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Optomechanical coupling behavior of multilayer nano-waveguides

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Abstract

The all-optical nano-switch has aroused considerable attention due to its fast switching and potential applications in silicon integrated photonics. The high power-consuming, however, limits its implementation, which can be avoided by mechanical Kerr effect. Multilayered structures could significantly enhance mechanical Kerr effect. In this paper, we propose a general method for analyzing optomechanical behavior of multilayer nano-waveguides. Moreover, we design three stacked ways for multilayer nano-waveguides: periodic stack, arithmetic stack, and geometric stack. An interesting result is that the optical gradient force and bending deflection will converge to a stable value if the stacked layer number is, respectively, larger than 26, 28, and 26, for the three stacked ways. This indicates that if the stacked layer number goes beyond the certain number, increasing the number of layers is useless for enhancing optical gradient forces and bending deflection. We further find that for arithmetic stack, the stable values of optical gradient forces and bending deflection are independent of common difference factor. The present method and results may offer a promising pathway for the design and optimization of multilayer all-optical nano-switches driven by optical gradient forces.Please check the edit made in the article title.Done.

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References

  1. Sacher, W.D., Mikkelsen, J.C., Huang, Y., Mak, J.C.C., Yong, Z., Luo, X., Li, Y., Dumais, P., Jiang, J., Goodwill, D., Bernier, E., Lo, P.G.-Q., Poon, J.K.S.: Monolithically integrated multilayer silicon nitride-on-silicon waveguide platforms for 3-D photonic circuits and devices. Proc. IEEE 106(12), 2232–2245 (2018)

    Google Scholar 

  2. Keyes, R.W.: Power dissipation in information processing. Science 168(3933), 796–801 (1970)

    Google Scholar 

  3. Chu, T., Yamada, H., Ishida, S., Arakawa, Y.: Thermooptic switch based on photonic-crystal line-defect waveguides. IEEE Photonics Technol. Lett. 17(10), 2083–2085 (2005)

    Google Scholar 

  4. Van Campenhout, J., Green, W.M.J., Vlasov, Y.A.: Design of a digital, ultra-broadband electro-optic switch for reconfigurable optical networks-on-chip. Opt. Express 17(26), 23793–23808 (2009)

    Google Scholar 

  5. Ren, M., Huang, J., Cai, H., Tsai, J.M., Zhou, J., Liu, Z., Suo, Z., Liu, A.Q.: Nano-optomechanical actuator and pull-back instability. ACS Nano 7(2), 1676–1681 (2013)

    Google Scholar 

  6. Braje, D.A., Balic, V., Yin, G.Y., Harris, S.E.: Low-light-level nonlinear optics with slow light. Phys. Rev. A 68(4), 041801 (2003)

    Google Scholar 

  7. Dawes, A.M.C., Illing, L., Clark, S.M., Gauthier, D.J.: All-optical switching in rubidium vapor. Science 308(5722), 672–674 (2005)

    Google Scholar 

  8. Dawes, A.M.C., Gauthier, D.J., Schumacher, S., Kwong, N.H., Binder, R., Smirl, A.L.: Transverse optical patterns for ultra-low-light-level all-optical switching. Laser Photonics Rev. 4(2), 221–243 (2010)

    Google Scholar 

  9. Pernice, W.H.P., Li, M., Tang, H.X.: A mechanical Kerr effect in deformable photonic media. Appl. Phys. Lett. 95(12), 123507 (2009)

    Google Scholar 

  10. Ren, L., Xu, X., Zhu, S., Shi, L., Zhang, X.: Experimental realization of on-chip nonreciprocal transmission by using the mechanical Kerr effect. ACS Photonics 7(11), 2995–3002 (2020)

    Google Scholar 

  11. Ma, J., Povinelli, M.L.: Mechanical Kerr nonlinearities due to bipolar optical forces between deformable silicon waveguides. Opt. Express 19(11), 10102–10110 (2011)

    Google Scholar 

  12. Almeida, V.R., Panepucci, R.R.: Nano-opto-electro-mechanical devices based on silicon slot-waveguides structures. In: 2009 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC), IEEE, Belem, Brazil, pp 560–563. 03–06 November 2009

  13. Pernice, W.H.P., Li, M., Tang, H.X.: Optomechanical coupling in photonic crystal supported nanomechanical waveguides. Opt. Express 17(15), 12424–12432 (2009)

