 1500 nm, and the substrate with a dielectric constant of 2.4 is placed on the side adjacent to the large end of hole, for Al PACAH (the CAHs arranged in a triangular array), the average forward transmittance and the average transmission ratio (the ratio of forward transmittance to backward one) in the region of 400 nm-600 nm are 28.4% and 7.6, respectively. Particularly, the forward transmittance and the transmission ratio at 448 nm are 43.0% and 12.4 respectively. And for Ag PACAH (the CAHs arranged in a square array), the average forward transmittance and the average transmission ratio in the region of 550 nm-800 nm are 25.4% and 5.7, respectively. Particularly, the forward transmittance and the transmission ratio at 611 nm are 36.5% and 8.5, respectively. This metal PACAH shows potential of application in secrecy equipment, such as a unidirectional optical transmission wall.
© 2014 Optical Society of America
1. Introduction
An optical device which implements asymmetric transmission is an important component of modern information processors. In recent decades, many researchers have made great efforts to find this kind of optical devices with good performance. They took advantages of various kinds of materials, such as nonlinear [1,2], magneto-optic [3,4], liquid crystal [5], left-handed [6], photonic crystal [7–11], and metal [12–18] materials, to generate the asymmetric optical transmission effect. Among these fantastic designs, the ones characteristics of miniature and integration have a distinct advantage for application in high-integrated information processors. For instance, the one based on asymmetric photonic crystal [7–11] and another based on a metal film with asymmetric structure [12–18] are both with micro-nano scale. However, there still exist some situations under which this optical device is expected to be larger. On this requirement, we came up with an idea that if the metal CAH [17,18] is made in a periodic array manner, an optical device implementing asymmetric transmission of larger size is possibly obtained. To avoid confusion, we set the forward direction along the axis of the cone, from the large end to the small one, and vice versa. As shown in Fig. 1, when the light is normally incident onto the CAH, for forward propagation, some of incident light will be reflected by the inclined wall of the CAH. Therefore, the forward propagation light wave at the edge of small end of CAH would involve zero order mode and some high order ones, which would excite more localized surface plasmon (LSP) modes at the edge of the small end of CAH. While for backward propagation case, there’s only the zero order mode of light wave at the edge of the small end of CAH, which will result in much weaker LSP resonance than forward propagation case. So the forward transmission is much larger than the backward one since the LSP resonance is the main contributor to the optical transmission of the metal CAH [17]. In addition, periodic arrangement of micro-nano metal structures would result in the generation of new surface plasmon (SP) resonance modes [19], so that new peaks will appear in the transmission spectrum and accompany with much evident asymmetric optical transmission. In this paper, we construct periodic arrays of metal CAHs and investigate their forward and backward transmission properties under various conditions (different periods, periodic arrangements, and substrates) and search the optimal structure for asymmetric optical transmission, via the method of numerical simulation (3D FDTD [20], meep software [21]). In calculation, the time steps were set to be 10000. And the size of mesh was determined by the automatically iterative process. The initial mesh size was set to be 15 nm and then decreased by 1 nm gradually. And after one time of degression, we made comparison between the calculated results corresponding to last two series of mesh. If the relative deviation between these two results is less than 5%, the iterative process will be terminated and the last result is that to be reported. We found that the finalized mesh size is 5 nm, which is much smaller than the skin depth of metal.
Fig. 1 A sketch of light propagating through the metal CAH, where the dark blue and light blue arrows denote forward and backward propagations, respectively.
