Skip to main content
Log in

Imaginary modulation inducing giant spatial Goos–Hänchen shifts in one-dimensional defective photonic lattices

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

We investigate the spatial Goos–Hänchen (GH) shifts in one-dimensional defective photonic lattices by modulating the imaginary part of refractive index, namely, the imaginary modulation. The reflection spectra possess two singular points under imaginary modulation when the reflectance is infinite or vanishing. These two points correspond to the coherent-perfect-absorption-laser (CPA-LP) point and defect mode (MD) in the parameter space composed of the incident angle and refractive index. We show the spatial GH shifts are extremely giant in the vicinity of CPA-LP and MD as the phase of reflection coefficients dislocate. Moreover, the GH shifts are sensitive to the incident angle and the refractive index of defect. The sensitivity coefficients can reach as high as 106. The study may find potential applications in highly sensitive sensors.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Abbas, M., Qamar, S.: Amplitude control of the Goos-Hänchen shift via a Kerr nonlinearity. Laser Phys. Lett. 11, 5201 (2014)

    Article  Google Scholar 

  • Anicin, B.A., Fazlic, R., Kopric, M.: Theoretical evidence for negative Goos-Haenchen shifts. J. Phys. A 11(8), 1657–1662 (1978)

    Article  ADS  Google Scholar 

  • Bliokh, K.Y., Aiello, A.: Goos–Hänchen and Imbert–Fedorov beam shifts: an overview. J. Opt. 15(1), 014001 (2013)

    Article  ADS  Google Scholar 

  • Chan, C.C., Tamir, T.: Angular shift of a Gaussian beam reflected near the Brewster angle. Opt. Lett. 10(8), 378–380 (1985)

    Article  ADS  Google Scholar 

  • Chen, X., Shen, M., Zhang, Z.F., Li, C.F.: Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals. J. Appl. Phys. 104(12), 123101 (2008)

    Article  ADS  Google Scholar 

  • Chen, J., Wang, K., Long, H., Han, X., Hu, H., Liu, W., Wang, B., Lu, P.: Tungsten disulfide-gold nanohole hybrid metasurfaces for nonlinear metalenses in the visible region. Nano Lett. 18, 1344–1350 (2018)

    Article  ADS  Google Scholar 

  • Cheng, M., Fu, P., Chen, X., Zeng, X., Feng, S., Chen, R.: Giant and tunable Goos-Hanchen shifts for attenuated total reflection structure containing graphene. JOSA B 31(10), 2325–2329 (2014)

    Article  ADS  Google Scholar 

  • Chuang, Y.L., Lee, R.K.: Giant Goos-Hänchen shift using PT symmetry. Phys. Rev. A 92(1), 013815 (2015)

    Article  ADS  Google Scholar 

  • Götte, J.B., Dennis, M.R.: Generalized shifts and weak values for polarization components of reflected light beams. New J. Phys. 14(7), 073016 (2012)

    Article  ADS  Google Scholar 

  • Grosche, S., Ornigotti, M., Szameit, A.: Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces. Opt. Express 23(23), 30195–30203 (2015)

    Article  ADS  Google Scholar 

  • Gui, D., Ji, L., Muhammad, A., Li, W., Cai, W., Li, Y., Li, X., Wu, X., Lu, P.: Jahn-Teller effect on framework flexibility of hybrid organic–inorganic perovskites. J. Phys. Chem. Lett. 9(4), 751–755 (2018)

    Article  Google Scholar 

  • Hashimoto, T., Yoshino, T.: Optical heterodyne sensor using the Goos-Hänchen shift. Opt. Lett. 14(17), 913–915 (1989)

    Article  ADS  Google Scholar 

  • He, J., Yi, J., He, S.: Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index. Opt. Express 14(7), 3024–3029 (2006)

    Article  ADS  Google Scholar 

  • He, M., Li, Y., Zhou, Y., Li, M., Cao, W., Lu, P.: Direct visualization of valence electron motion using strong-field photoelectron holography. Phys. Rev. Lett. 120(13), 133204 (2018)

    Article  ADS  Google Scholar 

  • Jiang, L., Wang, Q., Xiang, Y., Dai, X., Wen, S.: Electrically tunable Goos-Hänchen shift of light beam reflected from a graphene-on-dielectric surface. IEEE Photonics J. 5, 6500108 (2013)

    Article  ADS  Google Scholar 

  • Ke, S., Liu, J., Liu, Q., Zhao, D., Liu, W.: Strong absorption near exceptional points in plasmonic wave guide arrays. Opt. Quantum Electron. 50, 318 (2018a)

