Skip to main content
Log in

Implementing fractional Fourier transform using SH0 wave computational metamaterials in space domain

  • Letter
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Landy N, Smith D R. A full-parameter unidirectional metamaterial cloak for microwaves. Nat Mater, 2013, 12: 25–28

    Article  Google Scholar 

  2. Li Y, Zhu K J, Peng Y G, et al. Thermal meta-device in analogue of zero-index photonics. Nat Mater, 2019, 18: 48–54

    Article  Google Scholar 

  3. Zigoneanu L, Popa B I, Cummer S A. Three-dimensional broadband omnidirectional acoustic ground cloak. Nat Mater, 2014, 13: 352–355

    Article  Google Scholar 

  4. Xu T, Lezec H J. Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial. Nat Commun, 2014, 5: 4141

    Article  Google Scholar 

  5. Xu Y, Gu C, Hou B, et al. Broadband asymmetric waveguiding of light without polarization limitations. Nat Commun, 2013, 4: 2561

    Article  Google Scholar 

  6. Larouche S, Tsai Y J, Tyler T, et al. Infrared metamaterial phase holograms. Nat Mater, 2012, 11: 450–454

    Article  Google Scholar 

  7. Mosk A P, Lagendijk A, Lerosey G, et al. Controlling waves in space and time for imaging and focusing in complex media. Nat Photon, 2012, 6: 283–292

    Article  Google Scholar 

  8. Melde K, Mark A G, Qiu T, et al. Holograms for acoustics. Nature, 2016, 537: 518–522

    Article  Google Scholar 

  9. Zhang W, Cheng K, Wu C, et al. Implementing quantum search algorithm with metamaterials. Adv Mater, 2018, 30: 1703986

    Article  Google Scholar 

  10. Zhang W, Qu C, Zhang X. Solving constant-coefficient differential equations with dielectric metamaterials. J Opt, 2016, 18: 075102

    Article  Google Scholar 

  11. Silva A, Monticone F, Castaldi G, et al. Performing mathematical operations with metamaterials. Science, 2014, 343: 160–163

    Article  MathSciNet  Google Scholar 

  12. Zangeneh-Nejad F, Fleury R. Topological analog signal processing. Nat Commun, 2019, 10: 2058

    Article  Google Scholar 

  13. Liu W, Li M, Guzzon R S, et al. A fully reconfigurable photonic integrated signal processor. Nat Photon, 2016, 10: 190–195

    Article  Google Scholar 

  14. Zuo S, Wei Q, Tian Y, et al. Acoustic analog computing system based on labyrinthine metasurfaces. Sci Rep, 2018, 8: 10103

    Article  Google Scholar 

  15. Zuo S Y, Tian Y, Wei Q, et al. Acoustic analog computing based on a reflective metasurface with decoupled modulation of phase and amplitude. J Appl Phys, 2018, 123: 091704

    Article  Google Scholar 

  16. Zhu Y, Hu J, Fan X, et al. Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase. Nat Commun, 2018, 9: 1632

    Article  Google Scholar 

  17. Ghaffarivardavagh R, Nikolajczyk J, Glynn Holt R, et al. Horn-like space-coiling metamaterials toward simultaneous phase and amplitude modulation. Nat Commun, 2018, 9: 1349

    Article  Google Scholar 

  18. Qiu H, Chen M, Huan Q, et al. Steering and focusing of fundamental shear horizontal guided waves in plates by using multiple-strip metasurfaces. EPL, 2019, 127: 46004

    Article  Google Scholar 

  19. Cegla F B. Energy concentration at the center of large aspect ratio rectangular waveguides at high frequencies. J Acoust Soc Am, 2008, 123: 4218–4226

    Article  Google Scholar 

  20. Almeida L B. The fractional Fourier transform and time-frequency representations. IEEE Trans Signal Process, 1994, 42: 3084–3091

    Article  Google Scholar 

  21. Sejdić E, Djurović I, Stanković L. Fractional fourier transform as a signal processing tool: An overview of recent developments. Signal Process, 2011, 91: 1351–1369

    Article  Google Scholar 

  22. Chinchilla L, Sierra D A, Torres R. A time-variant filtering approach for non-stationary random signals based on the fractional convolution. Signal Process, 2016, 119: 92–101

    Article  Google Scholar 

  23. Gómez-Echavarría A, Ugarte J P, Tobón C. The fractional fourier transform as a biomedical signal and image processing tool: A review. Biocybern Biomed Eng, 2020, 40: 1081–1093

    Article  Google Scholar 

  24. Lohmann A W. Image rotation, Wigner rotation, and the fractional Fourier transform. J Opt Soc Am A, 1993, 10: 2181–2186

    Article  Google Scholar 

  25. Namias V. The fractional order fourier transform and its application to quantum mechanics. IMA J Appl Math, 1980, 25: 241–265

    Article  MathSciNet  Google Scholar 

  26. Raymer M G, Beck M, McAlister D. Complex wave-field reconstruction using phase-space tomography. Phys Rev Lett, 1994, 72: 1137–1140

    Article  MathSciNet  Google Scholar 

  27. Bernardo L M, Soares O D D. Fractional Fourier transforms and imaging. J Opt Soc Am A, 1994, 11: 2622–2626

    Article  Google Scholar 

  28. Liu S, Ren H, Zhang J, et al. Image-scaling problem in the optical fractional fourier transform. Appl Opt, 1997, 36: 5671–5674

    Article  Google Scholar 

  29. McBride A C, Kerr F H. On Namias’s fractional Fourier transforms. IMA J Appl Math, 1987, 39: 159–175

    Article  MathSciNet  Google Scholar 

  30. Mendlovic D, Ozaktas H M. Fractional Fourier transforms and their optical implementation: I. J Opt Soc Am A, 1993, 10: 1875–1881

    Article  Google Scholar 

  31. Ozaktas H M, Mendlovic D. Fractional Fourier transforms and their optical implementation: II. J Opt Soc Am A, 1993, 10: 2522–2531

    Article  Google Scholar 

  32. Orazbayev B, Pacheco-Peña V, Beruete M, et al. Exploiting the dispersion of the double-negative-index fishnet metamaterial to create a broadband low-profile metallic lens. Opt Express, 2015, 23: 8555–8564

    Article  Google Scholar 

  33. Pacheco-Peña V, Orazbayev B, Beaskoetxea U, et al. Zoned near-zero refractive index fishnet lens antenna: Steering millimeter waves. J Appl Phys, 2014, 115: 124902

    Article  Google Scholar 

  34. Lv Z, Ding Y, Pei Y. Temporal differential elastic wave computational metamaterials. J Appl Phys, 2020, 127: 203104

    Article  Google Scholar 

  35. Hughes S A. Wave momentum flux parameter: A descriptor for nearshore waves. Coast Eng, 2004, 51: 1067–1084

    Article  Google Scholar 

  36. Xie Y, Wang W, Chen H, et al. Wavefront modulation and sub-wavelength diffractive acoustics with an acoustic metasurface. Nat Commun, 2014, 5: 5553

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to YongMao Pei.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12025201, 11521202, 11890681 and 11522214). Calculations are supported by High-Performance Computing Platform of Peking University, China.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lv, Z., Ding, Y., Li, H. et al. Implementing fractional Fourier transform using SH0 wave computational metamaterials in space domain. Sci. China Technol. Sci. 64, 2560–2565 (2021). https://doi.org/10.1007/s11431-021-1846-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-021-1846-x

Navigation