On the similarity of particle and photon tunneling and multiple internal reflections in one-dimensional, two-dimensional and three-dimensional photon tunneling

Abstract

The formal mathematical analogy between time-dependent quantum equation for the nonrelativistic particles and time-dependent equation for the propagation of electromagnetic waves had been studied in [A. I. Akhiezer and V. B. Berestezki, Quantum Electrodynamics (FM, Moscow, 1959) [in Russian] and S. Schweber, An Introduction to Relativistic Quantum Field Theory, Chap. 5.3 (Row, Peterson & Co, Ill, 1961)]. Here, we deal with the time-dependent Schrödinger equation for nonrelativistic particles and with time-dependent Helmholtz equation for electromagnetic waves. Then, using this similarity, the tunneling and multiple internal reflections in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) particle and photon tunneling are studied. Finally, some conclusions and future perspectives for further investigations are presented.