Waveguide Analog of Tunneling through Quantum Potential Barriers

Abstract

Expressions are derived for the electromagnetic fields of guided waves which are analogous to the quantum-mechanical equations representing barrier tunneling. This analogy is achieved by comparing the propagation constant of the Schrödinger time-independent wave equation with that of the electromagnetic wave equation in waveguide and by comparing the de Broglie wavelength of a particle with the wavelength of the waves that propagate the energy. This results in an expression relating the form of an arbitrary one-dimensional energy barrier to the physical dimensions of a section of waveguide. The analogy is tested by the propagation of energy in the TE10 mode at both the 3- and 6-cm bands for the cases of rectangular and hyperbolic barriers. Although evanescent modes are present at the discontinuous regions, the analog for the rectangular barrier, which is considered to be the worse case, is verified when an effective barrier length leff of about 1.2l is used. This experimental verification demonstrates the possibility of waveguide simulation of quantum-mechanical energy barriers and the practicality of utilizing an electromagnetic analog for demonstrating the tunneling phenomenon and provides a method for measurement of the transmission coefficient through an arbitrarily shaped barrier.

Alternative perspective on photonic tunneling

“…Traditionally, the propagation of electromagnetic wave packets through an undersized waveguide is interpreted in terms of "photonic tunneling", which is based on a mathematical analogy between the Helmholtz equation describing evanescent modes and the nonrelativistic Schrödinger equation describing a quantum-mechanical tunneling [1][2][3].…”

A black potential for spin less particles

“…Waveguide analogy [44] of a quantum mechanical potential is very useful to study the problem in classical regime. In this section we prescribe the cross-sectional view of the waveguide which is analogous to this relativistic non-Hermitian Hulthen potential.…”

“…For mathematical simplicity we select the T E 10 mode of the plane electromagnetic wave[44] whose electric and magnetic field components are oriented in a such a way that E x = H y = E z = 0. The time-independent electromagnetic wave equation for this T E 10 wave propagation through a waveguide is written in Eq.…”

Mathematical-Physics of propagating modes in planar waveguides

“…A typical situation of this approach can be found in Optics when studying the modes in planar wave guides and in Quantum Mechanics when analyzing square potential wells [3][4][5][6][7][8][9][10][11][12].…”