Gain and loss have always been the main themes of nature and our life. Generally speaking, loss brings negative impacts and thus has to be eliminated or compensated for. Particularly in optics and photonics, loss exists in almost every optical device and system, which deteriorates their performance, generates heating problems, accelerates their aging, and causes severe energy waste. Except in some specific application scenarios, including optical absorbers and attenuators, losses are always among the key challenges to be overcome. For example, optical sensors are fundamental in detecting various types of information, such as chemical^[1,2], biological^[3,4], refractive index^[5,6], and even movements and rotations^[7]. For decades, scientists have been working on new device configurations and manufacturing technologies to reduce the losses for higher sensitivity, lower power consumption, and improved overall performances^[8–10]. In laser science and technology, optical losses have to be suppressed to achieve higher output power, smaller footprints, and faster operation speeds^[11–13]. Last but not least, in the emerging field of optical quantum computing, suppressing losses has been a long-term challenge. Having low-loss photon sources and detectors is critical for not only increasing accuracy but also promoting the scalability of the system^[14,15].

Losses can be classified into non-radiative losses associated with material absorptions and radiative losses. While the former can be effectively suppressed with advanced low-loss materials and better processing techniques, the latter is fundamentally inevitable for practical systems. Every device needs to interact with the external environment through leakage waves, either for the input and output of information or for the exchange of energies. Consequently, the systems have to be open and nonconservative, which can be described by non-Hermitian Hamiltonians with complex eigenvalues and non-orthogonal eigenstates^[16]. To balance the energy reduction caused by those losses, gain materials are usually incorporated into the systems. If the distribution of gains and losses satisfies the commutative law $\widehat{H}\widehat{P}\widehat{T}=\widehat{P}\widehat{T}\widehat{H}$, where $\widehat{P}$ is the parity operator reversing the physical coordinates and $\widehat{T}$ is the time operator that works effectively as a complex conjugate operation, the system is said to be parity-time ($\mathcal{PT}$)-symmetric. According to the first mathematical discussion by Bender and Boettcher^[17], such systems would exhibit completely real eigenvalue spectra while being non-conservative. Moreover, with certain configurations, both the eigenvalues and the eigenstates of a non-Hermitian system can coalesce or degenerate at some points in the parameter space, which are referred to as exceptional points (EPs). The occurrence of EPs is a unique phenomenon in non-Hermitian systems, with no counterpart in Hermitian systems^[18]. One significance of the EPs is that they are the transformation point between $\mathcal{PT}$-symmetry and $\mathcal{PT}$-symmetry-broken phases^[19]. Within the proximity of these transition points, several intriguing phenomena may occur, including phase transitions, asymmetric mode switching, and eigenfrequency splitting under perturbations^[20].

Although the EP concept and $\mathcal{PT}$-symmetry were first proposed in the context of quantum physics, it was soon observed in experiments in the microwave^[21] and optical regimes^[18,22]. The underlying reasons lie in the similarity between the Schrödinger wave equation and the paraxial electromagnetic wave equations^[23], as well as the ease of implementing suitable gains and losses in those systems^[24]. Nonetheless, practical implementations of this idea are inevitably limited by several fundamental physical nonidealities, including fabrication imperfections, instability, and noises^[19]. To overcome those limitations, researchers have proposed various mechanisms, such as building exceptional surfaces and making use of non-reciprocity and/or nonlinearity^[25,26]. Among all the methods, there is one counterintuitive proposal of deliberately adding losses into the system for better overall performance. By carefully arranging the locations and strengths of lossy components, intriguing phenomena can arise, such as improved light confinement in lasers^[27], loss-induced transparency in optomechanics^[28], and optical nonreciprocity^[29]. Those judiciously engineered losses can also give rise to abnormal behaviors of light not achievable with traditional EP devices, such as extremely asymmetry retroreflections with high efficiency^[30].

In this review, we will focus on the development of loss-assisted EP devices, which outperform their ordinary EP counterparts in many cases by providing anomalous functionalities without the need for gain materials. We first briefly introduce the fundamental mechanism of EPs and elaborate on the reason why losses are desired in some cases. We then provide a comprehensive review of different lossy EP devices based on different structural platforms, including cavities, waveguides, and metasurfaces. In the final part, some outlooks are given regarding the potential developments and applications for lossy EP devices.

