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OPTICS LETTERS / Vol. 39, No. 16 / August 15, 2014
One-way optical transmission in silicon grating-photonic crystal structures Yanyu Zhang,1 Qiang Kan,2 and Guo Ping Wang1,3,* 1
2
School of Physics and Technology, Wuhan University, Wuhan 430072, China Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China 3
College of Electronic Science and Technology, Shenzhen University, Shenzhen 518060, China *Corresponding author: [email protected] Received May 14, 2014; revised July 2, 2014; accepted July 15, 2014; posted July 16, 2014 (Doc. ID 212072); published August 15, 2014
One-way optical transmission through a composite structure of grating-photonic crystal (PC) is presented. This unidirectional transportation property originates from the diffraction of grating to change the direction of light incident into the PC from pseudobandgaps to passbands of the PC. Numerical simulation shows that a light beam in a certain range of frequencies can transmit the composite structure when it is incident from the grating interface but is completely reflected by the structure when it is incident from the PC interface, which is further verified experimentally. The present structure may provide another more compact way for designing on-chip optical diode-like integrated devices. © 2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.5298) Photonic crystals; (230.1950) Diffraction gratings. http://dx.doi.org/10.1364/OL.39.004934
Recently, much research has been devoted to all-optical devices due to their important potential applications in optical communication and quantum computers [1,2]. A unidirectional transmission device, which allows light to pass in one direction but be blocked in the opposite direction, is a fundamental element among them. In order to realize unidirectional propagation, magneto-optic materials [3–5], optics nonlinearity [6–8], metamaterials [9–11], and indirect interband photonic transition [12], etc., have been employed. On the other hand, structures like dielectric or metal gratings [13–15], parity time symmetry waveguides [16,17], plasmonic subwavelength slits [18,19], and photonic crystals (PCs) with pseudobandgaps [20–22] have been reported. However, grating and PC slab structures may be a little more complicated to realize in experiment or have lower one-way contrast ratio and higher loss. Plasmonic subwavelength slits usually work in a narrow band of frequency. In this Letter, we present a simple and compact composite structure of silicon grating-PC to realize one-way transmission in a wideband range of frequency with reasonable highcontrast ratio and low loss. Figure 1(a) shows the schematic configuration of the present composite grating-PC structure. It consists of a rectangular grating and a two-dimensional PC with the same height (h 320 nm). The PC has a square lattice constructed with circular silicon rods. The lattice constant is a 600 nm, and the radius of the silicon rods is r 225 nm. The thickness of the rectangular silicon grating is t 210 nm, and the grating constant is ag 1800 nm, with slit width w 600 nm. The distance between the grating and PC is d, which is a variation in the following discussion. Figure 1(b) shows the simulated transmission spectra of a transverse magnetic (TM) polarized plane light normally incident from the grating interface (forward, red solid line) and PC interface (backward, blue dash line), respectively, by using the finite-difference time-domain (FDTD) method [23]. In the simulations, the refractive index of silicon is set to 3.49 at 1400 nm and the distance 0146-9592/14/164934-04$15.00/0
