The quantum tunnel effect of photon in one-dimensional photonic crystals

TL;DR

This paper investigates the quantum tunneling effect of photons in one-dimensional photonic crystals, analyzing transmissivity, probability density, and current density, revealing conditions for quantum tunneling and periodic behaviors.

Contribution

It introduces a quantum theoretical approach to analyze photon behavior in photonic crystals, demonstrating the quantum tunnel effect and its relation to transmissivity and incident parameters.

Findings

Quantum transmissivity matches classical transmissivity.

Probability density and current density show periodic changes with incident angle and periodic number.

Photon tunneling occurs at frequencies where transmissivity is zero.

Abstract

In the paper, we have given the quantum transmissivity, probability density and probability current density of photon in one-dimensional photonic crystals $(AB)^N$ with the quantum theory approach. We find the quantum transmissivity is identical to the classical transmissivity. When the incident angle $\theta$ and periodic number $N$ change the probability density and probability current density are approximate periodic change, and their amplitude are increased with the incident angles $\theta$ and periodic number $N$ increasing. Otherwise, we find when the frequency of incident photon is corresponding to transmissivity $T=1$, the amplitude of the probability density is the largest. When the frequency of incident photon is corresponding to transmissivity $T=0$, the amplitude of the probability density attenuate rapidly to zero, it indicates that there is the quantum tunnel effect of photon in photonic crystals.