Abstract

Transition radiation (TR) induced by electron–matter interaction usually demands vast accelerating voltages, and the radiation angle cannot be controlled. Here we present a mechanism of direction controllable inverse transition radiation (DCITR) in a graphene-dielectric stack excited by low-velocity electrons. The revealed mechanism shows that the induced hyperbolic-like spatial dispersion and the superposition of the individual bulk graphene plasmons (GPs) modes make the fields, which are supposed to be confined on the surface, radiate in the stack along a special radiation angle normal to the Poynting vector. By adjusting the chemical potential of the graphene sheets, the radiation angle can be controlled. And owing to the excitation of bulk GPs, only hundreds of volts for the accelerating voltage are required and the field intensity is dramatically enhanced compared with that of the normal TR. Furthermore, the presented mechanism can also be applied to the hyperbolic stack based on semiconductors in the infrared region as well as noble metals in the visible and ultraviolet region. Accordingly, the presented mechanism of DCITR is of great significance in particle detection, radiation emission, and so on.

© 2019 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
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  44. T. Ochiai, “Efficiency and angular distribution of graphene-plasmon excitation by electron beam,” J. Phys. Soc. Jpn. 83, 054705 (2014).
    [Crossref]
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    [Crossref]
  46. K.-C. Zhang, X.-X. Chen, C.-J. Sheng, K. J. A. Ooi, L. K. Ang, and X.-S. Yuan, “Transition radiation from graphene plasmons by a bunch beam in the terahertz regime,” Opt. Express 25, 20477–20485 (2017).
    [Crossref]
  47. K. Akbari, Z. L. Mišković, S. Segui, J. L. Gervasoni, and N. R. Arista, “Energy losses and transition radiation in multilayer graphene traversed by a fast charged particle,” ACS Photon. 4, 1980–1992 (2017).
    [Crossref]
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    [Crossref]

2019 (1)

Y. Zhang, C.-K. Lim, Z. Dai, G. Yu, J. W. Haus, H. Zhang, and P. N. Prasad, “Photonics and optoelectronics using nano-structured hybrid perovskite media and their optical cavities,” Phys. Rep. 795, 1–51 (2019).
[Crossref]

2018 (4)

S. Das, A. Salandrino, and R. Hui, “Tunable hyperbolic photonic devices based on periodic structures of graphene and HfO2,” J. Opt. Soc. Am. B 35, 2616–2624 (2018).
[Crossref]

M. V. Tsarev and P. Baum, “Characterization of non-relativistic attosecond electron pulses by transition radiation from tilted surfaces,” New J. Phys. 20, 033002 (2018).
[Crossref]

X. Lin, S. Easo, Y. Shen, H. Chen, B. Zhang, J. D. Joannopoulos, M. Soljačić, and I. Kaminer, “Controlling Cherenkov angles with resonance transition radiation,” Nat. Phys. 14, 816–821 (2018).
[Crossref]

J. S. T. Smalley, F. Vallini, X. Zhang, and Y. Fainman, “Dynamically tunable and active hyperbolic metamaterials,” Adv. Opt. Photon. 10, 354–408 (2018).
[Crossref]

2017 (4)

F. Liu, L. Xiao, Y. Ye, M. Wang, K. Cui, X. Feng, W. Zhang, and Y. Huang, “Integrated Cherenkov radiation emitter eliminating the electron velocity threshold,” Nat. Photonics 11, 289–292 (2017).
[Crossref]

K.-C. Zhang, X.-X. Chen, C.-J. Sheng, K. J. A. Ooi, L. K. Ang, and X.-S. Yuan, “Transition radiation from graphene plasmons by a bunch beam in the terahertz regime,” Opt. Express 25, 20477–20485 (2017).
[Crossref]

K. Akbari, Z. L. Mišković, S. Segui, J. L. Gervasoni, and N. R. Arista, “Energy losses and transition radiation in multilayer graphene traversed by a fast charged particle,” ACS Photon. 4, 1980–1992 (2017).
[Crossref]

