Abstract

The hybrid multiplexing technique reactivates optical interconnect as it offers multiple dimensions to dramatically enhance the data capacity of a single wavelength carrier. A straightforward method to realize hybrid multiplexing is to perform polarization multiplexing for mode-multiplexed signals, by utilizing a mode-transparent polarization beam splitter (MTPBS), which can process multiple modes simultaneously. However, present PBSs mainly work in the single-mode regime, and it is not easy to redesign the conventional PBS to accommodate multiple modes, due to the severe mode dispersion. Here, a novel MTPBS, which can tackle a group of modes simultaneously, is proposed and demonstrated. As a demonstration, the MTPBS supporting a total channel number of 13 is experimentally achieved, with low insertion loss and low modal/polarization cross talk. This work provides a new insight to realize hybrid multiplexing and represents a solution for high-density and large-capacity photonic integration.

© 2020 Chinese Laser Press

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2020 (1)

2018 (4)

2017 (4)

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

J. R. Ong, T. Y. L. Ang, E. Sahin, B. Pawlina, G. F. R. Chen, D. T. H. Tan, S. T. Lim, and C. E. Png, “Broadband silicon polarization beam splitter with a high extinction ratio using a triple-bent-waveguide directional coupler,” Opt. Lett 42, 4450–4453 (2017).
[Crossref]

H. Wu, Y. Tan, and D. X. Dai, “Ultra-broadband high-performance polarizing beam splitter on silicon,” Opt. Express 25, 6069–6075 (2017).
[Crossref]

D. Guo and T. Chu, “Silicon mode (de)multiplexers with parameters optimized using shortcuts to adiabaticity,” Opt. Express 25, 9160–9170 (2017).
[Crossref]

2016 (3)

2015 (2)

2014 (4)

J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de)multiplexer enabling simultaneous mode- and polarization-division-multiplexing,” Laser Photonics Rev. 8, L18–L22 (2014).
[Crossref]

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Y. Li, C. Li, C. Li, B. Cheng, and C. Xue, “Compact two-mode (de)multiplexer based on symmetric Y-junction and multimode interference waveguides,” Opt. Express 22, 5781–5786 (2014).
[Crossref]

L. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

2013 (2)

2007 (1)

1986 (1)

S. Zhu, A. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[Crossref]

1948 (1)

K. Artmann, “Calculation of the lateral shift of totally reflected beams,” Ann. Phys. 437, 87–102 (1948).
[Crossref]

An, S.

Ang, T. Y. L.

J. R. Ong, T. Y. L. Ang, E. Sahin, B. Pawlina, G. F. R. Chen, D. T. H. Tan, S. T. Lim, and C. E. Png, “Broadband silicon polarization beam splitter with a high extinction ratio using a triple-bent-waveguide directional coupler,” Opt. Lett 42, 4450–4453 (2017).
[Crossref]

Artmann, K.

K. Artmann, “Calculation of the lateral shift of totally reflected beams,” Ann. Phys. 437, 87–102 (1948).
[Crossref]

Bergmen, K.

L. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

Calabro, S.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

Cao, R.

Chang, W.

Chen, C. P.

L. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

Chen, G.

Chen, G. F. R.

J. R. Ong, T. Y. L. Ang, E. Sahin, B. Pawlina, G. F. R. Chen, D. T. H. Tan, S. T. Lim, and C. E. Png, “Broadband silicon polarization beam splitter with a high extinction ratio using a triple-bent-waveguide directional coupler,” Opt. Lett 42, 4450–4453 (2017).
[Crossref]

Chen, W.

Chen, X.

Cheng, B.

Cheng, M.

Chu, T.

Correa, R. A.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Da Ros, F.

Dai, D.