Assuming an electromagnetic system supporting two resonances with a certain amount of coupling between them, it can be described by an effective Hamiltonian according to the standard coupled-mode theory as^[31]$$\widehat{H}=\left(\begin{array}{cc}{\omega }_1-i{\gamma }_1& \kappa \\ \kappa & {\omega }_2-i{\gamma }_2\end{array}\right),$$(1)where ${\omega }_{1,2}$ are the resonance frequencies of the two modes, $\kappa$ is the coupling coefficient, and ${\gamma }_{1,2}$ are the gain or loss acting on the two resonances, respectively. A positive (negative) ${\gamma }_{1,2}$ stands for a finite loss (gain). The eigenvalues of this Hamiltonian can be derived as $$E={\omega }_{\mathrm{ave}}-i{\gamma }_{\mathrm{ave}}\pm \sqrt{{({\omega }_{\mathrm{diff}}-i{\gamma }_{\mathrm{diff}})}^2+{\kappa }^2},$$(2)where ${\omega }_{\mathrm{ave}}=({\omega }_1+{\omega }_2)/2$, ${\gamma }_{\mathrm{ave}}=({\gamma }_1+{\gamma }_2)/2$, ${\omega }_{\mathrm{diff}}=({\omega }_1-{\omega }_2)/2$, and ${\gamma }_{\mathrm{diff}}=({\gamma }_1-{\gamma }_2)/2$. When the system is $\mathcal{PT}$-symmetric, the Hamiltonian will return to itself after a parity transformation $\mathcal{P}$ and a time-reversal transformation $\mathcal{T}$. The former exchanges the spatial position of the two modes while the latter acts as a complex conjugate. Applying the commutation law, $[\widehat{H},\widehat{P}\widehat{T}]=\widehat{H}\widehat{P}\widehat{T}-\widehat{P}\widehat{T}\widehat{H}=0$^[19]. Consequently, $$\widehat{P}\widehat{T}\widehat{H}{(\widehat{P}\widehat{T})}^{-1}=\left(\begin{array}{cc}{\omega }_2+i{\gamma }_2& \kappa \\ \kappa & {\omega }_1+i{\gamma }_1\end{array}\right).$$(3)

For the system to be $\mathcal{PT}$-symmetric, ${\omega }_1={\omega }_2=\omega$ and ${\gamma }_1=-{\gamma }_2=\gamma$. Substituting these conditions into Eq. (2), we have $E=\omega \pm \sqrt{{\kappa }^2-{\gamma }^2}$. When $|\kappa |>|\gamma |$, the system is said to be in the $\mathcal{PT}$-symmetric phase, with separated real parts and degenerated imaginary parts (= 0) for the eigenvalues. When $|\kappa |<|\gamma |$, the system enters the $\mathcal{PT}$-symmetry-broken phase. The eigenvalues will have the same real parts but different imaginary components. In the special case of $|\kappa |=|\gamma |$, the real and imaginary parts of the eigenvalue will coalesce at the same time, effectively showing only one distinct eigenvalue and one linearly independent eigenvector ${[1,i]}^T$. Such a degeneracy point is referred to as an exceptional point. Several advantages can already be achieved by operating the system in the vicinity of an EP. For instance, compared with those conventional degeneracies in Hermitian systems, referred to as diabolic points (DPs), EPs will provide stronger responses of the eigenvalue splitting when subjected to small external perturbations^[32]. In the following sections, we will analyze different works to prove that purely passive EPs with deliberately added losses can help us better utilize those advantages.

A typical configuration of an active EP system is schematically shown in the upper panel of Fig. 1(a). It generally contains two parts, one providing active gain while the other is lossy. If we specify the resonant frequencies of the two components to be the same, the system will become $\mathcal{PT}$-symmetric when the loss is exactly balanced by the gain, as it is invariant under simultaneous $\mathcal{P}$ and $\mathcal{T}$ transformations [see the upper panel of Fig. 1(a)]. Figure 1(b) indicates the EP as the transition point between $\mathcal{PT}$-symmetric and $\mathcal{PT}$-broken phase, as mentioned in the discussion of Eq. (3). However, incorporating gain into the system can sometimes bring great challenges. It has been shown that due to the existence of noise, an active EP system can be easily rendered to instability^[33]. Besides, the device will become much more complex, especially in cases of metasurfaces and photonic crystals, where the active material has to be inserted into each unit cell. In the microwave and terahertz regime, this problem is of even greater concern as individual circuitry is needed for each unit cell^[34]. Those circuits generally require transistors and external bias for active gain, which increases the difficulty when manufacturing a large-area device. To solve this problem, researchers have proposed the idea of removing gain elements and building the device with parts having different loss rates. Assuming that ${\gamma }_{1,2}>0$ and ${\gamma }_1\ne {\gamma }_2$ in Eq. (1), the Hamiltonian, when $\mathcal{PT}$-symmetric, can be transformed into $$\widehat{H}=\left(\begin{array}{cc}\omega -i{\gamma }_1& \kappa \\ \kappa & \omega -i{\gamma }_2\end{array}\right)=\left(\begin{array}{cc}\omega +i\beta & \kappa \\ \kappa & \omega -i\beta \end{array}\right)+\left(\begin{array}{cc}-i\chi & 0\\ 0& -i\chi \end{array}\right),$$(4)where $\chi =({\gamma }_1+{\gamma }_2)/2$ is the average loss rate and $\beta =({\gamma }_2-{\gamma }_1)/2$ is the difference in losses^[22]. Consequently, the dynamics of this purely lossy system are equivalent to those of a balanced gain-loss system with a uniform exponential decay applied. This configuration is schematically illustrated in the lower panel of Fig. 1(a). The feasibility of such all-passive $\mathcal{PT}$-symmetric devices has been demonstrated both theoretically and experimentally in various configurations^[35,36]. In the following section, we will introduce several representative realizations of EPs in lossy systems of different dimensions including cavities, waveguides, and metasurfaces [see Fig. 1(c)].