2. Analysis and discussion
In previous work, we have studied in detail the transmission properties of the metal CAH [17,18]. The results indicate that, in the middle-long wave band of visible light, the asymmetric optical transmission effect of Ag CAH is the most obvious [18], and for single Ag CAH, when RL = 600 nm, RS = 150 nm, and t = 1500 nm, the asymmetric optical transmission effect is optimal near 605 nm [17]. So we construct the Ag PACAH by combining many of such single Ag CAH in a periodic array; and then investigate its transmission properties in the middle-long wave band. As is well known, for a metal film perforated with a hole array of period a, the transmission peak positions λmax for normal incidence can be identified approximately from the SP dispersion relation, and they are given by:
where i and j are the scattering orders of the array, εm and εd are the dielectric constants of the metal and the medium in contact with the metal, respectively [22,23]. Equations (1) and (2) indicate that, at normal incidence, as the metal and the medium are specified, the peak positions λmax corresponding to (i, j) mode are only determined by the period a. In addition, the peak positions λmax are proportional to the period a. To verify whether Eqs. (1) and (2) also apply to the Ag PACAH, we calculate the transmission spectra of the Ag PACAHs (both the square and triangular cases) with different periods. For simplification, the medium outside the metal is set to be air. In the calculation, the dielectric constants of metals are characterized by the Drude-Lorentz model [24]. And the conditions of linearly polarized incident light, uniaxial perfectly matched layer absorbing boundary and bloch periodic boundary [20,21] are used. The optical transmittance through a PACAH is defined as the ratio of the power flux integrated at Plane 2 to that integrated at Plane 1, where Plane 1 is a plane 400 nm away from the entrance of hole, and Plane 2 400 nm off the exit of hole. Figure 2 shows the calculation details for the forward propagation case. And it’s a similar situation for the backward propagation case. Figures 3(a)–3(d) show the forward and backward transmission spectra of Ag PACAHs for the square arrays, and Figs. 3(e)–3(h) for the triangular case. Among them, the period for Figs. 3(a)–3(b)/3(e)–3(f) is 1400 nm, and the period for Figs. 3(c)–3(d)/3(g)–3(h) is 1600 nm. For Figs. 3(a)/3(c)/3(e)/3(g), RL = 600 nm, RS = 150 nm, and t = 1500 nm, while for Figs. 3(b)/3(d)/3(f)/3(h), RL = 480 nm, RS = 120 nm, and t = 1200 nm. As shown in Figs. 3(a)–3(h), the variation of CAH’s structure parameters doesn’t result in the displacement of the primary extremum positions in the Ag PACAH’s transmission spectrum, provided that the periodic manner of CAH is determined (square or triangular) and the period are fixed. This is coincident with Eqs. (1) and (2): at normal incidence, the transmission peaks λmax of Ag PACAH are only determined by the period a. The red arrows in Figs. 3(a)/3(c)/3(e)/3(g) denote the transmission peaks corresponding to (i, j) mode. As is well known, Eqs. (1) and (2) do not take into account the presence of the holes and the associated scattering losses, so the wavelengths of transmission peaks calculated from Eqs. (1) and (2) are shorter than the practical ones. Just as shown in Figs. 3(a)/3(c)/3(e)/3(g), the positions pointed by red arrows have a blue-shift compared to the transmission peaks from the numerical calculation. Besides, there exist other transmission peaks different from (i, j) modes. This is because, in the derivation of Eqs. (1) and (2), the thickness of the metal film is regarded as zero, which means that the condition of normal incidence implies normal emergence of light. But practically, the light experiences multiple reflections in a CAH when it passes through the CAH. When the light reaches the exit of a CAH, its traveling direction is changed. So the condition of normal emergence is not satisfied anymore. Equations (1) and (2) can’t describe all the transmission peaks of Ag PACAH (for the square case or the triangular one) in this case, and there are other peaks relative to situations of other emergence angles. These new transmission peaks are shown in Figs. 3(a)/3(c)/3(e)/3(g), without the red arrows. Furthermore, with the same CAHs, when the period a increases, the density of CAHs becomes small, which results in the decrease of transmittance in visible range. And from Eqs. (1) and (2), the increase of period a also enlarges the wavelength of transmission peaks, λmax, corresponding to (i, j) mode, leading to the redshift of transmission spectrum. For the square array, as shown in Figs. 3(a)/3(c), when the period increases from 1400 nm to 1600 nm, the max forward transmittance of Ag PACAH goes from 46.9% to 29.7%, and the transmission peaks corresponding to (i, j) mode in visible range are all red shifted. And for the triangular array, as shown in Figs. 3(e)/3(g), when the period increases from 1400 nm to 1600 nm, the max forward transmittance drops from 54.6% to 34.3%, and the transmission peaks are all red shifted, too.Fig. 3 Transmission spectra of Ag PACAHs. (a)-(b): Square arrays with a period of 1400 nm. (c)-(d): Triangular arrays with a period of 1400 nm. (e)-(f): Square arrays with a period of 1600 nm. (g)-(h): Triangular arrays with a period of 1600 nm. For (a)/(c)/(e)/(g), RL = 600 nm, RS = 150 nm, and t = 1500 nm. While for (b)/(d)/(f)/(h), RL = 480 nm, RS = 120 nm, and t = 1200 nm. The dark blue and light blue lines denote the forward and backward transmission curves respectively (similarly hereinafter).