D. Dai, C. Li, S. Wang, H. Wu, Y. Shi, Z. Wu, S. Gao, T. Dai, H. Yu, and H.-K. Tsang, “10-channel mode (de)multiplexer with dual polarizations,” Laser Photonics Rev. 12, 1700109 (2018).
[Crossref]

J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de)multiplexer enabling simultaneous mode- and polarization-division-multiplexing,” Laser Photonics Rev. 8, L18–L22 (2014).
[Crossref]

Dai, D. X.

Dai, T.

D. Dai, C. Li, S. Wang, H. Wu, Y. Shi, Z. Wu, S. Gao, T. Dai, H. Yu, and H.-K. Tsang, “10-channel mode (de)multiplexer with dual polarizations,” Laser Photonics Rev. 12, 1700109 (2018).
[Crossref]

W. Chen, P. Wang, T. Yang, G. Wang, T. Dai, Y. Zhang, L. Zhou, X. Jiang, and J. Yang, “Silicon three-mode (de)multiplexer based on cascaded asymmetric Y junctions,” Opt. Lett. 41, 2851–2854 (2016).
[Crossref]

De Man, E.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

de Waardt, H.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Ding, Y.

Fan, X.

B. Xu, X. Fan, S. Wang, and Z. He, “Simultaneous 40-channel DWDM-DPSK signal monitoring system realized by using single-channel linear optical sampling technique,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M4G.3.

Feiste, U.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Gabrielli, L. H.

L. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

Gao, S.

D. Dai, C. Li, S. Wang, H. Wu, Y. Shi, Z. Wu, S. Gao, T. Dai, H. Yu, and H.-K. Tsang, “10-channel mode (de)multiplexer with dual polarizations,” Laser Photonics Rev. 12, 1700109 (2018).
[Crossref]

Guo, D.

Guo, X.

Hawley, D.

S. Zhu, A. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[Crossref]

He, S.

J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de)multiplexer enabling simultaneous mode- and polarization-division-multiplexing,” Laser Photonics Rev. 8, L18–L22 (2014).
[Crossref]

He, Y.

He, Z.

B. Xu, X. Fan, S. Wang, and Z. He, “Simultaneous 40-channel DWDM-DPSK signal monitoring system realized by using single-channel linear optical sampling technique,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M4G.3.

Huang, B.

Huang, H. Y.

Huijskens, F. M.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Jiang, X.

Khanna, G.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

Kim, D. W.

Kim, K. H.

Kim, S.

Kim, Y.

Koonen, A. M. J.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Lee, M. H.

Li, C.

Li, D.

Li, G.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Li, M.

Li, W.

Li, Y.

Lim, S. T.

J. R. Ong, T. Y. L. Ang, E. Sahin, B. Pawlina, G. F. R. Chen, D. T. H. Tan, S. T. Lim, and C. E. Png, “Broadband silicon polarization beam splitter with a high extinction ratio using a triple-bent-waveguide directional coupler,” Opt. Lett 42, 4450–4453 (2017).
[Crossref]

Lipson, M.

L. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

Liu, D.

Liu, K.

Lopez, E. A.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Lu, L.

Luo, L.

L. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

Ma, Q.

Mu, S.

Nelson, L. E.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Nordin, G. P.

Okonkwo, C. M.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Ong, J. R.

J. R. Ong, T. Y. L. Ang, E. Sahin, B. Pawlina, G. F. R. Chen, D. T. H. Tan, S. T. Lim, and C. E. Png, “Broadband silicon polarization beam splitter with a high extinction ratio using a triple-bent-waveguide directional coupler,” Opt. Lett 42, 4450–4453 (2017).
[Crossref]

Ophir, N.

L. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

Ou, H.

Pagano, A.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

Pan, Z.

Pawlina, B.

J. R. Ong, T. Y. L. Ang, E. Sahin, B. Pawlina, G. F. R. Chen, D. T. H. Tan, S. T. Lim, and C. E. Png, “Broadband silicon polarization beam splitter with a high extinction ratio using a triple-bent-waveguide directional coupler,” Opt. Lett 42, 4450–4453 (2017).
[Crossref]

Peucheret, C.

Piat, A. C.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

Png, C. E.