A microcavity provides an ideal platform for investigating EP photonics because it can support multiple resonances with decent quality factors, covering frequencies from radio-frequency and microwave^[37] to terahertz^[38] and optical^[39]. By judiciously designing microcavity structures, many important functionalities can be achieved, such as coherent perfect absorption^[40–43], loss-induced transparency^[28,44–47], ultrasensitive detections^[48–51], and loss-induced nonreciprocity^[52,53]. Among them, coherent perfect absorption (CPA) refers to the complete absorption of electromagnetic waves achieved by the interference of multiple incident waves^[54]. This technique can be critical in promoting efficiencies in applications such as photodetectors and solar cells^[55,56]. Through their equivalence with the time-inversed process of lasing, it is clear that most conventional CPA devices are subject to very sharp and narrow absorption characteristics. However, it was proven that an EP could widen the absorption line shape of the original optical loss if the latter was tuned to the vicinity of the EP. To demonstrate this effect, Ref. [40] used two coupled whispering gallery mode (WGM) resonators to build a purely passive EP-supporting device. According to the temporal coupled-mode theory (TCMT), the system shown in Fig. 2(a) could be described by a Hamiltonian similar to that in Eq. (4). In this case, the WGM cavities had fixed radiative loss rates ${\gamma }_{1,2}$ and no gain elements. The overall dissipation rate of the system was tuned by adjusting the inter-cavity coupling strength $\kappa$. A generic CPA EP could be reached in the ${\gamma }_{c1}-\kappa$ parameter space, where ${\gamma }_{c1}$ is the coupling rate between the waveguide and cavity 1, when the following conditions were satisfied: $${\gamma }_{c1}={\gamma }_1+{\gamma }_2,$$(5a)$$\kappa =\left|\frac{{\gamma }_{c1}+{\gamma }_2-{\gamma }_1}{4}\right|.$$(5b)

The transmission spectrum at this state is shown in Fig. 2(b), which can be fitted by a quartic function instead of a Lorentzian one. This anomalous broadening of the absorption line shape was attributed to the coalescence of the S-matrix zeros at the real frequency axis, which resulted from the total intrinsic loss being balanced by the total radiative coupling loss. Similar broadening effects were also observed in Ref. [41], where a single microsphere was coupled with a tapered fiber. A tunable reflecting mirror was placed at one end of the fiber to facilitate a unidirectional coupling from the clockwise to counterclockwise modes inside the microsphere [Fig. 2(c)]. With the introduced asymmetrical coupling, the system had an effective Hamiltonian as $${\widehat{H}}_{\mathrm{ES}}=\left(\begin{array}{cc}{\omega }_0-i\mathrm{\Gamma }& 0\\ \kappa & {\omega }_0-i\mathrm{\Gamma }\end{array}\right),$$(6)where $\mathrm{\Gamma }=({\gamma }_0+{\gamma }_1)/2$, ${\gamma }_1$ is the coupling loss between the waveguide and the cavity, and ${\gamma }_0$ is the summation of all other resonator-related losses (scattering, material absorption, etc.). $\kappa$ represents the CW-to-CCW coupling rate brought by the mirror. Although the diagonal elements were balanced as both the CW and CCW modes would experience the same loss rate, the unbalanced off-diagonal elements would create an EP in this purely passive system. Perfect absorption with a quartic lineshape would appear when the system was at the critical coupling state, i.e., ${\gamma }_0={\gamma }_1$ [Figs. 2(d) and 2(e)]. Moreover, the EP would only be lifted when the CCW-to-CW coupling is nonzero, effectively forming an exceptional surface (ES) in the parameter spaces. As a result, the absorption feature was robust against manufacturing fluctuations, imperfections in materials, etc.

