Expansion of Metasurface Technology: Exploring Picophotonics in Optical Precision Metrology

Abstract

With the progression of photolithography processes, the present technology nodes have attained 3 nm and even 2 nm, necessitating a transition in the precision standards for displacement measurement and alignment methodologies from the nanometer scale to the subnanometer scale. Metasurfaces, owing to their superior light field manipulation capabilities, exhibit significant promise in the domains of displacement measurement and positioning, and are anticipated to be applied in the advanced alignment systems of lithography machines. This paper primarily provides an overview of the contemporary alignment and precise displacement measurement technologies employed in photolithography stages, alongside the operational principles of metasurfaces in the context of precise displacement measurement and alignment. Furthermore, it explores the evolution of metasurface systems capable of achieving nano/subnano precision, and identifies the critical issues associated with subnanometer measurements using metasurfaces, as well as the principal obstacles encountered in their implementation within photolithography stages. The objective is to provide initial guidance for the advancement of photolithography technology.

Keywords

metasurfaces / lithography machine / optical precision metrology

1 Introduction

In the last century, researchers have demonstrated that metamaterials can be engineered to exhibit electromagnetic properties not found in nature \(\left\lbrack {1 - 3}\right\rbrack\) , which enables unprecedented light-matter interactions and energy manipulation through tailored structural configurations. With the advancement of research, scientists have further developed the concept of metasurfaces [ 4 - 8 ], which inherit the unique electromagnetic properties of metamaterials while emphasizing the characteristics of two-dimensional structures. In the field of electromagnetics, the nanoscale matching of metasurfaces with light wavelengths enables the precise design of nanostructures by adjusting their geometric shape, periodicity, and materials, based on physical mechanisms such as resonance phase, geometric phase, and waveguide transmission phase. The advantages of metasurfaces, including high integration, low energy loss, and light weight, have led to their widespread application in fields such as imaging [ 9 - 11 ], encryption [ 12 - 14 ], and vectorial light field generation [ 10 ] , substantially advancing progress in these domains.

Picophotonics is a field dedicated to the study of optical phenomena at extremely small scales, typically on the order of \({10}^{-{12}}\mathrm{\;m}\left\lbrack {22}\right\rbrack\) , corresponding to the atomic scale (with the typical size of an atom being approximately 200 picome-ters). An aspect of picophotonics lies in achieving deep-subwavelength optical field manipulation. In conventional optics, diffraction fundamentally restricts positional accuracy and imaging resolution when the wavelength becomes comparable to the object’s dimensions. Picopho-tonics harnesses expertise from various disciplines, including metamaterials, nanophotonics, and plasmonics, to circumvent these fundamental constraints. For instance, the sub-nanometer architectures of metamaterials facilitate the nanoscale manipulation of light, while plasmon-ics capitalizes on the properties of plasmonic oscillations to govern the propagation of light. These phenomena serve as precision surgical knives, providing critical support for picometer-scale optical research [ 23 ].

Lithography plays a pivotal role in the fabrication of integrated circuits. The exposure light source, the optical system, and the dual-stage wafer stage constitute the three core components that are essential for the optimal performance of a lithography machine. Among these, the ultra-precise displacement measurement and alignment of the wafer stage are pivotal steps in enhancing the accuracy of the photolithography process. These aspects also represent key challenges that require addressing and are currently the subject of intensive research efforts in China. To achieve high-precision photolithography, lithography machines utilize a range of complex and voluminous optical components, such as lenses and gratings. These components must be individually installed and aligned, which complicates efforts to miniaturize and integrate them into the equipment. Metasurfaces, characterized by their monolithic single-layer or multi-layer configurations, offer enhanced flexibility in manipulating light fields while preserving a compact form to conserve space within the optical system. In photolithography, to facilitate the acquisition of alignment information at various positions and to enhance alignment accuracy, smaller alignment marks are frequently necessary without compromising the richness of the alignment information. This presents a substantial challenge for conventional alignment mark designs. However, since the precise control of electromagnetic waves by the sub-wavelength structures of metasurfaces, they are capable of effectively addressing the challenges as process node requirements grow increasingly stringent. The phase modulation, polarization control, and beam shaping facilitated by this precise control confer metasurfaces with numerous innovative properties, thus providing additional opportunities for the design of alignment systems in lithography machines. Furthermore, the light fields generated by metasurfaces demonstrate remarkable stability, which is particularly advantageous for positioning schemes utilizing structured light, mitigating the influence of light field intensity variations on positioning accuracy. In fact, the utilization of metasurfaces for alignment applications is supported by a robust theoretical and experimental foundation. Nevertheless, a considerable gap persists that needs to be addressed to extend metasurface-based solutions to fulfill the multi-degree-of-freedom (DOF) displacement measurement requirements in photolithography.

This paper initially introduces the contemporary alignment requirements and displacement measurement parameters for lithography machines. Subsequently, it elucidates the various principles underlying metasurface-based displacement measurement and positioning, encompassing polarization encoding [ 24 , 25 - 27 ], non-Hermitian exceptional points [ 28 ], micro nano structure scattering [ 29 ] , and superoscillation [ 40 ]. It subsequently systematizes contemporary scientific breakthroughs. Conclusively, the review synthesizes and discusses the critical challenges that require addressing, along with the emerging future trends in this domain, as shown in Fig. 1 .

2 Alignment and Precision Displace- ment Measurement Requirements of Lithography Machines

The technology node of lithography machines can be obtained from the International Roadmap for Devices and Systems (IRDS), which has succeeded the International Technology Roadmap for Semiconductors (ITRS). The IRDS delineates the lithography processes, critical dimensions, and overlay requirements for each generation of technology nodes, as illustrated in Tab. 1 . It is important to note that, with advancements in lithographic processes, the technology node no longer directly corresponds to the actual feature size. Technical nodes in logic devices are utilized to characterize the gate length. At the \({32}\mathrm{\;{nm}}\) technology node, the gate length of a logic device is approximately \({29}\mathrm{\;{nm}}\) , and the pitch of the gate layer is around \({130}\mathrm{\;{nm}}\) . And dense pattern period in logic devices is significantly greater than that in memory devices at the same technology node.