between grating and PC is d 93 nm. From the figure, we can see that there exists an asymmetric transmission region ranging from 1355 to 1375 nm (gray region). For instance, at wavelength 1360 nm, the forward transmission of light forms a peak with a transmittance T (transmitted light intensity divided by the incident light intensity) of about 95% (black arrow), while the transmittance of light in the backward direction is around 1%, indicating that the incident light can only pass through the composite structure in the forward direction. On the other hand, we can also see that the transmission of light ranging from 1470 to 1630 nm (green slashed region) is around zero from either the forward and backward direction, which indicates that light with wavelength falling into this range of frequency shows no unidirectional transmission. Figures 1(c) and 1(d) show the simulated electrical field intensity distributions of a TM light at 1360 nm incident in the forward [Fig. 1(c)] and backward [Fig. 1(d)] directions, respectively. The arrows indicate the directions of the incident light. We can see that when the light is incident from the grating interface into the composite structure (forward) it can pass through the grating-PC structure to the outside [Fig. 1(c)]. However, when the light is incident from the PC interface into the structure (backward), it is reflected back completely by several layers of PC [Fig. 1(d)]. To understand the physics underlying the above oneway transportation of light, we calculate the TM-mode band structure of the PC (see Fig. 2) by using the plane-wave expansion method [24]. The frequency is normalized by, where is the incident wavelength.a From the band structure, we can see that there exists a directional bandgap (gray region) between the third and fourth bands, ranging from ωα∕2πc 0.4428 to ωα∕2πc 0.4086 (from 1355 to 1470 nm in wavelength). Such a gap stops the propagation of light along the Γ − X direction but allows the propagation of light along the Γ − M direction. Therefore, by using a grating to change the direction of light (ranging from 1355 to 1375 nm) incident © 2014 Optical Society of America
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
Fig. 1. (a) Schematic geometry of the composite grating-PC structure. (b) Simulated transmission spectra of a TM-polarized light in the forward (red solid line) and backward (blue dashed line) directions, respectively. The gray and green slashed regions denote the one-way transmission and full bandgap regions, respectively. (c), (d) Calculated electric-field distributions of light at 1360 nm [see arrow in (b)] in the forward and backward directions, respectively. Blue arrowed lines indicate the direction of the incident light.
into the PC from the Γ − X direction (stopband) to the Γ − M direction (passband), we can make the light pass through the composite structure. In contrast, if light is directly incident into the PC in the Γ − X direction, it will be reflected completely since its frequency falls in the range of the stopband of the PC. As a result, when light is incident from the grating interface (forward direction), transmission is permitted. But for the light incident from the PC interface (backward direction), transmission is forbidden. On the other hand, in the PC there also exists an omnidirectional bandgap [green slashed region in Fig. 3] ranging from ωα∕2πc 0.4086 to ωα∕2πc 0.3682 (from 1470 to 1630 nm in wavelength), in which the incident light from any direction is forbidden. This is the reason light beams ranging from 1470 to 1630 nm [Fig. 1(b), green-slashed region] always show a transmittance of
Fig. 2. Calculated TM-mode band structure of PC. The grayand green-slashed regions denote the directional bandgap and a full bandgap, respectively.
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Fig. 3. (a) SEM image of the fabricated grating-PC structure. Inset, an enlarged view. (b) Simulated (forward: red solid line and backward: blue dashed line) and measured transmission spectra (forward: red circle, solid line and backward: blue x dashed line) of light ranging from 1355 to 1375 nm. Inset, simulated (forward: red solid line and backward: blue dashed line) and measured (forward: red circle, solid line and backward: blue x dashed line) transmittance spectra of light ranging from 1470 to 1500 nm. (c) Measured one-way contrast-ratio dependence on the distances between grating and PC. The wavelength of the incident light is at 1360 nm (red square, dotted line), 1370 nm (blue circle, dashed line), and 1375 nm (green asterisk, dashed line), respectively.
