{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:58:29Z","timestamp":1760147909675,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T00:00:00Z","timestamp":1678320000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council, Taiwan","award":["NSTC-110-2221-E-A49-057-MY3","NSTC-109-2221-E-009-155-MY3"],"award-info":[{"award-number":["NSTC-110-2221-E-A49-057-MY3","NSTC-109-2221-E-009-155-MY3"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Due to the popularity of different high bandwidth applications, it is becoming increasingly difficult to satisfy the huge data capacity requirements, since the traditional electrical interconnects suffer significantly from limited bandwidth and huge power consumption. Silicon photonics (SiPh) is one of the important technologies for increasing interconnect capacity and decreasing power consumption. Mode-division multiplexing (MDM) allows signals to be transmitted simultaneously, at different modes, in a single waveguide. Wavelength-division multiplexing (WDM), non-orthogonal multiple access (NOMA) and orthogonal-frequency-division multiplexing (OFDM) can also be utilized to further increase the optical interconnect capacity. In SiPh integrated circuits, waveguide bends are usually inevitable. However, for an MDM system with a multimode bus waveguide, the modal fields will become asymmetric when the waveguide bend is sharp. This will introduce inter-mode coupling and inter-mode crosstalk. One simple approach to achieve sharp bends in multimode bus waveguide is to use a Euler curve. Although it has been reported in the literature that sharp bends based on a Euler curve allow high performance and low inter-mode crosstalk multimode transmissions, we discover, by simulation and experiment, that the transmission performance between two Euler bends is length dependent, particularly when the bends are sharp. We investigate the length dependency of the straight multimode bus waveguide between two Euler bends. High transmission performance can be achieved by a proper design of the waveguide length, width, and bend radius. By using the optimized MDM bus waveguide length with sharp Euler bends, proof-of-concept NOMA-OFDM experimental transmissions, supporting two MDM modes and two NOMA users, are performed.<\/jats:p>","DOI":"10.3390\/s23062965","type":"journal-article","created":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T02:01:47Z","timestamp":1678327307000},"page":"2965","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Design Consideration, Numerical and Experimental Analyses of Mode-Division-Multiplexed (MDM) Silicon Photonics Integrated Circuit with Sharp Bends"],"prefix":"10.3390","volume":"23","author":[{"given":"Pin-Cheng","family":"Kuo","sequence":"first","affiliation":[{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7488-2611","authenticated-orcid":false,"given":"Chi-Wai","family":"Chow","sequence":"additional","affiliation":[{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan-Zeng","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wahyu Hendra","family":"Gunawan","sequence":"additional","affiliation":[{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tun-Yao","family":"Hung","sequence":"additional","affiliation":[{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yin-He","family":"Jian","sequence":"additional","affiliation":[{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guan-Hong","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ching-Wei","family":"Peng","sequence":"additional","affiliation":[{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Department of Photonics & Graduate Institute of Electro-Optical Engineering, College of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"Philips Electronics Ltd., N.T., Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6482-8534","authenticated-orcid":false,"given":"Chien-Hung","family":"Yeh","sequence":"additional","affiliation":[{"name":"Department of Photonics, Feng Chia University, Taichung 40724, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"C35","DOI":"10.1364\/JOCN.1.000C35","article-title":"Key technologies of WDM-PON for future converged optical broadband access networks","volume":"1","author":"Chang","year":"2009","journal-title":"J. Opt. Commun. Netw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1364\/OL.35.000279","article-title":"Bidirectional hybrid CATV\/radio-over-fiber WDM transport system","volume":"35","author":"Lu","year":"2010","journal-title":"Opt. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"8622","DOI":"10.1364\/OE.21.008622","article-title":"20-Gbps WDM-PON transmissions employing weak-resonant-cavity FPLD with OFDM and SC-FDE modulation formats","volume":"21","author":"Lu","year":"2013","journal-title":"Opt. Exp."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1109\/LPT.2018.2882766","article-title":"Polarization-tracking-free PDM supporting hybrid digital-analog transport for fixed-mobile systems","volume":"31","author":"Shen","year":"2018","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"A143","DOI":"10.1364\/JOCN.440798","article-title":"4G to 6G: Disruptions and drivers for optical access [Invited]","volume":"14","author":"Ranaweera","year":"2022","journal-title":"J. Opt. Comm. Netw."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Lipson, M., Miller, S.A., Phare, C.T., Chang, Y.C., Ji, X., Gordillo, O.A.J., Mohanty, A., Roberts, S.P., Shin, M.C., and Stern, B. (2018, January 23\u201327). Silicon photonics integration for future generation optical network. Proceedings of the 2018 European Conference on Optical Communication (ECOC), Rome, Italy.","DOI":"10.1109\/ECOC.2018.8535125"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Andrade, H., Xia, Y., Maharry, A., Valenzuela, L., Buckwalter, J.F., and Schow, C.L. (2021, January 13\u201316). 