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Recently, quantum computing and information processing based on photons has become one research frontier, attracting significant attentions. The optical asymmetric transmission devices (OATD), having similar function to the diode in electric circuitry, will find important applications. In particular, the OATDs based on nanophotonic structures are preferred due to their potential applications in the on-chip integration with other photonic devices. Therefore, there have been numerous applications of OATDs based on different nanostructures, including composite grating structures, metasurfaces, surface plasmon polaritons, metamaterials, photonic crystals (PhCs). However, in general, those designs show relatively low forward transmittance (< 0.5) and narrow working bandwidth (< 100 nm), and they are able to work with only one polarization state. This makes the current OATDs unsuitable for many applications. To solve this challenge, here we design a two-dimensional (2D) PhC heterostructure based on the self-collimating effect and bandgap properties. The PhC heterostructure is composed of two square lattice 2D PhCs (PhC 1 and PhC 2) on a silicon substrate with different lattice shapes and lattice constants. The PhC 1 is composed of periodically arranged silicon cylinders in air. Meanwhile, the PhC 2 is an square air hole array embedding in silicon. The two PhCs are integrated with an inclined interface with an angle of 45° with respect to the direction of incident light. The plane wave expansion method is used to calculate the band diagrams and equal frequency contours (EFCs) of the two PhCs. As the propagation directions of light waves in PhCs are determined by the gradient direction of the EFCs, we are able to control the light propagation by controlling the EFCs of PhCs. By engineering the EFCs, the PhC 2 shows strong self-collimation effect in a broad wavelength range with a central wavelength of 1550 nm for both TE and TM polarization. By self-collimating the forward incident light from different incident angles to couple to the output waveguide, we are able to significantly increase the forward transmittance to > 0.5 for both TE and TM polarized light. Meanwhile, the backward transmittance can be effectively cut off by the unique dispersion properties of the PhC heterostructures. In this way, the heterostructure is able to achieve polarization independent asymmetric transmission of light waves in a broad wavelength range. To visualize the light propagation in the PhC heterostructure, we use the finite-difference-time-domain method to calculate the electric intensity distributions of the forward and backward propagation light of both TE and TM polarization at a wavelength of 1550 nm. Strong self-collimation effect of forward propagation light and the nearly complete blockage of backward propagation light can be identified unambiguously in the intensity plots, confirming the theoretical analysis. The calculation of transmittance and contrast ratio spectra show that the asymmetric transmission wavelength bandwidth can reach 532 nm with the forward transmittance and contrast ratio being 0.693 and 0.946 at an optical communication wavelength of 1550 nm for TE polarized light. On the other hand, for the TM polarized light, the asymmetric transmission wavelength bandwidth is 128 nm, the forward transmittance and contrast ratio are 0.513 and 0.972, respectively, at 1550 nm wavelength. Thus, it is confirmed that the PhC heterostructure achieves highly efficient, broadband and polarization independent asymmetric transmission. Finally, to further improve the forward transmittance of the TE polarized light, we modulate the radius of the front row of photonic lattice of PhC 1 at the interface. It shows that the forward transmittance can be further improved to a record high value of 0.832 with a bandwidth of 562 nm for TE polarized light. Our design opens up new possibilities for designing OATDs based on PhCs, and will find broad applications, for the design can be realized by current nanofabrication techniques.
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Keywords:
- self-collimation /
- photonic bandgap /
- heterostructure /
- asymmetric transmission
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图 1 硅基光子晶体异质结构示意图
Figure 1. Schematic of photonic crystal heterostructure based on silicon.
图 2 (a) PhC 1能带图; (b) PhC 2能带图, 插图为PhC 2在Γ—X方向的能带; (c) PhC 1在TE偏振模式第一条能带EFC; (d) PhC 2在TE偏振光下第四条能带EFC (蓝线表示TE偏振光1550 nm处的频带); (e) PhC 1在TM偏振光第一条能带EFC; (f) PhC 2在TM偏振光第三条能带EFC (红线表示TM模式1550 nm处的频带)
Figure 2. (a) Photonic band diagrams of PhC 1; (b) the photonic band diagrams of PhC 2, where the insert shows the energy band of PhC 2 in Γ－X direction; (c) the first band EFC of PhC 1 under TE polarized light; (d) the fourth band EFC of PhC 2 under TE polarized light (blue lines represent TE mode at the wavelength of 1550 nm); (e) the first band EFC of PhC 1 under TM polarized light; (f) the third band EFC of PhC 2 under TM polarized light (red lines represent TM mode at 1550 nm).
图 3 1550 nm波长处正向入射场强图和反向入射场强图 (a) TE偏振光正向; (b) TE偏振光反向; (c) TM偏振光正向; (d) TM偏振光反向
Figure 3. Electric field intensity distribution of forward transmission and backward transmission at the wavelength of 1550 nm: (a) Forward transmission of TE polarized light; (b) backward transmission of TE polarized light; (c) forward transmission of TM polarized light; (d) backward transmission of TM polarized light.
