The multifunctional process of resonance scattering and generation of oscillations by nonlinear layered structures

Figures & data

Figure 1. The nonlinear dielectric layered structure.

Figure 2. The geometry of the two-sheeted Riemann surfaces H_nκ.

Figure 3. Relative portion of energy generated in the third harmonic $W_{3\mathit{\kappa }}/W_{\mathit{\kappa }}$, the scattering $R_{\mathit{\kappa }}^{+},R_{\mathit{\kappa }}^{-}$ and generation $R_{3\mathit{\kappa }}^{+}{R}_{3\mathit{\kappa }}^{-}$ coefficients for α = −0.01 (left top/bottom) and for α = +0.01 (right top/bottom).

Figure 4. Curves at $a_{\mathit{\kappa }}^{\text{inc}}=24$, ϕ_κ = 0° for α = −0.01 (left) and at $a_{\mathit{\kappa }}^{\text{inc}}=14$, ϕ_κ = 66° for α = +0.01 (right): 1 – ${\mathit{\epsilon }}^{\left(\text{L}\right)}$, 2 – $\left|U\left(\mathit{\kappa };z\right)\right|$, 3 – $\left|U\left(3\mathit{\kappa };z\right)\right|$, 4 – $\text{Re}\left({\mathit{\epsilon }}_{\mathit{\kappa }}\right)$, 5 – $\text{Im}\left({\mathit{\epsilon }}_{\mathit{\kappa }}\right)$, 6 – $\text{Re}\left({\mathit{\epsilon }}_{3\mathit{\kappa }}\right)$, 7 – $\text{Im}\left({\mathit{\epsilon }}_{3\mathit{\kappa }}\right)\equiv 0$.

Figure 5. Scattered $\left|U_{\mathit{\kappa }}\left[a_{\mathit{\kappa }}^{\text{inc}},z\right]\right|$ and generated $\left|U_{3\mathit{\kappa }}\left[a_{\mathit{\kappa }}^{\text{inc}},z\right]\right|$ fields in the nonlinear layer at ϕ_κ = 0° for α = −0.01 (left) and ϕ_κ = 60° for α = +0.01 (right).

Figure 6. Curves at ϕ_κ = 0°, for α = −0.01 (left) and at ϕ_κ = 60° for α = +0.01 (right): 1 – $R_{\mathit{\kappa }}^{+}$, 2 – $R_{\mathit{\kappa }}^{-}$, 3 – $R_{2\mathit{\kappa }}^{+}\equiv 0$, 4 – $R_{2\mathit{\kappa }}^{-}\equiv 0$, 5 – $R_{3\mathit{\kappa }}^{+}$, 6 – $R_{3\mathit{\kappa }}^{-}$, 7 – $W_{3\mathit{\kappa }}/W_{\mathit{\kappa }}$.

Figure 7. Curves at ϕ_κ = 0° (left) and ϕ_κ = 60° (right): 1 … $\mathit{\kappa }={\mathit{\kappa }}^{\text{inc}}=0.375$, 2 … $3\mathit{\kappa }={\mathit{\kappa }}^{\text{gen}}=3{\mathit{\kappa }}^{\text{inc}}$; 3.1 … $\text{Re}\left({\mathit{\kappa }}_1^{\left(\text{L}\right)}\right)$, 3.2 … $\text{Im}\left({\mathit{\kappa }}_1^{\left(\text{L}\right)}\right)$, 4.1 … $\text{Re}\left({\mathit{\kappa }}_3^{\left(\text{L}\right)}\right)$, 4.2 … $\text{Im}\left({\mathit{\kappa }}_3^{\left(\text{L}\right)}\right)$ for α ≡ 0; 5.1 … $\text{Re}\left({\mathit{\kappa }}_1^{\left(\text{NL}\right)}\right)$, 5.2 … $\text{Im}\left({\mathit{\kappa }}_1^{\left(\text{NL}\right)}\right)$, 6.1 … $\text{Re}\left({\mathit{\kappa }}_3^{\left(\text{NL}\right)}\right)$, 6.2 … $\text{Im}\left({\mathit{\kappa }}_3^{\left(\text{NL}\right)}\right)$ for α = −0.01 (left) and for α = +0.01 (right).

