Photonics Research, 2018, 6 (4): 040000A1, Published Online: Jul. 10, 2018
Dispersive non-Hermitian optical heterostructures
Figures & Tables
Fig. 2. Absorption coefficient | α 1 | and parameter Δ ϵ as the functions of frequency at α 2 = 0.2 (solid red line), α 2 = 2 (dashed black line), and α 2 = 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 ω 01 = 1 PHz , ω 02 = 1.2 PHz , γ 1 = 0.067 PHz , γ 2 = 0.14 PHz , | α 1 | = 20.86 , α 2 = 2 , ϵ 01 = 2 , ϵ 02 = 3.22 , and d g = d l = 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 ω 01 = 1 PHz , ω 02 = 2 PHz , γ 1 = 0.067 PHz , γ 2 = 0.14 PHz , α 1 = 2 , ϵ 01 = 2 , ϵ 02 = 2.2 , and d g = d l = 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 α 2 = 92.3 (solid green line) and α 2 = 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 d g = 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 d g = d l = 250 nm , geometry of the system is presented in (a); dashed blue curves, six layers with thicknesses d g 1 = d g 3 = d l 1 = d l 3 = 200 nm and d g 2 = d l 2 = 100 nm , geometry of the stack is presented in (b); solid green curves, six layers with thicknesses d g 1 = d g 2 = 200 nm , d l 1 = d l 2 = d g 3 = 100 nm , and d l 3 = 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 ω 01 = ω 02 = ω = 1 PHz , γ 1 = γ 2 = 0.067 PHz , ϵ 01 = ϵ 02 = 2 , and d g = d l = 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 ω 01 = 1 PHz , ω 02 = 2 PHz , γ 1 = 0.067 PHz , γ 2 = 0.14 PHz , α 1 = 2.4 , ϵ 01 = 2 , ϵ 02 = 2.2 , and d g = d l = 500 nm at ω = 2.65 PHz and Θ = 0 ° . Red and blue lines correspond to the eigenvalues λ 1 and λ 2 . Vertical dashed lines indicate the position of EPs.
O. V. Shramkova, K. G. Makris, D. N. Christodoulides, G. P. Tsironis. Dispersive non-Hermitian optical heterostructures[J]. Photonics Research, 2018, 6(4): 040000A1.