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Composite optical interference in non-unitary and unitary beam-splitter systems

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Abstract

In this paper, we theoretically propose and demonstrate a non-unitary beam-splitter (BS) by introducing coupling losses at the interface of the plasmonic waveguide and multimode dielectric waveguide (DW). The coupling losses enable us to modify the reflection and transmission factors, which can result in arbitrary shift of interference curves of two outputs. Specially, the lossy non-unitary BS can tune the amplitudes and phases of two outputs, even making them change synchronously, regardless of input phase differences. After a \(\pi /2\) phase delay in one arm, these two outputs are fed into another multimode DW. This DW is a normal unitary BS, working like the Michelson interferometer, where anti-synchronous interference can take place. At last, the whole device outputs an invariant zero energy state in one port, exhibiting a phase-insensitive performance. Our study provides a versatile design platform to realize non-unitary/unitary BS and construct more multi-functional devices.

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References

  1. D. Dai, W. Zhi, J. Peters, J.E. Bowers, Compact polarization beam splitter using an asymmetrical Machczehnder interferometer based on silicon-on-insulator waveguides. IEEE Photon. Technol. Lett. 24, 673–675 (2012)

    Article  ADS  Google Scholar 

  2. Y. Xu, J. Xiao, X. Sun, Compact polarization beam splitter for silicon-based slot waveguides using an asymmetrical multimode waveguide. J. Lightw. Technol. 32, 4884–4890 (2014)

    Article  Google Scholar 

  3. Z. Guo, J. Xiao, Ultracompact silicon-based polarization beam splitter using subwavelength gratings. IEEE Photon. Technol. Lett. 29, 1800–1803 (2017)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. C. He, X. Chen, M. Lu, X. Li, W. Wan, X. Qian, R. Yin, Y. Chen, Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal. Appl. Phys. Lett. 96, 111111 (2010)

    Article  ADS  Google Scholar 

  6. W. Jia, J. Deng, H. Wu, X. Li, A.J. Danner, Design and fabrication of high-efficiency photonic crystal power beam splitters. Opt. Lett. 36, 4077–4079 (2011)

    Article  ADS  Google Scholar 

  7. S.I. Bozhevolnyi, V.S. Volkov, E. Devaux, J.Y. Laluet, T.W. Ebbesen, Channel plasmon subwavelength waveguide components including interferometers and ring resonators. Nature 440, 508–511 (2006)

    Article  ADS  Google Scholar 

  8. J.T. Kim, S. Park, Vertical polarization beam splitter using a hybrid long-range surface plasmon polariton waveguide. J. Opt. 16, 025501 (2014)

    Article  ADS  Google Scholar 

  9. A.L. Stepanov, J.R. Krenn, H. Ditlbacher, A. Hohenau, A. Drezet, B. Steinberger, A. Leitner, F.R. Aussenegg, Quantitative analysis of surface plasmon interaction with silver nanoparticles. Opt. Lett. 30, 1524–1526 (2005)

    Article  ADS  Google Scholar 

  10. F. Gan, C. Sun, H. Li, Q. Gong, J. Chen, On-chip polarization splitter based on a multimode plasmonic waveguide. Photon. Res. 6, 47–53 (2018)

    Article  Google Scholar 

  11. S. Liu, T. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. Tang, C. Ouyang, X. Zhou, H. Yuan, H. Ma, W. Jiang, J. Han, W. Zhang, Q. Cheng, Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves. Light: Sci. Appl. 5, e16076 (2016)

    Article  Google Scholar 

  12. O. Wolf, S. Campione, A. Benz, A.P. Ravikumar, S. Liu, T.S. Luk, E.A. Kadlec, E.A. Shaner, J.F. Klem, M.B. Sinclair, I. Brener, Phased-array sources based on nonlinear metamaterial nanocavities. Nat. Commun. 6, 7667 (2015)

    Article  ADS  Google Scholar 

  13. P.V. Kapitanova, P. Ginzburg, D.S. Filonov, P.M. Voroshilov, P.A. Belov, A.N. Poddubny, Y.S. Kivshar, G.A. Wurtz, A.V. Zayats, Photonic spin hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes. Nat. Commun. 5, 4226 (2014)

    Article  Google Scholar 

  14. M. Kim, D. Lee, T.H. Kim, Y. Yang, H.J. Park, J. Rho, Observation of enhanced optical spin hall effect in a vertical hyperbolic metamaterial. ACS Photon. 6, 2530–2536 (2019)

    Article  Google Scholar 

  15. Y. Chen, J. Gu, F. Wang, Y. Cai, Self-splitting properties of a Hermite–Gaussian correlated Schell-model beam. Phys. Rev. A 91, 013823 (2015)

    Article  ADS  Google Scholar 

  16. W. Zhu, J. Yu, H. Guan, H. Lu, Z. Chen, Large spatial and angular spin splitting in a thin anisotropic near-zero metamaterial. Opt. Express 25, 5196 (2017)