J. Yao, Y. Chen, L. Ye, N. Liu, G. Cai, and Q. H. Liu, “Multiple resonant excitations of surface plasmons in a graphene stratified slab by Otto configuration and their independent tuning,” Photon. Res. 5, 377–384 (2017).
[Crossref]

2016 (2)

L. Tengfei and J. B. Khurgin, “Hyperbolic metamaterials: beyond the effective medium theory,” Optica 3, 1388–1396 (2016).
[Crossref]

I. Kaminer, M. Mutzafi, A. Levy, G. Harari, H. H. Sheinfux, S. Skirlo, J. Nemirovsky, J. D. Joannopoulos, M. Segev, and M. Soljačić, “Quantum Čerenkov radiation: spectral cutoffs and the role of spin and orbital angular momentum,” Phys. Rev. X 6, 011006 (2016).
[Crossref]

2015 (3)

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

T. Galfsky, H. N. S. Krishnamoorthy, W. Newman, E. E. Narimanov, Z. Jacob, and V. M. Menon, “Active hyperbolic metamaterials: enhanced spontaneous emission and light extraction,” Optica 2, 62–65 (2015).
[Crossref]

J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic plasmons and topological transitions over uniaxial metasurfaces,” Phys. Rev. Lett. 114, 233901 (2015).
[Crossref]

2014 (5)

T. Xu and H. J. Lezec, “Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial,” Nat. Commun. 5, 4141 (2014).
[Crossref]

A. A. Orlova, S. V. Zhukovsky, I. V. Iorsh, and P. A. Belov, “Controlling light with plasmonic multilayers,” Photon. Nanostr. Fundam. Appl. 12, 213–230 (2014).
[Crossref]

S. Liu, C. Zhang, M. Hu, X. Chen, P. Zhang, S. Gong, T. Zhao, and R. Zhong, “Coherent and tunable terahertz radiation from graphene surface plasmon polaritons excited by an electron beam,” Appl. Phys. Lett. 104, 201104 (2014).
[Crossref]

S. Gong, M. Hu, R. Zhong, X. Chen, P. Zhang, T. Zhao, and S. Liu, “Electron beam excitation of surface plasmon polaritons,” Opt. Express 22, 19252–19261 (2014).
[Crossref]

T. Ochiai, “Efficiency and angular distribution of graphene-plasmon excitation by electron beam,” J. Phys. Soc. Jpn. 83, 054705 (2014).
[Crossref]

2013 (3)

F. J. G. De Abajo, “Multiple excitation of confined graphene plasmons by single free electrons,” ACS Nano 7, 11409–11419 (2013).
[Crossref]

O. Lundh, C. Rechatin, J. Lim, V. Malka, and J. Faure, “Experimental measurements of electron-bunch trains in a laser-plasma accelerator,” Phys. Rev. Lett. 110, 065005 (2013).
[Crossref]

T. J. Maxwell, C. Behrens, Y. Ding, A. S. Fisher, J. Frisch, Z. Huang, and H. Loos, “Coherent-radiation spectroscopy of few-femtosecond electron bunches using a middle-infrared prism spectrometer,” Phys. Rev. Lett. 111, 184801 (2013).
[Crossref]

2012 (4)

I. Georgescu, “Čerenkov radiation: light from ripples,” Nat. Phys. 8, 704 (2012).
[Crossref]

S. Liu, P. Zhang, W. Liu, S. Gong, R. Zhong, Y. Zhang, and M. Hu, “Surface polariton Cherenkov light radiation source,” Phys. Rev. Lett. 109, 153902 (2012).
[Crossref]

I. Iorsh, A. Poddubny, A. Orlov, P. Belov, and Y. S. Kivshar, “Spontaneous emission enhancement in metal-dielectric metamaterials,” Phys. Lett. A 376, 185–187 (2012).
[Crossref]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37, 1856–1858 (2012).
[Crossref]

