Skip to main content
SpringerLink
Log in

The Talbot effect in a metamaterial

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

The effect of anisotropy and spatial dispersion of a metamaterial on the Talbot effect may be engineered in principle. This has profound implications for applications of the Talbot effect such as the design of a multimode interference coupler (MMI). The paper describes how a metamaterial can suppress the modal phase error which otherwise limits the scaling of MMI port dimension. A binary multilayer dielectric material described by the Kronig–Penney model is shown to provide a close approximation to the required dispersion relation. Results of simulations of a multi-slotted waveguide MMI engineered to provide a polarising beam splitter function are given as an example of the method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. D.A.B. Miller, Silicon photonics: Meshing optics with applications. Nat. Photonics 11, 403–404 (2017)

    Article  ADS  Google Scholar 

  2. T.J. Hall, M. Hasan, Universal discrete Fourier optics RF photonic integrated circuit architecture. Opt. Express 24(7), 7600–7610 (2016)

    Article  ADS  Google Scholar 

  3. H. Nikkhah, T.J. Hall, Subwavelength grating waveguides for integrated photonics. Appl. Phys. A 122(4), 1–6 (2016)

    Article  Google Scholar 

  4. H. Nikkhah, T.J. Hall, Metamaterial Lüneburg lens for Fourier optics on-a-chip. Proc. SPIE OPTO, Integrated Optics: Devices, Materials, and Technologies, Photonics, West San Francisco (2014), 89880J–89880J

  5. A. Maese-Novo, R. Halir, S. Romero-García, D. Pérez-Galacho et al., Wavelength independent multimode interference coupler. Opt. Express 21(6), 7033–7040 (2013)

    Article  ADS  Google Scholar 

  6. L. Auslander, R. Tolimieri, Is computing with the finite Fourier transform pure or applied mathematics? Bull. Am. Math. Soc. 1(6), 847–897 (1979)

    Article  MathSciNet  Google Scholar 

  7. H. Nikkhah, Q. Zheng, I. Hassan, S. Abdul-Majid, T.J. Hall, The Free Space and Waveguide Talbot Effect: Phase Relations and Planar Light Circuit Applications. (Photonics North, Montreal, 2012), pp 841217–841217

    Google Scholar 

  8. J.Z. Huang, R. Scarmozzino, R.M. Osgood, A new design approach to large input/output number multimode interference couplers and its application to low-crosstalk WDM routers. IEEE Photonics Technol. Lett. 10(9), 1292–1294 (1998)

    Article  ADS  Google Scholar 

  9. A. Molina-Fernandez, J.G. Ortega-Moñux, Wangüemert-Pérez, Improving multimode interference couplers performance through index profile engineering. J. Lightwave Technol. 27(10), 1307–1314 (2009)

    Article  ADS  Google Scholar 

  10. R. Halir, G. Roelkens, A. Ortega-Moñux, J.G. Wangüemert-Pérez, High-performance 90 hybrid based on a silicon-on-insulator multimode interference coupler. Opt. Lett. 36(2), 178–180 (2011)

    Article  ADS  Google Scholar 

  11. A. Ortega-Monux, L. Zavargo-Peche, A. Maese-Novo et al., High-performance multimode interference coupler in silicon waveguides with subwavelength structures. IEEE Photonics Technol. Lett. 23(19), 1406–1408 (2011)

    Article  ADS  Google Scholar 

  12. D. Pérez-Galacho, R. Halir, A. Ortega-Moñux, C. Alonso-Ramos et al., Integrated polarization beam splitter with relaxed fabrication tolerances. Opt. Express 21(12), 14146–14151 (2013)

    Article  ADS  Google Scholar 

  13. R. Halir, P. Cheben, J.M. Luque-González, J.D. Sarmiento-Merenguel et al., Ultra-broadband nanophotonic beam splitter using an anisotropic sub-wavelength metamaterial. Laser Photonics Rev. 10(6), 1039–1046 (2016)

    Article  ADS  Google Scholar 

  14. S. Jahani, Z. Jacob, Transparent subdiffraction optics: nanoscale light confinement without metal. Optica 1(2), 96–100 (2014)

    Article  ADS  Google Scholar 

  15. B. Wolf, Fourier transform in metaxial geometric optics. JOSA A 8(9), 1399–1403 (1991)

    Article  ADS  Google Scholar 

  16. D. Landau, E.M. Lifshitz, Course of Theoretical Physics. Electrodynamics of Continuous Media. Oxford, 1960

  17. A. Markel, I. Tsukerman, Current-driven homogenization and effective medium parameters for finite samples. Phys. Rev. B 88(12), 125131 (2013)

    Article  ADS  Google Scholar 

  18. R. Iwanow, D.A. May-Arrioja, D.N. Christodoulides, G.I. Stegeman, Y. Min, W. Sohler, Discrete Talbot effect in waveguide arrays. Phys. Rev. Lett. 95(5), 053902 (2005)

    Article  ADS  Google Scholar 

  19. L. Garanovich, A.A. Sukhorukov, Y.S. Kivshar, Broadband diffraction management and self-collimation of white light in photonic lattices. Phys. Rev. E 74(6), 066609 (2006)

    Article  ADS  Google Scholar 

  20. K. Patorski, I the self-imaging phenomenon and its applications. Progress Opt. 27, 1–108 (1989)

    Article  ADS  Google Scholar 

  21. H.F. Talbot, LXXVI. Facts relating to optical science. No. IV. Lond. Edinb. Philos. Mag. J. Sci. 9(56) 401–407 (1836)

    Google Scholar 

  22. L. Rayleigh, XXV. On copying diffraction-gratings, and on some phenomena connected therewith. Lond. Edinb. Dublin Philos. Mag. J. Sci. 11(67) 196–205 (1881)

    Article  Google Scholar 

  23. R.D.L. Kronig, W.G. Penney, Quantum mechanics of electrons in crystal lattice. Proc. R. Soc. Lond. Ser. A 130, 499–513 (1930)

    Article  ADS  Google Scholar 

  24. P. Yeh, A. Yariv, C.S. Hong, Electromagnetic propagation in periodic stratified media. I. General theory. JOSA 67(4) 423–438 (1977)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    H. Nikkhah, M. Hasan & T. J. Hall

Authors
  1. H. Nikkhah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Hasan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. J. Hall
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Nikkhah.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nikkhah, H., Hasan, M. & Hall, T.J. The Talbot effect in a metamaterial. Appl. Phys. A 124, 106 (2018). https://doi.org/10.1007/s00339-017-1521-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-017-1521-1

Search

Navigation