    Article  ADS  Google Scholar 

  17. S. Taravati, A.A. Kishk, Dynamic modulation yields one-way beam splitting. Phys. Rev. B 99, 075101 (2019)

    Article  ADS  Google Scholar 

  18. S. Samanta, P.K. Dey, P. Banerji, P. Ganguly, A 1 \(\times \) 2 polarization-independent power splitter using three-coupled silicon rib waveguides. J. Opt. 20, 095801 (2018)

    Article  ADS  Google Scholar 

  19. A. Zeilinger, General properties of lossless beam splitters in interferometry. Am. J. Phys. 49, 882–883 (1981)

    Article  ADS  Google Scholar 

  20. V. Degiorgio, Phase shift between the transmitted and the reflected optical fields of a semireflecting lossless mirror is \(\pi /2\). Am. J. Phys. 48, 81–82 (1980)

    Article  ADS  Google Scholar 

  21. H. Ditlbacher, J.R. Krenn, G. Schider, A. Leitner, F.R. Aussenegg, Two-dimensional optics with surface plasmon polaritons. Appl. Phys. Lett. 81, 1762–1764 (2002)

    Article  ADS  Google Scholar 

  22. K. Sun, R.L. Byer, All-reflective Michelson, Sagnac, and Fabryc–Perot interferometers based on grating beam splitters. Opt. Lett. 23, 567–569 (1998)

    Article  ADS  Google Scholar 

  23. Z.Y. Ou, J.K. Rhee, L.J. Wang, Observation of four-photon interference with a beam splitter by pulsed parametric down-conversion. Phys. Rev. Lett. 83, 959–962 (1999)

    Article  ADS  Google Scholar 

  24. Y.S. Kim, O. Kwon, S.M. Lee, H. Kim, S.K. Choi, H.S. Park, Y.H. Kim, Observation of young’s double-slit interference with the three-photon noon state. Opt. Express 19, 24957–24966 (2011)

    Article  ADS  Google Scholar 

  25. L. Li, Z. Liu, X. Ren, S. Wang, V.C. Su, M.K. Chen, C.H. Chu, H.Y. Kuo, B. Liu, W. Zang, G. Guo, L. Zhang, Z. Wang, S. Zhu, D.P. Tsai, Metalens-arraycbased high-dimensional and multiphoton quantum source. Science 368, 1487–1490 (2020)

    Article  ADS  Google Scholar 

  26. Y. Zhang, K. Wei, F. Xu, Generalized Hong-Ou-Mandel quantum interference with phase-randomized weak coherent states. Phys. Rev. A 101, 033823 (2020)

    Article  ADS  Google Scholar 

  27. S. Ding, G. Wang, Extraordinary reflection and transmission with direction dependent wavelength selectivity based on parity-time-symmetric multilayers. J. Appl. Phys. 117, 31 (2015)

    Article  Google Scholar 

  28. H. Fan, J. Chen, Z. Zhao, J. Wen, Y. Huang, Anti-parity-time symmetry in passive nanophotonics. ACS Photon. 7, 3035–3041 (2020)

    Article  Google Scholar 

  29. B. Vest, M.C. Dheur, E. Devaux, A. Baron, E. Rousseau, J.P. Hugonin, J.J. Greffet, G. Messin, F. Marquier, Anti-coalescence of bosons on a lossy beam splitter. Science 356, 1373–1376 (2017)

    Article  ADS  Google Scholar 

  30. R. Wen, C. Zou, X. Zhu, P. Chen, Z.Y. Ou, J.F. Chen, W. Zhang, Non-Hermitian magnon-photon interference in an atomic ensemble. Phys. Rev. Lett. 122, 253602 (2019)

    Article  ADS  Google Scholar 

  31. Y. Wang, T. Li, L. Wang, H. He, L. Li, Q. Wang, S. Zhu, Plasmonic switch based on composite interference in metallic strip waveguides. Laser Photon. Rev. 8, 47–51 (2014)

    Article  ADS  Google Scholar 

  32. L.B. Soldano, E.C.M. Pennings, Optical multi-mode interference devices based on self-imaging: principles and applications. J. Lightw. Technol. 13, 615–627 (1995)

    Article  ADS  Google Scholar 

  33. M. Bachmann, P.A. Besse, H. Melchior, General self-imaging properties in \(n \times n\) multimode interference couplers including phase relations. Appl. Opt. 33, 3905–3911 (1994)

    Article  ADS  Google Scholar 

  34. H. Lu, Z. Cao, H. Li, Q. Shen, Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide. Appl. Phys. Lett. 85, 4579–4581 (2004)

    Article  ADS  Google Scholar 

  35. A. Panda, P. Sarkar, G. Palai, Studies on coupling of optical power in fiber to semiconductor waveguide at wavelength 1550 nm for photonics integrated circuits. Optik 157, 944–950 (2018)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 11804157). The computational resources generously provided by High Performance Computing Center of Nanjing Tech University are greatly appreciated.

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Correspondence to Yulin Wang.

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Li, Z., Wang, Y., Li, T. et al. Composite optical interference in non-unitary and unitary beam-splitter systems. J Opt 50, 495–501 (2021). https://doi.org/10.1007/s12596-021-00728-5

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