- Email: [email protected]
Wideband high-contrast optical diode and unidirectional beam splitters via near-infrared metallic photonic crystals
Optics Communications 289 (2013) 144–148
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Wideband high-contrast optical diode and unidirectional beam splitters via near-infrared metallic photonic crystals Shuai Feng a,n, Cheng Ren b, Wenzhong Wang a, Yiquan Wang a a b
School of Science, Minzu University of China, Beijing100081, PR China School of Opto-Electronic Information Science and Technology, Yantai University, Yantai 264005, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 March 2012 Received in revised form 28 September 2012 Accepted 5 October 2012 Available online 22 October 2012
A novel nanoscale all-optical photonic crystal diode consisting of rectangular and square metals immersed in silicon is reported. This wideband high-contrast diode based on the self-collimation behavior can confine the light beams travel along a certain direction. So it works well needless of the input and output waveguides and is more feasible to combine with other functional devices in the complex integrated optical circuits. And through a simple design of two photonic crystals’ interface, unidirectional beam splitters owing to the directional band gap can also be obtained. & 2012 Elsevier B.V. All rights reserved.
Keywords: Photonic crystal All-optical diode Light beam splitter
1. Introduction Owing to the capability of unidirectional movement of the current flux, electrical diode plays a basic role in electronic circuits, which has significantly revolutionized fundamental science and advanced technology. The unidirectional propagation of electromagnetic waves has attracted peoples’ much attention due to its important applications in the fields of optical computing, optical interconnection networks and integrated photonic circuits. The propagation of light in photonic crystal (PC) is just like the movement of electron in semiconductors, which is to say that photonic forbidden bands exist in PCs. And considerable efforts have been dedicated to the study of the nonreciprocal transmission of electromagnetic waves in the different kinds of PC heterostrcutures [1–11]. Various schemes have been proposed to design all-optical diode in nonlinear and magnetic PCs with broken time reversal symmetry [1–4]. Due to the relatively small nonlinear susceptibility and magneto–optical coefficient of conventional materials, above all optical diodes works well only if the operating light intensity or magnetic field is very strong, which restricts its actual applications in many fields. Hwang et al. [5] reported an electrotunable optical isolator by combining the photonic band gap effect and the unique interface properties of asymmetric liquidcrystal photonic band gap heterostructure, showing nonreciprocal transmission of circularly polarized light in photonic band gap regions. But the large size of liquid crystal is unsuitable for
n
Corresponding author. Tel.: þ86 10 68932205; fax: þ86 10 68932205. E-mail address: [email protected] (S. Feng).
0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.10.006
the practical integration applications. Wang et al. [6] realized unidirectional transmission of electromagnetic chiral-edge states in a magneto–optical PC within the microwave region, which works well in a strong magnetic field environment. Recently, Cakmakyapan et al. [7] reported the strong directional selectivity of a single subwavelength slit in nonsymmetric metallic gratings with double-side corrugations at the microwave frequencies. Lu et al. [8,9] realized a low-power high-contrast all-optical diode in a two-dimensional (2D) PC heterostructure with broken spatial inversion symmetry experimentally. Wang et al. [10] reported a unidirectional on-chip optical diode in silicon based on the directional band gap difference of the near-infrared square-lattice photonic crystals comprising a heterojunction structure and the break of the spatial inversion symmetry. Li et al. [11] utilized a sonic-crystal-based acoustic diode that had broken spatial inversion symmetry and experimentally realized sound unidirectional transmission in this acoustic diode. In this paper, we designed a 2D square-lattice PC heterostructure consisting of rectangular and square metals immersed in silicon. For the near-infrared light waves around 1550 nm, the rectangular-metal PC works as a waveguide owing to its largeangle self-collimation behavior along the ! –X direction. For the square-metal PC, the light transmission characters are determined by both the incident light’s frequency and its incident angle. So it provides us great feasibility to design a composite PC structure and acquire the different transmission characteristics of the leftward and rightward incidence through the heterostructure composed of above two PCs. Moreover, through the design of two PCs’ interface, a kind of unidirectional beam splitter owing to the directional band gap is also obtained.