In above calculation, we have set the medium outside the metal as air for simplification. In practical applications, however, the metal film is generally attached to a substrate. And the substrate is usually the quartz glass, whose relative dielectric constant is in the range of 2.1-2.4. So we now consider a substrate and investigate its influence on the Ag PACAH’s transmission spectrum. According to the above discussion, for a single CAH structure with RL = 600 nm, RS = 150 nm, and t = 1500 nm, the corresponding Ag PACAH with a square period of 1400 nm shows an optimal effect of asymmetric optical transmission near 677 nm, where the forward and backward transmittances are 46.9% and 7.3% respectively. And the Ag PACAH with a triangular period of 1400 nm performs best near 666 nm, where the forward and backward transmittances are 54.4% and 7.5% respectively. On the basis of these two period structures, we set εS (the dielectric constant of the substrate) to be 2.1 and observe how the substrate affects the transmission spectrum of Ag PACAH. Figures 4(a)–4(d) show the forward and backward transmission spectra of Ag PACAHs for the square array, while Figs. 4(e)–4(h) show those for the triangular case. Here, Figs. 4(a)/4(e) are the substrate-free cases; Figs. 4(b)/4(f) are with substrate set on the side adjacent to the small end of hole; Figs. 4(c)/4(g) are with substrate set on the side adjacent to the large end of hole, and Figs. 4(d)/4(h) are the cases that the substrate is set on both sides. As seen from Figs. 4(b)/4(d)/4(f)/4(h), the forward and backward transmittances of Ag PACAHs are small if the substrate is set on the side adjacent to the small end of hole. Moreover, the positions of transmission extremums are changed dramatically, compared to those of the substrate-free cases [Figs. 4(a)/4(e)]. On the other hand, if the substrate is set on the side adjacent to the large end of hole, and the other side is air, as shown in Figs. 4(c)/4(g), the positions of some main transmission minimums remains the same, and most importantly, the forward and backward transmittances generally don’t change dramatically, compared to those of the substrate-free cases [Figs. 4(a)/4(e)]. So in practical use, it is best to set the substrate on the side adjacent to the large end of hole. In this way, the forward transmission peaks of Ag PACAH have still relatively large values, which lead to a better implementation of asymmetric optical transmission.
Fig. 4 Transmission spectra of Ag PACAHs with a period of 1400 nm. RL = 600 nm, RS = 150 nm, t = 1500 nm, and εS = 2.1. (a)-(d) are the square arrays, while (e)-(h) are the triangular cases. (a)/(e): Air on both sides. (b)/(f): Substrate on the side adjacent to the small end of hole, and air on the other side. (c)/(g): Substrate on the side adjacent to the large end of hole, and air on the other side. (d)/(h): Substrate on both sides.