J. R. Ong, T. Y. L. Ang, E. Sahin, B. Pawlina, G. F. R. Chen, D. T. H. Tan, S. T. Lim, and C. E. Png, “Broadband silicon polarization beam splitter with a high extinction ratio using a triple-bent-waveguide directional coupler,” Opt. Lett 42, 4450–4453 (2017).
[Crossref]

Poitras, C. B.

L. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

Qi, B.

Qi, M. H.

Qian, Y.

Qiu, C.

Rafique, D.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

Rahman, T.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

Ren, X.

Riccardi, E.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

Richardson, D. J.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).
[Crossref]

Roy, R.

S. Zhu, A. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: a demonstration and review,” Am. J. Phys. 54, 601–607 (1986).
[Crossref]

Sahin, E.

J. R. Ong, T. Y. L. Ang, E. Sahin, B. Pawlina, G. F. R. Chen, D. T. H. Tan, S. T. Lim, and C. E. Png, “Broadband silicon polarization beam splitter with a high extinction ratio using a triple-bent-waveguide directional coupler,” Opt. Lett 42, 4450–4453 (2017).
[Crossref]

Schülzgen, A.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Sheng, Z.

Shi, Y.

D. Dai, C. Li, S. Wang, H. Wu, Y. Shi, Z. Wu, S. Gao, T. Dai, H. Yu, and H.-K. Tsang, “10-channel mode (de)multiplexer with dual polarizations,” Laser Photonics Rev. 12, 1700109 (2018).
[Crossref]

Song, J.

Sorger, V. J.

Spinnler, B.

G. Khanna, T. Rahman, E. De Man, E. Riccardi, A. Pagano, A. C. Piat, S. Calabro, B. Spinnler, D. Rafique, and U. Feiste, “Single-carrier 400 G 64QAM and 128QAM DWDM field trial transmission over metro legacy links,” IEEE Photonics Technol. Lett. 29, 189–192 (2017).
[Crossref]

Su, Y.

Sun, C.

Tan, D. T. H.

J. R. Ong, T. Y. L. Ang, E. Sahin, B. Pawlina, G. F. R. Chen, D. T. H. Tan, S. T. Lim, and C. E. Png, “Broadband silicon polarization beam splitter with a high extinction ratio using a triple-bent-waveguide directional coupler,” Opt. Lett 42, 4450–4453 (2017).
[Crossref]

Tan, Y.

Tsang, H.-K.

D. Dai, C. Li, S. Wang, H. Wu, Y. Shi, Z. Wu, S. Gao, T. Dai, H. Yu, and H.-K. Tsang, “10-channel mode (de)multiplexer with dual polarizations,” Laser Photonics Rev. 12, 1700109 (2018).
[Crossref]

van Uden, R. G. H.

R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8, 865–870 (2014).
[Crossref]

Wang, G.

Wang, J.

J. Wang, Y. Xuan, M. H. Qi, H. Y. Huang, Y. Li, M. Li, X. Chen, Z. Sheng, A. Wu, and W. Li, “Broadband and fabrication-tolerant on-chip scalable mode-division multiplexing based on mode-evolution counter-tapered couplers,” Opt. Lett. 40, 1956–1959 (2015).
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B. Xu, X. Fan, S. Wang, and Z. He, “Simultaneous 40-channel DWDM-DPSK signal monitoring system realized by using single-channel linear optical sampling technique,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M4G.3.

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Other (1)

B. Xu, X. Fan, S. Wang, and Z. He, “Simultaneous 40-channel DWDM-DPSK signal monitoring system realized by using single-channel linear optical sampling technique,” in Optical Fiber Communication Conference (Optical Society of America, 2018), paper M4G.3.

