Abstract

We propose and analyze a compact polarizing beam splitter (PBS) based on a metal-insulator-metal (MIM) structure inserted into a multimode interference coupler (MMI). Owing to the MIM structure, the TE polarized state is reflected by the cut-off condition while the TM polarized state is transmitted by the surface plasmon polariton, and the two polarized states can thus be separated. In this paper, the dependence of the reflected TE and transmitted TM field intensities on the MIM length and the gap thickness has been studied systematically. The proposed PBS structure, with a total size of 4 × 0.7 × 44 µm3 is designed with MIM length, gap thickness, and metal thickness of 0.6 µm, 0.5 µm, and 0.05 µm, respectively. In the designed PBS, the transmittance for the TM polarized light, reflectance for the TE polarized light, extinction ratio, and insertion losses of the TE and TM modes are obtained using a 3D finite-difference time-domain method to be 0.9, 0.88, 12.55 dB, and 1.1 dB and 0.9 dB, respectively. The designed PBS has a much shorter length, 44 µm, compared to previous PBS devices.

© 2013 OSA

1. Introduction

Integrated polarization beam splitters (PBSs) are frequently implemented in access network applications because of their low cost, compactness, and potential integration with other photonic and electronic components. These features are significantly relevant to the fabrication process as well as compound materials used for the integrated devices. In realizing integrated PBS, multimode interference (MMI)-based devices [1, 2] are more desirable than many other conventional directional couplers [36] because MMI-based devices are smaller and have a better tolerance in fabrication with particular principles of light splitting-recovering. A PBS based on MMI couplers commonly requires a certain MMI length after the width and thickness are specifically determined. Since the device length is usually a multiple of the beat length for two polarization terms, a long device length is usually required to obtain the common multiples for polarization separation. Compared to grating-assisted or photonic crystal (PhC)-assisted MMI couplers [715], PBS structures have been proposed to dramatically shorten the device length [8, 10]. Owing to the dispersive nature of the underlying principles, Bragg grating-based and PhC-based PBSs do not provide wideband operation. Furthermore, the PBS fabrication process does not easily allow these to be made compact. The Bragg grating-based and PhC-based PBSs require a stringent fabrication tolerance. Excessive loss and errors may occur as a result of the side-walls not being perpendicular, being too rough, or having different hole array and hole-shaped of compound arrays. Moreover, the PhC-based devices have a lower limit on their total size because they require several periodic holes to generate the characteristics of the photonic bandgap. In contrast, a plasmonic-based structure [7] requires maintaining a specific incident angle in order to confine, or not confine, a polarization. The thin metal film is also concerned for preventing a small resonance angle and large absorption. To overcome these obstacles, a novel PBS structure utilizing a metal-insulator-metal (MIM) structure has recently been developed [16]. The MIM-based structure was used to separate the reflected TE polarized state and transmitted TM polarized state. In this paper, as illustrated in Fig. 1(a), a compact PBS employing the polarization separation property of a MIM embedded in a MMI coupler is proposed and analyzed. The MIM structure is composed of two silver layers and a silicon oxide layer in between and is simple to fabricate. Another advantage of this structure is that the input TE and TM ports can be assigned separately by utilizing MMI. Therefore, the designed device could be utilized in many applications such as an isolator with mode selection, polarizer, and light mode splitter.

 

Fig. 1 (a) 3D configuration of the PBS structure with an embedded MIM, (b) 2D cross section schematic of MIM-embedded slab waveguide.

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In the configuration, TE and TM polarized modes are defined the same as in a single slab waveguide. Transmittance and reflectance of the TE modes are dominated by the gap thickness (GM) and the length (LM) of the MIM. Conversely, those of the TM modes are not sensitive to the gap, because of the presence of the surface plasmon polariton (SPP). These facts were considered in the design of the PBS based on MIM-embedded MMI. The position of the MIM in the MMI coupler is determined to maximize the polarization separation. Furthermore, appropriate metal thickness of the MIM is also examined to gain high polarization separation and to determine the propagation length (LWG).

This paper is organized as follows. First, we examine the propagating property of the TE and TM polarized modes in the MIM-embedded slab waveguide, focusing on the cut-off condition of the TE polarized mode. Then, the reflection properties of the TE polarized mode and transmission properties of the TM polarized mode are investigated to maximize polarization separation. Next, the propagation properties of the TE and TM polarized modes in the MIM-embedded MMI are studied by varying the MIM position. The effect of the metal thickness is also studied and discussed. Conclusions are presented in the last section.

2. Design and Analysis of MIM-embedded MMI PBS

In contrast to the Bragg grating-assisted MMI or the PhC-assisted MMI [8, 13], the MIM is introduced to construct a compact PBS device. Utilizing the polarization-sensitive characteristic of the MIM structure, the TE polarized mode (Hx , Ey, Hz) and the TM polarized mode (Ex, Hy, Ez) are split inside MMI coupler. The 3D schematic of a MIM-embedded MMI for PBS is shown in Fig. 1(a). As shown, the MMI coupler is composed of four access ports but only three access ports are used for the PBS device. In this study, we set the operation wavelength to 1.55 μm, the MMI coupler width (WWG) to 4 μm, and the thickness (HWG) to 0.7 μm. The width of the access port (Wac) is set to 1 μm with a separation distance (Sac) of 0.4 μm. The waveguide is composed of silicon (n1 = 3.48) on silicon oxide (SOI), while the MIM is composed of silver (n3 = 0.54 + j10.832) and silicon dioxide (n2 = 1.45) layers.