We further study the influence of the substrate’s dielectric constant on the transmission spectrum of Ag PACAH. The two period structures mentioned in the last paragraph are still taken for examples, with a period of 1400 nm. We set the substrate on the side adjacent to the large end of hole and inspect how the change of εS affects the transmission spectrum of Ag PACAH. Figures 5(a)–5(d) show the transmission spectra of Ag PACAHs for the square array, where εS = 2.1, 2.2, 2.3, and 2.4, respectively. And Figs. 5(e)–5(h) are the corresponding triangular cases. As illustrated in Fig. 5, since the substrate is set on the side adjacent to the large end of hole, the variation of εS doesn’t change the positions of some main transmission minimums but make some influence on the forward transmission peaks, whether for the square arrays or the triangular ones. Therefore, with the whole period structure determined, we still can fine tune the transmission spectrum of Ag PACAH by adjusting εS, to optimize the effect of asymmetric optical transmission.
Fig. 5 Transmission spectra of Ag PACAHs with a period of 1400 nm. RL = 600 nm, RS = 150 nm, and t = 1500 nm. And the substrate is set on the side adjacent to the large end of hole. (a)-(d): Square arrays with εS = 2.1, 2.2, 2.3, and 2.4, respectively. (e)-(h): Triangular arrays with εS = 2.1, 2.2, 2.3, and 2.4, respectively.
It is found that in the short wave band of visible light, Al CAH shows the most obvious effect of asymmetric optical transmission [18]. So we also investigate the asymmetric optical transmission of Al PACAH. Figures 6(a)–6(h) show the forward and backward transmission spectra of Al PACAHs, whose structure parameters are set to be the same as those corresponding to Figs. 5(a)–5(h). According to the discussion above, with the structure parameters of single CAH and the period determined, we can also optimize the effect of asymmetric optical transmission of Al PACAH by changing the arrangement of CAHs and εS. As shown in Fig. 6(a), the Al PACAH for the square array performs an optimal effect of asymmetric optical transmission at 407 nm, where the forward and backward transmittances are 36.9% and 3.4%, respectively. By changing the period arrangement from the square array to the triangular one, the optimized effect of asymmetric optical transmission is moved to 552 nm, where the forward and backward transmittances are 42.3% and 4.9% respectively, as illustrated in Fig. 6(e). And by varying εS from 2.1 to 2.4, the optimized effect of asymmetric optical transmission is moved to 448 nm, where the forward and backward transmittances are 43.0% and 3.5% respectively, as shown in Fig. 6(h). One sees that the Al PACAH is suitable for the use of short wave band in visible region.
Fig. 6 Transmission spectra of Al PACAHs with a period of 1400 nm. RL = 600 nm, RS = 150 nm, and t = 1500 nm. And the substrate is set on the side adjacent to the large end of hole. (a)-(d): Square arrays with εS = 2.1, 2.2, 2.3, and 2.4, respectively. (e)-(h): Triangular arrays with εS = 2.1, 2.2, 2.3, and 2.4, respectively.
3. Conclusion
In conclusion, the metal PACAH can also implement asymmetric optical transmission. With the single CAH structure determined, we can still optimize the effect of asymmetric optical transmission at a specific wavelength in visible region, via changing the metal, the period, the periodic manner of CAHs and the substrate’s dielectric constant. This kind of metal PACAH can serve as a unidirectional optical transmission wall, with stable performance, being expected to be a great potential for applications.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grants No. 11274401 and No. U0934002), the National Basic Research Program of China (Grant No. 2010CB923200), the Ministry of Education of China (Grant No. V200801), the Guangdong Province Key Laboratory of Computational Science, and the Guangdong Province Computational Science Innovative Research Team.
References and links
1. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Appl. Phys. Lett. 79(3), 314 (2001). [CrossRef]
2. W. L. She, Q. X. Li, Z. X. Yu, Z. L. Gao, Q. L. Zhang, and H. C. Chen, “Optical diode effect induced by two laser beams in a Mn-doped KNSBN crystal,” Chin. Phys. 12(4), 820 (1992).