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Figures (7)

Fig. 1.
Fig. 1. (a) Schematic of the MTPBS based on multimode bus waveguides, which support multiple mode channels. The modes are indistinguishable, while light can be distinguished by the polarization state. Dual-polarization MDM signals can be split into TE and TM polarizations. TE MDM signals are reflected at 90°, while TM MDM signals are transmitted straightly. The bi-trench coupler consists of a pair of total internal reflection (TIR) mirrors separated by fully etched trenches. (b) Cube PBS as an analogy of MTPBS. The cube PBS consists of a pair of right-angle prisms separated by a polarization-dependent dielectric coating on the hypotenuse of one of the prisms. P-polarized light is turned with 90°, while S-polarized light is transmitted straightly.
Fig. 2.
Fig. 2. (a) Calculated effective indices of eigenmodes in the waveguide with different widths. The square-curves and triangle-curves are for TE and TM polarizations, respectively. (b) The simulated power transmission efficiency at through port versus different trench widths for TE0 and TM0 modes by using single-trench, bi-trench, and tri-trench couplers. The FDTD numerical method and transfer matrix theory are utilized for simulation at 1550 nm as a comparison. The trench width is the same as the gap between neighboring trenches. (c) The schematics of these three kinds of trench couplers. (d) The FDTD simulated power transmission efficiency at the through port for TE0TE6 and TM0TM5 modes for the bi-trench coupler at 1550 nm. The simulated mode transmission efficiency when inputting (e) TE0, TE6 and (f) TM0, TM5 modes from 1500 to 1600 nm. In the legend “TM0TM1T,” the TM0 mode stands for the input mode, while the TM1 mode stands for the output mode. The letter “T” refers to the through port, and the letter “C” refers to the cross port.
Fig. 3.
Fig. 3. Simulated light propagation in the MTPBS for (a) TM0, (b) TM5, (c) TE0, and (d) TE6 modes at the wavelength of 1550 nm. White-solid lines indicate the location of waveguides.
Fig. 4.
Fig. 4. (a) Microscope view of the tested device with an input port and two output ports. Two tested devices with the same geometry but different mode multiplexers are needed for complete characterization. (b) Seven-TE-mode (de)multiplexer and (c) six-TM-mode (de)multiplexer are utilized to obtain single-polarization MDM signals individually. The adiabatic taper connects the TE/TM mode (de)multiplexer with the MTPBS. (d) Zoom-in view of MTPBS, where the TM grating is used to filter out the scattering light from TM polarization.
Fig. 5.
Fig. 5. (a) Schematic of ith adiabatic coupler (AC) for TE0-TEi mode conversion; two reversely tapered waveguides (access waveguide and bus waveguide) are placed closely to form a coupling region. The seven-TE-mode (de)multiplexer is composed of six cascaded ACs, which are used to excite TE1TE6 modes. (b) Schematic of ith asymmetric directional coupler (ADC) to realize TM0-TMi mode conversion. The six-TM-mode (de)multiplexer consists of five cascaded ADCs, which are used to excite TM1TM5 modes. (c) Detailed parameters for TE and TM mode multiplexers.
Fig. 6.
Fig. 6. Normalized spectra of the MTPBS when injecting TE0TE6 modes. For a given inputting mode, the spectra for these seven modes at through and cross ports are measured successively. In the legend “TE1C,” the TE1 mode stands for the output mode, while the letter “C” refers to the cross port. In the legend “Cross talk-T,” “Cross talk” refers to the maximal cross talk at the through port which mainly comes from the adjacent modes, while the letter “T” refers to the through port.
Fig. 7.
Fig. 7. Normalized spectra of the MTPBS when injecting TM0TM5 modes. For a given inputting mode, the spectra for these seven modes at through and cross ports are measured successively. In the legend “TM1T,” the TM1 mode stands for the output mode, while the letter “T” refers to the through port. In the legend “Cross talk-C,” “Cross talk” refers to the maximal cross talk at the cross port which mainly comes from the adjacent modes, while the letter “C” refers to the cross port.

Equations (2)

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d=qcosθik0(neff2sin2θincl2)1/2,
q=ncl2sin2θi(neff2+ncl2)ncl2.

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