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  One-way optical transmission in silicon grating-photoniccrystal structures Yanyu Zhang, 1 Qiang Kan, 2 and Guo Ping Wang 1,3, * 1 School of Physics and Technology, Wuhan University, Wuhan 430072, China 2 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: Received May 14, 2014; revised July 2, 2014; accepted July 15, 2014;posted July 16, 2014 (Doc. ID 212072); published August 15, 2014One-way optical transmission through a composite structure of grating-photonic crystal (PC) is presented. This uni-directional transportation propertysrcinates from the diffraction of grating to change the direction of light incidentinto the PC from pseudobandgaps to passbands of the PC. Numerical simulation shows that a light beamin a certainrange of frequencies can transmit the composite structure when it is incident from the grating interface but is com-pletely 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 integrateddevices. © 2014 Optical Society of America OCIS codes:  (130.3120) Integrated optics devices; (230.5298) Photonic crystals; (230.1950) Diffraction gratings. Recently, much research has been devoted to all-opticaldevices due to their important potential applications inoptical communication and quantum computers [1,2].  A unidirectional transmission device, which allows lightto pass in one direction but be blocked in the oppositedirection, is a fundamental element among them. In order to realize unidirectional propagation, magneto-optic ma-terials [3 – 5], optics nonlinearity [6 – 8], metamaterials[9 – 11], and indirect interband photonic transition [12], etc., have been employed. On the other hand, structureslike dielectric or metal gratings [13 – 15], parity time sym-metry waveguides [16,17], plasmonic subwavelength slits [18,19], and photonic crystals (PCs) with pseudobandg- aps [20 – 22] have been reported. However, grating andPC slab structures may be a little more complicated torealize in experiment or have lower one-way contrastratio and higher loss. Plasmonic subwavelength slits usu-ally 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 high-contrast 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 thesame height ( h    320  nm). The PC has a square latticeconstructed with circular silicon rods. The lattice con-stant is  a    600  nm, and the radius of the silicon rodsis  r     225  nm. The thickness of the rectangular silicongrating is  t    210  nm, and the grating constant is a  g    1800  nm, with slit width  w    600  nm. The distancebetween the grating and PC is  d , which is a variation inthe following discussion.Figure 1(b) shows the simulated transmission spectra of a transverse magnetic (TM) polarized plane light nor-mally incident from the grating interface (forward, redsolid line) and PC interface (backward, blue dash line),respectively, by using the finite-difference time-domain(FDTD) method [23]. In the simulations, the refractiveindex of silicon is set to 3.49 at 1400 nm and the distancebetween grating and PC is  d    93  nm. From the figure,we can see that there exists an asymmetric transmissionregion ranging from 1355 to 1375 nm (gray region).For instance, at wavelength 1360 nm, the forward trans-mission of light forms a peak with a transmittance  T  (transmitted light intensity divided by the incident lightintensity) of about 95% (black arrow), while the transmit-tance of light in the backward direction is around 1%, in-dicating that the incident light can only pass through thecomposite structure in the forward direction.On the other hand, we can also see that the transmis-sion of light ranging from 1470 to 1630 nm (green slashedregion) is around zero from either the forward andbackward direction, which indicates that light withwavelength falling into this range of frequency showsno unidirectional transmission.Figures 1(c) and 1(d) show the simulated electrical field intensity distributions of a TM light at 1360 nm in-cident in the forward [Fig. 1(c)] and backward [Fig. 1(d)] directions, respectively. The arrows indicate the direc-tions of the incident light. We can see that when the lightis incident from the grating interface into the compositestructure (forward) it can pass through the grating-PCstructure to the outside [Fig. 1(c)]. However, when thelight is incident from the PC interface into the structure(backward), it is reflected back completely by severallayers of PC [Fig. 1(d)].To understand the physics underlying the above one-way transportation of light, we calculate the TM-modeband structure of the PC (see Fig. 2) by using the plane-wave expansion method [24]. The frequency is nor-malized by, where is the incident wavelength.a From theband structure, we can see that there exists a directionalbandgap (gray region) between the third and fourthbands, ranging from  ωα  ∕ 2 π  c    0 . 4428  to  ωα  ∕ 2 π  c   0 . 4086  (from 1355 to 1470 nm in wavelength). Such a gap stops the propagation of light along the  Γ − X direc-tion but allows the propagation of light along the  Γ − Mdirection. Therefore, by using a grating to change the di-rection of light (ranging from 1355 to 1375 nm) incident 4934 OPTICS LETTERS / Vol. 39, No. 16 / August 15, 20140146-9592/14/164934-04$15.00/0 © 2014 Optical Society of America   into the PC from the  Γ − X direction (stopband) to the Γ − M direction (passband), we can make the light passthrough the composite structure. In contrast, if light is di-rectly incident into the PC in the Γ − X direction, it will bereflected completely since its frequency falls in the rangeof the stopband of the PC. As a result, when light isincident from the grating interface (forward direction),transmission is permitted. But for the light incident fromthe PC interface (backward direction), transmission isforbidden.On the other hand, in the PC there also exists an omni-directional bandgap [green slashed region in Fig. 3] rang-ing from  ωα  ∕ 2 π  c    0 . 4086  to  ωα  ∕ 2 π  c    0 . 