Overlay serves as a critical performance metric in the alignment process of lithography machines, typically quantified by \(\left|\text{mean}\right|+ {3\sigma }\) , where |mean| represents the average value from multiple measurements, and \({3\sigma }\) denotes three times the standard deviation. When the overlay exceeds acceptable limits, it may result in misalignment between the lithographic layers on the wafer, leading to short circuits or open circuits in the chips, which in turn reduces the product yield. In general, the overlay should not exceed one-fifth of the minimum feature pitch.

Alignment is an essential step for minimizing overlay in lithography. Among these, the alignment mark functions as the reference standard for the lithography machine and must fulfill criteria including process compatibility, detectability, structural consistency, and robustness throughout the manufacturing process. The design and layout of the alignment marks and patterns vary slightly, depending on the alignment principle. Alignment marks designed according to the principle of phase gratings are presented as grating patterns. To mitigate interference nulls resulting from the depth of the grating grooves and to enhance precision, most alignment systems of this type necessitate the use of multiple wavelengths, thereby increasing system complexity. Alignment marks based on image processing and differential interference principles exhibit a similar appearance, typically manifesting as grid-like or grating patterns oriented in various directions. Fig. 2 provides an illustration of field image alignment (FIA) technology, wherein search alignment marks are utilized to determine the rotation of the silicon wafer, whereas enhanced global alignment (EGA) marks are employed to ascertain the displacement of the silicon wafer in the \(X\) and \(Y\) directions. With the rapid advancement of technology and the diminution of mark dimensions, asymmetry resulting from the manufacturing process has emerged as a principal factor limiting alignment accuracy due to disrupting the original symmetrical diffracted light correlation.

The fabrication of semiconductor chips requires not only precision but also considerations for the speed and stability of the alignment process. To ensure continuous productivity, lithography machine must operate around the clock. For instance, the most recent generation of lithography systems can achieve a throughput of \({11}\mathrm{\;s}/\) wafer, indicating that the exposure of a \({300}\mathrm{\;{mm}}\) wafer is completed within \({11}\mathrm{\;s}\) . The mask stage of the lithography machines must achieve an acceleration of approximately \({100}\mathrm{\;m}/{\mathrm{s}}^{2}\) . The subsequent generation of lithography machines’ mask stage may potentially reach accelerations as high as \({150}\mathrm{\;m}/{\mathrm{s}}^{2}\) . In comparison, the acceleration of a jet fighter catapult typically ranges around \({44}\mathrm{\;m}/{\mathrm{s}}^{2}\) . To meet these stringent requirements, the lithography machine’s wafer stage and mask stage must attain a sensor positioning measurement frequency of 2000 times/s, with an accuracy of \({60}\mathrm{{pm}}\) . Simultaneously, the time required for measuring the alignment marks during the alignment process must not surpass the time needed for the exposure of the preceding batch of silicon wafers. Therefore, in the latter stages of design, it is also necessary to optimize the mark layout to achieve a balance between alignment accuracy and production efficiency. The general design specifications that the lithography machine stage must fulfill are detailed in Tab. 2 [ 44 ].

To design suitable spatial alignment marks and displacement measurement optical paths, the spatial dimensions of the stage must be taken into account. Given that the wafer size is \({300}\mathrm{\;{mm}}\) , the spatial clearance above the worktable is typically less than \({15}\mathrm{\;{mm}}\) . This necessitates a precision displacement sensing range for the worktable exceeding \({300}\mathrm{\;{mm}}\) , while ensuring that the imaging distance of the alignment system and the overall device dimensions remain within acceptable limits. In general, the optical path of the alignment and optical metrology system utilizing metasurfaces must satisfy the aforementioned requirements to ensure proper functionality in lithography machines.

3 Principle of Ultra Precision Dis- placement Detection and Position- ing Based on Metasurfaces

Owing to recent advancements in nanotechnol-ogy, metasurfaces have demonstrated exceptional controllability over light-field manipulation coupled with superior integration capabilities compared to conventional gratings. These developments have not only established novel research pathways in precision measurement but also enabled innovative instrumental approaches for achieving displacement measurements with enhanced precision and sensitivity. Based on distinct operational principles, this technology can be broadly categorized into four main approaches: polarization encoding techniques [ 24 - 27 ], non Hermitian exceptional points technology [ 28 ], micro nano structure scattering [ 29 - 39 ], and superoscillation [ 40 ].

3.1 Polarization Encoding

Polarization encoding technology integrates displacement information into the polarization state of light, thereby enabling sub-nanometer positioning accuracy [ 24 - 27 ]. Although different devices might exhibit distinct implementation specifics, the underlying principles of encoding remain consistent.

For the sake of clarity, we shall use the g-plate as an illustrative example in Fig. 3 . A patterned liquid crystal panel, referred to as a g-plate, has its liquid crystal molecule orientations established through the application of the subsequent design formula

(1) \[\alpha \left({x, y}\right)= \frac{\pi }{\Lambda }x +{\alpha }_{0}\]

where \(\Lambda\) represents the spatial period of the liquid crystal, and \({\alpha }_{0}\) denotes the compensation angle. Upon exiting the g-plate, the polarization of the light follows to the subsequent expression

(2) \[\left|{H\rangle \rightarrow }\right|\Lambda \rangle =\cos \left\lbrack {{2\alpha }\left( x\right)}\right\rbrack \left|{H\rangle +\sin \left\lbrack {{2\alpha }\left( x\right)}\right\rbrack }\right| V\rangle \]

Here, \(|V\rangle\) represents the linear polarization state along the vertical direction, and \(|\Lambda \rangle\) denotes the linear variation in the polarization direction of the structured light along the \(x\) -axis with a spatial period of \(\Lambda /2\) . Upon a lateral displacement of \({\Delta x}\) for the second g-plate relative to the first g-plate, the resulting output light field is given by the following expression

(3) \[\left|{\Lambda \rangle \rightarrow }\right|\theta \rangle =\cos \left\lbrack {\Delta \theta }\right\rbrack \left|{H\rangle +\sin \left\lbrack {\Delta \theta }\right\rbrack }\right| V\rangle \]

This represents a uniformly linearly polarized beam, wherein the polarization direction is rotated by an angle \({\Delta \theta }\) relative to the initial state. The relationship between \({\Delta \theta }\) and the displacement can be described as follows

(4) \[{\Delta \theta }= \frac{2\pi \Delta x}{\Lambda }\]

This effect can be enhanced by decreasing the spatial period \(\Lambda\) of the g-plate. Similarly, to prevent diffraction interference caused by the g-plate, the separation between the two g-plates must be sufficiently small, and the following conditions should generally be satisfied