Another intriguing behavior that can be achieved with EPs is loss-induced transparency. Traditional realizations usually require the breaking of reciprocity by employing magneto-optic materials^[57] or nonlinear materials^[58], which, however, are not compatible with on-chip integrated devices. Cavity-based passive systems supporting EPs provide ideal platforms to study electromagnetically induced transparency (EIT) and its potential applications as their resonance spectrum can be manipulated directly through optical states supported without introducing external noises and instabilities^[46]. They can also be integrated with other physics, such as optomechanics, for even more flexible control of optical responses. As an example, Ref. [28] reported that by enhancing the optical loss using an external nanotip, optical transparency could emerge at the otherwise strongly absorptive regime in an optomechanically induced transparency (OMIT) setup. The system also consisted of WGM resonators, as illustrated in Fig. 2(f). The resonator on the left supports a mechanical mode of frequency ${\omega }_m$ and an effective mass $m$. The additional optical loss applied on the right resonator could be precisely tuned by varying the size and distance of the nanotip. The spectrum in Fig. 2(g) shows that at certain frequency detunings ($\pm 11\mathrm{MHz}$), the strong absorption regime became transparent with the increase of tip loss ${\gamma }_{\mathrm{tip}}$. Meanwhile, in the vicinity of the EP, the transmission first dropped and then increased again for more tip loss, which aligned with the features of LIT in purely optical systems [Fig. 2(h)]. Another uncommon characteristic observed is the switching of slow-to-fast light with the tip loss at the EP. The group delay of the probe light varied drastically from negative to positive with a slight increase of ${\gamma }_{\mathrm{tip}}$. It demonstrated another interesting application of this passive EP cavity device as a coherent group-velocity switch. Following a very similar mechanism, increased losses could lead to both suppression and revival of lasing action, as demonstrated by Ref. [47]. The proposed schematic shown in Fig. 3(a) also consisted of two WGM resonators coupled with fibers. An additional loss rate of ${\gamma }_{\mathrm{tip}}$ was introduced by placing a Cr nanotip absorber close to one of the resonators. When increasing the loss rate, the total field intensity in the cavities would first decrease and then increase, regardless of which of the cavities had a higher loss [Fig. 3(b)]. The researchers found that if ${\gamma }_{\mathrm{tip}}$ was increased from zero while fixing $\kappa$ at the EP value, the lasing action would first be suppressed and then revived again. As indicated by the Raman spectra in Fig. 3(c), the recovered intensity could even exceed the original value, counterintuitively, when the loss rate increased. The experiments provide strong evidence for the practical application of purely lossy EP cavities and may lead to enhanced performance compared with active counterparts.

Last but not least, EP-supporting lossy cavities can facilitate ultrasensitive sensing. As discussed in previous sections, the eigenfrequency splitting near a second-order EP follows a square-root dependence against the variation of external parameters. Referring to Fig. 3(d), for sufficiently small perturbations, the energy difference is much larger compared to the conventional diabolic case in Hermitian systems^[48]. Based on this principle, EP sensors have been proposed for detecting various kinds of quantities, including particles^{[48,50,59–61]}, rotation^[7,62–64], temperature^[65], and so on. For instance, by combining polarization-dependent losses with magneto-optical (MO) effects, Ref. [51] successfully demonstrated the detection of subtle magnetic field variations in a strong background. Referring to the schematic in Fig. 3(e), the device was based on a Fabry-Pérot cavity that contained a kind of MO material, namely, terbium gallium garnet (TGG). The polarization-dependent losses were provided by liquid crystal (LC) cells, which could be electrically tuned according to various levels of background magnetic fields. Compared with conventional Hermitian counterparts, the addition of losses broke the parity symmetry, leading to a pair of non-orthogonal eigenmodes. When the real and imaginary parts of their frequencies coalesce, an EP would be reached. The dynamic response of the frequency split under a small perturbation $\mathrm{\Delta }B$ would be amplified by a factor of approximately $\sqrt{B_{\mathrm{EP}}/2\mathrm{\Delta }B}$. Experiments confirmed the square-root response near the EP, as indicated in Fig. 3(f). The sensitivity of the sensor was improved by three times compared to the conventional Hermitian counterparts, even after taking noises into account [Fig. 3(g)].