    Google Scholar 

  14. Yu, Y.F., Zhang, J.B., Bourouina, T., Liu, A.Q.: Optical-force-induced bistability in nanomachined ring resonator systems. Appl. Phys. Lett. 100(9), 093108 (2012)

    Google Scholar 

  15. Dong, B., Cai, H., Ng, G.I., Kropelnicki, P., Tsai, J.M., Randles, A.B., Tang, M., Gu, Y.D., Suo, Z.G., Liu, A.Q.: A nanoelectromechanical systems actuator driven and controlled by Q-factor attenuation of ring resonator. Appl. Phys. Lett. 103(18), 181105 (2013)

    Google Scholar 

  16. Povinelli, M.L., Loncar, M., Ibanescu, M., Smythe, E.J., Johnson, S.G., Capasso, F., Joannopoulos, J.D.: Evanescent-wave bonding between optical waveguides. Opt. Lett. 30(22), 3042–3044 (2005)

    Google Scholar 

  17. Li, M., Pernice, W., Xiong, C., Baehr-Jones, T., Hochberg, M., Tang, H.: Harnessing optical forces in integrated photonic circuits. Nature 456(7221), 480–484 (2008)

    Google Scholar 

  18. Li, M., Pernice, W.H.P., Tang, H.X.: Tunable bipolar optical interactions between guided lightwaves. Nat. Photonics 3(8), 464–468 (2009)

    Google Scholar 

  19. Roels, J., De Vlaminck, I., Lagae, L., Maes, B., Van Thourhout, D., Baets, R.: Tunable optical forces between nanophotonic waveguides. Nat. Nanotechnol. 4(8), 510–513 (2009)

    Google Scholar 

  20. Jackson, J. D. Classical electrodynamics. American Association of Physics Teachers (1999)

  21. Van Thourhout, D., Roels, J.: Optomechanical device actuation through the optical gradient force. Nat. Photonics 4(4), 211–217 (2010)

    Google Scholar 

  22. Rodriguez, A.W., Hui, P.-C., Woolf, D.P., Johnson, S.G., Lončar, M., Capasso, F.: Classical and fluctuation-induced electromagnetic interactions in micron-scale systems: designer bonding, antibonding, and Casimir forces. Ann. Phys. 527(1–2), 45–80 (2015)

    Google Scholar 

  23. Pernice, W.H.P., Li, M., Fong, K.Y., Tang, H.X.: Modeling of the optical force between propagating lightwaves in parallel 3D waveguides. Opt. Express 17(18), 16032–16037 (2009)

    Google Scholar 

  24. Miri, M.A., Cotrufo, M., Alu, A.: Optical gradient forces between evanescently coupled waveguides. Opt. Lett. 43(17), 4104–4107 (2018)

    Google Scholar 

  25. Rosenberg, J., Lin, Q., Painter, O.: Static and dynamic wavelength routing via the gradient optical force. Nat. Photonics 3(8), 478–483 (2009)

    Google Scholar 

  26. Tao, J.F., Cai, H., Yu, A.B., Zhang, Q.X., Wu, J., Xu, K., Lin, J.T., Lo, G.Q., Kwong, D.L., Liu, A.Q.: A NEMS optical switch driven by optical force. In: TRANSDUCERS 2011–2011 16th International Solid-State Sensors, Actuators and Microsystems Conference, IEEE, Beijing, China, pp 1753–1756. 5–9 June 2011

  27. Cai H, Xu KJ, Tao JF, Ding L, Tsai JM, Lo GQ, Kwong DL (2012) A nano-optical switch driven by optical force using a laterally coupled double-ring resonator. In: 2012 IEEE 25th International Conference on Micro Electro Mechanical Systems, IEEE, Paris, France, pp 1297–1300. 29 Jan.–2 Feb. 2012

  28. Fan, X., Kong, S., Fang, W., Niu, H., Chen, N., Bai, C., IEEE: A novel miniaturized all-optical switch based on optical gradient force. In: 2018 Asia Communications and Photonics Conference, Hangzhou, China, Asia Communications and Photonics Conference and Exhibition. IEEE, pp 1–3. 26–29 October 2018

  29. Srivastava, T., Jha, R., Das, R.: High-performance bimetallic spr sensor based on periodic-multilayer-waveguides. IEEE Photonics Technol. Lett. 23(20), 1448–1450 (2011)

    Google Scholar 

  30. Enami, Y., Yuan, B., Tanaka, M., Luo, J., Jen, A.K.Y.: Electro-optic polymer/TiO2 multilayer slot waveguide modulators. Appl. Phys. Lett. 101(12), 123509 (2012)