around zero from both the forward and backward directions. Experimentally, we fabricated a series of such composite grating-PC structures to verify the one-way transmission. The structure patterns are firstly defined in the photoresist covered on the top layer of the siliconon-insulator (SOI) by using electron-beam lithography (EBL). The patterns in the photoresist are then etched into the silicon layer using the inductively coupled plasma reactive-ion etching (ICP) technique. Figure 3(a) presents the scanning electron microscopy (SEM) image of the fabricated grating-PC structure. The inset shows the enlarged view of the structure. The distance d between the grating and the PC is changed from 93 to 220 nm (93, 108, 130, 150, 170, 186, 210, and 220 nm). We use near-field scanning optical microscopy (Multiview 2000, Nanonics Imaging LTD., Israel) to measure the transmission spectra of the composite structure. The illumination light is a TM-polarized light beam from a tunable infrared laser (8164A/B, Agilent, USA). The light is coupled into the grating-PC structure by a lens. Each result is obtained by averaging measurements over three times. Because of the limit of the tunable wavelength range of the laser system, we only measured the transmittance of light ranging from 1355 to 1375 nm (within the directional bandgap of the PC, see Fig. 2, gray region) and 1470 to 1500 nm (full bandgap, Fig. 2, green slashed
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region). Figure 3(b) shows the measured transmission spectra of light incident into the composite structure with d 93 nm in the forward (red circle, solid line) and backward directions (blue x dashed line). For comparison, the simulated transmission of light beam from the forward (red solid line) and backward directions (blue dashed line) are also presented in the figure. We see that, at wavelength 1360 nm, nearly 75% of the incident light is passed through the grating-PC structure in the forward direction, while only around 1% of the light can transmit the structure as it is incident in the backward direction, indicating that the light can propagate through the structure in one incident direction, but will be reflected in the opposite direction. The difference between the experimental measurement and numerical simulation [95% transmittance of light in the forward direction; see Fig. 1(b)] can be attributed to the fact that a part of the incident light is leaked out from the structure surface in experiments. We also measured the transmission spectra of the incident light ranging from 1470 to 1500 nm (within the full bandgap of the PC) [see inset of Fig. 3(b)]. We can see that it does not matter whether the illumination is in the forward or backward directions, the transmittance of the light is no more than 2%, indicating that the light shows no one-way transmission but instead is completely forbidden by the composite structure in both forward and backward directions. We also investigate the effect of distance d between grating and PC on the one-way transmission. We introduce a one-way contrast ratio C s as C s T F − T B ∕ T F T B [25], where T F and T B are the forward and backward transmittances, respectively. Figure 3(c) shows the C s dependence on d as the incident light is set at three wavelengths. We can see from the figure that the one-way contrast ratio shows little dependence on the distance between grating and PC when the incident light is at different wavelengths. For example, as the incident light is at 1360 nm, the C s is around 0.73 and 0.75 as d 170 nm and 93 nm, respectively (red square, dotted line). From this, we can conclude that the present composite grating-PC structure shows good properties in one-way transmission as the distance between grating and PC is changed within a certain value of ranges. On the other hand, when the thickness of grating is changed, it mainly influences the transmittance of the unidirectional transmission of the structure. This is because the thickness of gratings will, in general, affect the diffraction efficiency of light, so as to change the intensity of light incident into the PC. While the grating constant is changed, it will change the direction and diffraction efficiency of illumination light incident into the PC. If it makes the wave vector of light into the PC still fall in the stopband of the PC after diffracted by the grating, the structure will show no unidirectional propagation. Otherwise, unidirectional transmission appears. Our calculations (not shown here) reveal that, although some grating constants still make the oneway transmission of structure work, it may reduce the transmittance of the structure. This means that the grating constant may affect both the function of