S. Feng et al. / Optics Communications 289 (2013) 144–148
2. Unidirectional light transmission through metallic PC heterostructures At first, we consider a PC structure consisting of square metal rods immersed in silicon. The length of the PC’s lattice constant is a¼400 nm, and the refractive index of the background material is 3.45. The side length of the square metal is 0.25a and the sides are placed along the ! –X direction of the PC. Drude dispersion model is adopted to describe the permittivity of the metal, which is depicted as o2 eðoÞ ¼ e0 1 oðo þp igÞ . In the above equation, op is the plasma frequency and g is the damping coefficient. The metal studied in paper is Ag, the corresponding values are op ¼ 1:37 1016 Hz and
g ¼ 2:73 1013 Hz, which can reproduce the corresponding experiment results well within the near-infrared wavelengths around 1550 nm. Ignoring the absorption of the metal to the light beams, the calculated band structure for the several lowest photonic bands is shown in Fig. 1(a) for the TM modes. The first and second lowest bands are even-mode bands, which can be easily coupled by the incident light beams, while the third lowest band is an odd-mode band. It is well known that the propagation direction of light is
145
identical to the direction of group velocity of light given by vg ¼ rko(k), which means that the group velocity is perpendicular to the equal-frequency surface contour (EFC). Through analysis of the EFC as a function of k, we can find the frequency range in which the self-collimation phenomenon occurs and the propagation direction of light beam. The several EFCs in the second TM bands are shown in Fig. 1(b). It can be seen that the most part of the EFS contours around the frequency 0.24 c/a (c is the velocity of light in vacuum), which are centered at the ! –X line, are quite flat and have the surface normal pointing to the ! –X direction. As the group velocity for a give Bloch mode characterized by K is parallel to the EFS normal at this K point, we can see that the group velocities of the excited Bloch wave modes centered around the ! –X line point towards the ! –X direction, and corresponding to an apparent self-collimation effect for the PC slab, whose surface normal is parallel to the ! –X direction. In the other small part centered at the ! –M line, the curve is convex with respect to the ! point, which means a negative refractive direction. With the increasing of the frequency, the ratio of self-collimation EFS region reduces and the negative-refractive effects enhances. When the square metals are replaced by rectangular metals with the longer sides pointing to the ! X direction of the PC, whose two side lengths are 340 nm and 140 nm, the calculated TM-polarized band structure
Fig. 1. TM-polarized photonic band structures of the 2D square-lattice metallic PCs consisting of (a) square and (c) rectangular metals. And the several equal-frequency surface contours within the second photonic band of the PCs consisting of (b) square and (d) rectangular metals. The length of the square lattice is 400 nm. The side length of the square metals is 100 nm, and the two side lengths of the rectangular metals are 340 nm and 140 nm.
146
S. Feng et al. / Optics Communications 289 (2013) 144–148
and the several EFCs in the second band are shown in Fig. 1(c and d). It is shown that there is an apparent lifting of the lowest forbidden band owing to the increasing of the metal’s size. More important, it can be seen in Fig. 1(d) that the EFCs of the frequencies in the second band are quite flat, meaning that the self-collimating effect along the ! –X direction of the PC occurs. Based on the two PCs mentioned above, we constructed a PC heterojunction structure with the interface between PC1 and PC2 along the G–M direction, whose sketch map is shown in Fig. 2(a). Considering the actual absorption of the metal rods to the incident light waves, we simulated the transmission spectra for a TM light signal transporting along the forward (from right to left) and backward (from left to right) directions, which are obtained by dividing the light energy arrived at the opposite side by the incident light energy. There are 30 rows of rectangular metals and 40 rows of square metals on the center line along the light propagation direction. Fig. 2(b) shows the calculated forward and backward transmission spectra by the solid line (a) and dotted line (b), respectively. It is clearly seen that there exists an isolation band ranging from 0.245 c/a to 0.286 c/a (the wavelength region is from 1399 nm to 1633 nm), where the transmission contrast defined as the ratio of maximum transmission in one direction to the corresponding transmission in the inverse direction exceeds 100. In order to have a visual sight of the one-way transmission characteristics of the light waves through above heterostructure, the spatial light intensity distributions of the rightward and leftward light at normal incidence at the frequencies 0.245,
Fig. 2. (a) The sketch map of the heterostructure consisting of two square-lattice PCs with rectangular and square metals immersed in silicon, and (b) light transmission spectra through the heterostructure with 30 rows of rectangular metals and 40 rows of square metals along the central line. The solid line (a) represents the transmittance spectrum when the light beam is incident leftwards, and the dotted line (b) shows that in the case of rightward incidence.