50 GBaud QPSK 0.98 pJ\/bit Receiver in 45 nm CMOS and 90 nm Silicon Photonics. Proceedings of the 2021 European Conference on Optical Communication (ECOC), Bordeaux, France.","DOI":"10.1109\/ECOC52684.2021.9606026"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Lockwood, D.J., and Pavesi, L. (2021). Silicon Photonics IV, Springer. Topics in Applied Physics.","DOI":"10.1007\/978-3-030-68222-4"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2550","DOI":"10.1109\/JLT.2013.2270277","article-title":"Compatibility of silicon Mach-Zehnder modulators for advanced modulation formats","volume":"31","author":"Xu","year":"2013","journal-title":"J. Light. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2935","DOI":"10.1364\/OL.460602","article-title":"C-band 67\u2005GHz silicon photonic microring modulator for dispersion-uncompensated 100 Gbaud PAM-4","volume":"47","author":"Chan","year":"2022","journal-title":"Opt. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7900105","DOI":"10.1109\/JPHOT.2020.3043592","article-title":"DP-QPSK coherent detection using 2D grating coupled silicon based receiver","volume":"13","author":"Peng","year":"2021","journal-title":"IEEE Photonics J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Hung, T.Y., Chen, G.H., Lin, Y.Z., Chow, C.W., Jian, Y.H., Kuo, P.C., Peng, C.W., Tsai, J.F., Liu, Y., and Yeh, C.H. (2023). Wideband and channel switchable mode division multiplexing (MDM) optical power divider supporting 7.682 Tbit\/s for on-chip optical interconnects. Sensors, 23.","DOI":"10.3390\/s23020711"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3069","DOI":"10.1038\/ncomms4069","article-title":"WDM-compatible mode-division multiplexing on a silicon chip","volume":"5","author":"Luo","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"129104","DOI":"10.1109\/ACCESS.2019.2939715","article-title":"Mode-division-multiplexing (MDM) of 9.4-Tbit\/s OFDM signals on silicon-on-insulator (SOI) platform","volume":"7","author":"Chen","year":"2019","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"10940","DOI":"10.1364\/OE.19.010940","article-title":"Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires","volume":"19","author":"Dai","year":"2011","journal-title":"Opt. Express"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1631\/FITEE.1800386","article-title":"Ten-channel mode-division-multiplexed silicon photonic integrated circuit with sharp bends","volume":"20","author":"Li","year":"2019","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1422","DOI":"10.1364\/OL.38.001422","article-title":"Silicon mode (de)multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light","volume":"38","author":"Dai","year":"2013","journal-title":"Opt. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1109\/LPT.2018.2829508","article-title":"2.6 Tbit\/s on-chip optical interconnect supporting mode-division-multiplexing and PAM-4 signal","volume":"30","author":"Hsu","year":"2018","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"219881","DOI":"10.1109\/ACCESS.2020.3041418","article-title":"Compact mode division MUX\/DEMUX using enhanced evanescent-wave coupling on silicon-on-insulator (SOI) platform for 11-Tbit\/s broadband transmission","volume":"8","author":"Chen","year":"2020","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.1109\/JLT.2017.2721955","article-title":"Power-division non-orthogonal multiple access (NOMA) in flexible optical access with synchronized downlink\/asynchronous uplink","volume":"35","author":"Lu","year":"2017","journal-title":"J. Light. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Gunawan, W.H., Chow, C.W., Liu, Y., Chang, Y.H., and Yeh, C.H. (2022). Optical beam steerable visible light communication (VLC) system supporting multiple users using RGB and orthogonal frequency division multiplexed (OFDM) non-orthogonal multiple access (NOMA). Sensors, 22.","DOI":"10.3390\/s22228707"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1109\/JLT.2008.2010061","article-title":"OFDM for optical communications","volume":"27","author":"Armstrong","year":"2009","journal-title":"J. Light. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1109\/JSAC.2010.100805","article-title":"Studies of OFDM signal for broadband optical access networks","volume":"28","author":"Chow","year":"2010","journal-title":"IEEE J. Sel. Areas Comm."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1038\/ncomms2232","article-title":"On-chip transformation optics for multimode waveguide bends","volume":"3","author":"Gabrielli","year":"2012","journal-title":"Nat. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"27524","DOI":"10.1364\/OE.22.027524","article-title":"Multimode optical waveguide enabling microbends with low inter-mode crosstalk for mode-multiplexed optical interconnects","volume":"22","author":"Dai","year":"2014","journal-title":"Opt. Express"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"17814","DOI":"10.1364\/OE.21.017814","article-title":"Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform","volume":"21","author":"Cherchi","year":"2013","journal-title":"Opt. Express"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/6\/2965\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:51:35Z","timestamp":1760122295000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/6\/2965"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,9]]},"references-count":26,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["s23062965"],"URL":"https:\/\/doi.org\/10.3390\/s23062965","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,3,9]]}}}