The designed device is a compact PBS that utilizes cost-effective materials and a simple fabrication process. For accurate analysis, a full 3D structure is considered. The dimension of the MMI coupler is first analyzed and optimized by modal field expansion [17] and the beam propagation method. In our design, the device length LWG is selected to allow the TM polarized light to transmit to the MMI port C. Length LA is designed to allow the reflection of the TE polarized light to port A, as seen in Fig. 1(a). Based on the self-imaging effect, the field evolution along a conventional MMI coupler is given by the superposition of all guided modal field distributions [17]:

E(y,x)=m=0M1cmψm(y)exp[jm(m+2)π3Lπx],
where cm and ψm denote the excitation coefficient and the modal field of the mth order mode, respectively. Here, Lπ is the wavelength-dependent beat length.

Moreover, the TE and TM polarized modes that propagate inside the MIM are reflected or transmitted depending on the dimensions of the MIM structure. In term of the input wavelength, the cut-off condition for the TE polarized mode is given by Coff=λoff/2ng,where λoff and ng are the cut-off wavelength and the refractive index of MIM gap material, respectively. The transmission and reflection of the TE modes are determined only by the GM, such that reflection occurs for GM < Coff while transmission occurs for GMCoff [16]. Therefore, the GM needs to be smaller than the cut-off condition of 0.534 μm to reflect the TE polarized mode. However, the propagation of the TM polarized state has little dependence on the cut-off condition and the GM because the presence of SPP of the TM polarized state [18]. Hence, high transmission of the TM polarized mode can occur. Nevertheless, the limitation of the gap thickness appears because the light beam needs to be smaller than the diffraction limit (λ/2n3)3in order to confine or squeeze the electromagnetic energy in the volume of the MIM [19]. Moreover, the selection of a gap material for the MIM is limited by the diffraction limit. That is why SiO2 (ng = n2) is selected for the gap material of MIM rather than Si.

The transmission and reflection coefficients in the MIM-embedded MMI can be defined as T(λ0) and Γ(λ0), respectively. The forward propagating field ETM(y, LWG) and the backward propagating field ETE(y,0) can be written as [20]

ETM(y,LWG)=T(λ0).m=0M1cmψm(y)exp[jm(m+2)π3LπLWG],
ETE(y,0)=Γ(λ0).m=0M1cmψm(y)exp[jm(m+2)π3LπLA],
Equation (2) indicates the self-imaging effect for the TM transmitted field ETM(y,LWG). Similarly, Eq. (3) reveals the self-imaging effect for the TE polarized reflected field ETE(y,0).

3. Simulation results and discussion

The MMI coupler is in the form of a slab waveguide which is made of silicon on silicon oxide with refractive indexes n1 = 3.48 and n2 = 1.45, respectively. The MIM structure is given by a gap material of SiO2 and two independent metal slabs of silver (n3 = 0.54 + j10.823) with a thickness of 0.2 μm.

We first investigate the transmittance properties of the MIM structure by varying the MIM length from 0.1 to 1 μm and the gap thickness from 0.1 to 1 μm with a 0.1-μm step. For simplicity, a MIM-embedded waveguide with a width of 1 μm and a height of 0.7 μm is considered. As shown in Fig. 2, transmittance results for the TE and TM modes are obtained with respect to the variations in the LM and the GM. Figure 2(a) shows that the transmittance of the TE polarized mode decreases for GM < 0.6 μm, owing to the cut-off condition. For GM > 0.6 μm, however, the penetrated field can be relatively high, and the TE transmittance peaks are observed for LM larger than 0.7 μm. This is because of the Fabry–Perot etalon effect in the MIM-embedded waveguide. In contrast, as shown in Fig. 2(b), the TM polarized intensity fluctuates according to LM and GM owing to the existence of SPP and the Fabry-Perot etalon effect. For LM = 0.6 μm and GM = 0.4 μm or 0.5 μm, there is the highest TM transmittance peak because highly confinement guiding of SPP and Fabry-Perot etalon effect are available. However, for GM > 0.5 μm, the decreased TM transmittance peak is due to low coupling from the waveguide to the MIM. For GM < 0.4 μm, the decreased TM transmittance peak is due to the diffraction limit. Consequently, the high reflectance of the TE polarized mode and the high transmittance of the TM polarized mode, which are desirable features for the PBS device, are obtained with GM = 0.4 μm or 0.5 μm and LM = 0.6 μm. In addition, Fig. 2(c) shows the Fabry-Perot etalon resonance of the TM transmittance for the case of GM = 0.5 μm. The peak intensities are slight decreased due to the propagation loss of SPP.

 

Fig. 2 Transmittance results of (a) TE mode and (b) TM mode for the MIM-embedded waveguide varying LM and GM. (c) TM mode, with GM = 0.5 μm, versus the MIM length from 0 to 2 μm.

