Open Access
Add to BibSonomyAbstract
We propose an ultra-small polarization splitter based on a resonant tunneling phenomenon. This polarization splitter consists of two identical horizontally oblong silicon wire waveguides separated by a vertical slot waveguide. The structural parameters of the central resonant slot waveguide are designed to couple only the TM-like mode between the left and right side silicon wire waveguides. Results from numerical simulation with the full-vectorial beam propagation method show that a 16-μm-long polarization splitter with extinction ratio better than −20 dB on the entire C-band is achieved.
©2009 Optical Society of America
1. Introduction
Silicon wire waveguides [1]-[3] have attracted great attention for the purpose of miniaturizing optical devices, due to their ability to achieve small bending radii. Moreover, they can confine light in a small region because of their large index contrast. Various kinds of optical devices based on a silicon wire waveguide such as ring resonators [4], corner mirrors [5], and arrayed waveguide gratings [6] have been demonstrated so far. However, one of the main drawbacks of silicon wire waveguides is their strong polarization dependence. To overcome this issue, polarization diversity systems [7] consisting of two polarization splitters [8], [9] and two polarization rotators [10] have been proposed and a polarization independent filter with polarization diversity system was demonstrated [11]. A schematic drawing of a polarization diversity system is shown in Fig. 1 . In polarization diversity systems, incident light is separated into a TE-like mode and a TM-like mode by a polarization splitter, and the TM-like mode (or TE-like mode) is rotated 90 degrees by the first polarization rotator. After this process, separated beams are inputted into functional devices. Finally, the TE-like mode (or TM-like mode) is rotated 90 degrees by the second polarization rotator, and these two modes are combined by a polarization combiner which has the same structure of the polarization splitter. In this way, a polarization independent functional device is achieved. Therefore the polarization splitter is one of the essential components in a polarization diversity system. An ultra small and easy to fabricate polarization splitter based on directional coupler with two rectangular silicon wire cores was proposed, previously [9]. However the extinction ratio of this polarization splitter is about 13 dB because this is based on a difference of coupling length between TE-like mode and TM-like mode, therefore, further improvements of device length and polarization extinction ratio are highly expected.
In this paper, we propose a novel polarization splitter based on resonant coupling [12] between silicon wire and slot waveguides. The polarization splitter consists of two silicon wire waveguides separated by a slot waveguide [13]. The device operation is based on the phenomenon of resonant tunneling. The structural parameters of the central resonant slot waveguide are designed to couple only the TM-like mode between the left and right side silicon wire waveguides, by using a finite element method (FEM) [14]. Numerical simulations using a full-vectorial beam propagation method (BPM) [15] demonstrate that it is possible to obtain a 16-μm-long polarization splitter with extinction ratio better than −20 dB on the entire C-band.
2. Design of polarization splitter based on the resonant tunneling phenomenon
Figure 2 shows the schematic cross-section of the proposed polarization splitter based on Si wire waveguides. The substrate and the cover cladding are assumed to be silica with refractive index equal to 1.444, and air with refractive index equal to 1, respectively, while the silicon core index is 3.475. It consists of two identical rectangular waveguides, WG1 and WG3, separated by a slot waveguide WG2. The input/output waveguides WG1 and WG3 are horizontally oblong structures with width and height of 400 nm and 250 nm, respectively. The waveguide width and the slot width of WG2 are defined as w and g, respectively, and the height of WG2 is equal to 250 nm. The gap between WG1 and WG2, and WG2 and WG3, is defined as d.
Fig. 2 Cross section of the proposed polarization splitter consisting of two identical Si wire waveguides (WG1 and WG3) separated by a slot waveguide (WG2).
