Fig. 1. (a) Illustration of a PT-symmetric metasurface system composed of a nonmagnetic slab sandwiched by two ultrathin metasurfaces satisfying PT symmetry in a symmetric environment. (b) Absolute values of scattering matrix eigenvalues s1,2 with the increasing absolute value of imaginary part of the metasurfaces’ relative permittivity |Im(εms)| for different values of relative permittivity ε of the sandwiched slab. (c) and (d) Simulated Ez/E0 under the illumination of a planar wave incident from the left air region when ε=10−4, d=λ0, εms=1±159i, and dms=10−3λ0. The line profiles display |E|/E0 (red) and |H|/H0 (blue) along the edge of the simulation model. In (c), there is no impurity. In (d), a spherical dielectric impurity (relative permittivity 10, radius 0.2λ0) is positioned inside the sandwiched slab.

Fig. 2. (a) Schematic graph of the transformation of an ultrathin metasurface into a bulky slab via stretching spatial transformation along the x direction. (b) Illustration of the GPT-symmetric system composed of a lossy metasurface and a stretched gain metasurface separated by a slab. (c)–(e) Simulated Ez/E0 (color map), |E|/E0 (red lines), and |H|/H0 (blue lines) under the illumination of a planar wave incident from the left air region when ε=10−4 and d=λ0. The relevant parameters are εms=1+159i and dms=10−3λ0 for the lossy metasurface and εms′=0.001−0.159i, μms′=0.001, and dms′=λ0 for the stretched gain metasurface. In (c), there is no impurity. In (d) and (e), a spherical dielectric impurity (relative permittivity 10, radius 0.2λ0) is embedded inside the sandwiched slab. In (e), the metasurfaces are removed. (f) Transmittance through the models in (d) and (e) as a function of εimp of the embedded impurity.

Fig. 3. (a) Schematic graph the transformation of a loss/gain-less ZIM (εZIM=μZIM→0) into an effective uniform ZIM with complex εeff via a cylindrical dopant (relative permittivity εd, radius of circular cross section rd) oriented along the z direction. (b) and (c) Contour maps of (b) log(|Re(εeff)|) and (c) log(|Im(εeff)|) as a function of Re(εd) and |Im(εd)| when rd=0.35λ0. Both points P1 (εd=3.06−0.91i) and P2 (εd=10.18−0.85i) correspond to εeff≈0.159i. (d) and (e) Simulated Ez/E0 (color map), |E|/E0 (red lines), and |H|/H0 (blue lines) under the illumination of a planar wave incident from the left air region at the coalesced EP. The models in (d) and (e) are the same as those in Fig. 2(d), except that the stretched gain metasurface is replaced by a same-sized ZIM (εZIM=μZIM=10−4) doped with a cylindrical gain dopant, corresponding to parameters at points P1 and P2, respectively.

Fig. 4. (a) Schematic graph of a practical implementation for electromagnetic impurity-immunity. The lossy metasurface on the left is made of a conductive film. The sandwiched slab is implemented by type I PhC slab, at the center of which a cubic impurity is embedded. The stretched gain metasurface on the right is implemented by type II PhC slab doped with a cylindrical gain dopant. The right insets illustrate the unit cell of the two types of PhCs. (b) and (c) Photonic band structures (left) and effective parameters (right) for (b) type I and (c) type II PhCs. (d) and (e) Simulated Ez/E0 under the illumination of a planar wave incident from the left air region. In (e), the conductive film and doped type II PhC slab are removed. (f) Transmittance through the models in (d) and (e) as a function of εimp of the cubic impurity.

Fig. 5. (a) Illustration of a GPT-symmetric system composed of a lossy metasurface and a stretched gain metasurface separated by a slab in an asymmetric environment. (b) Required |Im(εms′)| of the stretched gain metasurface with varying εb2 when dms′=λ0. The marked dot denotes the values of εb2=0.6 and |Im(εms′)|=0.123. (c), (e) Simulated Ez/E0 (color map), |E|/E0 (red lines), and |H|/H0 (blue lines) under the illumination of a planar wave incident from the left air region when ε=10−4 and d=λ0. A spherical dielectric impurity (relative permittivity 10, radius 0.2λ0) is embedded inside the sandwiched slab. The lossy metasurface is characterized by εms=1+159i and dms=10−3λ0. In (c), the stretched gain metasurface is characterized by εms′=10−3−0.123i, μms′=10−3, and dms′=λ0. In (d), the stretched gain metasurface is implemented by a same-sized ZIM doped with a cylindrical gain dopant with rd=0.35λ0 and εd=10.18−0.65i.

Fig. 6. Contour maps of (a) log(|Re(εeff)|) and (b) log(|Im(εeff)|) of the doped type II PhC slab as functions of Re(εd) and |Im(εd)| of the cylindrical dopant.

Fig. 7. (a) Schematic graph of a GPT-symmetric system in the presence of variations of δ1 and δ2 in permittivities for the loss metasurface and stretched gain metasurface. The model is the same as that in Fig. 2(d) except for the variations in permittivities. (b) Simulated Ez/E0 (color map), |E|/E0 (red lines), and |H|/H0 (blue lines) under the illumination of a planar wave incident from the left air region in the presence of imperfections, that is, δ1/εms,0=5% and δ2/εms,0′=5%. Here, εms,0=1+159i and εms,0′=0.001–0.159i, which are the original relative permittivities of the loss metasurface and stretched gain metasurface. Computed (c) reflectance and (d) transmittance for left incidence as functions of δ1/εms,0 and δ2/εms,0′.