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For the design of MIM-embedded MMI PBS, the effect of MIM position on the PBS performance is first investigated. Using the same device parameters mentioned above, GM and LM of the MIM are selected to be 0.5 μm and 0.6 μm, respectively, according to the results of Fig. 2. Then, the MIM position (LA) is varied from 5 to 35 μm with a 1-μm step. For the PBS device, the three access ports A, B, and C are assigned to the reflection of the TE polarized state, the input light, and the transmission of the TM polarized state, respectively, as indicated in Fig. 1(a). From Fig. 3(a), it can be seen that the normalized field intensities of the TE and TM modes fluctuate by varying LA. The intensity of the TE mode in port A highly fluctuates between 0.22 and 0.88 with a low insertion loss of 1.1 dB. The field intensity in port C is extremely low because of the cut-off condition. Conversely, for the TM mode, the high transmitted intensity in port C fluctuates with a low insertion loss of 0.9 dB, and the low reflected intensity in port A also slightly fluctuates. Therefore, the TE reflectance peak in port A and the TM transmittance peak in port C can be obtained in our PBS structure when LA varies from 21 to 23 μm. To validate the length of the MMI coupler, the propagating field profile along the MMI coupler is monitored by the FDTD method. As shown in Fig. 3(b), the first single folded image distance of the TM transmittance peak corresponds to a MMI length of 44 μm when LA is 21μm.

 

Fig. 3 (a) Normalized intensities of the TE and TM modes according to the variation in the MIM position (LA) from 5 to 35 μm. Other design parameters are GM = 0.5 μm, LM = 0.6 μm, WWG = 4 μm, and HWG = 0.7 μm. (b) Propagating field profile along the MMI with a length (LWG) of 44 μm. The MIM position LA is 21 μm, and port A, B, and C are assigned for reflected TE mode, light source, and transmitted TM mode, respectively.

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Figure 4 shows the reflected field profiles of the TE polarized mode in the cross-section of port A. The three different reflected field profiles correspond to LAs of 21, 22, and 23 μm, respectively. The apparent differences are because the phase-matching is significantly affected by the MIM position. When LA is 22 μm, the beam profile is poor as illustrated in Fig. 4(b). The poor beam profile refers to the fact that the phase-matching of the field distribution does not occurred at the center of port A, resulting in a non-Gaussian profile. For the other LAs of 21 and 23 μm, however, strong phase-matching and a Gaussian field profile can be built as shown in Figs. 4(a) and 4(c).

 

Fig. 4 TE field profiles in the cross-section of port A for different MIM positions in the MMI coupler. The figures represent the MIM position (LA) of (a) 21 μm, (b) 22 μm and (c) 23 μm.

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For this structure, the high polarization splitting property occurs both for GM = 0.4 and 0.5 μm. For the design of PBS based on MMI, MIM properties embedded in MMI need to be carefully examined, though they should be similar to the case in a slab waveguide. Figures 5(a) and 5(b) reveal the TE and TM intensities in port A and C, respectively. With the same LM of 0.6 μm, GM of 0.4, 0.5, and 0.6 μm are considered. As shown in Fig. 5(a), the highest intensities of the TE modes occur in port A for GM = 0.5 μm, while the lowest intensities occur in port C for GM = 0.4 μm. For the TM modes, shown in Fig. 5(b), both the highest intensities in port C and the lowest in port A occur for only GM = 0.5 μm. The degradation for GM = 0.4 μm of MIM-embedded in the MMI structure is because the MMI coupler experiences multimode waveguide property. Therefore, the high polarization splitting property can be obtained in a MIM-embedded MMI if GM = 0.5 μm and LM = 0.6 μm.

 

Fig. 5 Normalized intensity of (a) TE mode (b) TM mode in port A and C versus MIM position LA = 21 μm, 22 μm, and 23 μm with the MIM length LM = 0.6 μm and varied gap thickness GM = 0.4 μm, 0.5 μm, and 0.6 μm

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Another interesting effect of the metal thickness (TM) is investigated by changing TM in the MIM-embedded MMI. The parameters of MIM are GM = 0.5 μm, LM = 0.6 μm, and LA = 21 μm, and those of MMI coupler are the same as WWG = 4 μm, HWG = 0.7 μm, and LWG = 44 μm. The normalized TE and TM intensities are then obtained by varying TM. As shown in Fig. 6, TE intensities at port A and C are not clearly separated when TM is zero because of the non-metallic mirror. For TM intensities at port A and C, they are not clearly separated when TM is ranged from 0 to 25 nm, because of low confinement of SPP due to inappropriate thin metal thickness. The SPP is the main reason for the high confinement of the TM mode when the phase-matching of SPP at the metal/dielectric interface is satisfied by the corresponding incident angle, wavelength, and metal thickness. Consequently, the high TM intensity at port C is about 0.9 for TM = 50 nm, and slightly decreases as TM increases. The TE intensity at port C is extremely low, whereas that in port A is about 0.88 and slightly reduces for TM larger than 50 nm. Therefore, metal thickness is a critical parameter for obtaining high polarized modes owing to the guiding of SPP and metallic mirror. When TM = 50 nm, a TM intensity peak is caused by the high confinement of SPP, whereas the TE intensity peak is related to the good metallic mirror of the MIM structure. Accordingly, a high extinction ratio of 12.55 dB can be achieved.

 

Fig. 6 Results of the normalized TE and TM intensities as a function of MIM metal thickness.

