Characterization of trapped 3D kink modes in solar coronal slabs. A density contrast of ρ_i/ρ_e = 3 is chosen for illustrative purposes. Plotted in each panel are the dependences on the out-of-plane wavenumber (k_y) of the mode frequency of the transverse fundamental (with transverse order j = 1, the black solid curve) and the first overtone (j = 2, black dash-dotted). The hatched portions in any k_y − ω plane represent where trapped modes are forbidden, with four curves serving as the relevant borders (labeled in panel c1). Curves 0, 1, 2₀, and 3 correspond to where ${\kappa }_{\mathrm{i}}^2:=k_z^2-{\omega }^2/v_{\mathrm{Ai}}^2=0$, κ_e² := k_z² − ω²/v_Ae² = 0, n_i² := ω²/v_Ai² − (k_y² + k_z²) = 0, and m_e² := k_y² + k_z² − ω²/v_Ae² = 0, respectively. The curves labeled 2_Jπ (J = 1/2, 1, 3/2) further correspond to where n_i = Jπ. These curves pertain to the characterization of the j = 1 and j = 2 modes, whose dispersive behavior is typified by different panels where the dimensionless axial wavenumber (k_zd) increases sequentially (see text for more details).