0.255 and 0.265 c/a are calculated and the results are shown in Figs. 3 and 4. In Fig. 3(a), the light wave resonant at the frequency 0.245 c/a goes straight in PC1 and reaches the heterojunction interface. Refraction occurs at the interface, but the intensity of the refractive light beam within the PC2 region is much weaker comparing with the incident light’s intensity. When the incident light’s frequency is increased to be 0.255 and 0.265 c/a, it can be seen from Fig. 3(b and c) that apparent negative refraction behaviors occur at the interface, which can be understood by the analysis of EFS’s contours shown in Fig. 1(b). In Fig. 4(a and b), light goes straight in PC2 from the right side of the heterostructure owing to the self-collimation effect. Light refraction and reflection behaviors occur at the interface of the PC1 and PC2, and the reflective light beam travels downward. The refractive light beam propagates into the PC1 region owing to the large-angle self-collimation characteristics along the ! –X direction of the PC1, and finally the light beam is exported from the left side of PC heterostructure. When the frequency becomes 0.265 c/a, it can be
Fig. 3. Steady spatial distributions of light intensity at the frequencies (a) 0.245, (b) 0.255, and (c) 0.265 c/a through the heterostructure at normal incidence of light source rightward.
S. Feng et al. / Optics Communications 289 (2013) 144–148
147
Fig. 5. (a) Sketch map of the heterostructure consisting of two PCs with rectangular and square metals immersed in silicon, respectively, and (b) light transmittances through the 40-row-metal PC heterostructure. The solid line (a) represents the transmittance spectrum when the light beam is incident from the left side, and the dotted line (b) shows that in leftward incidence. Fig. 4. Steady spatial distributions of light intensity at the frequencies (a) 0.245, (b) 0.255, and (c) 0.265 c/a through the heterostructure when the light is incident from the right side.
seen from Fig. 4(c) the width of the light beam increases with the light’s propagation distance within PC2 owing to the weaken of self-collimation effect. The self-collimation behavior along the G–X direction of PC1 is not influenced by the alteration of the incident angle from 01 to 451, while the light propagation characteristics within PC2 are determined by the incident angle of the light beam. It is obvious that the forward and backward light paths are quite different. We also constructed another kind of heterostructure by interlacing the rectangular and square metals at interface vertical to the light propagation direction, whose sketch map is shown in Fig. 5(a). The lattice constant of square-lattice PC is changed to be 650 nm, and the two side lengths of rectangular metal are 0.85 a and 0.25 a, while the side length of the square metal is still 0.25 a. Fig. 5(b) shows the calculated forward (from left to right) and backward (from right to left) transmission spectra by the solid line (a) and dotted line (b), respectively. It is clearly seen that there exists an isolation band ranging from 0.398 c/a to 0.428 c/a (the corresponding wavelength region is from 1519 nm to 1633 nm), where the transmission contrast exceeds 200 with a maximum about 10,000. For a certain frequency 0.41 c/a (the corresponding wavelength is 1585 nm), the steady light intensity distributions through the composite structure in forward and backward
directions are shown in Fig. 6(a and b), respectively. It can be seen from Fig. 6(a) that the light wave radiated from the left side travels through the heterostructure and finally is split into two output light beams with a certain angle between them. Fig. 6(b) shows the light wave radiated from the right side of the structure cannot travel through PC2 owing to the directional band gap along the ! –X direction. As far as we know, the unidirectional beam splitter is firstly achieved through a simple adjustment of the two PCs’ interface. To understand the splitter behavior through above heterostructure, the light transmittances at normal incidence through the 40-row-metal square-metal PCs with a surface normal along the ! –X direction and ! –M direction are calculated and the results are shown by the solid line (a) and dotted line (a) in Fig. 7, respectively. Through interlacing the rectangular and square metals at the interface between PC1 and PC2, the refractive light from PC1 to PC2 have light wave vector components pointing to different directions. Owing to the tangential component conservation of the wave vector k and band gap of PC1 in ! –X direction, the output light is finally split into two light beams.