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As have been well summarized in ref [7], the extinction ratios of PBS using photonic crystal, directional coupler, and plasmonic waveguide are ranged from 10 to 20 dB. Compared to these values, our data is not sufficient as it is. However, if we employ an optimized MMI coupler with tapered access ports reinforcing field intensity and polarization splitting, the extinction ratio is potentially improved up to 20 dB as indicated in Figs. 2(a) and 2(b) (PTM = 0.98 and PTE = 0.01). In addition, it is believed that high quality PBS based on MIM-embedded MMI can be easily fabricated by using a dry etching, for sharp sidewall of MIM, followed by MMI layer depositions. The high image resolution, high extinction ratio, and low insertion loss are due to the properties of the MIM structure and the MMI coupler. Therefore, the proposed device needs further development and research.

4. Conclusion

In this paper, a novel compact PBS based on a MIM-embedded MMI has been proposed and analyzed. We examine the reflection and transmission of the TE mode in terms of the cut-off condition in the MIM-embedded slab waveguide, and then investigate the PBS in MMI. The TE polarized state is reflected by the cut-off condition while the TM polarized state is transmitted by the SPP in MIM structure. By employing a MMI coupler, the reflected and transmitted fields can be easily separated into different ports. Our results show that the PBS design has superior characteristics such as a low insertion loss of 1.1 dB for the TE mode and 0.9 for the TM mode, a high extinction ratio of 12.55 dB, and a high image resolution. With parameters of SiO2 MIM gap thickness GM = 0.5 μm, MIM length LM = 0.6 μm, MIM position LA = 21 μm, and silver thickness TM = 50 nm, very compact three dimensional size of the PBS can be designed only by 4 × 0.7 × 44 µm3. The designed PBS structure can therefore be used in photonic integrated circuits (PICs) as a polarizer, laser isolator with mode selection, mode splitter, and so on.

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MISP) (No. NRF-2011-0012201), (No. NRF-2012R1A2A1A01011488), and Chung-Ang University through the CAYSS program.

References and links

1. J. M. Hong, H. H. Ryoo, S. G. Lee, E.-H. Lee, D. Woo, and S. Kim, “Novel design of polarization splitter based on a quasi-state multimode interference coupler,” in Proceedings of CLEO 2002 Tech. Dig. 1, 194–195 (2002).

2. J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett. 15(1), 72–74 (2003). [CrossRef]  

3. L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett. 6(3), 402–405 (1994). [CrossRef]  

4. P. Wei and W. Wang, “A TE-TM mode splitter on lithium niobate using Ti, Ni, and MgO diffusions,” IEEE Photon. Technol. Lett. 6(2), 245–248 (1994). [CrossRef]  

5. M. H. Hu, Z. Huang, R. Scarmozzino, M. Levy, and R. M. Osgood Jr., “Tunable Mach–Zehnder polarization splitter using height-tapered Y-branches,” IEEE Photon. Technol. Lett. 9(6), 773–775 (1997). [CrossRef]  

6. I. Kiyat, A. Aydinli, and N. Dagli, “A compact silicon-on-insulator polarization splitter,” IEEE Photon. Technol. Lett. 17(1), 100–102 (2005). [CrossRef]  

7. C.-Y. Tai, S. H. Chang, and T. C. Chiu, “Design and analysis of an ultra-compact and ultra-wideband polarization beam splitter based on coupled plasmonic waveguide arrays,” IEEE Photon. Technol. Lett. 19(19), 1448–1450 (2007). [CrossRef]  

8. L. Zhu, Y. Huang, and A. Yariv, “Integration of a multimode interference coupler with a corrugated sidewall Bragg grating in planar polymer waveguides,” IEEE Photon. Technol. Lett. 18(6), 740–742 (2006). [CrossRef]  

9. S. Kim, G. P. Nordin, J. Cai, and J. Jiang, “Ultracompact high-efficiency polarizing beam splitter with a hybrid photonic crystal and conventional waveguide structure,” Opt. Lett. 28(23), 2384–2386 (2003). [CrossRef]   [PubMed]  

10. T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Design of a compact photonic-crystal-based polarizing beam splitter,” IEEE Photon. Technol. Lett. 17(7), 1435–1437 (2005). [CrossRef]  

11. T. Yu, X. Jiang, Q. Liao, W. Qi, J. Yang, and M. Wang, “Self-imaging effect in photonic crystal multimode waveguides exhibiting no band gaps,” Chin. Opt. Lett. 5(12), 690–692 (2007).

12. Z. Qiang, W. Zhou, and R. A. Soref, “Optical add-drop filters based on photonic crystal ring resonators,” Opt. Express 15(4), 1823–1831 (2007). [CrossRef]   [PubMed]  

13. Y. Shi, D. Dai, and S. He, “Proposal for an ultra-compact polarization-beam splitter based on a photonic-crystal-assisted multimode interference coupler,” IEEE Photon. Technol. Lett. 19(11), 825–827 (2007). [CrossRef]  

14. M. Djavid, A. Ghaffari, and M. S. Abrishamian, “Coupled mode analysis of photonic crystal add-drop filters based on ring resonators,” J. Opt. Soc. Am. B 25(11), 1829–1832 (2008). [CrossRef]  

15. Y. Morita, Y. Tsuji, and K. Hirayama, “Proposal for a compact resonant-coupling-type polarization splitter based on photonic crystal waveguide with absolute photonic bandgap,” IEEE Photon. Technol. Lett. 20(2), 93–95 (2008). [CrossRef]  

16. C. Son, B. Kim, J. Shin, and N. Dagli, “Very compact metal slab waveguide reflectors as integrated high reflectivity mirrors on high index contrast waveguides,” J. Lightwave Technol. 29(19), 2999–3003 (2011). [CrossRef]  

17. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: Principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]  

18. J. Park, H. Kim, I.-M. Lee, S. Kim, J. Jung, and B. Lee, “Resonant tunneling of surface plasmon polariton in the plasmonic nano-cavity,” Opt. Express 16(21), 16903–16915 (2008). [CrossRef]   [PubMed]  

19. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer Science & Business Media LLC), Chap. 2.