图 4 异质结构透射谱 (a) TE偏振光; (b) TM偏振光; 其中灰色区域表示结构工作带宽
Figure 4. Transmittance spectra of heterostructure: (a) TE polarized light, (b) TM polarized light. The grey region represents the asymmetric transmission working wavelength range, where forward transmission is higher than 0.5.
图 5 光子晶体异质结优化示意图, 其中被优化的光子晶体结构通过红色长方形标注
Figure 5. Schematic of optimization of photonic crystal heterostructure, where the row of photonic lattice is highlighted by the red square is optimized.
图 6 异质结构界面处PhC 1不同半径硅圆柱TE偏振光透射谱 (a) R = 55 nm; (b) R = 65 nm; (c) R = 70 nm; (d) R = 75 nm
Figure 6. Transmittance spectra of the TE polarized light with different radii of PhC 1 photonic lattice at heterostructure interface: (a) R = 55 nm; (b) R = 65 nm; (c) R = 70 nm; (d) R = 75 nm.
表 1 异质界面处PhC 1硅圆柱不同半径的非对称传输性能
Table 1. Asymmetric transmission performance with different radii of PhC 1 at heterostructure interface.
R/nm 1550 nm正向
透射率透射对比度 非对称传输
带宽/nm55 0.579 0.941 448 60 0.693 0.946 532 65 0.789 0.947 556 70 0.832 0.944 562 75 0.803 0.942 568 
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[1] Espinola R L, Izuhara T, Tsai M C, Osgoode R M 2004 Opt. Lett. 29 941
Google Scholar
[2] Zhou X, Wang Y, Leykam D, Chong Y D 2017 New J. Phys. 19 095002
Google Scholar
[3] Fan L, Wang J, Varghese L T, Shen H, Niu B, Xuan Y, Weiner A M, Qi M 2012 Science 335 447
Google Scholar
[4] Kuzmiak V, Maradudin A A 2015 Phys. Rev. A 92 013615
Google Scholar
[5] Stolarek M, Yavorskiy D, Kotyński R, Zapata R, Carlos J, Łusakowski J, Szoplik T 2013 Opt. Lett. 38 839
Google Scholar
[6] Xiao Z Y, Zou H L, Xu K K, Tang J Y 2018 J. Magn. Magn. Mater. 449 278
Google Scholar
[7] Ozer A, Kocer H, Kurt H 2018 J. Opt. Soc. Am. B 35 2111
Google Scholar
[8] Zhang L, Mei S, Huang K, Qiu C W 2016 Adv. Opt. Mater. 4 818
Google Scholar
[9] Ling Y H, Lirong H, Wei H, Tongjun L, Yali S, Jing L, Gang Y 2017 Opt. Express 25 13648
Google Scholar
[10] Peng Y X, Wang K J, He M D, Luo J H, Zhang X M, Li J B, Tan S H, Liu J Q, Hu W D, Chen X S 2018 Opt. Commun. 412 1
Google Scholar
[11] Li X F, Rui F, Ding W 2018 J. Phys. D: Appl. Phys. 51 145304
Google Scholar
[12] Bai Y, Chen Y, Zhang Y, Wang Y, Aba T, Li H, Wang L, Zhang Z 2018 J. Phys. Condens. Matter 30 114001
Google Scholar
[13] Stephen L, Yogesh N, Subramanian V 2018 J. Appl. Phys. 123 033103
Google Scholar
[14] Xu T, Lezec H J 2014 Nat. Commun. 5 4141
Google Scholar
[15] Soltani A, Ouerghi F, AbdelMalek F, Haxha S, Ademgil H, Akowuah E K 2017 Opt. Commun. 392 147
Google Scholar
[16] Wu Z, Chen J, Ji M, Huang Q, Xia J, Wu Y, Wang Y 2015 Appl. Phys. Lett. 107 221102
Google Scholar
[17] Zhang Y, Li D, Zeng C, Huang Z, Wang Y, Huang Q, Wu Y, Yu J, Xia J 2014 Opt. Lett. 39 1370
Google Scholar
[18] Zhang Y, Kan Q, Wang G P 2014 Opt. Lett. 39 4934
Google Scholar
[19] Serebryannikov A E, Alici K B, Magath T, Cakmak A O, Ozbay E 2012 Phys. Rev. A 86 053835
Google Scholar
[20] Wang C, Zhou C Z, Li Z Y 2011 Opt. Express 19 26948
Google Scholar
[21] 刘丹, 胡森, 肖明 2017 物理学报 66 054209
Google Scholar
Liu D, Hu S, Xiao M 2017 Acta Phys. Sin. 66 054209
Google Scholar
[22] 费宏明, 徐婷, 刘欣, 林瀚, 陈智辉, 杨毅彪, 张明达, 曹斌照, 梁九卿 2017 物理学报 66 204103
Google Scholar
Fei H M, Xu T, Liu X, Lin H, Chen Z H, Yang Y B, Zhang M D, Cao B Z, Liang J Q 2017 Acta Phys. Sin. 66 204103
Google Scholar
[23] Fei H M, Wu M, Xu T, Lin H, Yang Y B, Liu X, Zhang M D, Cao B Z 2018 J. Opt. 20 095004
Google Scholar
[24] Bourzac K 2012 Nature 483 388
Google Scholar
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