3. Conclusions In conclusion, we have studied a high-contrast broadband alloptical diode in a PC heterostructure consisting of rectangular and
148
S. Feng et al. / Optics Communications 289 (2013) 144–148
Fig. 7. Light transmittances through the 40-row-metal PC at the normal incidence along the ! –X direction and ! –M direction, which are shown by the solid line (a) and the dotted line (b), respectively. The side length of the square metal is 0.25 a, and the lattice constant is 650 nm.
Acknowledgment Project supported by the National Natural Science Foundation of China with Grant nos. 10904176 and 11004169, the Fundamental Research Funds for the Central Universities, the ‘‘985 Project’’ and the ‘‘211 Project’’ of the Ministry of Education of China.
References
Fig. 6. Steady spatial distributions of light intensity at the frequency 0.41 c/a through the heterostructure, whose sketch map is shown in Fig. 5, from the (a) left and (b) right sides of the structure.
square metals immersed in silicon. Comparing with the previous PC all-optical diode based on the directional band gap mismatch, the working frequencies in our proposed structure are within the passband of the PC structures. Owing to the self-collimation characteristics of light propagation in our proposed heterostructure, this kind of diode can confine the light wave travel along a certain direction needless of input and output waveguides. And unidirectional beam splitters are also obtained through simple design of a composite PC structure. These calculated results may be utilized in the future complex photonic circuits.
[1] J.Y. Chen, L.W. Chen, Optics Express 14 (22) (2006) 10733. [2] Z. Wang, J.D. Chong, J.D. Joannopoulos, M. Soljacic, Physical Review Letters 100 (2008) 013905. [3] R.L. Espinola, T. Izuhara, M.C. Tsai, R.M. Osgood Jr., H. Dotsch, Optics Letters 29 (9) (2004) 941. [4] M.A. Levy, Journal of the Optical Society of America B 22 (1) (2005) 254. [5] J. Hwang, M.H. Song, B. Park, S. Nishimura, T. Toyooka, J.W. Wu, Y. Takanishi, K. Ishikawa, H. Takezoe, Nature Materials 4 (5) (2005) 383. [6] Z. Wang, Y.D. Chong, J.D. Joannopoulos, M. Soljacic, Nature 461 (2009) 772. [7] S. Cakmakyapan, H. Caglayan, A.E. Serebryannikov, E. Ozbay, Applied Physics Letters 98 (2011) 051103. [8] C.C. Lu, X.Y. Hu, Y.B. Zhang, Z.Q. Li, X.A. Xu, H. Yang, Q.H. Gong, Applied Physics Letters 99 (2011) 051107. [9] C.C. Lu, X.Y. Hu, H. Yang, Q.H. Gong, Optics Letters 36 (2011) 4668. [10] C. Wang, C.Z. Zhou, Z.Y. Li, Optics Express 19 (2011) 26948. [11] X.F. Li, X. Ni, L. Feng, M.H. Lu, C. He, Y.F. Chen, Physical Review Letters 106 (2011) 084301.