In the vertical slot waveguide WG2, due to the refractive index discontinuity, the TE-like mode is strongly confined in a narrow slot region, whereas the TM-like mode is confined in the entire WG2 region. Therefore, the condition in which the effective refractive index of the TE-like mode is smaller than that of the TM-like mode is achievable with a proper choice of the structural parameters of the WG2. On the other hand, in WG1 and WG3, the effective refractive index of the TM-like mode is much smaller than that of the TE-like mode. The structural parameters of WG2 are determined such that its TM-like mode is almost resonant with the TM-like mode of the outer WG1 and WG3. Due to the large difference between the effective refractive index of the TE-like mode in WG2 and that of the same mode in WG1 and WG3, the TE-like mode of WG2 will be completely nonresonant with respect to those of the outside waveguides. Figure 3 shows the effective refractive indices of the TE- and TM-like modes as a function of the waveguide width w in the central WG2 for several incremental values of the slot width g calculated through a full-vector modal solver based on FEM [14], where the dotted and dashed lines represent the effective refractive indices of TE- and TM-like modes equal to 2.228 and 1.704 in both horizontally-oblong side waveguides (WG1 and WG3), respectively, at the 1550 nm operating wavelength. We can see that, when the structural parameters in WG2 are set as w ≈580 nm and g ≈60 nm, the effective refractive index of the TM-like mode in WG2 becomes equal to that in WG1 and WG3, namely the dashed line and the red curve intersect (solid circle in Fig. 3(b)), whereas the effective refractive index of the TE-like mode in WG2 is much different from those in WG1 and WG3 as shown in Fig. 3(a). In other words, the TM-like mode inputted to WG1 can resonantly couple into WG3 through WG2, while the TE-like mode in the same situation hardly couples into WG2 and propagates in WG1, resulting in a polarization splitting operation on a wide wavelength range with high extinction ratio.
Fig. 3 Effective refractive indices of (a) TE-like mode and (b) TM-like mode as a function of the waveguide width w in the central WG2 with 250 nm height for several incremental values of the slot width g, where the dotted line in (a) and the dashed line in (b) represent the effective refractive indices of TE- and TM-like modes in the horizontally oblong side waveguides (WG1 and WG3) with 400 nm width and 250 nm height, respectively, at the 1550 nm operating wavelength.
The operation of this polarization splitter can also be explained in terms of the supermodes of the three-core directional coupler. If the individual isolated cores of the coupler are single moded, the coupled structure supports three modes, two symmetric and one antisymmetric. In Fig. 4 , the electric field distributions of the TM-like supermodes at 1550 nm are shown. Let neff ,1, neff ,2, and neff ,3 represent the effective refractive indices of the two symmetric modes and of the one antisymmetric mode, respectively, for the TM-like wave. If we choose the structural parameters of WG2 to satisfy the condition at the resonant wavelength λR:
the power transfer efficiency from one outside waveguide to the other can be maximized [12] and the coupling length L can be calculated using the following equation:where the coupling length can be controlled by the gap distance, d, between the central waveguide and the outer waveguide. To achieve short device size, we assumed gap distance d = 300 nm. Figure 5 shows the w dependence of the value of for g = 60 nm. We can see that when the structural parameters in WG2 are defined as w ≈600 nm, the Eq. (1) is satisfied. Estimated coupling length from Eq. (2) is about 16 μm.Fig. 4 The electric field distributions of three supermodes at 1550 nm for the TM-like wave in a three-core directional coupler. This structure supports three modes, two symmetric (a), (b) and one antisymmetric (c).
Fig. 5 The WG2 width dependency of the value of 2n eff,3−n eff,1−n eff,2 for g = 60 nm. When the waveguide width in WG2 is defined as w ≈600 nm, the Eq. (1) is satisfied for the TM-like mode at 1550 nm.
3. Characteristics of polarization splitter
In order to show the applicability of the proposed polarization splitter, we confirmed that the polarization splitter shown in Fig. 2 could split TE- and TM-like modes, using the full vectorial BPM [15]. The TE- and TM-like modes at 1550 nm are inputted into WG1 in Fig. 2 and the beam propagation analysis is performed. Figures 6(a) and (b) show the normalized power variation versus the propagation distance in WG1 and WG3, respectively, where w = 600 nm, g = 60 nm, and d = 300 nm. We find that the TE-like mode launched into WG1 does not couple into WG3, while the TM-like mode completely couples into WG3. The separation of TE- and TM-like modes is achieved at a propagation distance of ~16 μm. This result is in good agreement with the coupling length estimated by using Eq. (2). The electric field distributions of the TE- and TM-like modes at the propagation distance of 0 μm, 8 μm and 16 μm are shown in Figs. 7(a), (b), and (c) , respectively. From these results we can also confirm that the TE-like mode launched into WG1 does not couple into WG3, while the TM-like mode completely couples into WG3.