2011 (3)

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5, 411–415 (2011).
[Crossref]

J. Chen, Y. Wang, B. Jia, T. Geng, X. Li, L. Feng, W. Qian, B. Liang, X. Zhang, M. Gu, and S. Zhuang, “Observation of the inverse Doppler effect in negative-index materials at optical frequencies,” Nat. Photonics 5, 239–245 (2011).
[Crossref]

O. Lundh, J. Lim, C. Rechatin, L. Ammoura, A. Ben-Ismail, X. Davoine, G. Gallot, J.-P. Goddet, E. Lefebvre, V. Malka, and J. Faure, “Few femtosecond, few kiloampere electron bunch produced by a laser-plasma accelerator,” Nat. Phys. 7, 219–222 (2011).
[Crossref]

2010 (1)

F. J. G. De Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys. 82, 209–275 (2010).
[Crossref]

2009 (4)

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19, 3077–3083 (2009).
[Crossref]

A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103, 095003 (2009).
[Crossref]

G. Adamo, K. F. MacDonald, Y. H. Fu, C.-M. Wang, D. P. Tsai, F. J. García de Abajo, and N. I. Zheludev, “Light well: a tunable free-electron light source on a chip,” Phys. Rev. Lett. 103, 113901 (2009).
[Crossref]

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: emission spectrum,” Phys. Rev. A 79, 013829 (2009).
[Crossref]

2008 (2)

A. Yurtsever, M. Couillard, and D. A. Muller, “Formation of guided Cherenkov radiation in silicon-based nanocomposites,” Phys. Rev. Lett. 100, 217402 (2008).
[Crossref]

Y. Zhang, Z. D. Gao, Z. Qi, S. N. Zhu, and N. B. Ming, “Nonlinear Čerenkov radiation in nonlinear photonic crystal waveguides,” Phys. Rev. Lett. 100, 163904 (2008).
[Crossref]

2006 (2)

S. Lazar, G. A. Botton, and H. W. Zandbergen, “Enhancement of resolution in core-loss and low-loss spectroscopy in a monochromated microscope,” Ultramicroscopy 106, 1091–1103 (2006).
[Crossref]

C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler radiation emitted by an oscillating dipole moving inside a photonic band-gap crystal,” Phys. Rev. Lett. 96, 043903 (2006).
[Crossref]

2005 (1)

I. Adam, R. Aleksan, L. Amerman, E. Antokhin, D. Aston, P. Bailly, C. Beigbeder, M. Benkebil, P. Besson, G. Bonneaud, and M. Zito, “The DIRC particle identification system for the BaBar experiment,” Nucl. Instrum. Methods Phys. Res. A 538, 281–357 (2005).
[Crossref]

2002 (1)

G. L. Orlandi, “Coherence effects in the transition radiation spectrum and practical consequences,” Opt. Commun. 211, 109–119 (2002).
[Crossref]

1996 (2)

N. Yamamoto, A. Toda, and K. Axaya, “Imaging of transition radiation from thin films on a silicon substrate using a light detection system combined with TEM,” Microscopy 45, 64–72 (1996).
[Crossref]

N. Yamamoto, H. Sugiyama, and A. Toda, “Cherenkov and transition radiation from thin plate crystals detected in the transmission electron microscope,” Proc. R. Soc. London 452, 2279–2301 (1996).
[Crossref]

1991 (1)

C. J. Hirschmugl, M. Sagurton, and G. P. Williams, “Multiparticle coherence calculations for synchrotron-radiation emission,” Phys. Rev. A 44, 1316–1320 (1991).
[Crossref]

1982 (1)

V. L. Ginzburg, “Transition radiation and transition scattering,” Phys. Scripta T2A, 182–191 (1982).
[Crossref]

1965 (1)

