Photonic tunneling can be regarded as an optical analog for the quantum-mechanical barrier penetration of material particles. As the photon field has no charge and is not subject to the Pauli exclusion principle, some physical problems (such as tunneling time) become easier to study through photonic quantum tunneling, arousing great interest in the study of the quantum tunneling effect of photons. However, up to now, the quantum resonance tunneling phenomena of photons through a double-barrier have not been studied thoroughly. Photons in a state of quantum tunneling correspond to evanescent waves (i.e., surface plasmon polaritons) that are the core concept of nanooptics. Thus, research on photonic resonance tunneling can reveal new physical laws in nanooptics and has potential application value in optical devices (such as optical sensors and optical transistors). Therefore, it is necessary to develop a systematic theory of photonic resonance tunneling through a double-barrier. The application of the resonance tunneling effect of photons in the design of pulse and phase laser ranging systems is an important subject worth studying.

A photonic double-barrier structure is formed by a rectangular waveguide with dielectric discontinuities (Fig. 1). Seeing that the electromagnetic waves propagating along the waveguide satisfy the Helmholtz equation and can be expanded as a superposition of the waveguide modes transverse electric (TE) and transverse magnetic (TM), one can take the TE₁₀ mode as an example. In this case, the electric field component and its first derivative for z are continuous at the boundaries between the two different media inside the waveguide, based on which and using the concept of the Poynting vector one can obtain the quantum tunneling probability formula of photons through the double-barrier. By employing the analytic method and numerical simulation, we can obtain the physical conditions required for the resonance penetration effect of propagating-wave and evanescent-wave photons, respectively. In addition, we can clarify the dependence of the tunneling probability on the geometric size of the double-barrier, the refractive index of the filling medium, and the photon frequency. The parameters in the tunneling probability expression of photons through the double-barrier are related to each other. As a result, the parameter design makes it easy to make a mistake in the numerical analysis, which can be overcome by resorting to the original definitions of these parameters. To explore the potential application of the quantum resonance tunneling effect of photons in optical devices, we provide two new designs for the receivers of pulse and phase laser ranging systems (Figs. 6 and 7). To be specific, the double-barrier structure shown in Fig. 1 is placed in the receiving device of the laser ranging system. Its geometric sizes and the refractive index of the filling media are designed so that the resonant tunneling frequency is equal to the center frequency of the output signal of the laser ranging system.

The quantum tunneling probability of evanescent-wave photons through the double-barrier is given by Eq. (7), and in this case, the double-barrier corresponds to the two cut-off waveguides. The quantum tunneling probability of propagating-wave photons through the double-barrier is given by Eq. (9), and the double-barrier is formed by two normal-sized waveguides. Both Eq. (7) and Eq. (9) show that there are resonant penetration effects, namely that, the tunneling probability can be equal to one and photons can pass through the double-barrier completely. The resonant tunneling conditions of evanescent-wave photons are presented in Eq. (10), while the resonant penetration conditions of propagating-wave photons are provided in Eq. (11) or Eq. (12). The numerical simulation results are given in Figs. 2-5, where the tunneling probability curves containing resonance peaks show that their full widths at half maximum decrease sharply with the variation of parameters (such as the barrier width, the refractive index of the filling medium, and the photon frequency). In particular, when the double-barrier is formed by two cut-off waveguides, a tiny change in frequency or the structure parameters of the double-barrier can make a huge impact on the tunneling probability of photons. As for the laser ranging systems shown by Figs. 6 and 7, the resonant frequency is equal to the center frequency of the output signal. Since the frequency of the echo signal reflected by a static target is basically unchanged, the echo signal can smoothly pass through the double-barrier and enter the next module to complete the timing or phase measurement. Other light waves from the environment, with frequencies usually different from the working frequency of the laser ranging system, will be filtered out by the double-barrier structure. Thus, the received echo signal can be guaranteed to be true. On the other hand, the laser pulse has a non-zero spectral width (there is a frequency distribution around its central frequency). The closer the frequency of a component in the pulse is to the center frequency, the more likely it is to pass through the double-barrier. Therefore, when the echo signal passes through the double-barrier structure, its spectrum becomes narrowed, and its monochromaticity is enhanced. When the object to be measured is a moving object, the influence of the Doppler effect on this design is typically negligible.

A photonic double-barrier can be constructed via an electromagnetic waveguide with dielectric discontinuities. For a given frequency, by choosing appropriate parameters, the tunneling probability of photons through the double-barrier structure can be equal to one (resonant penetration effect). When the resonance phenomenon occurs, a small change in the frequency or structural parameters of the double-barrier can significantly influence the tunneling probability of photons through the double-barrier. These physical properties may provide some new-type design principles for some optical devices, such as band-pass filters, optical sensors, and optical transistors. Especially, it can present a new design for the receiving device of a laser ranging system, which is conducive to ruling out spurious returning signals and enhancing the monochromaticity of the true returning signals.