Fig. 6 Normalized power variation along the propagation distance (a) in WG1 and (b) WG3. We find that the TE-like mode launched into WG1 does not couple into WG3, while the TM-like mode completely couples into WG3. The separation of TE- and TM-like modes is achieved at a propagation distance of ~16 μm.
Fig. 7 The electric field distributions at the propagation distance of (a) 0 μm, (b) 8 μm, and (c) 16 μm at the 1550 nm operating wavelength. The left and right panels show the TE-like and TM-like modes, respectively. The TE-like mode launched into WG1 does not couple into WG3, while the TM-like mode completely couples into WG3 with a propagation length of about 16 μm.
Figure 8 shows the wavelength dependence of the extinction ratios in WG1, ER1, and WG3, ER3, for a fixed device length of 16 μm, where w = 600 nm, g = 60 nm, and d = 300 nm. The extinction ratios ER1 and ER3 are defined as follows:
Fig. 8 The wavelength dependence of the extinction ratios in WG1, ER1, and WG3, ER3, at a fixed device length of 16 μm. The bandwidth of −20 dB extinction ratio is almost 58 nm, from 1523 nm to 1581 nm.
The bandwidth where we have –20 dB extinction ratio is almost 58 nm, i.e., from 1523 nm to 1581 nm. If the TM- and TE-like modes are separately launched into WG1 and WG3, respectively, the TM-like mode couples into WG3 where the TE-like mode propagates and the two modes completely combine at the coupling length of the TM-like mode. In this case the three-core Si wire waveguide can be used as a polarization combiner.
Figure 9 shows the wavelength dependence of the insertion losses for the TE- and TM-like modes, for a fixed device length of 16 μm, where w = 600 nm, g = 60 nm, and d = 300 nm. The insertion losses are calculated as difference between input power and output power in each output port. The insertion loss for the TM-like mode is almost two orders of magnitude larger than that for the TE-like mode. The polarization dependent loss of this device is almost same value as the insertion loss for the TM-like mode and less than 0.4 dB on the entire C-band.
Fig. 9 The wavelength dependence of insertion losses for the TE- and TM-like modes at a fixed device length of 16 μm. The polarization dependent loss of this device is less than 0.4 dB for the entire C-band.
The extinction ratios at 1550 nm as a function of WG2 width w, slot width g, and gap distance d are shown in Figs. 10(a)-(c) , respectively. When WG2 width w is changed, the wavelength which satisfies Eq. (1) is changed. As a result, the extinction ratio is impaired. Similarly, when the slot width g is changed, the extinction ratio is also impaired. The tolerance of manufacturing error for w and g would be about 5 nm and 3 nm, respectively. In contrast, the extinction ratio is not sensitive to variations in the gap distance d.
Fig. 10 The extinction ratios in WG1, ER1, and WG3, ER3, as a function of (a) WG2 width w, (b) slot width g, and (c) gap distance d.
In Fig. 11 , the WG2 width w and the slot width g dependency of the extinction ratio in WG1 at the wavelength of 1550 nm is shown. We plot only extinction ratio in WG1, because the extinction ration in WG3 is less sensitive. The dashed lines represent the structure with −20 dB extinction ratio. It can be seen that the region of good performance with better than −20 dB extinction ratio is belt-shaped. Usually, etching errors for slot width and waveguide width are opposite direction, however, we can say that when the structural parameters g and w are simultaneously changed by more than 5 nm due to the fabrication errors, if the errors for g and w have the same direction, the extinction ratio is not degraded so strongly.