20. T. Augustsson, “Bragg grating–assisted MMI-coupler for add-drop multiplexing,” J. Lightwave Technol. 16(8), 1517–1522 (1998). [CrossRef]  

References

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  1. J. M. Hong, H. H. Ryoo, S. G. Lee, E.-H. Lee, D. Woo, and S. Kim, “Novel design of polarization splitter based on a quasi-state multimode interference coupler,” in Proceedings of CLEO 2002 Tech. Dig. 1, 194–195 (2002).
  2. J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
    [CrossRef]
  3. L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett.6(3), 402–405 (1994).
    [CrossRef]
  4. P. Wei and W. Wang, “A TE-TM mode splitter on lithium niobate using Ti, Ni, and MgO diffusions,” IEEE Photon. Technol. Lett.6(2), 245–248 (1994).
    [CrossRef]
  5. M. H. Hu, Z. Huang, R. Scarmozzino, M. Levy, and R. M. Osgood., “Tunable Mach–Zehnder polarization splitter using height-tapered Y-branches,” IEEE Photon. Technol. Lett.9(6), 773–775 (1997).
    [CrossRef]
  6. I. Kiyat, A. Aydinli, and N. Dagli, “A compact silicon-on-insulator polarization splitter,” IEEE Photon. Technol. Lett.17(1), 100–102 (2005).
    [CrossRef]
  7. C.-Y. Tai, S. H. Chang, and T. C. Chiu, “Design and analysis of an ultra-compact and ultra-wideband polarization beam splitter based on coupled plasmonic waveguide arrays,” IEEE Photon. Technol. Lett.19(19), 1448–1450 (2007).
    [CrossRef]
  8. L. Zhu, Y. Huang, and A. Yariv, “Integration of a multimode interference coupler with a corrugated sidewall Bragg grating in planar polymer waveguides,” IEEE Photon. Technol. Lett.18(6), 740–742 (2006).
    [CrossRef]
  9. S. Kim, G. P. Nordin, J. Cai, and J. Jiang, “Ultracompact high-efficiency polarizing beam splitter with a hybrid photonic crystal and conventional waveguide structure,” Opt. Lett.28(23), 2384–2386 (2003).
    [CrossRef] [PubMed]
  10. T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Design of a compact photonic-crystal-based polarizing beam splitter,” IEEE Photon. Technol. Lett.17(7), 1435–1437 (2005).
    [CrossRef]
  11. T. Yu, X. Jiang, Q. Liao, W. Qi, J. Yang, and M. Wang, “Self-imaging effect in photonic crystal multimode waveguides exhibiting no band gaps,” Chin. Opt. Lett.5(12), 690–692 (2007).
  12. Z. Qiang, W. Zhou, and R. A. Soref, “Optical add-drop filters based on photonic crystal ring resonators,” Opt. Express15(4), 1823–1831 (2007).
    [CrossRef] [PubMed]
  13. Y. Shi, D. Dai, and S. He, “Proposal for an ultra-compact polarization-beam splitter based on a photonic-crystal-assisted multimode interference coupler,” IEEE Photon. Technol. Lett.19(11), 825–827 (2007).
    [CrossRef]
  14. M. Djavid, A. Ghaffari, and M. S. Abrishamian, “Coupled mode analysis of photonic crystal add-drop filters based on ring resonators,” J. Opt. Soc. Am. B25(11), 1829–1832 (2008).
    [CrossRef]
  15. Y. Morita, Y. Tsuji, and K. Hirayama, “Proposal for a compact resonant-coupling-type polarization splitter based on photonic crystal waveguide with absolute photonic bandgap,” IEEE Photon. Technol. Lett.20(2), 93–95 (2008).
    [CrossRef]
  16. C. Son, B. Kim, J. Shin, and N. Dagli, “Very compact metal slab waveguide reflectors as integrated high reflectivity mirrors on high index contrast waveguides,” J. Lightwave Technol.29(19), 2999–3003 (2011).
    [CrossRef]
  17. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: Principles and applications,” J. Lightwave Technol.13(4), 615–627 (1995).
    [CrossRef]
  18. J. Park, H. Kim, I.-M. Lee, S. Kim, J. Jung, and B. Lee, “Resonant tunneling of surface plasmon polariton in the plasmonic nano-cavity,” Opt. Express16(21), 16903–16915 (2008).
    [CrossRef] [PubMed]
  19. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer Science & Business Media LLC), Chap. 2.
  20. T. Augustsson, “Bragg grating–assisted MMI-coupler for add-drop multiplexing,” J. Lightwave Technol.16(8), 1517–1522 (1998).
    [CrossRef]

2011 (1)

2008 (3)

2007 (4)