unidirectional transmission and the transmittance of grating-PC structures. When the light source is tilted, it may fall into the passband of the PC. Hence, even when there is no grating in front of the PC, light may pass through the structure no matter what (forward or backward) direction of light is incident, indicating that one-way transmission phenomenon will disappear. In the case of grating being present, tilted illumination will affect the contrast ratio of oneway transmission and even destroy the unidirectional transmission, because it will modulate the direction of light incident into the PC. This is in principle similar to the case where grating constant in front of PC is changed. In conclusion, we have demonstrated both numerically and experimentally a simple and compact grating-PC structure for wideband and high-contrast asymmetric optical transmission. Such a unidirectional optical transportation property originates from the role the grating played in changing the direction of light incident into the PC from the pseudobandgap to the passbands of the PC. The present structure may provide another more effective way for designing on-chip optical diode-like integrated devices. This work was supported by 973 Program (2011CB933600) and National Natural Science Foundation of China (Grant 11274247). References 1. J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003). 2. E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001). 3. L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nat. Photonics 5, 758 (2011). 4. M. Levy, J. Opt. Soc. Am. B 22, 254 (2005). 5. T. R. Zaman, X. Guo, and R. J. Ram, Appl. Phys. Lett. 90, 023514 (2007). 6. M. Soljačić, C. Luo, J. D. Joannopoulos, and S. Fan, Opt. Lett. 28, 637 (2003). 7. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001). 8. L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012). 9. Y. D. Xu, C. D. Gu, B. Hou, Y. Lai, J. S. Li, and H. Y. Chen, Nat. Commun. 4, 2561 (2013). 10. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, Phys. Rev. Lett. 108, 213905 (2012). 11. C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010). 12. Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009). 13. Z. H. Zhu, K. Liu, W. Xu, Z. Luo, C. C. Guo, B. Yang, T. Ma, X. D. Yuan, and W. M. Ye, Opt. Lett. 37, 4008 (2012). 14. W. M. Ye, X. D. Yuan, and C. Zeng, Opt. Lett. 36, 2842 (2011). 15. C. Cheng, J. Chen, Q. Y. Wu, F. F. Ren, J. Xu, Y. X. Fan, and H. T. Wang, Appl. Phys. Lett. 91, 111111 (2007). 16. H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. A 82, 043803 (2010). 17. L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, and Y. F. Chen, Science 333, 729 (2011). 18. E. Battal, T. A. Yogurt, and A. K. Okyay, Plasmonics 8, 509 (2013).
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS 19. S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, Opt. Lett. 35, 2597 (2010). 20. A. E. Serebryannikov, Phys. Rev. B 80, 155117 (2009). 21. C. C. Lu, X. Y. Hu, H. Yang, and Q. H. Gong, Opt. Lett. 36, 4668 (2011). 22. C. Wang, C. Z. Zhou, and Z. Y. Li, Opt. Express 19, 26948 (2011).
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23. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method, 2nd ed. (Artech House, 2000). 24. K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990). 25. X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, Phys. Rev. Lett. 106, 084301 (2011).
OPTICS LETTERS / Vol. 39, No. 16 / August 15, 2014
One-way optical transmission in silicon grating-photonic crystal structures Yanyu Zhang,1 Qiang Kan,2 and Guo Ping Wang1,3,* 1
2
School of Physics and Technology, Wuhan University, Wuhan 430072, China Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China 3
College of Electronic Science and Technology, Shenzhen University, Shenzhen 518060, China *Corresponding author: [email protected] Received May 14, 2014; revised July 2, 2014; accepted July 15, 2014; posted July 16, 2014 (Doc. ID 212072); published August 15, 2014
One-way optical transmission through a composite structure of grating-photonic crystal (PC) is presented. This unidirectional transportation property originates from the diffraction of grating to change the direction of light incident into the PC from pseudobandgaps to passbands of the PC. Numerical simulation shows that a light beam in a certain range of frequencies can transmit the composite structure when it is incident from the grating interface but is completely reflected by the structure when it is incident from the PC interface, which is further verified experimentally. The present structure may provide another more compact way for designing on-chip optical diode-like integrated devices. © 2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.5298) Photonic crystals; (230.1950) Diffraction gratings. http://dx.doi.org/10.1364/OL.39.004934
Recently, much research has been devoted to all-optical devices due to their important potential applications in optical communication and quantum computers [1,2]. A unidirectional transmission device, which allows light to pass in one direction but be blocked in the opposite direction, is a fundamental element among them. In order to realize unidirectional propagation, magneto-optic materials [3–5], optics nonlinearity [6–8], metamaterials [9–11], and indirect interband photonic transition [12], etc., have been employed. On the other hand, structures like dielectric or metal gratings [13–15], parity time symmetry waveguides [16,17], plasmonic subwavelength slits [18,19], and photonic crystals (PCs) with pseudobandgaps [20–22] have been reported. However, grating and PC slab