F. G. Bass and V. M. Yakovenko, “Theory of radiation from a charge passing through an electrically inhomogeneous medium,” Sov. Phys. Usp. 8, 420 (1965).
[Crossref]

1953 (1)

W. Galbraith and J. V. Jelley, “Light pulses from the night sky associated with cosmic rays,” Nature 171, 349–350 (1953).
[Crossref]

1937 (1)

I. Frank and I. Tamm, “Coherent visible radiation from fast electrons passing through matter,” C.R. Acad. Sci. USSR 14, 109–114 (1937).
[Crossref]

1934 (1)

P. A. Cherenkov, “Visible emission of clean liquids by action of γ radiation,” Doklady Akademii Nauk SSSR 2, 451 (1934).

Adam, I.

I. Adam, R. Aleksan, L. Amerman, E. Antokhin, D. Aston, P. Bailly, C. Beigbeder, M. Benkebil, P. Besson, G. Bonneaud, and M. Zito, “The DIRC particle identification system for the BaBar experiment,” Nucl. Instrum. Methods Phys. Res. A 538, 281–357 (2005).
[Crossref]

Adamo, G.

G. Adamo, K. F. MacDonald, Y. H. Fu, C.-M. Wang, D. P. Tsai, F. J. García de Abajo, and N. I. Zheludev, “Light well: a tunable free-electron light source on a chip,” Phys. Rev. Lett. 103, 113901 (2009).
[Crossref]

Akbari, K.

K. Akbari, Z. L. Mišković, S. Segui, J. L. Gervasoni, and N. R. Arista, “Energy losses and transition radiation in multilayer graphene traversed by a fast charged particle,” ACS Photon. 4, 1980–1992 (2017).
[Crossref]

Aleksan, R.

I. Adam, R. Aleksan, L. Amerman, E. Antokhin, D. Aston, P. Bailly, C. Beigbeder, M. Benkebil, P. Besson, G. Bonneaud, and M. Zito, “The DIRC particle identification system for the BaBar experiment,” Nucl. Instrum. Methods Phys. Res. A 538, 281–357 (2005).
[Crossref]

Alù, A.

J. S. Gomez-Diaz, M. Tymchenko, and A. Alù, “Hyperbolic plasmons and topological transitions over uniaxial metasurfaces,” Phys. Rev. Lett. 114, 233901 (2015).
[Crossref]

Amerman, L.

I. Adam, R. Aleksan, L. Amerman, E. Antokhin, D. Aston, P. Bailly, C. Beigbeder, M. Benkebil, P. Besson, G. Bonneaud, and M. Zito, “The DIRC particle identification system for the BaBar experiment,” Nucl. Instrum. Methods Phys. Res. A 538, 281–357 (2005).
[Crossref]

Ammoura, L.

O. Lundh, J. Lim, C. Rechatin, L. Ammoura, A. Ben-Ismail, X. Davoine, G. Gallot, J.-P. Goddet, E. Lefebvre, V. Malka, and J. Faure, “Few femtosecond, few kiloampere electron bunch produced by a laser-plasma accelerator,” Nat. Phys. 7, 219–222 (2011).
[Crossref]

Ang, L. K.

Antokhin, E.

I. Adam, R. Aleksan, L. Amerman, E. Antokhin, D. Aston, P. Bailly, C. Beigbeder, M. Benkebil, P. Besson, G. Bonneaud, and M. Zito, “The DIRC particle identification system for the BaBar experiment,” Nucl. Instrum. Methods Phys. Res. A 538, 281–357 (2005).
[Crossref]

Arista, N. R.

K. Akbari, Z. L. Mišković, S. Segui, J. L. Gervasoni, and N. R. Arista, “Energy losses and transition radiation in multilayer graphene traversed by a fast charged particle,” ACS Photon. 4, 1980–1992 (2017).
[Crossref]

Aston, D.