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Wideband high-contrast optical diode and unidirectional beam splitters via near-infrared metallic photonic crystals Shuai Feng a,n, Cheng Ren b, Wenzhong Wang a, Yiquan Wang a a b
School of Science, Minzu University of China, Beijing100081, PR China School of Opto-Electronic Information Science and Technology, Yantai University, Yantai 264005, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 March 2012 Received in revised form 28 September 2012 Accepted 5 October 2012 Available online 22 October 2012
A novel nanoscale all-optical photonic crystal diode consisting of rectangular and square metals immersed in silicon is reported. This wideband high-contrast diode based on the self-collimation behavior can confine the light beams travel along a certain direction. So it works well needless of the input and output waveguides and is more feasible to combine with other functional devices in the complex integrated optical circuits. And through a simple design of two photonic crystals’ interface, unidirectional beam splitters owing to the directional band gap can also be obtained. & 2012 Elsevier B.V. All rights reserved.
Keywords: Photonic crystal All-optical diode Light beam splitter
1. Introduction Owing to the capability of unidirectional movement of the current flux, electrical diode plays a basic role in electronic circuits, which has significantly revolutionized fundamental science and advanced technology. The unidirectional propagation of electromagnetic waves has attracted peoples’ much attention due to its important applications in the fields of optical computing, optical interconnection networks and integrated photonic circuits. The propagation of light in photonic crystal (PC) is just like the movement of electron in semiconductors, which is to say that photonic forbidden bands exist in PCs. And considerable efforts have been dedicated to the study of the nonreciprocal transmission of electromagnetic waves in the different kinds of PC heterostrcutures [1–11]. Various schemes have been proposed to design all-optical diode in nonlinear and magnetic PCs with broken time reversal symmetry [1–4]. Due to the relatively small nonlinear susceptibility and magneto–optical coefficient of conventional materials, above all optical diodes works well only if the operating light intensity or magnetic field is very strong, which restricts its actual applications in many fields. Hwang et al. [5] reported an electrotunable optical isolator by combining the photonic band gap effect and the unique interface properties of asymmetric liquidcrystal photonic band gap heterostructure, showing nonreciprocal transmission of circularly polarized light in photonic band gap regions. But the large size of liquid crystal is unsuitable for
n
Corresponding author. Tel.: þ86 10 68932205; fax: þ86 10 68932205. E-mail address: [email protected] (S. Feng).
0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.10.006
the practical integration applications. Wang et al. [6] realized unidirectional transmission of electromagnetic chiral-edge states in a magneto–optical PC within the microwave region, which works well in a strong magnetic field environment. Recently, Cakmakyapan et al. [7] reported the strong directional selectivity of a single subwavelength slit in nonsymmetric metallic gratings with double-side corrugations at the microwave frequencies. Lu et al. [8,9] realized a low-power high-contrast all-optical diode in a two-dimensional (2D) PC heterostructure with broken spatial inversion symmetry experimentally. Wang et al. [10] reported a unidirectional on-chip optical diode in silicon based on the directional band gap difference of the near-infrared square-lattice photonic crystals comprising a heterojunction structure and the break of the spatial inversion symmetry. Li et al. [11] utilized a sonic-crystal-based acoustic diode that had broken spatial inversion symmetry and experimentally realized sound unidirectional transmission in this acoustic diode. In this paper, we designed a 2D square-lattice PC heterostructure consisting of rectangular and square metals immersed in silicon. For the near-infrared light waves around 1550 nm, the rectangular-metal PC works as a waveguide owing to its largeangle self-collimation behavior along the ! –X direction. For the square-metal PC, the light transmission characters are determined by both the incident light’s frequency and its incident angle. So it provides us great feasibility to design a composite PC structure and acquire the different transmission characteristics of the leftward and rightward incidence through the heterostructure composed of above two PCs. Moreover, through the design of two PCs’ interface, a kind of unidirectional beam splitter owing to the directional band gap is also obtained.