structures may be a little more complicated to realize in experiment or have lower one-way contrast ratio and higher loss. Plasmonic subwavelength slits usually work in a narrow band of frequency. In this Letter, we present a simple and compact composite structure of silicon grating-PC to realize one-way transmission in a wideband range of frequency with reasonable highcontrast ratio and low loss. Figure 1(a) shows the schematic configuration of the present composite grating-PC structure. It consists of a rectangular grating and a two-dimensional PC with the same height (h 320 nm). The PC has a square lattice constructed with circular silicon rods. The lattice constant is a 600 nm, and the radius of the silicon rods is r 225 nm. The thickness of the rectangular silicon grating is t 210 nm, and the grating constant is ag 1800 nm, with slit width w 600 nm. The distance between the grating and PC is d, which is a variation in the following discussion. Figure 1(b) shows the simulated transmission spectra of a transverse magnetic (TM) polarized plane light normally incident from the grating interface (forward, red solid line) and PC interface (backward, blue dash line), respectively, by using the finite-difference time-domain (FDTD) method [23]. In the simulations, the refractive index of silicon is set to 3.49 at 1400 nm and the distance 0146-9592/14/164934-04$15.00/0
between grating and PC is d 93 nm. From the figure, we can see that there exists an asymmetric transmission region ranging from 1355 to 1375 nm (gray region). For instance, at wavelength 1360 nm, the forward transmission of light forms a peak with a transmittance T (transmitted light intensity divided by the incident light intensity) of about 95% (black arrow), while the transmittance of light in the backward direction is around 1%, indicating that the incident light can only pass through the composite structure in the forward direction. On the other hand, we can also see that the transmission of light ranging from 1470 to 1630 nm (green slashed region) is around zero from either the forward and backward direction, which indicates that light with wavelength falling into this range of frequency shows no unidirectional transmission. Figures 1(c) and 1(d) show the simulated electrical field intensity distributions of a TM light at 1360 nm incident in the forward [Fig. 1(c)] and backward [Fig. 1(d)] directions, respectively. The arrows indicate the directions of the incident light. We can see that when the light is incident from the grating interface into the composite structure (forward) it can pass through the grating-PC structure to the outside [Fig. 1(c)]. However, when the light is incident from the PC interface into the structure (backward), it is reflected back completely by several layers of PC [Fig. 1(d)]. To understand the physics underlying the above oneway transportation of light, we calculate the TM-mode band structure of the PC (see Fig. 2) by using the plane-wave expansion method [24]. The frequency is normalized by, where is the incident wavelength.a From the band structure, we can see that there exists a directional bandgap (gray region) between the third and fourth bands, ranging from ωα∕2πc 0.4428 to ωα∕2πc 0.4086 (from 1355 to 1470 nm in wavelength). Such a gap stops the propagation of light along the Γ − X direction but allows the propagation of light along the Γ − M direction. Therefore, by using a grating to change the direction of light (ranging from 1355 to 1375 nm) incident © 2014 Optical Society of America
August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
Fig. 1. (a) Schematic geometry of the composite grating-PC structure. (b) Simulated transmission spectra of a TM-polarized light in the forward (red solid line) and backward (blue dashed line) directions, respectively. The gray and green slashed regions denote the one-way transmission and full bandgap regions, respectively. (c), (d) Calculated electric-field distributions of light at 1360 nm [see arrow in (b)] in the forward and backward directions, respectively. Blue arrowed lines indicate the direction of the incident light.
into the PC from the Γ − X direction (stopband) to the Γ − M direction (passband), we can make the light pass through the composite structure. In contrast, if light is directly incident into the PC in the Γ − X direction, it will be reflected completely since its frequency falls in the range of the stopband of the PC. As a result, when light is incident from the grating interface (forward direction), transmission is permitted. But for the light incident from the PC interface (backward direction), transmission is forbidden. On the other hand, in the PC there also exists an omnidirectional bandgap [green slashed region in Fig. 3] ranging from ωα∕2πc 0.4086 to ωα∕2πc 0.3682 (from 1470 to 1630 nm in wavelength), in which the incident light from any direction is forbidden. This is the reason light beams ranging from 1470 to 1630 nm [Fig. 1(b), green-slashed region] always show a transmittance of
Fig. 2. Calculated TM-mode band structure of PC. The grayand green-slashed regions denote the directional bandgap and a full bandgap, respectively.
