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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 23, NO. 13, JULY 1, 2011
High Efficient Subwavelength Binary Blazed Grating Beam Splitter via Vertical Coupling Junbo Yang, Zhiping Zhou, Wei Zhou, Xueao Zhang, and Honghui Jia
Abstract—We propose a novel broadband beam splitter (BS) with a single-layer and compact grating vertical coupling structure, which is based on the form birefringence of subwavelength binary blazed grating and effective-medium theory. Rigorous coupled-wave analysis is used to optimize the design of this beam splitter. The simulation and analysis show that the BS for transverse electric (TE) light are designed to split the incident light beam into two beams of equal power (nearly 50% split), which travel in opposite directions in the waveguide. The coupling length is about 9 m. The coupling efficiency for the right and the left branches of waveguide are 47% and 52%, respectively. The power difference of two output ports is less than 15% over a 75-nm wavelength bandwidth range. Index Terms—Beam splitter, blazed grating, nanowaveguide.
I. INTRODUCTION
O
PTICAL beam splitter (BS) is a fundamental component for optical instrumentation and has vast applications in scientific researches and information technology related industries. Conventional beam splitters have been based on the natural birefringent effects, the refraction effect at multilayer dielectric coatings, the absorption effect of a dichroic polarizer, the diffraction effect of grating structures, or a combination of several of these effects, which are bulky, heavy, expensive, and not suitable for integrated optical circuits. An alternative way of creating polarization components is based on form birefringence exhibited in subwavelength gratings, which is several times larger than natural birefringence in crystals. This type of subwavelength grating splitter adopts silicon-on-insulator (SOI) material and structure. SOI is emerging as a very important material platform for integrated nanophotonics due to the high refractive index contrast between the silicon core and the oxide cladding ( ) [1]. This material Manuscript received November 02, 2010; revised March 23, 2011; accepted April 02, 2011. Date of publication April 15, 2011; date of current version June 08, 2011. This work was supported by the National Natural Science Foundation of China (60977018, 60907003, 61007047) and by the Foundation of National University of Defense Technology (JC09-02-12). J. Yang is with the State Key Laboratory on Advanced Optical Communication Systems and Networks, Peking University, Beijing 100871, China, and also with the National University of Defense Technology, Center of Material Science, Changsha 410073, China. Z. Zhou is with the State Key Laboratory on Advanced Optical Communication Systems and Networks, Peking University, Beijing 100871, China, and also with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail:
[email protected]). W. Zhou, X. Zhang, and H. Jia are with the National University of Defense Technology, Center of Material Science, Changsha 410073, China. Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2011.2142298
system is very well suited for high density integration of photonic components and circuits which can be fabricated by standard complementary metal oxide semiconductor (CMOS) technology. Owing to the subwavelength nature of the binary blazed grating, all the diffractive orders can be made evanescent so that only one order is present outside the grating structure. In addition, due to the matter of shadowing effect and waveguide feature, binary blazed grating exhibits higher diffraction efficiency than the others. In the past few years, Tyan et al. produced a multilayer Si and SiO subwavelength grating that acted as a high efficiency polarization beam splitter [2]. Pajewski et al. proposed a polarization beam splitter with high diffractive efficiency using binary blazed grating [3]. Their drawbacks are to need oblique incidence for the total internal reflection condition or Brewster angle. Feng et al. also proposed a two-layer grating coupler used as a polarization beam splitter which comprises two-layer polarization sensitive subwavelength grating couples [4]. The upper layer is designed for TE mode coupling, while the lower layer is for the transverse magnetic (TM) mode. However, this type of structure is complicated and difficult to fabricate and design in practical applications. Thus, they are not easy to integrate with other devices due to without vertical coupling between fiber and waveguide. In addition, beam splitter which are based on the form birefringence of subwavelength multilayer binary gratings, have been proposed [5]. However, it is difficult to fabricate due to the multilayer structure. Prisms and slabs made of high-refractive-index materials such as ZnSe, Ge, and Si can be designed as beam splitters for obliquely incident -polarized light in the near-and mid-IR [6]. The split beams travel in orthogonal directions when light is incident at the Brewster angle. For example, total internal reflection at the Si-SiO interface at an angle of incidence near 33 . Thus, this beam splitter is difficult to integrate