Meanwhile, using a similar structure, recent works also demonstrated lossy EPs could boost the precision of nanometrology down to a 2-nm scale^[66]. The intermodal coupling and losses were, in this configuration, provided by an electrically driven movable mirror and an ${\mathrm{Er}}^{3+}$-doped optical absorber. Instead of resolving eigenfrequencies and measuring splittings, the researchers directly evaluated the transmission peak shifts as the gauge of nanometric displacements. This method eliminated the need for reference signals and avoided any spectral fitting errors. Experiment results demonstrated an enhancement in sensitivity of more than 86 times. Since the device was not working on the exact spot of EP, the divergence of noise level due to deep mode non-orthogonality was avoided, leading to a five-fold enhancement of signal-to-noise ratio (SNR).

Apart from the abovementioned examples, cavity-based EP devices can also achieve different functionalities when combined with various technologies^[67,68]. For instance, Mie scatterers could be used to break the rotational symmetry of microring resonators and tune the system to an EP. The devices can thus provide chiral optical transmission or chiral electro-optical modulation with high contrasts. In the quantum realm, researchers have discovered that single- or two-photon blockades may emerge when EP-induced asymmetric coupling is delicately combined with resonators with Kerr nonlinearity^[69]. With proper loss engineering, EPs have also been configured in cavity magnomechanical systems to facilitate magnon-photon and magnon-phonon couplings. Those systems can offer flexible and powerful control of light, including transmission spectra, group velocity, nonreciprocity, and so on^[70–73].

Optical waveguides are another paradigmatic system for inducing photonic EPs. As compared to microcavities, which support only one system state at any fixed time point, waveguides can help observe the transition between two or more modes thanks to the added spatial degree of freedom. System parameters, such as shape, loss rates, and refractive indices, can now vary along the propagation path, corresponding to different points in the parameter space. For instance, they can be tuned to form loops and encircle the EPs^[74–76], which are conceptually illustrated in Fig. 4(a). One particularly intriguing feature of dynamically encircling EPs is its chiral response, where the final output state depends only on the encircling direction, regardless of the input state^[19,20]. This phenomenon led to intensive studies regarding the development of devices with asymmetric mode-switching or mode-locking capabilities^{[20,74,77–80]}.

As an example, Ref. [77] mapped the encircling path to an L-shaped waveguide supporting two orthogonal eigenmodes. Compared with previous works, a novel encircling path crossing the infinite boundary of the parameter space was enabled after converting the detuning-loss parameter space into a Riemann sphere [inset box of Fig. 4(b)]. The loss was introduced by placing a second waveguide nearby so that energy exchange with the main waveguide could happen. The geometries of the waveguides were varied continuously to dynamically adjust detuning frequencies, loss rates, and coupling strengths to the two eigenmodes propagating along [see Figs. 4(b) and 4(c)]. A near-unity asymmetric conversion ratio was achieved with mode crosstalk below $-20\mathrm{dB}$ at 1550 nm in silicon waveguides [Fig. 4(d)]. The device could be easily integrated with photonic chips and opened up the opportunity for mass application of gain-free, broadband asymmetric polarization conversion. Utilizing the same principle of EP encircling, Ref. [79] also demonstrated waveguide-based asymmetric mode converters experimentally. The designed encircling paths involved, likewise, the boundary of parameter spaces, which relaxed the constraint of adiabaticity and enabled fast parametric evolution [Fig. 4(e)]. The path was mapped to a double-coupled silicon waveguide (DSW) system, where the position-dependent loss rate was introduced using a layer of chromium [Fig. 4(f)]. As can be seen from Fig. 4(g), when ${\mathrm{TE}}_0$ mode was injected into the left port, the conversion efficiency to ${\mathrm{TE}}_1$ mode remained near unity within the wavelength range of 1520–1580 nm. The evolution process represented the clockwise (CW) encircling direction around the EP, with mode crosstalk lower than $-15\mathrm{dB}$. The inclusion of parameter space boundaries in the loop efficiently aided in shrinking the device length to 57 µm, with numerical results further supporting a device of 30 µm. The abovementioned demonstrations of waveguide-based asymmetric mode converters, where losses are added deliberately, significantly promoted the feasibility of applying the EP principle in practical scenarios, especially for on-chip integrations.