C.-Y. Tai, S. H. Chang, and T. C. Chiu, “Design and analysis of an ultra-compact and ultra-wideband polarization beam splitter based on coupled plasmonic waveguide arrays,” IEEE Photon. Technol. Lett.19(19), 1448–1450 (2007).
[CrossRef]

Y. Shi, D. Dai, and S. He, “Proposal for an ultra-compact polarization-beam splitter based on a photonic-crystal-assisted multimode interference coupler,” IEEE Photon. Technol. Lett.19(11), 825–827 (2007).
[CrossRef]

Z. Qiang, W. Zhou, and R. A. Soref, “Optical add-drop filters based on photonic crystal ring resonators,” Opt. Express15(4), 1823–1831 (2007).
[CrossRef] [PubMed]

T. Yu, X. Jiang, Q. Liao, W. Qi, J. Yang, and M. Wang, “Self-imaging effect in photonic crystal multimode waveguides exhibiting no band gaps,” Chin. Opt. Lett.5(12), 690–692 (2007).

2006 (1)

L. Zhu, Y. Huang, and A. Yariv, “Integration of a multimode interference coupler with a corrugated sidewall Bragg grating in planar polymer waveguides,” IEEE Photon. Technol. Lett.18(6), 740–742 (2006).
[CrossRef]

2005 (2)

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Design of a compact photonic-crystal-based polarizing beam splitter,” IEEE Photon. Technol. Lett.17(7), 1435–1437 (2005).
[CrossRef]

I. Kiyat, A. Aydinli, and N. Dagli, “A compact silicon-on-insulator polarization splitter,” IEEE Photon. Technol. Lett.17(1), 100–102 (2005).
[CrossRef]

2003 (2)

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

S. Kim, G. P. Nordin, J. Cai, and J. Jiang, “Ultracompact high-efficiency polarizing beam splitter with a hybrid photonic crystal and conventional waveguide structure,” Opt. Lett.28(23), 2384–2386 (2003).
[CrossRef] [PubMed]

1998 (1)

1997 (1)

M. H. Hu, Z. Huang, R. Scarmozzino, M. Levy, and R. M. Osgood., “Tunable Mach–Zehnder polarization splitter using height-tapered Y-branches,” IEEE Photon. Technol. Lett.9(6), 773–775 (1997).
[CrossRef]

1995 (1)

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: Principles and applications,” J. Lightwave Technol.13(4), 615–627 (1995).
[CrossRef]

1994 (2)

L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett.6(3), 402–405 (1994).
[CrossRef]

P. Wei and W. Wang, “A TE-TM mode splitter on lithium niobate using Ti, Ni, and MgO diffusions,” IEEE Photon. Technol. Lett.6(2), 245–248 (1994).
[CrossRef]

Abrishamian, M. S.

Augustsson, T.

Aydinli, A.

I. Kiyat, A. Aydinli, and N. Dagli, “A compact silicon-on-insulator polarization splitter,” IEEE Photon. Technol. Lett.17(1), 100–102 (2005).
[CrossRef]

Cai, J.

Chang, S. H.

C.-Y. Tai, S. H. Chang, and T. C. Chiu, “Design and analysis of an ultra-compact and ultra-wideband polarization beam splitter based on coupled plasmonic waveguide arrays,” IEEE Photon. Technol. Lett.19(19), 1448–1450 (2007).
[CrossRef]

Chiu, T. C.

C.-Y. Tai, S. H. Chang, and T. C. Chiu, “Design and analysis of an ultra-compact and ultra-wideband polarization beam splitter based on coupled plasmonic waveguide arrays,” IEEE Photon. Technol. Lett.19(19), 1448–1450 (2007).
[CrossRef]

Dagli, N.

Dai, D.

Y. Shi, D. Dai, and S. He, “Proposal for an ultra-compact polarization-beam splitter based on a photonic-crystal-assisted multimode interference coupler,” IEEE Photon. Technol. Lett.19(11), 825–827 (2007).
[CrossRef]

de Vreede, A. I.

L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett.6(3), 402–405 (1994).
[CrossRef]

Djavid, M.

Fallahi, M.

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Design of a compact photonic-crystal-based polarizing beam splitter,” IEEE Photon. Technol. Lett.17(7), 1435–1437 (2005).
[CrossRef]

Ghaffari, A.

Green, F. H.

L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett.6(3), 402–405 (1994).
[CrossRef]

He, S.

Y. Shi, D. Dai, and S. He, “Proposal for an ultra-compact polarization-beam splitter based on a photonic-crystal-assisted multimode interference coupler,” IEEE Photon. Technol. Lett.19(11), 825–827 (2007).
[CrossRef]

Hirayama, K.

Y. Morita, Y. Tsuji, and K. Hirayama, “Proposal for a compact resonant-coupling-type polarization splitter based on photonic crystal waveguide with absolute photonic bandgap,” IEEE Photon. Technol. Lett.20(2), 93–95 (2008).
[CrossRef]

Hong, J. M.

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

Hu, M. H.

M. H. Hu, Z. Huang, R. Scarmozzino, M. Levy, and R. M. Osgood., “Tunable Mach–Zehnder polarization splitter using height-tapered Y-branches,” IEEE Photon. Technol. Lett.9(6), 773–775 (1997).
[CrossRef]

Huang, Y.

L. Zhu, Y. Huang, and A. Yariv, “Integration of a multimode interference coupler with a corrugated sidewall Bragg grating in planar polymer waveguides,” IEEE Photon. Technol. Lett.18(6), 740–742 (2006).
[CrossRef]

Huang, Z.