    Google Scholar 

  31. Kurnosov, V.D., Kurnosov, K.V.: Numerical simulation of the divergence and optical confinement factor of a semiconductor laser with an asymmetric periodic multilayer AlGaInAs/InP waveguide. Quantum Electron. 50(9), 816–821 (2020)

    Google Scholar 

  32. Peng, W., Zhang, G., Lv, Y., Qin, L., Qi, K.: Ultra-narrowband absorption filter based on a multilayer waveguide structure. Opt. Express 29(10), 14582–14600 (2021)

    Google Scholar 

  33. Anemogiannis, E., Glytsis, E.N.: Multilayer waveguides: efficient numerical analysis of general structures. J. Lightwave Technol. 10(10), 1344–1351 (1992)

    Google Scholar 

  34. Kwon, M.S., Shin, S.Y.: Simple and fast numerical analysis of multilayer waveguide modes. Opt. Commun. 233(1–3), 119–126 (2004)

    Google Scholar 

  35. Libman M, Kondratyev NM, Gorodetsky ML (2018) Semi-analytical Model for a Slab One-dimensional Photonic Crystal. In: 4th International Conference on Quantum Technologies (ICQT), Moscow, Russia, 2018. AIP Conference Proceedings, vol 1. p 020004. AIP Publishing LLC, (2017)

  36. Sun, B., Cai, C., Venkatesh, B.S.: Matrix method for two-dimensional waveguide mode solution. J. Mod. Opt. 65(8), 914–919 (2018)

    MathSciNet  Google Scholar 

  37. Sharma, D., Verma, A., Prajapati, Y.K., Singh, V., Saini, J.P.: Forward and backward wave propagation in multilayer planar waveguide using metamaterials layer. Opt. Quant. Electron. 45(2), 105–114 (2013)

    Google Scholar 

  38. Midolo, L., Schliesser, A., Fiore, A.: Nano-opto-electro-mechanical systems. Nat. Nanotechnol. 13(1), 11–18 (2018)

    Google Scholar 

  39. Pattnaik PK, Vijayaaditya B, Srinivas T, Selvarajan A Optical MEMS pressure sensor using ring resonator on a circular diaphragm. In: 2005 International Conference on MEMS, NANO and Smart Systems, Banff, Canada, IEEE, pp 277–280. 24–27 Jul 2005

  40. Huang JG, Dong B, Tang M, Gu YD, Wu JH, Chen TN, Yang ZC, Yin YF, Hao YL, Kwong DL, Liu AQ (2015) NEMS actuator driven by electrostatic and optical force with nano-scale resolution. Paper presented at the 2015 Transducers-2015 18th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), Anchorage, AK, 2015 Jun 21–25

  41. Intaraprasonk, V., Fan, S.: Nonvolatile bistable all-optical switch from mechanical buckling. Appl. Phys. Lett. 98(24), 241104 (2011)

    Google Scholar 

  42. Tao, J.F., Cai, H., Yao, L.N., Lee, T., Gu, Y.D.: A novel low-light-level optical switch by using nano-opto-mechanics technology. In: 2017 IEEE 30th International Conference on Micro Electro Mechanical Systems (MEMS), IEEE, Las Vegas, USA, pp 936–939. 22–26 January 2017

  43. Cai, H., Dong, B., Tao, J.F., Ding, L., Tsai, J.M., Lo, G.Q., Liu, A.Q., Kwong, D.L.: A nanoelectromechanical systems optical switch driven by optical gradient force. Appl. Phys. Lett. 102(2), 023103 (2013)

    Google Scholar 

  44. Cai, H., Lin, J.X., Wu, J.H., Dong, B., Gu, Y.D., Yang, Z.C., Jin, Y.F., Hao, Y.L., Kwong, D.L., Liu, A.Q., IEEE.: NEMS optical cross connect (OXC) driven by opticl force. In: 2015 28th IEEE International Conference on Micro Electro Mechanical Systems, Estoril, PORTUGAL, Proceedings IEEE Micro Electro Mechanical Systems. IEEE, pp 57–60. 18–22 January 2015

  45. Wang, K.F., Wang, B.L., Zheng, L., Zhang, Y., Zhang, C.W.: Bending behavior and its effect on switching performance of an all-optical switch. J. Phys. D Appl. Phys. 54(15), 155108 (2021)