3682  (from1470 to 1630 nm in wavelength), in which the incidentlight from any direction is forbidden. This is the reasonlight beams ranging from 1470 to 1630 nm [Fig. 1(b),green-slashed region] always show a transmittance of around zero from both the forward and backwarddirections.Experimentally, we fabricated a series of suchcomposite grating-PC structures to verify the one-waytransmission. The structure patterns are firstly definedin the photoresist covered on the top layer of the silicon-on-insulator (SOI) by using electron-beam lithography(EBL). The patterns in the photoresist are then etchedinto the silicon layer using the inductively coupled plasma reactive-ion etching (ICP) technique. Figure 3(a) presents the scanning electron microscopy (SEM) imageof the fabricated grating-PC structure. The inset showsthe enlarged view of the structure. The distance  d  be-tween the grating and the PC is changed from 93 to220 nm (93, 108, 130, 150, 170, 186, 210, and 220 nm).We use near-field scanning optical microscopy (Multi- view 2000, Nanonics Imaging LTD., Israel) to measure thetransmission spectra of the composite structure. The il-lumination light is a TM-polarized light beam from a tun-able infrared laser (8164A/B, Agilent, USA). The light iscoupled into the grating-PC structure by a lens. Each re-sult is obtained by averaging measurements over threetimes. Because of the limit of the tunable wavelengthrange of the laser system, we only measured the transmit-tance of light ranging from 1355 to 1375 nm (within thedirectional bandgap of the PC, see Fig. 2, gray region)and 1470 to 1500 nm (full bandgap, Fig. 2, green slashed Fig. 1. (a) Schematic geometry of the composite grating-PCstructure. (b) Simulated transmission spectra of a TM-polarizedlight in the forward (red solid line) and backward (blue dashedline) directions, respectively. The gray and green slashed re-gions denote the one-way transmission and full bandgapregions, respectively. (c), (d) Calculated electric-field distribu-tions of light at 1360 nm [see arrow in (b)] in the forward andbackward directions, respectively. Blue arrowed lines indicatethe direction of the incident light.Fig. 2. Calculated TM-mode band structure of PC. The gray-and green-slashed regions denote the directional bandgapand a full bandgap, respectively.Fig. 3. (a) SEM image of the fabricated grating-PC structure.Inset, an enlarged view. (b) Simulated (forward: red solid lineand backward: blue dashed line) and measured transmissionspectra (forward: red circle, solid line and backward: blue xdashed line) of light ranging from 1355 to 1375 nm. Inset, simu-lated (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 from1470 to 1500 nm. (c) Measured one-way contrast-ratio depend-ence on the distances between grating and PC. The wavelengthof 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. August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS 4935  region). Figure 3(b) shows the measured transmissionspectra of light incident into the composite structure with d    93  nm in the forward (red circle, solid line) andbackward directions (blue x dashed line). For compari-son, the simulated transmission of light beam from theforward (red solid line) and backward directions (bluedashed 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 forwarddirection, while only around 1% of the light can transmitthe structure as it is incident in the backward direction,indicating that the light can propagate through the struc-ture in one incident direction, but will be reflected in theopposite direction. The difference between the experi-mental measurement and numerical simulation [95% transmittance of light in the forward direction; seeFig. 1(b)] can be attributed to the fact that a part of the incident light is leaked out from the structure surfacein experiments.We also measured the transmission spectra of the in-cident light ranging from 1470 to 1500 nm (within the fullbandgap of the PC) [see inset of Fig. 3(b)]. We can seethat it does not matter whether the illumination is inthe forward or backward directions, the transmittanceof the light is no more than 2%, indicating that the lightshows no one-way transmission but instead is completelyforbidden by the composite structure in both forwardand backward directions.We also investigate the effect of distance  d  betweengrating and PC on the one-way transmission. We intro-duce 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 andbackward transmittances, respectively. Figure 3(c)shows the  C  s  dependence on  d  as the incident light isset at three wavelengths. We can see from the figure thatthe one-way contrast ratio shows little dependence onthe distance between grating and PC when the incidentlight is at different wavelengths. For example, as the in-cident light is at 1360 nm, the  C  s  is around 0.73 and 0.75as  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 be-tween grating and PC is changed within a certain valueof ranges.On the other hand, when the thickness of grating ischanged, it mainly influences the transmittance of theunidirectional transmission of the structure. This is be-cause the thickness of gratings will, in general, affectthe diffraction efficiency of light, so as to change the in-tensity of light incident into the PC. While the grating con-stant is changed, it will change the direction anddiffraction efficiency of illumination light incident intothe PC. If it makes the wave vector of light into thePC still fall in the stopband of the PC after diffractedby the grating, the structure will show no unidirectional propagation. Otherwise, unidirectional transmission ap- pears. Our calculations (not shown here) reveal that,although some grating constants still make the one-way transmission of structure work, it may reduce thetransmittance of the structure. This means that thegrating 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 pass-band of the PC. Hence, even when there is no grating infront of the PC, light may pass through the structure nomatter what (forward or backward) direction of light isincident, indicating that one-way transmission phenome-non will disappear. In the case of grating being present,tilted illumination will affect the contrast ratio of one-way transmission and even destroy the unidirectionaltransmission, 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 ischanged.In conclusion, we have demonstrated both numericallyand experimentally a simple and compact grating-PCstructure for wideband and high-contrast asymmetricoptical transmission. Such a unidirectional optical trans- portation property srcinates from the role the grating played in changing the direction of light incident intothe PC from the pseudobandgap to the passbands of the PC. The present structure may provide another moreeffective way for designing on-chip optical diode-likeintegrated devices.This work was supported by 973 Program(2011CB933600) and National Natural Science Founda-tion 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. Solja  č i ć , 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. 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