3. M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J.-M. Lourtioz, “Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals,” Phys. Rev. B 80(12), 121102 (2009). [CrossRef]
4. Z. F. Yu, G. Veronis, Z. Wang, and S. H. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett. 100(2), 023902 (2008). [CrossRef] [PubMed]
5. A. E. Miroshnichenko, I. Pinkevych, and Y. S. Kivshar, “Tunable all-optical switching in periodic structures with liquid-crystal defects,” Opt. Express 14(7), 2839–2844 (2006). [CrossRef] [PubMed]
6. M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(3), 037602 (2005). [CrossRef] [PubMed]
7. S. O. Konorov, D. A. Sidorov-Biryukov, I. Bugar, M. J. Bloemer, V. I. Beloglazov, N. B. Skibina, D. Chorvat Jr, D. Chorvat, A. Scalora, and A. M. Zheltikov, “Experimental demonstration of a photonic-crystal-fiber optical diode,” Appl. Phys. B 78(5), 547–550 (2004). [CrossRef]
8. F. Biancalana, “All-optical diode action with quasiperiodic photonic crystals,” J. Appl. Phys. 104(9), 093113 (2008). [CrossRef]
9. C. C. Lu, X. Y. Hu, Y. B. Zhang, Z. Q. Li, X. A. Xu, H. Yang, and Q. H. Gong, “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011). [CrossRef]
10. C. C. Lu, X. Y. Hu, H. Yang, and Q. H. Gong, “Ultrahigh-contrast and wideband nanoscale photonic crystal all-optical diode,” Opt. Lett. 36(23), 4668–4670 (2011). [CrossRef] [PubMed]
11. C. Wang, C. Z. Zhou, and Z. Y. Li, “On-chip optical diode based on silicon photonic crystal heterojunctions,” Opt. Express 19(27), 26948–26955 (2011). [CrossRef] [PubMed]
12. S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “One-way transmission through the subwavelength slit in nonsymmetric metallic gratings,” Opt. Lett. 35(15), 2597–2599 (2010). [CrossRef] [PubMed]
13. S. Cakmakyapan, H. Caglayan, A. E. Serebryannikov, and E. Ozbay, “Experimental validation of strong directional selectivity in nonsymmetric metallic gratings with a subwavelength slit,” Appl. Phys. Lett. 98(5), 051103 (2011). [CrossRef]
14. J. Xu, C. Cheng, M. Kang, J. Chen, Z. Zheng, Y. X. Fan, and H. T. Wang, “Unidirectional optical transmission in dual-metal gratings in the absence of anisotropic and nonlinear materials,” Opt. Lett. 36(10), 1905–1907 (2011). [CrossRef] [PubMed]
15. M. Stolarek, D. Yavorskiy, R. Kotyński, C. J. Zapata Rodríguez, J. Łusakowski, and T. Szoplik, “Asymmetric transmission of terahertz radiation through a double grating,” Opt. Lett. 38(6), 839–841 (2013). [CrossRef] [PubMed]
16. H. Gao, Z. Y. Zheng, H. Y. Hao, A. G. Dong, Z. J. Fan, and D. H. Liu, “Mechanism of optical unidirectional transmission in subwavelength dual-metal gratings,” Appl. Phys. B 114(3), 401–406 (2014). [CrossRef]
17. N. Peng, X. K. Li, and W. L. She, “Nonreciprocal optical transmission through a single conical air hole in an Ag film,” Opt. Express 22(14), 17546–17552 (2014). [CrossRef] [PubMed]
18. N. Peng and W. L. She, “Near-ultraviolet to green and near-infrared asymmetric optical transmission of a single conical air hole in a metal film,” to be submitted.
19. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
20. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domian Method (Artech House, 2000).
21. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010). [CrossRef]
22. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]
23. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
24. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]