Apart from mode locking, unidirectional reflectionless propagation is another innovation that can be readily achieved with lossy EP waveguides. A waveguide as a general two-port optical scattering system can be described by the following scattering matrix $S$^[81]: $$\left(\begin{array}{c}{H}_R^{-}\\ H_L^{-}\end{array}\right)=S\left(\begin{array}{c}{H}_L^{+}\\ H_R^{+}\end{array}\right)=\left(\begin{array}{cc}t& r_b\\ r_f& t\end{array}\right)\left(\begin{array}{c}{H}_L^{+}\\ H_R^{+}\end{array}\right).$$(11)

In the above equation, $H_L$ and $H_R$ are the complex magnetic field amplitudes of the modes injected from left and right ports, with the +(−) sign indicating the incoming (outgoing) direction [Fig. 5(a)]. Similar to the Hamiltonian mentioned earlier, the eigenvalues of the scattering matrix can be found as ${\lambda }_S^{\pm }=t\pm \sqrt{r_f{r}_b}$. Therefore, when the two eigenvalues coalesce, unidirectional reflectionlessness will appear as either $r_f$ or $r_b$ will become zero. This results from the destructive interference of the two branch solutions at the EP, suppressing the reflection in one direction but not the other^[82]. Considering its importance in applications such as optical computation, communications, and on-chip photonic devices, unidirectional propagation has been studied in detail for a long time^[83–85]. Specifically, plasmonic devices involving active gain materials are proven to be effective and flexible platforms for such investigation^[86–89]. Nonetheless, purely passive meta-waveguides supporting EP-induced unidirectional reflectionlessness were also theoretically and experimentally demonstrated^[82,90,91]. For instance, Ref. [77] used germanium and chrome to periodically modulate the effective refractive index of a silicon waveguide and successfully resembled a loss-shifted $\mathcal{PT}$-symmetric system as described in the previous section [Fig. 5(b)]. The parity-time optical potentials were mimicked by the alternating arrangement of silicon and Ge/Cr structures on top of the waveguide, which introduced imaginary refractive indices that corresponded to energy dissipations [Figs. 5(c) and 5(d)]. The simulated field distribution and measured contrast ratio are depicted in Figs. 5(e) and 5(f), supporting the theoretical design with a maximum contrast ratio of 0.7 at the wavelength around 1550 nm.

Metasurfaces refer to sub-wavelength patterned layers that can interact strongly with electromagnetic waves and significantly alter their properties over a sub-wavelength thickness^[92–102]. Since the unit cells of metasurfaces, as well as their arrangement, can be designed arbitrarily, both the loss rate and coupling rate can be tailored at will along the metasurfaces, which offers large degrees of freedom for engineering EPs. Those devices may bring enhanced performance in many important applications, such as polarization control^[103–108], asymmetric reflection/transmission^{[30,109,110–117]}, and sensing^{[4,118–120]}. Polarization, as a vital characteristic of electromagnetic waves, can determine the way light interacts with matter and attracts intense attention in various applications including optical communication and biomedical sensing^[16,121]. By taking two different polarization states as the basis for the eigenvectors, the system can be described by a Hermitian similar to that in Eq. (1) as the loss rates and intermodal coupling are adjustable through engineering the unit cells. For instance, Ref. [103] configured an EP-supporting metasurface where the unit cells consisted of lossy coupled linear antennas [Fig. 6(a)]. Their EPs were associated with circularly polarized transmission eigenstates, which resulted from breaking the $x$- and $y$-mirror symmetries by displacement perturbations. The existence of EP in the parameter space formed by perturbations $\delta x/\delta y$ and frequency was indicated by the asymmetric transmission rate of circularly polarized light, as drawn in Fig. 6(b). Figure 6(c) shows the relationship between the Stokes parameters and frequency, indicating a nearly perfect circularly polarized eigenstate associated with maximally asymmetric transmission at the EP. This simple yet efficient methodology presented in this paper could greatly promote the application of EPs in optical beam shaping. To further increase the applicability and flexibility, scientists delved into the possibility of dynamic reconfigurability. Reference [107] successfully demonstrated a reconfigurable metasurface with adjustable eigen-polarizations. It was built using a hybridized structure containing gold circular resonators, which could be treated as orthogonal dipoles when excited with external fields, and the type-II superconductor NbN [Fig. 6(d)]. This special material had a temperature-dependent conductivity, which translated to a tunable loss rate in the system Hermitian matrix. In this case, the loss rate enabled the dynamic reconfiguration of polarization states. Polarization plots and the Poincare sphere depicted in Fig. 6(e) show a continuous evolution of the eigenstates with the temperature varying from 7 to 12 K. Besides controlling these polarization states near EPs, Ref. [108] has demonstrated a plasmonic topological metasurface that exhibits $2\pi$ topological phase accumulation in a reflection regime by choosing nanoantenna designs distributed along any arbitrarily closed parameter loop encircling the EP. They decoupled left circularly polarized (LCP) and right circularly polarized (RCP) channels by exploiting a linear combination of exceptional topological phase and PB phase, which enables independent manipulation of the wavefronts of LCP and RCP beams, as shown in Fig. 6(f).