Figure 8. The Q-factor and the relative Q-factor. Curves: 1 … $Q_{{\mathit{\kappa }}_1}$, 3 … $Q_{{\mathit{\kappa }}_3}$, and … $Q_{{\mathit{\kappa }}_1}/Q_{{\mathit{\kappa }}_3}$ at ${\mathit{\kappa }}^{\text{inc}}=0.375$, ${\mathit{\kappa }}_n={\mathit{\kappa }}_n^{\left(\text{NL}\right)}$, $n=1,3$, for ϕ_κ = 0°, α = −0.01 (left top/bottom) and for ϕ_κ = 60°, α = +0.01 (right top/bottom).

Figure 9. The properties of the nonlinear structure at incidence angles $\left\{{\mathit{\varphi }}_{\mathit{\kappa }},{180}^{\circ }-{\mathit{\varphi }}_{\mathit{\kappa }}\right\}$ with ${\mathit{\varphi }}_{\mathit{\kappa }}\in \left[0^{\circ }\right.,\left.{90}^{\circ }\right)$ for amplitudes $\left\{a_{\mathit{\kappa }}^{\text{inc}},b_{\mathit{\kappa }}^{\text{inc}}\right\}$: (top left/right) $a_{\mathit{\kappa }}^{\text{inc}}\ne 0$, $b_{\mathit{\kappa }}^{\text{inc}}=0$; (middle left/right) $a_{\mathit{\kappa }}^{\text{inc}}=38$, $b_{\mathit{\kappa }}^{\text{inc}}\ne 0$; (bottom left/right) $a_{\mathit{\kappa }}^{\text{inc}}=b_{\mathit{\kappa }}^{\text{inc}}$ here $R_{n\mathit{\kappa }}^{+}=R_{n\mathit{\kappa }}^{-}$, $n=1,3$.

Figure 10. Curves: 0 – $\left|U\left(\mathit{\kappa };z\right)\right|$ for $\mathit{\alpha }\left(z\right)\equiv 0$, 1 – ${\mathit{\epsilon }}^{\left(\text{L}\right)}$, 2 – $\left|U\left(\mathit{\kappa };z\right)\right|$, 3 – $\left|U\left(3\mathit{\kappa };z\right)\right|$, 4 – $\text{Re}\left({\mathit{\epsilon }}_{\mathit{\kappa }}\right)$, 5 – $\text{Im}\left({\mathit{\epsilon }}_{\mathit{\kappa }}\right)$, 6 – $\text{Re}\left({\mathit{\epsilon }}_{3\mathit{\kappa }}\right)$, 7 – $\text{Im}\left({\mathit{\epsilon }}_{3\mathit{\kappa }}\right)\equiv 0$, at $\left\{{\mathit{\varphi }}_{\mathit{\kappa }},{180}^{\circ }-{\mathit{\varphi }}_{\mathit{\kappa }}\right\}$ with ϕ_κ = 0° and (top left): $\left\{a_{\mathit{\kappa }}^{\text{inc}}=38,b_{\mathit{\kappa }}^{\text{inc}}=0\right\}$; (top right): $\left\{a_{\mathit{\kappa }}^{\text{inc}}=38,b_{\mathit{\kappa }}^{\text{inc}}=20\right\}$; (bottom left): $\left\{a_{\mathit{\kappa }}^{\text{inc}}=38,b_{\mathit{\kappa }}^{\text{inc}}=30\right\}$; (bottom right) $\left\{a_{\mathit{\kappa }}^{\text{inc}},b_{\mathit{\kappa }}^{\text{inc}}\right\}$ with $a_{\mathit{\kappa }}^{\text{inc}}=b_{\mathit{\kappa }}^{\text{inc}}=38$.