(5) \[ D \ll \frac{{w}_{0}\Lambda }{\Lambda }\]

where \({w}_{0}\) represents the beam waist radius, \(\lambda\) denotes the wavelength of the light, and \(D\) is the separation between the two plates. Finally, based on Malus’s law, the following formula for displacement can be derived

(6) \[ P\left({\Delta x}\right)= {p}_{0}{\cos }^{2}\left(\frac{2\pi \Delta x}{\Lambda }\right)\]

where \({p}_{0}\) represents the optical power of the input laser. By fine-tuning the polarization, the entire Malus curve can be maintained within its linear region, thereby achieving optimal sensitivity and leading to

(7) \[{P}_{lin}\cong {p}_{0}\left({\frac{1}{2}\pm \frac{2\pi }{\Lambda }{\Delta x}}\right)\]

The sensitivity of the system can be calculated as follows

(8) \[ S =\left|\frac{\mathrm{d}p}{\mathrm{\;d}{\Delta x}}\right|= \frac{{2\pi }{p}_{0}}{\Lambda }\]

To address the measurement ambiguity associated with a wide range, a dynamically rotating polarization analyzer may be employed to maintain the operating point within the linear region of the curve, thereby eliminating degeneracy through continuous tracking.

3.2 Non-Hermitian Exceptional Points

Exceptional points (EPs) originated as a concept in quantum mechanics, introduced within the framework of perturbation theory for non-Hermitian linear operators. They are characterized by the intersection of the eigenvalues and eigenstates of the system’s Hamiltonian [ 45 ]. Within the methodology of mathematical physics, the eigenstate can be described as a spatial distribution associated with a specific frequency. The so-called degenerate state occurs when the same frequency corresponds to two distinct spatial modes. An \(N\) th-order exceptional point generally corresponds to a frequency splitting \({\Delta \omega }\propto {\varepsilon }^{\frac{1}{N}},\varepsilon\) represents a small perturbation near the exceptional point [ 46 , 47 ] . Owing to this characteristic, even a minute perturbation can result in a substantial frequency splitting, thereby rendering the system highly sensitive in the vicinity of the exceptional point.

Under typical conditions, systems that exchange energy with their environment are classified as open systems, often referred to as non-Hermitian systems. The physical quantities within such systems are described by non-Hermitian operators, which generally exhibit complex eigenvalues and non-orthogonal eigenstates. As research advanced, Bender and Boettcher discovered that a system satisfying parity-time (PT) symmetry can support a real eigenvalue spectrum, even in the context of non-Hermitian systems [ 48 ].

Systems frequently employed for designing exceptional points are typically dual-coupled systems, a phenomenon that can be elucidated through the fundamental theory of coupled models [ 49 , 50 ] , as shown in Fig. 4 . In a two-level system comprising two coupled resonant units, the Hamiltonian is represented as

(9) \[\widehat{H}= \left(\begin{matrix}{\omega }_{1}- \mathrm{i}{\gamma }_{1}& \kappa \\\kappa &{\omega }_{2}- \mathrm{i}{\gamma }_{2}\end{matrix}\right)\]

where \({\omega }_{1,2}\) represent the resonant frequencies of the coupled resonant units, \({\gamma }_{1,2}\) denote the gain or loss coefficients, and \(\kappa\) signifies the coupling strength between the resonant units. The two eigenvalues of the Hamiltonian can be determined as follows

(10) \[{\omega }_{\pm }= {\omega }_{\text{ave }}- \mathrm{i}{\gamma }_{\text{ave }}\pm \sqrt{{\kappa }^{2}+ {\left({\omega }_{\text{diff }}+ \mathrm{i}{\gamma }_{\text{diff }}\right)}^{2}}\]

Each parameter can be calculated using the following formulas

\[{\omega }_{\text{ave }}= \frac{{\omega }_{1}+ {\omega }_{2}}{2}\\{\gamma }_{\text{ave }}= \frac{{\gamma }_{1}+ {\gamma }_{2}}{2}\\{\omega }_{\text{diff }}= \frac{{\omega }_{1}- {\omega }_{2}}{2}\\{\gamma }_{\text{diff }}= \frac{{\gamma }_{1}- {\gamma }_{2}}{2}\]

Fig. 4 The coupling theoretical model of non-Hermitian electromagnetic metasurfaces [ 49 ]:(a) left: a two-level system consisting of two coupled resonant units; right: evolution of eigenvalues;(b) left: a two-level system consisting of two dipoles with orthogonal excitation directions; right: evolution of eigenvalues

It is evident that when \({\kappa }^{2}+ {\left({\omega }_{\text{diff }}+ \mathrm{i}{\gamma }_{\text{diff }}\right)}^{2}=\) 0 , the two eigenvalues become identical, both equal to \({\omega }_{\text{ave }}- \mathrm{i}{\gamma }_{\text{ave }}\) , and the corresponding eigen-states are also identical, expressed as \({\left(\frac{{\omega }_{\text{diff }}- \mathrm{i}{\gamma }_{\text{diff }}}{2\kappa },1\right)}^{\mathrm{T}}\) . This particular degenerate point is known as an EP.

However, the aforementioned result involves a complex vector, which may pose challenges in practical applications. Consequently, researchers have discovered and proposed PT symmetry [ 51 - 54 ]. In this scenario, \({\omega }_{1}= {\omega }_{2}= {\omega }_{0}\) , and \({\gamma }_{1}= -{\gamma }_{2}= \gamma\) , and the Hamiltonian satisfies the condition \({PT}\widehat{H}= \widehat{H}{PT}\) , where \(P\) and \(T\) represent the parity and time-reversal operators, respectively. In electromagnetic systems, if the complex electromagnetic parameters exhibit a complex conjugate inversion symmetry, the non-Hermitian system can also support a real eigenvalue spectrum. The Hamiltonian for a PT-symmetric system can be formulated as follows

(11) \[{\widehat{H}}_{\mathrm{{PT}}}= \left(\begin{matrix}{\omega }_{0}- \mathrm{i}\gamma &\kappa \\\kappa &{\omega }_{0}+ \mathrm{i}\gamma \end{matrix}\right)\]

The eigenvalues of the PT-symmetric Hamiltonian can be determined as follows

(12) \[{\omega }_{\pm }= {\omega }_{0}\pm \sqrt{{\kappa }^{2}- {\gamma }^{2}}\]

When \(\left|\gamma \right|< \left|\kappa \right|\) , the system is in the PT-symmetric phase. In this regime, the electric field within the two resonant units is symmetrically distributed, and the total electromagnetic energy remains conserved. The eigenvalues are real, indicating that the system exhibits a balanced gain and loss. Conversely, when \(\left|\gamma \right|> \left|\kappa \right|\) , the electric field distribution becomes asymmetric, with the electric field predominantly localized in either the gain or the loss resonant unit. This asymmetry results in the non-conservation of the total electromagnetic energy, and the eigenvalues become complex.