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Fig. 3. (a) SEM image of the fabricated grating-PC structure. Inset, an enlarged view. (b) Simulated (forward: red solid line and backward: blue dashed line) and measured transmission spectra (forward: red circle, solid line and backward: blue x dashed line) of light ranging from 1355 to 1375 nm. Inset, simulated (forward: red solid line and backward: blue dashed line) and measured (forward: red circle, solid line and backward: blue x dashed line) transmittance spectra of light ranging from 1470 to 1500 nm. (c) Measured one-way contrast-ratio dependence on the distances between grating and PC. The wavelength of the incident light is at 1360 nm (red square, dotted line), 1370 nm (blue circle, dashed line), and 1375 nm (green asterisk, dashed line), respectively.
around zero from both the forward and backward directions. Experimentally, we fabricated a series of such composite grating-PC structures to verify the one-way transmission. The structure patterns are firstly defined in the photoresist covered on the top layer of the siliconon-insulator (SOI) by using electron-beam lithography (EBL). The patterns in the photoresist are then etched into the silicon layer using the inductively coupled plasma reactive-ion etching (ICP) technique. Figure 3(a) presents the scanning electron microscopy (SEM) image of the fabricated grating-PC structure. The inset shows the enlarged view of the structure. The distance d between the grating and the PC is changed from 93 to 220 nm (93, 108, 130, 150, 170, 186, 210, and 220 nm). We use near-field scanning optical microscopy (Multiview 2000, Nanonics Imaging LTD., Israel) to measure the transmission spectra of the composite structure. The illumination light is a TM-polarized light beam from a tunable infrared laser (8164A/B, Agilent, USA). The light is coupled into the grating-PC structure by a lens. Each result is obtained by averaging measurements over three times. Because of the limit of the tunable wavelength range of the laser system, we only measured the transmittance of light ranging from 1355 to 1375 nm (within the directional bandgap of the PC, see Fig. 2, gray region) and 1470 to 1500 nm (full bandgap, Fig. 2, green slashed
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region). Figure 3(b) shows the measured transmission spectra of light incident into the composite structure with d 93 nm in the forward (red circle, solid line) and backward directions (blue x dashed line). For comparison, the simulated transmission of light beam from the forward (red solid line) and backward directions (blue dashed line) are also presented in the figure. We see that, at wavelength 1360 nm, nearly 75% of the incident light is passed through the grating-PC structure in the forward direction, while only around 1% of the light can transmit the structure as it is incident in the backward direction, indicating that the light can propagate through the structure in one incident direction, but will be reflected in the opposite direction. The difference between the experimental measurement and numerical simulation [95% transmittance of light in the forward direction; see Fig. 1(b)] can be attributed to the fact that a part of the incident light is leaked out from the structure surface in experiments. We also measured the transmission spectra of the incident light ranging from 1470 to 1500 nm (within the full bandgap of the PC) [see inset of Fig. 3(b)]. We can see that it does not matter whether the illumination is in the forward or backward directions, the transmittance of the light is no more than 2%, indicating that the light shows no one-way transmission but instead is completely forbidden by the composite structure in both forward and backward directions. We also investigate the effect of distance d between grating and PC on the one-way transmission. We introduce a one-way contrast ratio C s as C s T F − T B ∕ T F T B [25], where T F and T B are the forward and backward transmittances, respectively. Figure 3(c) shows the C s dependence on d as the incident light is set at three wavelengths. We can see from the figure that the one-way contrast ratio shows little