47th Vietnam Conference on Theoretical Physics (VCTP47)
Hội nghị Vật lý lý thuyết Việt Nam lần thứ 47
Tuy Hòa, 14 August 2022

ProgrammeO.18  Oral, VCTP47 Date: Thursday, 4 August 2022 Time: 16:50  17:15 Investigating the inverse Klein tunneling effect in binary waveguide arraysMinh C. Tran (1,2,3) and Truong X. Tran (4) (1) Atomic Molecular and Optical Physics Research Group, Science and Technology Advanced Institute, Van Lang University, 69/68 Dang Thuy Tram street, Ho Chi Minh city, Vietnam (2) Faculty of Technology, Van Lang University, 69/68 Dang Thuy Tram street, Ho Chi Minh City, Vietnam (3) Nuclear Training Center, VINATOM, 140 Nguyen Tuan street, Ha Noi, Vietnam (4) Department of Physics, Le Quy Don Technical University, 236 Hoang Quoc Viet street, Ha Noi, Vietnam Waveguide array (WAs) is a candidate for studying many classic photonic phenomena, such as discrete diﬀraction [1], discrete solitons [2], and the generation of diﬀractive resonant radiation from discrete solitons [3]. Klein tunneling (KT)  another peculiar fundamental quantum relativistic effect  has also been investigated in BWAs both theoretically [4] and experimentally [5] and was predicted by O. Klein in 1929 [6]. According to Klein, relativistic fermions can tunnel through large repulsive potential steps, which are higher than the energy of the particle, without the exponential decaying expected in quantum nonrelativistic tunneling processes governed by the wellknown Schrödinger equation [6]. This phenomenon is due to the existence of negativeenergy solutions of the Dirac equation [7]. The potential step must be sufficiently steep for KT to be observed [8]; i.e., it must occur at a very narrow region comparable or shorter than the Compton wavelength. In this presentation, we show results that we investigated the inverse KT in BWAs. For observing KT in BWAs, one launches an incident beam belonging to the positive branch (or electron branch) of the dispersion relation so that it hits the potential step and generates the transmitted beam belonging to the negative branch (or positron branch). Inversely, to observe the inverse KT effect, we now propose to launch an incident beam belonging to the negative branch which hits the inverse potential step and generates the transmitted beam belonging to the positive branch. In this talk, we want to achieve two goals: (i) we show the analytical formulas for the inverse KT effect in two cases: discrete model and continuous model, and (ii) we verify these theoretical results for the inverse KT in BWAs by comparing them with the results obtained by the beam propagation method. REFERENCES [1] D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature (London) 424, 817 (2003). [2] D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988). [3] Tr. X. Tran and F. Biancalana, Phys. Rev. Lett. 110, 113903 (2013). [4] S. Longhi, Phys. Rev. B 81, 075102 (2010). [5] F. Dreisow, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, Europhys. Lett. 97, 10008 (2012). [6] O. Klein, Z. Phys. 53, 157 (1929). [7] H. Nitta, T. Kudo, and H. Minowa, Am. J. Phys. 67, 966 (1999). [8] F. Sauter, Z. Phys. 69, 742 (1931) Presenter: Trần Công Minh 
Institute of Physics, VAST

Center for Theoretical Physics 
Center for Computational Physics
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