I. Adam, R. Aleksan, L. Amerman, E. Antokhin, D. Aston, P. Bailly, C. Beigbeder, M. Benkebil, P. Besson, G. Bonneaud, and M. Zito, “The DIRC particle identification system for the BaBar experiment,” Nucl. Instrum. Methods Phys. Res. A 538, 281–357 (2005).
[Crossref]

Axaya, K.

N. Yamamoto, A. Toda, and K. Axaya, “Imaging of transition radiation from thin films on a silicon substrate using a light detection system combined with TEM,” Microscopy 45, 64–72 (1996).
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Figures (5)

Fig. 1.
Fig. 1. Schematic of the stacked graphene. The free electrons traverse the stack, which consists of periodically arranged alternative graphene sheets and dielectric buffer with permittivity εd and thickness h, along the Z (parallel to the electrons) direction. The excited GPs propagate along the X and Y (perpendicular to the electrons) directions.
Fig. 2.
Fig. 2. Dispersion curves of the stack and the poles distribution. (a) The frequency dispersion curves with normalized excitation probabilities in the logarithmic scale; h is 100 nm, εd and εsub are 2.1, and the chemical potential of the graphene sheets is 0.15 eV. There appear 10 curves around two fundamental modes for the stack with 10 layers of graphene sheets, induced by the GP coupling. (b) The GP pole distributions at 12, 15, and 17 THz.
Fig. 3.
Fig. 3. Contour maps of the electric field along the R direction for individual modes. (a) The contour map and field amplitude profile of the 4th mode at 12 THz, in which a TM4-like mode is formed by the coupling, indicating a hyperbolic-like spatial dispersion. (b) The contour map and field amplitude profile of the 10th mode at 12 THz, in which the fields are mainly confined on the upper surface, indicating a plasmonic-like spatial dispersion.
Fig. 4.
Fig. 4. DCITR from the individual bulk GP modes. (a) The contour map of the electric field along the R direction of DCITR at 12 THz, in which the field propagates along an radiation angle normal to the Poynting vector. The inset is that at 22 THz, which is confined on the first several graphene sheets. (b) The contour map of the TR in normal medium at 12 THz. (c) The electric field contour map of the GPs on the monolayer graphene sheet at 12 THz; (d) and (e) the normalized field intensity via the number of graphene sheet, in which the field intensity of DCITR attenuates in the form of an inverse proportional function of the graphene sheet number.
Fig. 5.
Fig. 5. Radiation angle and normalized field intensities. (a) The dependences of the field intensities and radiation angle on the frequencies. (b) The dependences of the field intensities on the electrons velocities at 12 and 15 THz, respectively. (c) The dependence of the field intensity on the chemical potential of the graphene sheets. (d) The dependence of the radiation angle on chemical potentials of the graphene sheets.

Equations (6)

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Eq(k,z,ω)i=jqku0ε0εi[(ωu0)2+k2k02εi]1ejωu0z,
[Eq|z=0inc+Ea|z=0incHϕq|z=0inc+Hϕa|z=0inc]=[10σ1][Eq|z=01+Ea|z=01Hϕq|z=01+Hϕa|z=01],
[Ea|z=01Hϕa|z=01]=i=1N1MipMib[Ea|z=dNsubHϕa|z=dNsub],
MipMib=[ejk//,ihi+ejk//,ihi2ejk//,ihiejk//,ihi2η0k//,iεik0ejk//,ihiejk//,ihi2εik0η0k//,iejk//ihi+ejk//,ihi2][10σ1],
Ea|z=dNsub=0[k2qJ1(kr)×k0(εdχincχ1εinc)u0ε0εdη0k//,incχ1χincχ1χincχincχ1σu0ε0εdχ2(εinck0η0k//,inc+σGra)(ϑa+ϑb)+εdk0η0k//,1(ϑaϑb)]dk,
Ea|z=dNsub=πi=1N[(kGSPsi)2H1(1)(kGSPsir)g(kGSPsi)f(kGSPsi)],

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