S. Feng et al. / Optics Communications 289 (2013) 144–148
2. Unidirectional light transmission through metallic PC heterostructures At first, we consider a PC structure consisting of square metal rods immersed in silicon. The length of the PC’s lattice constant is a¼400 nm, and the refractive index of the background material is 3.45. The side length of the square metal is 0.25a and the sides are placed along the ! –X direction of the PC. Drude dispersion model is adopted to describe the permittivity of the metal, which is depicted as o2 eðoÞ ¼ e0 1 oðo þp igÞ . In the above equation, op is the plasma frequency and g is the damping coefficient. The metal studied in paper is Ag, the corresponding values are op ¼ 1:37 1016 Hz and
g ¼ 2:73 1013 Hz, which can reproduce the corresponding experiment results well within the near-infrared wavelengths around 1550 nm. Ignoring the absorption of the metal to the light beams, the calculated band structure for the several lowest photonic bands is shown in Fig. 1(a) for the TM modes. The first and second lowest bands are even-mode bands, which can be easily coupled by the incident light beams, while the third lowest band is an odd-mode band. It is well known that the propagation direction of light is
145
identical to the direction of group velocity of light given by vg ¼ rko(k), which means that the group velocity is perpendicular to the equal-frequency surface contour (EFC). Through analysis of the EFC as a function of k, we can find the frequency range in which the self-collimation phenomenon occurs and the propagation direction of light beam. The several EFCs in the second TM bands are shown in Fig. 1(b). It can be seen that the most part of the EFS contours around the frequency 0.24 c/a (c is the velocity of light in vacuum), which are centered at the ! –X line, are quite flat and have the surface normal pointing to the ! –X direction. As the group velocity for a give Bloch mode characterized by K is parallel to the EFS normal at this K point, we can see that the group velocities of the excited Bloch wave modes centered around the ! –X line point towards the ! –X direction, and corresponding to an apparent self-collimation effect for the PC slab, whose surface normal is parallel to the ! –X direction. In the other small part centered at the ! –M line, the curve is convex with respect to the ! point, which means a negative refractive direction. With the increasing of the frequency, the ratio of self-collimation EFS region reduces and the negative-refractive effects enhances. When the square metals are replaced by rectangular metals with the longer sides pointing to the ! X direction of the PC, whose two side lengths are 340 nm and 140 nm, the calculated TM-polarized band structure
Fig. 1. TM-polarized photonic band structures of the 2D square-lattice metallic PCs consisting of (a) square and (c) rectangular metals. And the several equal-frequency surface contours within the second photonic band of the PCs consisting of (b) square and (d) rectangular metals. The length of the square lattice is 400 nm. The side length of the square metals is 100 nm, and the two side lengths of the rectangular metals are 340 nm and 140 nm.
146
S. Feng et al. / Optics Communications 289 (2013) 144–148
and the several EFCs in the second band are shown in Fig. 1(c and d). It is shown that there is an apparent lifting of the lowest forbidden band owing to the increasing of the metal’s size. More important, it can be seen in Fig. 1(d) that the EFCs of the frequencies in the second band are quite flat, meaning that the self-collimating effect along the ! –X direction of the PC occurs. Based on the two PCs mentioned above, we constructed a PC heterojunction structure with the interface between PC1 and PC2 along the G–M direction, whose sketch map is shown in Fig. 2(a). Considering the actual absorption of the metal rods to the incident light waves, we simulated the transmission spectra for a TM light signal transporting along the forward (from right to left) and backward (from left to right) directions, which are obtained by dividing the light energy arrived at the opposite side by the incident light energy. There are 30 rows of rectangular metals and 40 rows of square metals on the center line along the light propagation direction. Fig. 2(b) shows the calculated forward and backward transmission spectra by the solid line (a) and dotted line (b), respectively. It is clearly seen that there exists an isolation band ranging from 0.245 c/a to 0.286 c/a (the wavelength region is from 1399 nm to 1633 nm), where the transmission contrast defined as the ratio of maximum transmission in one direction to the corresponding transmission in the inverse direction exceeds 100. In order to have a visual sight of the one-way transmission characteristics of the light waves through above heterostructure, the spatial light intensity distributions of the rightward and leftward light at normal incidence at the frequencies 0.245,
Fig. 2. (a) The sketch map of the heterostructure consisting of two square-lattice PCs with rectangular and square metals immersed in silicon, and (b) light transmission spectra through the heterostructure with 30 rows of rectangular metals and 40 rows of square metals along the central line. The solid line (a) represents the transmittance spectrum when the light beam is incident leftwards, and the dotted line (b) shows that in the case of rightward incidence.
