(color online) (a) Physical model used to calculate the complex reflection and transmission coefficients at two interfaces. (b) Magnitudes and (c) phases of the reflection and transmission coefficients for the decoupled model, obtained by the numerical simulation. The coefficients of r₂₁ and t₁₂ (ϕ₂₁, are the magnitudes (phases) of reflection and transmission when the incident wave reaches the air (region 1)//dielectric interface. The coefficients of r₂₃ and t₂₃ (ϕ₂₃, are the magnitudes (phases) of reflection and transmission when the incident wave reaches the dielectric//air (region 3) interface. The β is the phase delay caused by the round propagation in the dielectric spacer. (d) Comparison between the full-wave simulation (black dash line) and theoretical calculation (red solid line) transmission coefficient S₂₁ of the proposed triple-band BPF.