M. H. Hu, Z. Huang, R. Scarmozzino, M. Levy, and R. M. Osgood., “Tunable Mach–Zehnder polarization splitter using height-tapered Y-branches,” IEEE Photon. Technol. Lett.9(6), 773–775 (1997).
[CrossRef]

Jeong, J. W.

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

Jiang, J.

Jiang, X.

Jung, J.

Kim, B.

Kim, H.

Kim, S.

Kiyat, I.

I. Kiyat, A. Aydinli, and N. Dagli, “A compact silicon-on-insulator polarization splitter,” IEEE Photon. Technol. Lett.17(1), 100–102 (2005).
[CrossRef]

Lee, B.

Lee, E.-H.

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

Lee, I.-M.

Lee, S. G.

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

Levy, M.

M. H. Hu, Z. Huang, R. Scarmozzino, M. Levy, and R. M. Osgood., “Tunable Mach–Zehnder polarization splitter using height-tapered Y-branches,” IEEE Photon. Technol. Lett.9(6), 773–775 (1997).
[CrossRef]

Liao, Q.

Liu, T.

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Design of a compact photonic-crystal-based polarizing beam splitter,” IEEE Photon. Technol. Lett.17(7), 1435–1437 (2005).
[CrossRef]

Mansuripur, M.

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Design of a compact photonic-crystal-based polarizing beam splitter,” IEEE Photon. Technol. Lett.17(7), 1435–1437 (2005).
[CrossRef]

Metaal, E. G.

L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett.6(3), 402–405 (1994).
[CrossRef]

Moloney, J. V.

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Design of a compact photonic-crystal-based polarizing beam splitter,” IEEE Photon. Technol. Lett.17(7), 1435–1437 (2005).
[CrossRef]

Morita, Y.

Y. Morita, Y. Tsuji, and K. Hirayama, “Proposal for a compact resonant-coupling-type polarization splitter based on photonic crystal waveguide with absolute photonic bandgap,” IEEE Photon. Technol. Lett.20(2), 93–95 (2008).
[CrossRef]

Nordin, G. P.

Osgood, R. M.

M. H. Hu, Z. Huang, R. Scarmozzino, M. Levy, and R. M. Osgood., “Tunable Mach–Zehnder polarization splitter using height-tapered Y-branches,” IEEE Photon. Technol. Lett.9(6), 773–775 (1997).
[CrossRef]

Park, J.

Park, S. R.

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

Park, S.-G.

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: Principles and applications,” J. Lightwave Technol.13(4), 615–627 (1995).
[CrossRef]

Qi, W.

Qiang, Z.

Ryu, H. H.

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

Scarmozzino, R.

M. H. Hu, Z. Huang, R. Scarmozzino, M. Levy, and R. M. Osgood., “Tunable Mach–Zehnder polarization splitter using height-tapered Y-branches,” IEEE Photon. Technol. Lett.9(6), 773–775 (1997).
[CrossRef]

Shi, Y.

Y. Shi, D. Dai, and S. He, “Proposal for an ultra-compact polarization-beam splitter based on a photonic-crystal-assisted multimode interference coupler,” IEEE Photon. Technol. Lett.19(11), 825–827 (2007).
[CrossRef]

Shin, J.

Smit, M. K.

L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett.6(3), 402–405 (1994).
[CrossRef]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: Principles and applications,” J. Lightwave Technol.13(4), 615–627 (1995).
[CrossRef]

L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett.6(3), 402–405 (1994).
[CrossRef]

Son, C.

Soref, R. A.

Tai, C.-Y.

C.-Y. Tai, S. H. Chang, and T. C. Chiu, “Design and analysis of an ultra-compact and ultra-wideband polarization beam splitter based on coupled plasmonic waveguide arrays,” IEEE Photon. Technol. Lett.19(19), 1448–1450 (2007).
[CrossRef]

Tsuji, Y.

Y. Morita, Y. Tsuji, and K. Hirayama, “Proposal for a compact resonant-coupling-type polarization splitter based on photonic crystal waveguide with absolute photonic bandgap,” IEEE Photon. Technol. Lett.20(2), 93–95 (2008).
[CrossRef]

Verbeek, B. H.

L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett.6(3), 402–405 (1994).
[CrossRef]

Wang, M.

Wang, W.

P. Wei and W. Wang, “A TE-TM mode splitter on lithium niobate using Ti, Ni, and MgO diffusions,” IEEE Photon. Technol. Lett.6(2), 245–248 (1994).
[CrossRef]

Wei, P.

P. Wei and W. Wang, “A TE-TM mode splitter on lithium niobate using Ti, Ni, and MgO diffusions,” IEEE Photon. Technol. Lett.6(2), 245–248 (1994).
[CrossRef]

Woo, D.

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

Yang, J.

Yariv, A.

L. Zhu, Y. Huang, and A. Yariv, “Integration of a multimode interference coupler with a corrugated sidewall Bragg grating in planar polymer waveguides,” IEEE Photon. Technol. Lett.18(6), 740–742 (2006).
[CrossRef]

Yu, T.

Zakharian, A. R.

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Design of a compact photonic-crystal-based polarizing beam splitter,” IEEE Photon. Technol. Lett.17(7), 1435–1437 (2005).
[CrossRef]

Zhou, W.