    Article  Google Scholar 

  • Ke, S., Zhao, D., Liu, Q., Liu, W.: Adiabatic transfer of surface plasmons in non-Hermitian graphene waveguides. Opt. Quantum Electron. 50, 393 (2018b)

    Article  Google Scholar 

  • Ke, S., Zhao, D., Liu, Q., Wu, S., Wang, B., Lu, P.: Optical imaginary directional couplers. J. Lightwave Technol. 36(12), 2510–2515 (2018c)

    Article  ADS  Google Scholar 

  • Ke, S., Liu, Q., Zhao, D., Liu, W.: Spectral discrete diffraction with non-Hermitian coupling. JOSA B 35(10), 2387–2393 (2018d)

    Article  ADS  Google Scholar 

  • Lai, H.M., Chan, S.W.: Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media. Opt. Lett. 27(9), 680–682 (2002)

    Article  ADS  Google Scholar 

  • Lai, H.M., Chan, S.W., Wong, W.H.: Nonspecular effects on reflection from absorbing media at and around Brewster’s dip. JOSA A 23(12), 3208–3216 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  • Li, C.F.: Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects. Phys. Rev. Lett. 91(13), 133903 (2003)

    Article  ADS  Google Scholar 

  • Liu, Q.J., Ke, S.L., Liu, W.W.: Mode conversion and absorption in an optical waveguide under cascaded complex modulations. Opt. Quantum Electron. 50, 356 (2018a)

    Article  Google Scholar 

  • Liu, J., Park, S., Nowak, D., Tian, M., Wu, Y., Long, H., Wang, K., Wang, B., Lu, P.: Near-field characterization of graphene plasmons by photo-induced force microscopy. Laser Photonics Rev. 12(8), 1800040 (2018b)

    Article  ADS  Google Scholar 

  • Liu, W., Li, X., Song, Y., Zhang, C., Han, X., Long, H., Wang, B., Wang, K., Lu, P.: Cooperative enhancement of two-photon-absorption-induced photoluminescence from a 2D perovskite-microsphere hybrid dielectric structure. Adv. Funct. Mater. 28(26), 1707550 (2018c)

    Article  Google Scholar 

  • Leung, P.T., Chen, C.W., Chiang, H.P.: Large negative Goos-Hanchen shift at metal surfaces. Opt. Commun. 276(2), 206–208 (2007)

    Article  ADS  Google Scholar 

  • Longhi, S., Della Valle, G., Staliunas, K.: Goos-Hänchen shift in complex crystals. Phys. Rev. A 84(4), 042119 (2011)

    Article  ADS  Google Scholar 

  • Ma, P., Gao, L.: Large and tunable lateral shifts in one-dimensional PT-symmetric layered structures. Opt. Express 25(9), 9676–9688 (2017)

    Article  ADS  Google Scholar 

  • Ma, X., Zhou, Y., Chen, Y., Li, M., Li, Y., Zhang, Q., Lu, P.: Timing the release of the correlated electrons in strong-field nonsequential double ionization by circularly polarized two-color laser fields. Opt. Express 27(3), 1825–1837 (2019)

    Article  ADS  Google Scholar 

  • Merano, M.: Optical beam shifts in graphene and single-layer boron-nitride. Opt. Lett. 41(24), 5780–5783 (2016)

    Article  ADS  Google Scholar 

  • Qin, C., Wang, B., Lu, P.: Frequency diffraction management through arbitrary engineering of photonic band structures. Opt. Express 26(20), 25721–25735 (2018a)

    Article  ADS  Google Scholar 

  • Qin, C., Liu, Q., Wang, B., Lu, P.: Photonic Weyl phase transition in dynamically modulated brick-wall waveguide arrays. Opt. Express 26(16), 20929–20943 (2018b)

    Article  ADS  Google Scholar 

  • Qin, C., Zhou, F., Peng, Y., Sounas, D., Zhu, X., Wang, B., Dong, J., Zhang, X., Alù, A., Lu, P.: Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials. Phys. Rev. Lett. 120(13), 133901 (2018c)

    Article  ADS  Google Scholar 

  • Qin, C., Yuan, L., Wang, B., Fan, S., Lu, P.: Efective electric feld force for a photon in a synthetic frequency lattice created in a waveguide modulator. Phys. Rev. A 97, 063838 (2018d)

  • Snyder, A.W., Love, J.D.: Goos-Hänchen shift. Appl. Opt. 15(1), 236–238 (1976)

    Article  ADS  Google Scholar 

  • Tamir, T., Bertoni, H.L.: Lateral displacement of optical beams at multilayered and periodic structures. JOSA 61(10), 1397–1413 (1971)