with other elements. Recently, air hole 2-D photonic crystal and air slots have also been used to produce beam-splitters for power separators [7]. However, it is a potential challenge for this photonic crystal structure to realize beam-splitting operations. In this letter, we propose a planar waveguide beam splitter based on the subwavelength binary blazed grating. It is designed for the wavelength of 1.55 m under TE polarization with vertical coupling scheme. Since the grating length is only 9 m and the grating height is comparable with waveguide thickness, the finite difference time-domain (FDTD) method, a powerful and accurate method for finite size structure, is chosen to simulate and design the binary blazed grating splitter. II. ANALYSIS According to planar waveguide theory, the effective re) of TE mode as a function of fractive indices (ERIs, wavelength and the depth of waveguide satisfy the following
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YANG et al.: HIGH EFFICIENT SUBWAVELENGTH BINARY BLAZED GRATING BEAM SPLITTER
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Fig. 2. Binary blazed grating beam splitter the period of grating m; m; the height of waveguide m; the depth of grating H m; the subperiods of the substructures are the length of beam splitter m and m. Fig. 1. Comparison of the different gratings.
equations:
(5) According to (3)–(5), we have
(1) is the depth of waveguide. and denote the refractive index at two sides of the waveguide, respectively. is the refractive index of waveguide. Thus, for SOI planar waveguide structure, Si , air , SiO , we can obtain the effective refractive index of TE mode when the depth of waveguide is equal to 220 nm, and nm. To meet the phase match condition between the grating and the waveguide modes, the grating period, denoted as , can be described as: (2) , , the When considering vertical coupling, i.e., grating period can be obtained based on above (1) and (2). The effective refractive indices ( ) of a single localized substructure, consisting of a ridge material and a spacing materials can be described as follows: (3) where is the fill factor, which is defined as the ratio of ridge width to grating subperiod. We can control the width of each ridge to obtain the desired refractive index distribution. For the subwavelength binary blazed gratings, rigorous diffraction theory must be applied to describe their behavior. The basic design procedure and discrete processing are shown in Fig. 1, and apply the rigorous diffraction analysis to the localized subwavelength features within the grating period, and optimize it by the simulated annealing method [8]. Assume that the conventional grating has an index of refraction and a height H . The surrounding medium has an index of refraction . The height of each of the discrete multilevel grating is ( ). H denotes the height of binary subwavelength blazed grating, and the fill factor of each subperiod is ( ), then
(4)
(6) With the assumptions and the calculations given above, a ridge-width-modulated grating with localized subwavelength features can be constructed through quantization of the conventional blazed grating. Subsequently, the finite-difference time-domain method is used to simulate this device. The input field is chosen to be TE mode ( m). Taking , we designed a binary blazed grating beam splitter as shown in Fig. 2. III. RESULTS Considering the TE mode and vertical coupling, we obtained the coupling efficiencies to the right and the left directions of the waveguide being 47% ( ) and 52% ( ), respectively. The relevant Poynting Vectors are given in Fig. 3. Obviously, after TE polarization beam is vertically coupled into planar waveguide by subwavelength binary blazed grating, it is well divided into two beams which correspond the right and the left branch of waveguide, respectively, and the difference of power value of them is only about 5%, which is enough small to be suitable for beam splitter. The mode-field distribution of the right and the left output ports of beam splitter are also discussed and analyzed. Their corresponding wave profiles are shown in Fig. 4. It is noted that TE light is imposed the stringent restrictions the range of waveguide 1.6–2.2 m. Thus, the simulation result is exactly the same as our theoretical result and practical design, because the spatial coordinates of the upper and the lower surface of Si waveguide in our design are 1.8 m and 2.02 m, respectively, and the width of waveguide is equal to 0.22 m. Fig. 4 shows the TE light is well coupled into the grating, split into right and left components, and then transmitted into the nongrating portion of the waveguide. Fig. 5 shows the simulation results of coupling efficiencies as a function of incident wavelengths at the right and the left output ports. The results show that the coupling efficiencies to the right and the left ports of waveguide are simultaneously decreased as the wavelength increases (the wavelength varies between 1.50 and 1.575 m). For example, the coupling efficiency is ranging from 0.27 to 0.5 at the right branch while is varies
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 23, NO. 13, JULY 1, 2011
Fig. 5. Coupling efficiency as a function of wavelength.
