Fig. 1. Conceptual illustrations of the combination of loss and exceptional point. (a) Schematic illustrations of traditional active EP systems (upper panel) and purely passive EP systems with losses (lower panel). By adding losses, the gain elements can be replaced. The passive system will also be invariant under PT transformation as long as a proper exponential decay is included. (b) The real and imaginary parts of the eigenvalue against the variation of relative loss difference (γdiff/κ) when the two modes have the same resonant frequency. The EP serves as the transition point between PT-symmetry (left) and PT-symmetry-broken (right) phases. (c) Examples of typical EP devices and several possible functionalities that can be achieved when loss is combined with the EP in traditional photonic systems: cavities, waveguides, and metasurfaces.

Fig. 2. Examples of cavity-based EP devices achieving coherent perfect absorption (CPA) and loss-induced transparency (LIT). (a) Schematic of a one-channel generic CPA EP. (b) Experimentally measured normalized output spectrum of the device in (a). Inset depicts a log-log plot of output versus frequency detuning, confirming the quartic dependence^[40]. (c) Schematic diagram of the experimental setup for a CPA device utilizing the tunable unidirectional coupling between the clockwise (CW) and counterclockwise (CCW) modes in a microsphere resonator. (d) Measured transmission (green), reflection (red), and absorption (purple) of the device with CW input under critical coupling. (e) Reflection spectrum obtained for a fully reflective mirror, showing the quartic behavior of the lineshape^[41]. (f) Schematic of the optomechanical hybrid system. (g) Transmission spectra under different loss rates γtip. (h) Enlarged transmission spectra around −3MHz detuning, clearly showing the suppression and revival process of LIT^[28].

Fig. 3. Cavity-based passive EP devices for lasing revival and sensing. (a) Schematic of the coupled WGM resonators with additional loss induced by a Cr nanotip. (b) Eigenfrequency surface in the parameter space formed by coupling rate κ and loss rate γ2′. (c) Raman lasing spectra of the resonators with different values of loss^[47]. (d) Topological surfaces formed by a diabolic point degeneracy (top) and an exceptional point degeneracy (bottom) when subject to a perturbation ϵ, showing the enhanced splitting near the EP^[48]. (e) Schematic of the experimental setup for the loss-enhanced magneto-optical (MO) effect as proposed in Ref. [51]. (f) Experimentally measured frequency splitting of the conventional and loss-enhanced MO effects, clearly indicating the square-root dependence brought by the EPs for the latter. (g) Sensitivity enhancement compared with Hermitian MO devices, showing a threefold improvement from EP2 data.

Fig. 4. EP encircling using waveguides. (a) Conceptual illustration of encircling an EP in the parameter space, demonstrating the idea of mode locking^[74]. (b) Schematic diagram of the designed L-shaped waveguide. The inset shows how the encircling path involving the infinite boundary of the parameter space is mapped onto a Riemann sphere. (c) Field distributions at different locations of the waveguide. Different input ports correspond to different encircling directions. The mode-locking phenomenon is observable at corresponding output ports. (d) The transmission spectra between different combinations of polarizations^[77]. (e) Another encircling loop across the parameter space boundary for fast evolution. (f) Schematic diagram of the proposed double-coupled silicon waveguides on silicon-on-insulator (SOI) wafer. (g) Simulation (left) and experimental (right) transmission spectra between different modes^[79].

Fig. 5. Unidirectional reflectionless propagation in passive waveguides based on EPs. (a) Two-port optical system modeling a waveguide. HL+(−) and HR+(−) are the complex magnetic field amplitudes of the incoming (outgoing) modes at the left and right ports, respectively^[81]. (b) Schematic and photo of the designed passive unidirectional reflectionless parity-time waveguide. (c) Designed spatially modulated effective indices (red line) and experimental implementations using sinusoidal-shaped Si (blue dots). (d) The indices of the Ge/Cr combination. (e) Simulated electric field amplitude distributions for forward/backward incidence. (f) The contrast ratio was experimentally obtained and calculated from the Gaussian fits of transmission spectra^[90].

Fig. 6. Examples of passive EP metasurfaces realizing polarization control. (a) Unit cell design of a chiral EP metasurface. (b) Circular polarization transmission asymmetry factor Λ plotted in the parameter space of frequency f and structural displacements δx and δy. (c) Evolution of transmission eigenvalues |λ±| and Stokes parameters as the frequency is swept across an EP at f=210THz^[103]. (d) Unit cell design (top) and microscopy image (bottom) of the proposed reconfigurable EP metasurface. (e) Eigen-polarization states of the transmission matrix at different temperatures (①–⑤: experiments, ⑥–❿: fitting results). Corresponding locations are indicated on the Poincare sphere on the right^[107]. (f) Schematics of the design implemented for combining the exceptional topological phase and PB phase control in the proposed plasmonic topological metasurface^[108].

Fig. 7. Passive EP metasurfaces realizing asymmetric reflection and transmission. (a) Fabricated metasurface with lossy and lossless regions indicated. The inset shows the supercell configuration consisting of three subunits with different gap opening angles. (b) Principle of realizing purely passive non-Hermitian metasurface, where the Hamiltonian is shifted by a nonzero base loss. (c) FEM-simulated reflectivities versus the length w of the slit on the back for different reflection orders. (d) FDTD-simulated far-field reflecting intensities for incident waves from left (top) to right (bottom)^[30]. (e) Schematic of the Ag-graphene hybrid metasurface for asymmetric reflection. (f) Topological surfaces of the eigenvalues in the parameter space of wavelength λ and graphene chemical potential μc, with intersections indicated by the red curves. (g) Normalized electric field intensities with normal incident light when the system is at either of the two EPs indicated in (f)^[112].

Fig. 8. Sensors utilizing exceptional sensitivity based on passive EP implementations. (a) Schematic illustrations of the symmetry-broken double-layer metasurface. (b) Real (left) and imaginary (right) parts of the eigenmodes of the device. (c) Simulation results of the frequency splitting Δω versus the index of the cladding surrounding the metal bar on the top. (d) Experimental results when the concentration of anti-IgG is varied from 100 to 1500 aM, where ϵ=(anti-IgG concentrationaM)/(1100aM)^[4]. (e) Unit cell design of the bifunctional sensing EP metasurface. One of the SRRs has VO2 within its resonating gap (red). (f) Derivatives of the phase change when the temperature varies near an EP. (g) Eigenfrequency splitting ΔωE versus the resonance shift Δωy^[118].