dependence on the distance between grating and PC when the incident light is at different wavelengths. For example, as the incident light is at 1360 nm, the C s is around 0.73 and 0.75 as d 170 nm and 93 nm, respectively (red square, dotted line). From this, we can conclude that the present composite grating-PC structure shows good properties in one-way transmission as the distance between grating and PC is changed within a certain value of ranges. On the other hand, when the thickness of grating is changed, it mainly influences the transmittance of the unidirectional transmission of the structure. This is because the thickness of gratings will, in general, affect the diffraction efficiency of light, so as to change the intensity of light incident into the PC. While the grating constant is changed, it will change the direction and diffraction efficiency of illumination light incident into the PC. If it makes the wave vector of light into the PC still fall in the stopband of the PC after diffracted by the grating, the structure will show no unidirectional propagation. Otherwise, unidirectional transmission appears. Our calculations (not shown here) reveal that, although some grating constants still make the oneway transmission of structure work, it may reduce the transmittance of the structure. This means that the grating constant may affect both the function of
unidirectional transmission and the transmittance of grating-PC structures. When the light source is tilted, it may fall into the passband of the PC. Hence, even when there is no grating in front of the PC, light may pass through the structure no matter what (forward or backward) direction of light is incident, indicating that one-way transmission phenomenon will disappear. In the case of grating being present, tilted illumination will affect the contrast ratio of oneway transmission and even destroy the unidirectional transmission, because it will modulate the direction of light incident into the PC. This is in principle similar to the case where grating constant in front of PC is changed. In conclusion, we have demonstrated both numerically and experimentally a simple and compact grating-PC structure for wideband and high-contrast asymmetric optical transmission. Such a unidirectional optical transportation property originates from the role the grating played in changing the direction of light incident into the PC from the pseudobandgap to the passbands of the PC. The present structure may provide another more effective way for designing on-chip optical diode-like integrated devices. This work was supported by 973 Program (2011CB933600) and National Natural Science Foundation of China (Grant 11274247). References 1. J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003). 2. E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001). 3. L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. A. Ross, Nat. Photonics 5, 758 (2011). 4. M. Levy, J. Opt. Soc. Am. B 22, 254 (2005). 5. T. R. Zaman, X. Guo, and R. J. Ram, Appl. Phys. Lett. 90, 023514 (2007). 6. M. Soljačić, C. Luo, J. D. Joannopoulos, and S. Fan, Opt. Lett. 28, 637 (2003). 7. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001). 8. L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, Science 335, 447 (2012). 9. Y. D. Xu, C. D. Gu, B. Hou, Y. Lai, J. S. Li, and H. Y. Chen, Nat. Commun. 4, 2561 (2013). 10. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, Phys. Rev. Lett. 108, 213905 (2012). 11. C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010). 12. Z. Yu and S. Fan, Nat. Photonics 3, 91 (2009). 13. Z. H. Zhu, K. Liu, W. Xu, Z. Luo, C. C. Guo, B. Yang, T. Ma, X. D. Yuan, and W. M. Ye, Opt. Lett. 37, 4008 (2012). 14. W. M. Ye, X. D. Yuan, and C. Zeng, Opt. Lett. 36, 2842 (2011). 15. C. Cheng, J. Chen, Q. Y. Wu, F. F. Ren, J. Xu, Y. X. Fan, and H. T. Wang, Appl. Phys. Lett. 91, 111111 (2007). 16. H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, Phys. Rev. A 82, 043803 (2010). 17. L. Feng, M. Ayache, J. Huang, Y. L. Xu, M. H. Lu, and Y. F. Chen, Science 333, 729 (2011). 18. E. Battal, T. A. Yogurt, and A. K. Okyay, Plasmonics 8, 509 (2013).
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