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.
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References
Abbas, M., Qamar, S.: Amplitude control of the Goos-Hänchen shift via a Kerr nonlinearity. Laser Phys. Lett. 11, 5201 (2014)
Anicin, B.A., Fazlic, R., Kopric, M.: Theoretical evidence for negative Goos-Haenchen shifts. J. Phys. A 11(8), 1657–1662 (1978)
Bliokh, K.Y., Aiello, A.: Goos–Hänchen and Imbert–Fedorov beam shifts: an overview. J. Opt. 15(1), 014001 (2013)
Chan, C.C., Tamir, T.: Angular shift of a Gaussian beam reflected near the Brewster angle. Opt. Lett. 10(8), 378–380 (1985)
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)
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)
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)
Chuang, Y.L., Lee, R.K.: Giant Goos-Hänchen shift using PT symmetry. Phys. Rev. A 92(1), 013815 (2015)
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)
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)
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)
Hashimoto, T., Yoshino, T.: Optical heterodyne sensor using the Goos-Hänchen shift. Opt. Lett. 14(17), 913–915 (1989)
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)
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)
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)
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)
Ke, S., Zhao, D., Liu, Q., Liu, W.: Adiabatic transfer of surface plasmons in non-Hermitian graphene waveguides. Opt. Quantum Electron. 50, 393 (2018b)
Ke, S., Zhao, D., Liu, Q., Wu, S., Wang, B., Lu, P.: Optical imaginary directional couplers. J. Lightwave Technol. 36(12), 2510–2515 (2018c)
Ke, S., Liu, Q., Zhao, D., Liu, W.: Spectral discrete diffraction with non-Hermitian coupling. JOSA B 35(10), 2387–2393 (2018d)
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)
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)
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)
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)
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)
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)
Leung, P.T., Chen, C.W., Chiang, H.P.: Large negative Goos-Hanchen shift at metal surfaces. Opt. Commun. 276(2), 206–208 (2007)
Longhi, S., Della Valle, G., Staliunas, K.: Goos-Hänchen shift in complex crystals. Phys. Rev. A 84(4), 042119 (2011)
Ma, P., Gao, L.: Large and tunable lateral shifts in one-dimensional PT-symmetric layered structures. Opt. Express 25(9), 9676–9688 (2017)
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)
Merano, M.: Optical beam shifts in graphene and single-layer boron-nitride. Opt. Lett. 41(24), 5780–5783 (2016)
Qin, C., Wang, B., Lu, P.: Frequency diffraction management through arbitrary engineering of photonic band structures. Opt. Express 26(20), 25721–25735 (2018a)
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)
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)
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)
Tamir, T., Bertoni, H.L.: Lateral displacement of optical beams at multilayered and periodic structures. JOSA 61(10), 1397–1413 (1971)
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)
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)
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)
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)
Wang, S., Wang, B., Lu, P.: PT-symmetric Talbot effect in a temporal mesh lattice. Phys. Rev. A 98(4), 043832 (2018b)
Wang, S., Qin, C., Wang, B., Lu, P.: Discrete temporal Talbot effect in synthetic mesh lattices. Opt. Express 26(15), 19235–19246 (2018c)
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)
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)
Yin, X., Hesselink, L.: Goos-Hänchen shift surface plasmon resonance sensor. Appl. Phys. Lett. 89(26), 261108 (2006)
Zhai, C., Zhang, Y., Zhang, Q.: Characterizing the ellipticity of an isolated attosecond pulse. Opt. Commun. 437, 104–109 (2019)
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)
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)
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)
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)
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)
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)
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).
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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
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DOI: https://doi.org/10.1007/s11082-019-1828-6