Fig. 11 The extinction ratio in WG1, ER1, as a function of the slot width g and the WG1 width w at the propagation length of 16 μm. The dashed lines represent the structure with extinction ratio of −20 dB.
When we set gap distance as d = 300 nm, we can achieve 58 nm bandwidth polarization splitter with coupling length of 16 μm. However there is trade-off relationship between extinction ratio and, coupling length and operating bandwidth. In other words, when we reduce gap distance, extinction ratio is impaired, while we can achieve polarization splitter with wide operating bandwidth and short device size. On the other hand, when we increase gap distance, device size becomes long and operating bandwidth becomes narrow, however extinction ratio can be improved. In Fig. 12 , the gap distance dependence of the operating bandwidth and coupling length estimated by Eq. (2) is shown. In this simulation, WG2 width is defined as satisfying Eq. (1) at 1550 nm wavelength, where the slot width g is fixed as 60 nm. We can see that the broader operating bandwidth and shorter device size are achieved by adopting smaller gap distance. However, if the gap distance d is smaller than 230 nm, we can’t input the field in the input waveguide appropriately, since the inputted mode will strongly overlap with neighboring waveguide. When the gap distance d equals 230 nm, the operating bandwidth and device size of this polarization splitter are 105 nm and 10.5 μm, respectively.
Fig. 12 Coupling length and operating wavelength as a function of gap distance d, where the slot width g is fixed as 60 nm.
Conclusion
In this paper, we have proposed a novel design of a polarization splitter based on the resonant tunneling phenomenon. The three waveguides consist of two identical horizontally oblong Si wire waveguides separated by a vertical slot waveguide. Results from numerical simulations with the full-vectorial BPM have been presented. The polarization splitter has an extinction ratio better than –20 dB over C band with a short length of less than 16 μm. The proposed polarization splitter could be used in the construction of ultra-compact polarization splitters/combiners in polarization diversity system.
References and links
1. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonic devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11(1), 232–240 (2005). [CrossRef]
2. K. Yamada, T. Tsuchizawa, T. Watanabe, J. Takahashi, E. Tamechika, M. Takahashi, S. Uchiyama, T. Shoji, H. Fukuda, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon wire waveguiding system,” IEICE Trans. Electron. E87-C, 351–358 (2004).
3. K. K. Lee, D. R. Lim, H.-C. Luan, A. Agarwal, J. Foresi, and L. C. Kimerling, “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000). [CrossRef]
4. B. E. Little, J. S. Foresi, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10(4), 549–551 (1998). [CrossRef]
5. R. U. Ahmed, F. Pizzuto, G. C. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood Jr., “Ultra-compact corner-mirrors and T-branches in silicon-on-insulator,” IEEE Photon. Technol. Lett. 14(1), 65–67 (2002). [CrossRef]
6. K. Sasaki, F. Ohno, A. Motegi, and T. Baba, “Arrayed waveguide grating of 70 × 60 μm2 size based on Si photonic wire waveguides,” Electron. Lett. 41(14), 801–802 (2005). [CrossRef]
7. T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007). [CrossRef]
8. M. Komatsu, K. Saitoh, K. Kakihara, and M. Koshiba, “Design of Ultra Small Polarization Splitter Based on Silicon wire Waveguides,” Integrated Photonics and Nanophotonics Research and Applications 2008 Technical Digest IMC6 (2008).
9. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Ultrasmall polarization splitter based on silicon wire waveguides,” Opt. Express 14(25), 12401–12408 (2006). [CrossRef] [PubMed]
10. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Polarization rotator based on silicon wire waveguides,” Opt. Express 16(4), 2628–2635 (2008). [CrossRef] [PubMed]
11. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express 16(7), 4872–4880 (2008). [CrossRef] [PubMed]
12. K. Saitoh, Y. Sato, and M. Koshiba, “Polarization splitter in three-core photonic crystal fibers,” Opt. Express 12(17), 3940–3946 (2004). [CrossRef] [PubMed]
13. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]
14. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38(7), 927–933 (2002). [CrossRef]
15. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19(3), 405–413 (2001). [CrossRef]