Zhu, L.

L. Zhu, Y. Huang, and A. Yariv, “Integration of a multimode interference coupler with a corrugated sidewall Bragg grating in planar polymer waveguides,” IEEE Photon. Technol. Lett.18(6), 740–742 (2006).
[CrossRef]

Chin. Opt. Lett. (1)

IEEE Photon. Technol. Lett. (10)

J. M. Hong, H. H. Ryu, S. R. Park, J. W. Jeong, S. G. Lee, E.-H. Lee, S.-G. Park, D. Woo, and S. Kim, “Design and fabrication of a significantly shortened multimode interference coupler for polarization splitter application,” IEEE Photon. Technol. Lett.15(1), 72–74 (2003).
[CrossRef]

L. B. Soldano, A. I. de Vreede, M. K. Smit, B. H. Verbeek, E. G. Metaal, and F. H. Green, “Mach–Zehnder interferometer polarization splitter in InGaAsP–InP,” IEEE Photon. Technol. Lett.6(3), 402–405 (1994).
[CrossRef]

P. Wei and W. Wang, “A TE-TM mode splitter on lithium niobate using Ti, Ni, and MgO diffusions,” IEEE Photon. Technol. Lett.6(2), 245–248 (1994).
[CrossRef]

M. H. Hu, Z. Huang, R. Scarmozzino, M. Levy, and R. M. Osgood., “Tunable Mach–Zehnder polarization splitter using height-tapered Y-branches,” IEEE Photon. Technol. Lett.9(6), 773–775 (1997).
[CrossRef]

I. Kiyat, A. Aydinli, and N. Dagli, “A compact silicon-on-insulator polarization splitter,” IEEE Photon. Technol. Lett.17(1), 100–102 (2005).
[CrossRef]

C.-Y. Tai, S. H. Chang, and T. C. Chiu, “Design and analysis of an ultra-compact and ultra-wideband polarization beam splitter based on coupled plasmonic waveguide arrays,” IEEE Photon. Technol. Lett.19(19), 1448–1450 (2007).
[CrossRef]

L. Zhu, Y. Huang, and A. Yariv, “Integration of a multimode interference coupler with a corrugated sidewall Bragg grating in planar polymer waveguides,” IEEE Photon. Technol. Lett.18(6), 740–742 (2006).
[CrossRef]

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Design of a compact photonic-crystal-based polarizing beam splitter,” IEEE Photon. Technol. Lett.17(7), 1435–1437 (2005).
[CrossRef]

Y. Shi, D. Dai, and S. He, “Proposal for an ultra-compact polarization-beam splitter based on a photonic-crystal-assisted multimode interference coupler,” IEEE Photon. Technol. Lett.19(11), 825–827 (2007).
[CrossRef]

Y. Morita, Y. Tsuji, and K. Hirayama, “Proposal for a compact resonant-coupling-type polarization splitter based on photonic crystal waveguide with absolute photonic bandgap,” IEEE Photon. Technol. Lett.20(2), 93–95 (2008).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (1)

Other (2)

J. M. Hong, H. H. Ryoo, S. G. Lee, E.-H. Lee, D. Woo, and S. Kim, “Novel design of polarization splitter based on a quasi-state multimode interference coupler,” in Proceedings of CLEO 2002 Tech. Dig. 1, 194–195 (2002).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer Science & Business Media LLC), Chap. 2.

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Figures (6)

Fig. 1
Fig. 1

(a) 3D configuration of the PBS structure with an embedded MIM, (b) 2D cross section schematic of MIM-embedded slab waveguide.

Fig. 2
Fig. 2

Transmittance results of (a) TE mode and (b) TM mode for the MIM-embedded waveguide varying LM and GM. (c) TM mode, with GM = 0.5 μm, versus the MIM length from 0 to 2 μm.

Fig. 3
Fig. 3

(a) Normalized intensities of the TE and TM modes according to the variation in the MIM position (LA) from 5 to 35 μm. Other design parameters are GM = 0.5 μm, LM = 0.6 μm, WWG = 4 μm, and HWG = 0.7 μm. (b) Propagating field profile along the MMI with a length (LWG) of 44 μm. The MIM position LA is 21 μm, and port A, B, and C are assigned for reflected TE mode, light source, and transmitted TM mode, respectively.

Fig. 4
Fig. 4

TE field profiles in the cross-section of port A for different MIM positions in the MMI coupler. The figures represent the MIM position (LA) of (a) 21 μm, (b) 22 μm and (c) 23 μm.

Fig. 5
Fig. 5

Normalized intensity of (a) TE mode (b) TM mode in port A and C versus MIM position LA = 21 μm, 22 μm, and 23 μm with the MIM length LM = 0.6 μm and varied gap thickness GM = 0.4 μm, 0.5 μm, and 0.6 μm

Fig. 6
Fig. 6

Results of the normalized TE and TM intensities as a function of MIM metal thickness.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E( y,x )= m=0 M1 c m ψ m ( y )exp[ j m( m+2 )π 3 L π x ],
E TM ( y, L WG )=T( λ 0 ). m=0 M1 c m ψ m ( y )exp[ j m( m+2 )π 3 L π L WG ],
E TE ( y,0 )=Γ( λ 0 ). m=0 M1 c m ψ m ( y )exp[ j m( m+2 )π 3 L π L A ],

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