0.255 and 0.265 c/a are calculated and the results are shown in Figs. 3 and 4. In Fig. 3(a), the light wave resonant at the frequency 0.245 c/a goes straight in PC1 and reaches the heterojunction interface. Refraction occurs at the interface, but the intensity of the refractive light beam within the PC2 region is much weaker comparing with the incident light’s intensity. When the incident light’s frequency is increased to be 0.255 and 0.265 c/a, it can be seen from Fig. 3(b and c) that apparent negative refraction behaviors occur at the interface, which can be understood by the analysis of EFS’s contours shown in Fig. 1(b). In Fig. 4(a and b), light goes straight in PC2 from the right side of the heterostructure owing to the self-collimation effect. Light refraction and reflection behaviors occur at the interface of the PC1 and PC2, and the reflective light beam travels downward. The refractive light beam propagates into the PC1 region owing to the large-angle self-collimation characteristics along the ! –X direction of the PC1, and finally the light beam is exported from the left side of PC heterostructure. When the frequency becomes 0.265 c/a, it can be
Fig. 3. Steady spatial distributions of light intensity at the frequencies (a) 0.245, (b) 0.255, and (c) 0.265 c/a through the heterostructure at normal incidence of light source rightward.
S. Feng et al. / Optics Communications 289 (2013) 144–148
147
Fig. 5. (a) Sketch map of the heterostructure consisting of two PCs with rectangular and square metals immersed in silicon, respectively, and (b) light transmittances through the 40-row-metal PC heterostructure. The solid line (a) represents the transmittance spectrum when the light beam is incident from the left side, and the dotted line (b) shows that in leftward incidence. Fig. 4. Steady spatial distributions of light intensity at the frequencies (a) 0.245, (b) 0.255, and (c) 0.265 c/a through the heterostructure when the light is incident from the right side.
seen from Fig. 4(c) the width of the light beam increases with the light’s propagation distance within PC2 owing to the weaken of self-collimation effect. The self-collimation behavior along the G–X direction of PC1 is not influenced by the alteration of the incident angle from 01 to 451, while the light propagation characteristics within PC2 are determined by the incident angle of the light beam. It is obvious that the forward and backward light paths are quite different. We also constructed another kind of heterostructure by interlacing the rectangular and square metals at interface vertical to the light propagation direction, whose sketch map is shown in Fig. 5(a). The lattice constant of square-lattice PC is changed to be 650 nm, and the two side lengths of rectangular metal are 0.85 a and 0.25 a, while the side length of the square metal is still 0.25 a. Fig. 5(b) shows the calculated forward (from left to right) and backward (from right to left) transmission spectra by the solid line (a) and dotted line (b), respectively. It is clearly seen that there exists an isolation band ranging from 0.398 c/a to 0.428 c/a (the corresponding wavelength region is from 1519 nm to 1633 nm), where the transmission contrast exceeds 200 with a maximum about 10,000. For a certain frequency 0.41 c/a (the corresponding wavelength is 1585 nm), the steady light intensity distributions through the composite structure in forward and backward
directions are shown in Fig. 6(a and b), respectively. It can be seen from Fig. 6(a) that the light wave radiated from the left side travels through the heterostructure and finally is split into two output light beams with a certain angle between them. Fig. 6(b) shows the light wave radiated from the right side of the structure cannot travel through PC2 owing to the directional band gap along the ! –X direction. As far as we know, the unidirectional beam splitter is firstly achieved through a simple adjustment of the two PCs’ interface. To understand the splitter behavior through above heterostructure, the light transmittances at normal incidence through the 40-row-metal square-metal PCs with a surface normal along the ! –X direction and ! –M direction are calculated and the results are shown by the solid line (a) and dotted line (a) in Fig. 7, respectively. Through interlacing the rectangular and square metals at the interface between PC1 and PC2, the refractive light from PC1 to PC2 have light wave vector components pointing to different directions. Owing to the tangential component conservation of the wave vector k and band gap of PC1 in ! –X direction, the output light is finally split into two light beams.