    Article  ADS  Google Scholar 

  • Tan, J., Zhou, Y., He, M., Chen, Y., Ke, Q., Liang, J., Zhu, X. Li, M. Lu, P.: Determination of the ionization time using attosecond photoelectron interferometry. Phys. Rev. Lett. 121, 253203 (2018)

  • Wang, L.G., Zhu, S.Y.: Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals. Opt. Lett. 31(1), 101–103 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  • Wang, L.G., Chen, H., Zhu, S.Y.: Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab. Opt. Lett. 30(21), 2936–2938 (2005)

    Article  ADS  Google Scholar 

  • Wang, Z., Wang, B., Long, H., Wang, K., Lu, P.: Surface plasmonic lattice solitons in semi-infinite graphene sheet arrays. J. Lightwave Technol. 35(14), 2960–2965 (2017)

    Article  ADS  Google Scholar 

  • Wang, D., Zhu, X., Li, L., Zhang, X., Liu, X., Lan, P., Lu, P.: Momentum gate for tunneling electrons with a circularly polarized control field. Phys. Rev. A 98(5), 053410 (2018a)

    Article  ADS  Google Scholar 

  • Wang, S., Wang, B., Lu, P.: PT-symmetric Talbot effect in a temporal mesh lattice. Phys. Rev. A 98(4), 043832 (2018b)

    Article  ADS  MathSciNet  Google Scholar 

  • Wang, S., Qin, C., Wang, B., Lu, P.: Discrete temporal Talbot effect in synthetic mesh lattices. Opt. Express 26(15), 19235–19246 (2018c)

    Article  ADS  Google Scholar 

  • Xu, S.L., Petrović, N., Belić, M.R., Hu, Z.L.: Light bullet supported by parity-time symmetric potential with power-law nonlinearity. Nonlinear Dyn. 84, 1877–1882 (2016a)

    Article  MathSciNet  Google Scholar 

  • Xu, S.L., Zhao, Y., Petrović, N.Z., Belić, M.R.: Spatiotemporal soliton supported by parity-time symmetric potential with competing nonlinearities. EPL 115, 14006 (2016b)

    Article  ADS  Google Scholar 

  • Yin, X., Hesselink, L.: Goos-Hänchen shift surface plasmon resonance sensor. Appl. Phys. Lett. 89(26), 261108 (2006)

    Article  ADS  Google Scholar 

  • Zhai, C., Zhang, Y., Zhang, Q.: Characterizing the ellipticity of an isolated attosecond pulse. Opt. Commun. 437, 104–109 (2019)

    Article  ADS  Google Scholar 

  • Zhang, X., Zhu, X., Wang, D., Li, L., Liu, X., Liao, Q., Lan, P., Lu, P.: Ultrafast oscillating-magnetic-field generation based on electronic-current dynamics. Phys. Rev. A 99(1), 013414 (2019)

    Article  ADS  Google Scholar 

  • Zhao, D., Wang, Z.Q., Long, H., Wang, K., Wang, B., Lu, P.X.: Optical bistability in defective photonic multilayers doped by graphene. Opt. Quantum Electron. 49(4), 163 (2017)

    Article  Google Scholar 

  • Zhao, D., Ke, S., Liu, Q., Wang, B., Lu, P.: Giant Goos-Hänchen shifts in non-Hermitian dielectric multilayers incorporated with graphene. Opt. Express 26(3), 2817–2828 (2018a)

    Article  ADS  Google Scholar 

  • Zhao, D., Liu, W.W., Ke, S.L., Liu, Q.J.: Large lateral shift in complex dielectric multilayers with nearly parity-time symmetry. Opt. Quantum Electron. 50, 323 (2018b)

    Article  Google Scholar 

  • Zhu, X.F.: Defect states and exceptional point splitting in the band gaps of one-dimensional parity-time lattices. Opt. Express 23(17), 22274–22284 (2015)

    Article  ADS  Google Scholar 

  • Zhu, Y., Hu, J., Fan, X., Yang, J., Liang, B., Zhu, X., Cheng, J.: Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase. Nat. Commun. 9(1), 1632 (2018)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the 973 Program (No. 2014CB921301), the National Natural Science Foundation of China (No. 11674117), Natural Science Foundation of Hubei Province (2015CFA040, 2016CFB515, 2017CFB526).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Weiwei Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, D., Zhong, D., Hu, Y. et al. Imaginary modulation inducing giant spatial Goos–Hänchen shifts in one-dimensional defective photonic lattices. Opt Quant Electron 51, 113 (2019). https://doi.org/10.1007/s11082-019-1828-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-019-1828-6

Keywords

Navigation