beam is equally split into two beams by the subwavelength binary blazed grating. The wavelength bandwidth of beam splitter can reach up to 75 nm while maintaining a relative small inequality between the split powers. IV. CONCLUSION Fig. 3. Calculated Poynting Vector component in SOI platform. (a) Distribution of Poynting Vector in waveguide. (b) Wave profile in waveguide.
We have demonstrated the operation of a novel subwavelength binary blazed grating that acts as a vertical coupler and as a beam splitter for the wavelengths ranging from 1.50 to 1.575 m (a bandwidth of 75 nm). We have used rigorous coupled-wave analysis for optimization and numerical characterization of the device. Relatively high coupling efficiencies (47% and 52%) and low power difference (5%) between two branches of the waveguide are achieved by this device according to FDTD simulations. The theoretical analysis is in good agreement with simulation result. This grating splitter is easy to fabricate using single etching step and integrate with other photoelectronic devices. Moreover, the proposed splitter can be placed anywhere on a chip because it allows vertical coupling and splitting, which makes the system design more flexible. REFERENCES
Fig. 4. Distribution of wave profile in waveguide. (a) Wave profile of the right branch in waveguide. (b) Wave profile of the left branch in waveguide.
from 0.27 to 0.65 at the left branch. The power difference between the two branches is getting smaller as the wavelength increases and is confined in a relative small range, i.e., . As seen in the Fig. 5, the difference is equal to zero at the wavelength of 1.575 m, but corresponding to the coupling efficiency of 0.27. In this case, TE polarization
[1] S. Scheerlinck and J. Schrauwen, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express, vol. 15, no. 15, pp. 9625–9630, 2007. [2] R.-C. Tyan and A. A. Salvekar, “Design, fabrication, and characterization of form-birefringent multilayer polarizing beam splitter,” J. Opt. Soc. Amer. A, vol. 14, no. 7, pp. 1627–1636, 1997. [3] L. Pajewski, R. Borghi, G. Schettini, F. Frezza, and M. Santarsiero, “Design of a binary grating with subwavelength features that acts as a polarizing beam splitter,” Appl. Opt., vol. 40, no. 32, pp. 5898–5905, 2001. [4] J. Feng and Z. Zhou, “Polarization beam splitter using a binary blazed grating coupler,” Opt. Lett., vol. 32, no. 12, pp. 1662–1664, 2007. [5] Y.-L. Liao, Z.-F. Han, and Z.-L. Cao, “Design of form-birefringent multilayer nonpolarizing beam splitter,” Opt. Commun., vol. 271, pp. 569–572, 2007. [6] R. M. A. Azzam, “Infrared broadband 50%–50% beam splitters for -polarized light,” Appl. Opt., vol. 45, no. 19, pp. 4572–4575, 2006. [7] P. Pottier, S. Mastroiacovo, and R. M. De La Rue, “Power and polarization beam-splitters, mirrors, and integrated interferometers based on air-hole photonic crystals and lateral large index-contrast waveguides,” Opt. Express, vol. 14, no. 12, pp. 5617–5633, 2006. [8] Z. Zhou and T. J. Drabik, “Optimized binary, phase-only, diffractive optical element with subwavelength features for 1.55 m,” J. Opt. Soc. Amer. A, vol. 12, no. 5, pp. 1104–1112, 1995.
