Fig. 1. Geometry of the problem.

Fig. 2. Absorption coefficient |α1| and parameter Δϵ as the functions of frequency at α2=0.2 (solid red line), α2=2 (dashed black line), and α2=5 (dash-dot blue line).

Fig. 3. (a) Reflectance [R(L)(ω)- solid red line and R(R)(ω)- dashed blue line] and transmittance (solid black line) of TM wave incident at Θ=15° on 1D system with ω01=1  PHz, ω02=1.2  PHz, γ1=0.067  PHz, γ2=0.14  PHz, |α1|=20.86, α2=2, ϵ01=2, ϵ02=3.22, and dg=dl=500  nm. (b) Real (solid lines) and imaginary (dashed lines) parts of dielectric permittivities of the layers near emission frequencies of the gain (red lines) and loss (black lines) regions. (c) Modulus of eigenvalues of S-matrix for 1D system as a function of frequency; red and blue lines correspond to the different eigenvalues of the same scattering matrix. The range of frequencies in (a) and (c) corresponding to the loss dominated system is gray shaded.

Fig. 4. (a) Reflectance [R(L)(ω)- solid red line and R(R)(ω)- dashed blue line] and transmittance (solid black line) of TM wave incident at Θ=0° and ω=0.92  PHz on non-Hermitian system with ω01=1  PHz, ω02=2  PHz, γ1=0.067  PHz, γ2=0.14  PHz, α1=2, ϵ01=2, ϵ02=2.2, and dg=dl=500  nm as a function of absorption coefficient. (b) Distribution of the energy flux density of an electromagnetic field in the system with the default parameters and α2=92.3 (solid green line) and α2=156.5 (dashed brown line); the area corresponding to gain material is red shaded, the area corresponding to loss material is green shaded. (c), (d) Transmittance of TM wave incident at Θ=0° (solid black line), Θ=30° (dash-dot green line), Θ=60° (dashed brown line), and dg=500  nm. The range of frequencies in (a), (c), and (d) corresponding to loss dominated system is gray shaded.

Fig. 5. (a) Geometry of non-Hermitian periodic stack. (b), (c) Geometries of non-Hermitian random stacks. (d), (e) Transmittance of TM wave through the stacks incident at ω=0.92  PHz and (d) Θ=0°, (e) Θ=60°; dash-dot black curve, four layers with dg=dl=250  nm, geometry of the system is presented in (a); dashed blue curves, six layers with thicknesses dg1=dg3=dl1=dl3=200  nm and dg2=dl2=100  nm, geometry of the stack is presented in (b); solid green curves, six layers with thicknesses dg1=dg2=200  nm, dl1=dl2=dg3=100  nm, and dl3=300  nm, geometry of the stack is presented in (c). The relevant layer parameters for the stacks are the same as in Fig. 4. The range of frequencies in (d) and (e) corresponding to loss dominated system is gray shaded.

Fig. 6. Eigenvalues of the S-matrix as a function of absorption coefficient for (a) PT-symmetric bilayer with ω01=ω02=ω=1  PHz, γ1=γ2=0.067  PHz, ϵ01=ϵ02=2, and dg=dl=500  nm at Θ=0° (solid and dashed lines of the same color correspond to the real and imaginary parts of eigenvalues) and (b) non-Hermitian bilayer with ω01=1  PHz, ω02=2  PHz, γ1=0.067  PHz, γ2=0.14  PHz, α1=2.4, ϵ01=2, ϵ02=2.2, and dg=dl=500  nm at ω=2.65  PHz and Θ=0°. Red and blue lines correspond to the eigenvalues λ1 and λ2. Vertical dashed lines indicate the position of EPs.