Another abnormal optical behavior enabled by EP metasurfaces is asymmetric transmission and/or reflection. For instance, unidirectional retro-reflection was realized by combining traditional phase-gradient metasurfaces with non-Hermiticity^[30]. The tri-meta-atom supercells provided a retro-reflection response, while leaky losses were introduced through the slits with varying widths in the metal base [Fig. 7(a)]. Lossless and lossy regions were balanced precisely to resemble a purely passive $\mathcal{PT}$-symmetry as described in previous sections, as indicated in Fig. 7(b). Both the reflectivity and the far-field response shown in Figs. 7(c) and 7(d) indicate a strong asymmetric retro-reflection behavior in the vicinity of EPs. Considering the polarization characteristics of electromagnetic waves, a fourth-order EP related to the collapsed EPs of a generalized $4\times 4$ non-Hermitian scattering matrix under TM and TE polarization states was first demonstrated in a similar non-Hermitian metasurface system^[109]. The device also consisted of tri-meta-atom supercells, where a polarization-insensitive unidirectional retroreflector was realized. Meanwhile, more peculiar behaviors can be achieved if the concept of EPs is combined with other optical singularities. One typical candidate is Fano resonances, which are generated when a narrowband resonant state interferes with a broadband continuum. Reference [112] provided such a design where the graphene was inserted between two layers of silver gratings as the lossy material [Fig. 7(e)]. Utilizing the tunable loss rate of the graphene layer, which could be changed by adjusting its chemical potential ${\mu }_c$, the topological nature of EPs was revealed [Fig. 7(f)]. Unidirectional invisibility was successfully demonstrated at the EP integrated with Fano resonances [Fig. 7(g)].

Like those cavity-based EP devices, EP metasurfaces can offer enhanced sensitivity and responsiveness with suitable designs. In Ref. [4], a novel kind of plasmonic EP was proposed and experimentally realized. The system was based on a multilayer plasmonic structure consisting of gold bars, which supported multiple plasmonic resonances with generally different loss rates. By hybridizing optically dissimilar resonators [Fig. 8(a)], the resonant frequencies and loss rates of several modes could become degenerate at the same spot in the parameter space, producing EPs [Fig. 8(b)]. At those states, this device would exhibit a square-root dependency in frequency splitting when subjected to external perturbations [Fig. 8(c)]. When the perturbation was caused by the change in the concentration of target molecules, e.g., anti-immunoglobulin G, this device could effectively work as a sensor with elevated sensitivity compared with conventional DP sensors, supported by the measurements shown in Fig. 8(d). Similarly, high-sensitivity sensing of temperature and refractive index was realized using a bilayer metasurface with two orthogonally oriented silver split-ring resonators (SRRs)^[118]. ${\mathrm{VO}}_2$, an insulator-to-metal phase-changing material, was inserted into the gap of the SRRs on one side of the metasurface [Fig. 8(e)]. The conductivity of ${\mathrm{VO}}_2$ would change with the temperature, which would translate to a variable loss rate controlled by the temperature. Consequently, the exact location of the transmission EPs would be affected, and the temperature variation could be read out by monitoring the giant transmission phase jump within the vicinity of the EP [Fig. 8(f)]. Meanwhile, changes in the refractive index (RI) of the surrounding medium would proportionally induce a shift in the resonance frequency, which would then cause the splitting of eigenfrequencies. Thanks to the square-root dependence of the splitting on the RI change, the sensitivity for small perturbations was greatly enhanced [Fig. 8(g)]. Utilizing the variable loss rate of ${\mathrm{VO}}_2$ and the EP mechanism, this purely passive device achieved both temperature and RI sensing simultaneously with one single structure.

Finally, apart from the abovementioned functionalities, EP-based passive metasurfaces can exhibit other interesting behaviors, which are useful in numerous applications such as imaging and holograms^[122–124], thermal emission^[125], and diffraction control^[115,126].