3.3 Micro Nano Structure Scattering

With the advancement of nanophotonics, nanoantennas have become an essential component in numerous devices. Commonly utilized antenna shapes include bowtie, bimetallic rod, cylindrical, and spherical configurations. The latter two configurations exhibit directional scattering and polarization-dependent spin-momentum locking coupling under specific conditions. When the Kerker condition is satisfied, the scattering phenomena can be explained by the Huygens dipole, leading to enhanced or suppressed forward or backward scattering. Based on this effect, it is feasible to achieve the localization of nanoparticles.

In 1983, Kerker proposed that the plane wave excitation of small spherical particles (with a radius much smaller than the wavelength, radius \(\ll \lambda\) ) results in asymmetric scattering in the forward and backward directions. The scattering perpendicular to the direction of beam propagation is referred to as transverse scattering [ 55 ], as shown in Fig. 5 . To achieve transverse Kerker scattering, high-refractive-index dielectric nanoparticles are typically employed, as they can support both electric and magnetic dipole modes of significant strength. These nanoparticles are then illuminated by tightly focused, radially polarized light. According to the generalized Mie theory, the contribution from magnetic quadrupoles in the main part of the spectrum can be neglected and the nanoparticle can be approximated as a dipole, where the induced dipole moment is proportional to the local electromagnetic field components [ 39 ].

(13) \[ p \propto {T}_{ED}E \]

(14) \[ m \propto {T}_{MD}H \]

Here, \(p\) and \(m\) represent the electric and magnetic dipole moments, respectively, while \({T}_{ED}\) and \({T}_{MD}\) are the scattering coefficients calculated using Mie scattering theory, which are related to the scattering cross section. In addition to the correlation between their amplitudes, there is a \(\pi /2\) phase difference between the electric and magnetic dipole moments under excitation at specific wavelengths. For an incident cylindrical vector field, the intensity and phase distribution of both the transverse and longitudinal field components exhibit cylindrical symmetry at the focal plane. At this point, the transverse components of the electric and magnetic fields are zero along the optical axis, and for positions very close to the axis \(\left({r \ll \lambda }\right)\) , these components can be approximated as increasing linearly with the radial distance. Meanwhile, the longitudinal component of the magnetic field (for azimuthally polarized light, or the longitudinal component of the electric field for radially polarized light) reaches its maximum on the optical axis and is significantly stronger than the transverse components for \(r \ll \lambda\) . Additionally, there is a \(\pm \pi /2\) phase delay between the longitudinal and transverse components. Combining this with the phase difference at specific wavelengths, it is possible to induce longitudinal and transverse dipole moments with a relative phase of 0 or \(\pi\) , thus producing transverse Kerker scattering. Simultaneously, adjusting the radial distance between the particle and the optical axis can also modify the relative amplitude between the longitudinal and transverse dipole moments, which forms the basis for measuring lateral displacement.

In experimental setups, nanoantennas are typically positioned at a dielectric interface. In the case of critical angle incidence, the outgoing light field can be derived using the principles of transverse Kerker scattering. In a typical experimental setup, a high NA objective lens is employed to focus light onto the scattering particle. A higher magnification objective lens is then utilized to collect the transmitted and forward-scattered light. A CCD camera is positioned at the back focal plane, and only the high-NA detection range is considered, ensuring that only the scattered field is detected, excluding any transmitted field. The difference in scattering intensity in opposite directions can be determined using the following expression

(15) \[{D}_{x}= \frac{{I}_{3}- {I}_{1}}{{I}_{\text{tot }}}\]

(16) \[{D}_{y}= \frac{{I}_{2}- {I}_{4}}{{I}_{\text{tot }}}\]

where \({I}_{i}, i = 1,2,3,4\) represents the average intensity in the \(i\) -th region on the back focal plane. Each region is within a range of 45 degrees apart. This division into four regions yields stronger and more uniform scattering signals. The total intensity, \({I}_{\text{tot }}\) is the sum of the intensities from all four regions. This configuration enables sub-nanometer resolution over a range of tens of nanometers, with precision reaching the picometer scale.

3.4 Superoscillation

The concept of superoscillation [ 56 , 57 ] originating in weak measurements in quantum mechanics, where the wavenumber values obtained from local spatial measurements may not be within the range of wavenumbers found in a global spatial measurement.

Super-oscillatory fields typically arise within a rather complex electromagnetic field; however, their amplitudes are often so small that they are frequently overlooked. Consider the following one-dimensional wave, which is composed of six spatial Fourier components:

(17) \[ f\left( x\right)= A{\mathrm{e}}^{\mathrm{i}\varphi }= \mathop{\sum }\limits_{{n = 0}}^{{n = 5}}\left({{a}_{n}{\mathrm{e}}^{\mathrm{i}{2\pi nx}}}\right)\]

Here, \({a}_{n}\) represents the Fourier coefficients, which are a set of predetermined values. \({a}_{0}= {19.0123},{a}_{1}= -{2.7348},{a}_{2}= -{15.7629},{a}_{3}=\) \(-{17.9047},{a}_{4}= - 1,{a}_{5}= {18.491}\) . As shown in Fig. 6 , it is straightforward to identify the fastest Fourier component \({k}_{\max }= {10\pi }\) . However, if one examines the low-intensity region near \(x = 0\) more closely, a very narrow peak can be observed that oscillates 10 times faster than the fastest Fourier component. Additionally, the characteristic strength of the super oscillation is notably low. There is a rapid phase variation within the super oscillation region.