3. Conclusions In conclusion, we have studied a high-contrast broadband alloptical diode in a PC heterostructure consisting of rectangular and
148
S. Feng et al. / Optics Communications 289 (2013) 144–148
Fig. 7. Light transmittances through the 40-row-metal PC at the normal incidence along the ! –X direction and ! –M direction, which are shown by the solid line (a) and the dotted line (b), respectively. The side length of the square metal is 0.25 a, and the lattice constant is 650 nm.
Acknowledgment Project supported by the National Natural Science Foundation of China with Grant nos. 10904176 and 11004169, the Fundamental Research Funds for the Central Universities, the ‘‘985 Project’’ and the ‘‘211 Project’’ of the Ministry of Education of China.
References
Fig. 6. Steady spatial distributions of light intensity at the frequency 0.41 c/a through the heterostructure, whose sketch map is shown in Fig. 5, from the (a) left and (b) right sides of the structure.
square metals immersed in silicon. Comparing with the previous PC all-optical diode based on the directional band gap mismatch, the working frequencies in our proposed structure are within the passband of the PC structures. Owing to the self-collimation characteristics of light propagation in our proposed heterostructure, this kind of diode can confine the light wave travel along a certain direction needless of input and output waveguides. And unidirectional beam splitters are also obtained through simple design of a composite PC structure. These calculated results may be utilized in the future complex photonic circuits.
[1] J.Y. Chen, L.W. Chen, Optics Express 14 (22) (2006) 10733. [2] Z. Wang, J.D. Chong, J.D. Joannopoulos, M. Soljacic, Physical Review Letters 100 (2008) 013905. [3] R.L. Espinola, T. Izuhara, M.C. Tsai, R.M. Osgood Jr., H. Dotsch, Optics Letters 29 (9) (2004) 941. [4] M.A. Levy, Journal of the Optical Society of America B 22 (1) (2005) 254. [5] J. Hwang, M.H. Song, B. Park, S. Nishimura, T. Toyooka, J.W. Wu, Y. Takanishi, K. Ishikawa, H. Takezoe, Nature Materials 4 (5) (2005) 383. [6] Z. Wang, Y.D. Chong, J.D. Joannopoulos, M. Soljacic, Nature 461 (2009) 772. [7] S. Cakmakyapan, H. Caglayan, A.E. Serebryannikov, E. Ozbay, Applied Physics Letters 98 (2011) 051103. [8] C.C. Lu, X.Y. Hu, Y.B. Zhang, Z.Q. Li, X.A. Xu, H. Yang, Q.H. Gong, Applied Physics Letters 99 (2011) 051107. [9] C.C. Lu, X.Y. Hu, H. Yang, Q.H. Gong, Optics Letters 36 (2011) 4668. [10] C. Wang, C.Z. Zhou, Z.Y. Li, Optics Express 19 (2011) 26948. [11] X.F. Li, X. Ni, L. Feng, M.H. Lu, C. He, Y.F. Chen, Physical Review Letters 106 (2011) 084301.