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Express"],"published-print":{"date-parts":[[2026,2,9]]},"abstract":"<jats:p>Mode-division multiplexing has emerged as a powerful strategy for enhancing the capacity of photonic integrated circuits, where compact and versatile mode manipulation devices in bus waveguides play a central role. In this work, we present the inverse design of two ultra-compact mode cyclic converters with size of only 7\u2005\u00b5m in length, enabled by the integration of the finite-element method, Bernstein polynomial\u2013based deformation parameterization, and the gradient-based method of moving asymptotes. The first device, a dual-mode cyclic converter (DMCC) with efficient TE0\/TE1 mutual conversion, is obtained within just 20 optimization iterations. Three-dimensional finite-difference time-domain simulations on a silicon-on-insulator platform confirm high conversion efficiencies of -0.053\u2005dB (TE0-to-TE1) and -0.043\u2005dB (TE1-to-TE0), with mode purities reaching 99.3%. Extending this approach, a triple-mode cyclic converter (TMCC) for TE0\/TE1\/TE2 cyclic conversion is realized through a two-stage optimization strategy, converging at around 100 iterations. The TMCC exhibits conversion efficiencies of -0.67\u2005dB (TE0-to-TE1), -1.1\u2005dB (TE1-to-TE2), and -0.67\u2005dB (TE2-to-TE0), accompanied by high mode purities of 96.4%, 93.6%, and 98.3%, respectively. Robustness analyses further demonstrate tolerance to fabrication deviations of \u00b110\u2005nm. These results highlight the potential of inverse design in deformed multimode silicon waveguides for realizing efficient mode cyclic conversion, thereby advancing mode-division multiplexing in photonic integrated circuits.<\/jats:p>","DOI":"10.1364\/oe.581899","type":"journal-article","created":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T15:00:08Z","timestamp":1767884408000},"page":"4092","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Inverse design of deformed silicon waveguides for multimode cyclic conversion"],"prefix":"10.1364","volume":"34","author":[{"given":"Zikang","family":"Hu","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04w9fbh59","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Songya","family":"Liu","sequence":"additional","affiliation":[{"name":"Beihang University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mingying","family":"Lan","sequence":"additional","affiliation":[{"name":"Beijing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yilin","family":"Wang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04w9fbh59","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1529-6700","authenticated-orcid":true,"given":"Lei","family":"Chen","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04w9fbh59","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9119-4781","authenticated-orcid":true,"given":"Han","family":"Ye","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04w9fbh59","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,1,28]]},"reference":[{"key":"oe-34-3-4092-R1","doi-asserted-by":"publisher","first-page":"3069","DOI":"10.1038\/ncomms4069","type":"journal-article","volume":"5","author":"Luo","year":"2014","journal-title":"Nat. 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