Researchers have conducted extensive studies on superoscillation functions to achieve controlled generation of superoscillation fields. The Paley-Wiener theorem establishes a correspondence between band-limited functions and exponential-type functions [ 59 ], Band-limited functions in the frequency domain are entirely analytic in the spatial domain, and altering the positions of a finite number of zeros of such functions does not affect the overall spectral width. Consequently, under the condition that the highest Fourier frequency of the function remains unchanged, any band-limited function can be transformed into a superoscillation function by altering the positions of its zero points. Additionally, in the presence of noise, the amplitudes of oversampled signals become statistically independent. At this point, oversampled signals with noise can also reconstruct super oscillations; Furthermore, Berry has proposed a method for constructing superoscillation functions based on clusters of optical vortices.

The formation of superoscillation fields is not limited to the near-field region; theoretically, it can achieve arbitrarily small light field structures in the far-field. Integrating superoscillation field illumination with deep learning algorithms can significantly enhance the resolution of optical imaging and the precision of micro- and nano-displacement detection. This opens up new possibilities for metasurface displacement and alignment. Additionally, superoscillation fields have significant applications in optical metrology [ 40 , 60 ], super-resolution imaging [ 58 ], and high density optical data storage [ 61 ].

4 Exploration of Cutting-Edge Applications of Metasurfaces in Photolithography Machines

Based on different physical mechanisms, metasur-faces used in optical metrology can be categorized to polarization encoding, singular points, scattering, and super-oscillations. However, the application of metasurfaces in the field of precision displacement and alignment remains relatively novel, with new physical mechanisms continually being proposed and implemented.

4.1 Polarization Encoding

In 2022, Raouf Barboza et al. introduced a polarization encoding technique known as linear photonic gears [ 27 ], designing a compact, fast, stable, and cost-effective device. On a substrate, liquid crystal molecules with varying orientations are arranged according to a specific pattern. The incident linearly polarized light rotates according to the molecular orientation. According to the Malus theorem, the relationship between optical power and displacement change follows a cosine squared dependence, enabling a resolution of \({400}\mathrm{{pm}}\) . Due to the inverse relationship between the phase change induced by displacement and the period of liquid crystal molecules, reducing the arrangement period of these molecules can directly enhance the detection resolution. Using this method, when the period of liquid crystal molecules is \({6\mu }\mathrm{m}\) , the theoretical resolution can reach \({50}\mathrm{{pm}}\) , as illustrated by the power variation curve with displacement in Fig. 7 . The sensitivity and stability of this method surpass those of amplitude encoding mode. However, due to limitations in the liquid crystal manufacturing process, the arrangement period of liquid crystal molecules cannot be minimized sufficiently, making it challenging to achieve nanometer-level sensitivity. Additionally, the optical properties of liquid crystals are highly sensitive to temperature variations, posing significant challenges to the stability and practical application of high-precision measurements.

In the same year, Haofeng Zang et al. significantly reduced the micro-nanostructure period of metasurfaces using photolithography technology, developing a novel method for lateral displacement measurement distinct from liquid crystal molecules [ 24 ]. This approach employs PB meta-surfaces to induce a linear polarization rotation in incident linearly polarized light over a range of several hundred micrometers due to lateral displacement. Since LCP and RCP are guided in different directions through the metasurface, the two metasurfaces must be positioned in close proximity. The experiment ingeniously employed a metasurface and a reflector to address this issue. Additionally, the reflective structure doubled the displacement sensitivity, achieving nanometer-level resolution with an uncertainty of only \({100}\mathrm{{pm}}\) , as illustrated in Fig. 8 .

In 2024, they achieved displacement measurement with a range of \({200\mu }\mathrm{m}\) and an accuracy of \({0.3}\mathrm{\;{nm}}\) in a two-dimensional plane using metasurfaces [ 26 ]. Unlike previous designs, the nanocolumn array on the metasurface decomposes incident light into different polarizations in various directions. The incident RCP and LCP light exhibit different PB phases, eliminating the measurement “dead zone” and extending the measurement range.

Polarization encoding technology based on metasurfaces primarily extracts displacement information from output optical power, rendering it suitable for high-speed and compact optical metrology. However, the reliance on the polarization state of light necessitates the inclusion of additional polarization elements. Additionally, the measurement range of this approach is constrained by the size of the metasurface, posing challenges for large-scale displacement measurement.

4.2 Non-Hermitian Exceptional Points

Due to the complex conditions required for observing singularities, they are typically confined to dielectric waveguide and resonator systems constrained by diffraction. This necessitates precise control over the spatial distribution of losses and gains at a microscale, which has led to limited attention in the field of optical metrology for an extended period. In 2020, Kanté et al. from the University of California, Berkeley, constructed an exceptional point (EP) in a plasma system based on detuned resonance hybridization within a multi-layer periodic plasma structure [ 28 ], and realized a second-order singular point system using a plasmonic metasurface composed of two layers of misaligned gold nanoar-rays to achieve symmetry breaking. As illustrated in Fig. 9 , a \(5\mathrm{\;{nm}}\) displacement of the unit structure due to manufacturing errors resulted in a \(6\mathrm{{THz}}\) mode splitting.

However, several challenges remain in singularity-based solutions: in extremely small perturbation sensing systems with inherent noise, the inevitable non-coupled resonator detuning during operation can readily alter the conditions of singularity points. Additionally, current theoretical derivations are predominantly based on phenomenological models, and the Hamiltonian operator does not account for the dispersion characteristics of materials. Furthermore, the impact of system size must also be considered. Overall, leveraging the singular points of non-Hermitian systems for optical metrology represents a novel development direction. Despite the existing limitations and challenges in both theoretical and technological aspects, the exceptional sensitivity of this approach demonstrates its considerable potential for practical applications.