    Google Scholar 

  46. Maleki, M., Naei, M.H., Hosseinian, E.: Exact three-dimensional interface stress and electrode-effect analysis of multilayer piezoelectric transducers under torsion. Int. J. Solids Struct. 49(17), 2230–2238 (2012)

    Google Scholar 

  47. Wang, Y., Li, Z., Chen, W., Zhang, C., Zhu, J.: Free vibration and active control of pre-stretched multilayered electroactive plates. Int. J. Solids Struct. 180, 108–124 (2019)

    Google Scholar 

  48. Kuo, H.Y., Shih, C.L., Pan, E.: Enhancing magnetoelectric effect in magneto-electro-elastic laminated composites via interface modulus and stress. Int. J. Solids Struct. 195, 66–73 (2020)

    Google Scholar 

  49. Wang, Y., Wang, K.F., Wang, B.L.: Bending mechanism of optically actuated all-optical mechanical switches composed of bilayer waveguides. Int. J. Mech. Sci. 222, 107234 (2022)

    Google Scholar 

  50. Rodrigues, J.R., Almeida, V.R.: Optical forces through the effective refractive index. Opt. Lett. 42(21), 4371–4374 (2017)

    Google Scholar 

  51. Zhu, L.: Frequency dependence of the optical force between two coupled waveguides. Opt. Lett. 34(18), 2870–2872 (2009)

    Google Scholar 

  52. Rodrigues, J.R., Rosa, F.S.S., Almeida, V.R.: Casimir and optical forces acting on a silicon NOEMS device based on slot-waveguide structure. IEEE Photonics Technol. Lett. 28(5), 589–592 (2016)

    Google Scholar 

  53. Schlereth, K.H., Tacke, M.: The complex propagation constant of multilayer waveguides: an algorithm for a personal computer. IEEE J. Quantum Electron. 26(4), 627–630 (1990)

    Google Scholar 

  54. Pernice, W.H.P., Li, M., Tang, H.X.: Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate. Opt. Express 17(3), 1806–1816 (2009)

    Google Scholar 

  55. Wang, K.F., Wang, B.L.: Approximate and explicit expression of optical forces and pull-in instability of a silicon nano-optomechanical device. Nanotechnology 30(8), 085502 (2019)

    Google Scholar 

  56. Rodrigues, J.R., Gusso, A., Rosa, F.S.S., Almeida, V.R.: Rigorous analysis of Casimir and van der Waals forces on a silicon nano-optomechanical device actuated by optical forces. Nanoscale 10(8), 3945–3952 (2018)

    Google Scholar 

  57. Burnett, J.H., Kaplan, S.G., Stover, E., Phenis, A.: Refractive index measurements of Ge. In: LeVan PD, Sood AK, Wijewarnasuriya P, Dsouza AI (eds) Conference on Infrared Sensors, Devices, and Applications VI, Proceedings of SPIE. International Society for Optics and Photonics, San Diego, USA, pp 222–232. 31 Aug.-01 Sep. 2016

  58. Palik, E.D.: Handbook of optical constants of solids, vol 3. Academic press (1998)

  59. Bochobza-Degani, O., Elata, D., Nemirovsky, Y.: An efficient DIPIE algorithm for CAD of electrostatically actuated MEMS devices. J. Microelectromech. Syst. 11(5), 612–620 (2002)

    Google Scholar 

  60. Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3), 139–147 (2000)

    Google Scholar 

  61. Wang, Y.-B., Wang, L.-F., Joyce, H.J., Gao, Q., Liao, X.-Z., Mai, Y.-W., Tan, H.H., Zou, J., Ringer, S.P., Gao, H.-J., Jagadish, C.: Super deformability and young’s modulus of GaAs nanowires. Adv. Mater. 23(11), 1356–1360 (2011)

    Google Scholar 

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Acknowledgements

This research was supported by Guangdong Basic and Applied Basic Research Foundation (Project Nos. 2022B1515020099), Shenzhen Science and Technology Program (Project No. JCYJ20220818102409020), and the National Natural Science Foundation of China (Project No. 11972137).

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  1. School of Science, Harbin Institute of Technology, Shenzhen, 518055, China

    Y. Wang, K. F. Wang & B. L. Wang

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Wang, Y., Wang, K.F. & Wang, B.L. Optomechanical coupling behavior of multilayer nano-waveguides. Arch Appl Mech 93, 4041–4064 (2023). https://doi.org/10.1007/s00419-023-02477-2

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