In this review, we provided a comprehensive examination of the development of purely passive devices supporting exceptional points, including cavities, waveguides, and metasurfaces. We first introduced the theoretical fundamentals of the formation of exceptional points and their relationship with the parity-time symmetry. We then evaluated the reason why losses can be beneficial within the vicinity of EPs, contradicting generally accepted intuitions. Several representative examples are given for different application scenarios of those EP devices with deliberately added losses. Those applications spanned from perfect absorption to asymmetric reflection and/or transmission, asymmetric mode conversion/locking, and polarization control, to list a few. Engineered losses effectively added another degree of freedom for light manipulation. It is worth noting that there have been some novel non-Hermitian effects recently that can be implemented in passive optical systems of different dimensions, such as the skin effect^[127,128], topology in quantum and photonics^[129,130], and so on.

We believe that passive EP devices will be especially advantageous when asymmetric responses, elevated sensitivities, or high-level operation stability are desired. So far, the debate on whether the EP mechanism can truly benefit applications such as lasing and sensing is still going on. Scientists have theoretically proved that for an active system, in the vicinity of EP, the non-orthogonality between the modes will bring excessive amounts of quantum and thermal noises^[19,26]. They will increase the linewidth of the resonances, making the frequency splitting unresolvable^[63,131] and bring no advantage for parameter sensing^[132]. Meanwhile, passive EP sensors are also being questioned regarding whether the $\sqrt{ϵ}$ bifurcation of eigenfrequencies is experimentally observable or not^[133,134]. Nonetheless, given all the existing demonstrations of passive EP sensors, such as those mentioned in earlier sections, we still believe that the combination of losses with EP is still worth investigating, with some of the reasons listed below. Firstly, optical nonreciprocity can be introduced within those lossy systems^[29], which may be a vital solution to noise problems as nonreciprocity can help break the fundamental limits of any conventional reciprocal sensor in non-Hermitian systems^[26]. Secondly, another significant benefit of loss-assisted EP systems over active counterparts is stability. Thermal noises and noises generated by external stabilization are completely unavoidable, especially in active systems with external biasing^[135]. It was proven that those temporal noises could easily render instability of the system^[33]. By adding dissipation, the instability can be compensated for. Hence, adding additional losses may be an essential step when building devices that are required to provide long-term stable operations.

Nonetheless, there are still several functionalities that are yet to be implemented in a purely passive way. As an example, active $\mathcal{PT}$-symmetric devices can provide powerful and comprehensive control over light such as reconfigurable light steering^[136]. Such functionalities have not been vastly observed with passive optical counterparts. Moreover, it was proven that if the order of the EP is $n$, the energy splitting will be further enhanced to be proportional to the $n$-th root of perturbation strength, bringing even further improvements for minuscule parameter changes^[137]. This trend has been confirmed by many EP sensors involving active gain^[137–139]. They are also proven feasible in other regimes such as electromechanical^[140], microwave^[141], and very high-frequency range^[119]. However, it remains a challenging task for EP systems without gain. There seem to be inadequate papers examining the configuration in a passive optical setting^[142], and the discussion is still limited to theories. To begin with, high-order EP devices are difficult to obtain in conventional EP devices involving gain. For instance, in cavity-based devices, the resonant frequencies of every cavity should be precisely tuned to the same value^[137,139], which naturally imposes more strict requirements for design and manufacturing. Another critical issue to be considered is, again, stability. An EP system with a higher order implies that it is even more vulnerable to parametric noises^[33], which would easily render the system to instability. In a passive setting, the difficulties may, in addition, include precise engineering of loss distributions. As shown in Eq. (4), more discrete levels of loss rates are required if the order of Hamiltonian is to be increased. The differences between the loss rates should be sufficiently large to distinguish different eigenmodes and obtain practically approachable EPs. However, the average loss rate $\chi$ should be limited to prevent the energy from dissipating too fast. Multi-dimensional parameter optimization is required before conducting experiments. Nonetheless, more investigations are still expected as successful implementations will help overcome some fundamental drawbacks of EP devices with active gains, such as instability and quantum noises mentioned earlier^{[32,33,63,133]}. One of the possible solutions may lie in the concept of exceptional surfaces, which has been proven feasible in second-order passive systems^[25,143,144]. Forming exceptional surfaces could relax the precision requirements during sample manufacturing. Another possible way to improve sensitivity and/or minimum detection limit is by taking advantage of plasmonic systems. For instance, in the microwave regime, surface plasmon resonators have successfully promoted the detection range of non-Hermitian sensors down to deep subwavelength levels and even enabled reconfigurability^[145–148]. Similar methodologies may apply to optical sensors with proper device designs. Last but not least, the EP concept may bring additional benefits to the research of various quantum effects, such as the quantum Mpemba effect^[149,150], and quantum coherence improvement^[151]. Although these are emerging fields even with conventional active EPs, they are worth studying in passive settings considering their potential advantages.