4.3 Micro Nano Structure Scattering

Owing to the field enhancement and strong coupling characteristics of micro-nanostructures, their scattering field is highly dependent on the phase distribution and relative position of the incident light field, offering new possibilities for optical metrology. Initially, to enhance detection power, nanoparticle positioning primarily utilized lasers with wavelengths below \({280}\mathrm{\;{nm}}\) [ 62 ] or high-power lasers [ 63 ]. However, this approach can also damage organic substrates [ 64 ]. Additionally, the requirement for multiple beams and detectors limits detection speed, making it challenging to meet the rapidly evolving demands of process development. To address these issues, S. Roy et al. from Delft University of Technology in the Netherlands proposed a novel detection scheme based on single-particle scattering in 2015 [ 38 ]. A high numerical aperture objective focuses the radially polarized beam onto the nanoparti-cle sample placed on the substrate. The scattering field interacts with the stray reflection field from the substrate, forming displacement-related directional scattering. In the detection optical path, the scattered beam is split into two orthogonal linearly polarized lights and captured by the camera, each carrying position information in the \(x\) and \(y\) directions. Experimental results demonstrate that particles with a size of \({\lambda }^{2}/{16}\) are sufficient to achieve a positioning uncertainty of \({10}^{-4}\) \({\lambda }^{2}\) . In 2016, Banzer et al. leveraged the resonance characteristics of high-refractive-index silicon nanoantennas, exhibiting both electrical and magnetic resonance [ 39 ], to enhance scattering directionality and achieve lateral positioning accuracy of several hundred picometers for nanoparticles. In the experiment, tightly focused radially polarized light was used to excite a spherical silicon nanoantenna. The longitudinal electric dipole mode and transverse magnetic dipole mode of high-refractive-index nanospheres were phase-adaptively excited, resulting in strong directionality in the far field, with a measurement position uncertainty of less than \({0.2}\mathrm{\;{nm}}\) . If antenna design and excitation fields are further optimized, positioning accuracy on the order of tens of picometers may be achievable. In the same year, Zheng Xi et al. employed a similar optical path [ 29 ], illuminating identical parallel metal nanorods separated by subwavelength distances using the V-point polarization singularity (i.e., the center of the focused spot) in the angularly polarized beam and the phase singularity in the Hermite-Gaussian beam. The electric field exhibits azimuthal polarization around the V-point polarization singularity. When the singularity and the center of the nanorods experience a small displacement, the symmetry of the light field is disrupted, resulting in the generation of resonant dipole moments within the nanorods. This mechanism underlies the significant scattering changes of the two nanorods in the far-field direction. In other words, if a beam with singularities is incident on a subwavelength-length antenna, the discontinuity of the incident field and the rapid phase change near the nanoan-tenna will result in the far-field scattering field exhibiting significant sensitivity to displacement at scales much smaller than the wavelength, as illustrated in Fig. 10 . Additionally, this work utilized the Richard Wolf diffraction integral model and the time-domain finite difference model to analyze the interaction of the beam with the nanorod, demonstrating that these models effectively explain the rapid changes in the scattering pattern caused by displacement, thereby validating the theoretical model.

In 2018, Tischler et al. proposed a displacement measurement scheme that eliminates the need for complex measuring devices [ 36 ], utilizing a scattering structure and a cylindrically symmetric incident field aligned along the same axis to construct a cylindrically symmetric system. When the scattering structure deviates from the axis center, an additional angular momentum component is generated, altering the scattering field mode and far-field scattering pattern. Since the scheme does not rely on specific scatterers or incident beams and depends solely on scattering intensity measurements, the complexity of system design is significantly reduced. The system implemented based on this scheme employed circularly polarized Gaussian beams to excite gold nanospheres, achieving a positioning accuracy of \({0.55}\mathrm{\;{nm}}\) . In the same year, Ankan Bag et al. designed and fabricated a \({156}\mathrm{\;{nm}}\) diameter silicon sphere with a \(6\mathrm{\;{nm}}\) silicon dioxide shell to scatter incident light fields [ 34 ], achieving a displacement resolution of \(3\mathrm{\;{nm}}\) and a measurement accuracy of \({0.6}\mathrm{\;{nm}}\) . To achieve enhanced on-chip integration, in 2020, they pioneered the use of Huygens dipoles in the directional coupling of photonic crystal waveguides [ 32 ], coupling the directional scattering induced by displacement into six cross waveguides, resulting in a micro-nano integrated nano-sensor structure. As illustrated in Fig. 11 , the displacement uncertainty within a \({600}\mathrm{\;{nm}}\) range is only \(\lambda /{300}\) , approximately \(6\mathrm{\;{nm}}\) .

Although the aforementioned work effectively addresses the issues of insufficient accuracy and resolution, the measurement range is limited, typically within a hundred nanometers, thereby increasing the complexity of the positioning system. In 2018, Lei Wei et al. employed the interference mode of evanescent waves in nanoan-tennas to achieve displacement and phase detection of nanoparticles [ 35 ]. By using interferometric evanescent waves as the excitation field for dipole nanoantennas, the rapid variations in the pure virtual Poynting vector due to lateral displacement or relative phase difference are transformed into changes in the Fourier spatial scattering direction. This method achieves extremely high displacement and phase sensitivity around specific positions and enables the angle in the scattered momentum space to track the displacement across the entire k-space. In 2019, Wuyun Shang et al. proposed a displacement sensor scheme with an adjustable range [ 33 ], achieving a maximum range of several micrometers. They exploited azimuthally polarized beam as the excitation field, which is incident on a single metal-dielectric nanoparticle consisting of a silver core and a dielectric shell. The excited longitudinal magnetic dipole and transverse electric dipole generate single cross-scattering. As the position of the incident light relative to the nanoparticles changes, the excited mode also changes, resulting in variations in the far-field scattering field. Based on this, they further adjusted the ratio of the outer to inner radius of the nanoparticles to achieve a range of several micrometers.

However, certain challenges may arise in practical applications. For instance, the subwave-length size of the nanoantenna structure results in very low scattering efficiency near the Kerker scattering conditions, making it challenging to detect scattered signals. To achieve strong focusing and scattering light intensity, high numerical aperture objective lenses are employed, which allows a significant amount of incident light introducing substantial noise to enter the detection system.

4.4 Superoscillation

Mechanical standard parts such as rulers are commonly used to measure displacement or length in daily life. Zheludev et al. utilized the singularity of the super-oscillatory field as a scale on a ruler to achieve atomic-scale resolution of \(\lambda /{4000}\) in 2019 [ 40 ], as illustrated in Fig. 12 . Specifically, the optical ruler employs a laser to irradiate the PB phase metasurface, and the interference of multiple light beams generates a free-space singular light field with rapid phase changes in the deep subwavelength region. This type of free-space light field can be imaged without resolution limitations, far exceeding the diffraction limit, and generates a super-oscillation subwavelength hotspot orthogonal to the incident polarization in the far field. The super-oscillation field with a significant phase gradient near this point shares the same polarization direction as the incident field. Finally, a high numerical aperture imaging system is employed to collect the light field, and the displacement size is determined through post-processing steps such as phase and gradient calculations.

In 2023, they further extended the application of the super-oscillation field [ 23 ] with projecting the super-oscillation field generated by a spatial light modulator onto a \({200}\mathrm{\;{nm}}\) wide nanowire, and then collecting scattered light and image it on a detector positioned at a distance of \(\lambda\) (approximately \({0.5\mu }\mathrm{m}\) ) utilizing a \({0.9}\mathrm{{NA}}\) microscope objective. Since optical metrology using scattered light in reverse can be simplified into a Fredholm integration problem, which has been demonstrated to be solvable through neural networks, they employed deep learning techniques to analyze and train the scattered light field, achieving an accuracy of \({92}\mathrm{{pm}}\) within a range of a few nanometers. The results are illustrated in Fig. 13 , and the measurement speed depends solely on camera performance, which represents a significant breakthrough in the field of picometer metrology.

While the superoscillation scheme offers nearly unlimited resolution and is resilient to mechanical and thermal instabilities, the detection optical path of typical metasurfaces requires complex optical systems, including polarizers, along with intricate post-processing and phase reconstruction algorithms, which presents chal-

lenges for practical applications.

4.5 Special Metasurface Optical Metrology Tech- nology

Due to the ongoing exploration of the diverse and unique physical mechanisms of metasurfaces, several optical metrology techniques distinct from the aforementioned schemes have emerged in recent years.

In addition to polarization encoding, position information can also be encoded in diffraction orders. Xi et al. from the Netherlands introduced a superstructure grating design for high-precision lateral position measurement in 2020 [ 31 ], encoding the position information of the superstructure grating around a specific point in the illumination field into reflection diffraction orders. By representing the scattered field of a single structure of a superstructure grating as a superposition of fields generated by a set of mul-tipoles, a phase vortex in the reflection order, arising from the resonance of these multipoles, can be utilized as a function of specific design parameters, thereby compressing the lateral position information of a specific point into a small number of detected photons. Subsequently, with power recovery technology, non-information photons not utilized for detection are recovered and directed to the FP cavity to detect phase shifts again to enhance the interferometer’s power, increase the number of effective detected photons, and reach the shot noise limit in lateral position measurement.

Random sub-nano undulations on the chip can also be utilized for displacement measurement without manually designed micro-nano structures. In 2022, Xuewen Chen et al. from Huazhong University of Science and Technology investigated the speckle patterns of substrates under an interference microscope and confirmed that roughness leading to noticeable far-field optical responses significantly smaller than \({0.5}\mathrm{\;{nm}}\) can produce distinct speckle patterns [ 30 ]. Furthermore, the sub-nanometer undulations on the surface morphology of each substrate region exhibit uniqueness resulting in unique speckle patterns. Consequently, this speckle image is defined as an optical fingerprint. This phenomenon inspired them to employ optical fingerprints for repeatable position recognition and unmarked lateral displacement detection, as illustrated in Fig. 14 . To enhance the signal-to-noise ratio, the reflected reference light and the scattered light from the sample were separated on the Fourier transform surface during the experiment. Partial attenuation plates (PBBs) were employed to selectively attenuate the intensity of the reference light to \(1/{400}\) , increasing the image contrast by approximately 20 times. Finally, cross-correlation was utilized to calculate the displacement of the image before and after movement, achieving an accuracy of \({0.22}\mathrm{\;{nm}}\) and a resolution of \(4\mathrm{\;{nm}}\) .

Maryam Ghahremani et al. successfully demonstrated sub-nanometer precision alignment in three-dimensional space through the implementation of interference holograms generated by metasurface labeling in 2024 [ 41 ]. The phase profiles of the two metasurface markers are designed as parallel telescope structures. Lateral displacement of the markers causes deflection of the outgoing beam, whereas longitudinal displacement leads to convergence and divergence of the outgoing beam wavefront. They achieved a lateral alignment accuracy of \(\lambda /{50000}\) and a longitudinal alignment accuracy of \(\lambda /{6300}\) by capturing and processing the outgoing beam. Additionally, only lasers and cameras are required to operate the equipment, which significantly reduces system costs.

Strictly speaking, the sub-nanometer-scale undulations of the substrate and the nanoan-tenna-based structures do not fall under the category of metasurfaces within the aforementioned approaches; however, both configurations exploit the unique properties of micro-nano architectures to engineer the light field. Based on this observation, we maintain that these approaches exhibit similarities with metasurfaces in terms of functionality and design principles, and consequently, they offer valuable insights for the potential future application of metasurfaces in achieving analogous functionalities.

5 Conclusions

In optical precision measurement systems, key performance metrics such as resolution, accuracy, and measurement range are critical parameters in determining the choice of a detection scheme. The micro nano structure scattering strategy utilizes the near-field interaction and coupling characteristics between individual nanostructures. Its operational range is limited by the size of a single unit cell and is confined to the submicron scale. While it is typically applicable for alignment, its measurement accuracy can achieve sub-nanometer levels due to the sensitive optical response. In contrast, the polarization-encoded strategy modulates the polarization state of incident light through the arrangement of metasur-face unit cells, enabling an easy-to-implement measurement range of hundreds of micrometers. This approach also exhibits more relaxed wavelength conditions compared to the micro nano structure scattering scheme. The superoscillation scheme theoretically offers resolution beyond the diffraction limit; however, due to noise and device limitations, its resolution and accuracy are restricted to sub-nanometer and tens of picometer levels in practical applications, respectively. This approach requires complex signal processing algorithms rather than direct intensity-based calculations unlike the scattering strategy, significantly increasing the system’s complexity. The sensing technology based on non-Hermitian exceptional points, although characterized by ultra-high sensitivity, is inherently limited by environmental noise obscuring the signal. Additionally, its position-sensitive nature strictly constrains its measurement range. Similar to the superoscillation scheme, it relies on complex signal processing algorithms to determine displacement, presenting a formidable challenge for practical applications. Nevertheless, its highly sensitive response to displacement demonstrates the immense potential of this approach, attracting considerable researchers’ interest in the field.

Overall, sub-nanometer accuracy can be achieved over ranges of several hundred micrometers by leveraging metasurface-based displacement measurement and positioning technology. This technology features a compact design that reduces the need for numerous optical components, offering a novel paradigm for the integration and simplification of precision measurement systems. However, significant challenges remain in the practical implementation of this technology within lithographic equipment.

1) The alignment range is limited, and system complexity is high due to the sub-wavelength dimensions of micro- and nano-structures, along with customized incident light fields. The measurable distance typically spans only a few hundred micrometers, or in some cases, just a few hundred nanometers. Although periodic modulation of structured light may extend the measurement range, this approach inevitably results in reduced scattering efficiency. Additionally, customized light fields generally require focusing through high-NA objective lenses, and the light’s wavelength must be precisely tuned to match the resonance frequencies of specific nanoantennas. In some scenarios, it also requires the use of sophisticated post-processing algorithms. These requirements not only increase the complexity of system design but also hinder the overall measurement speed.

2) High processing accuracy requirements and susceptibility to damage: In contrast to conventional grating structures, metasurfaces generally exhibit a higher degree of complexity. On one hand, optical metrology systems require high precision in the fabrication of these structures, as even minor variations can lead to significantly different responses. On the other hand, alignment and other processing steps can inadvertently damage micro- and nano-structures, complicating efforts to meet cost-effectiveness and reusability criteria in lithographic platforms.

3) Insufficient error analysis models and standardized system designs: Current metasur-face displacement measurement systems face challenges due to inadequate error analysis models and the lack of standardized designs. Most systems are developed independently, without enough focus on integrating with lithography stages. Furthermore, most existing solutions are limited to measuring only two degrees of freedom, necessitating further exploration of multi-DOF system solutions. Compared to the well-established error analysis models associated with grating-based measurement systems, the lack of comprehensive error modeling and metrological traceability for metasurface systems poses a significant challenge that must be addressed for the successful implementation of metasurfaces in lithography applications.

This review comprehensively discusses the positioning and precision displacement measurement requirements within the realm of precision manufacturing processes, and summarizes the current advancements in displacement detection and positioning metasurfaces. It serves as a valuable reference for researchers aiming to utilize metasurfaces to achieving high-precision displacement measurement and alignment capabilities.

References

[1] T. Cui , D. R. Smith , R. Liu . Metamaterials: Theory, Design, and Applications [M]. Springer Publishing Company, Incorporated , 2009 . 367 -

[2] N. Engheta R. W. Ziolkowski . Metamaterials: Physics and Engineering Explorations [M]. Wiley , 2006 .

[3] D. D. Paul . Optical metamaterials: Fundamentals and applications [J]. Physics Today , 2010 . 63 ( 9 ): 57 - 58 .

[4] Y. Ma Y. Gao . Metasurfaces: Design principles and application challenges (invited) [J]. Chinese Journal of Lasers , 2024 . 51 ( 1 ): 0103001 -

[5] E. Otte , C. Alpmann , C. Denz . Polarization singularity explosions in tailored light fields [J]. Laser &amp; Photonics Reviews , 2018 . 12 ( 6 ): 1700200 -

[6] X. Wang , Z. Nie , Y. Liang , J. Wang , T. Li , B. Jia . Recent advances on optical vortex generation [J]. Nanophotonics , 2018 . 7 ( 9 ): 1533 - 1556 .

[7] A. Forbes . Structured light from lasers [J]. Laser &amp; Photonics Reviews , 2019 . 13 ( 11 ): 1970043 -

[8] A. I. Kuznetsov , M. L. Brongersma , J. Yao , M. K. Chen , U. Levy , D. P. Tsai , N. I. Zheludev , A. Faraon , A. Arbabi , N. Yu , D. Chanda , K. B. Crozier , A. V. Kildishev , H. Wang , J. K. W. Yang , J. G. Valentine , P. Genevet , J. A. Fan , O. D. Miller , A. Majumdar , J. E. Fröch , D. Brady , F. Heide , A. Veeraraghavan , N. Engheta , A. Alù , A. Polman , H. A. Atwater , P. Thureja , R. Paniagua-Dominguez , S. T. Ha , A. I. Barreda , J. A. Schuller , I. Staude , G. Grinblat , Y. Kivshar , S. Peana , S. F. Yelin , A. Senichev , V. M. Shalaev , S. Saha , A. Boltasseva , J. Rho , D. K. Oh , J. Kim , J. Park , R. Devlin , R. A. Pala . Roadmap for optical metasurfaces [J]. ACS Photonics , 2024 . 11 ( 3 ): 816 - 865 .

[9] J. E. Fröch , L. Huang , Q. A. A. Tanguy , S. Colburn , A. Zhan , A. Ravagli , E. J. Seibel , K. F. Böhringer , A. Majumdar . Real time full-color imaging in a meta-optical fiber endoscope [J]. eLight , 2023 . 3 ( 1 ): 13 -

[10] A. Arbabi , Y. Horie , M. Bagheri , A. Faraon . Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission [J]. Nature Nanotech , 2015 . 10 ( 11 ): 937 - 943 .

[11] Q. Chen , Y. Gao , S. Pian , Y. Ma . Theory and fundamental limit of quasiachromatic metal-ens by phase delay extension [J]. Physical Review Letters , 2023 . 131 ( 19 ): 193801 -

[12] Α. Μ. Shaltout , V. M. Shalaev , M. L. Brongersma . Spatiotemporal light control with active metasurfaces [J]. Science , 2019 . 364 ( 6441 ): 648 -

[13] X. Fang , H. Ren , M. Gu . Orbital angular momentum holography for high-security encryption [J]. Nature Photonics , 2020 . 14 ( 2 ): 102 - 108 .

[14] F. Zhang , Y. Guo , M. Pu , L. Chen , M. Xu , M. Liao , L. Li , X. Li , X. Ma , X. Luo . Meta-optics empowered vector visual cryptography for high security and rapid decryption [J]. Nature Communications , 2023 . 14 ( 1 ): 1946 -

[15] T. Li , X. Hu , H. Chen , C. Zhao , G. Song . High-efficiency broadband vector beams using polarization rotation metasurfaces [J]. IEEE Photonics Technology Letters , 2017 . 29 ( 17 ): 1463 - 1466 .

[16] X. Yi , P. Huang , X. Huang , Z. Xu , C. Zhang , J. Zhao , X. Liu , Y. Ai , H. Chen . Operation of polarization order of vector beams with cascaded metasurfaces [J]. Applied Physics B-lasers And Optics , 2017 . 123 ( 9 ): 243 -

[17] Z. Shen , R. Li , Y. Xue , Z. Qiu , Z. Xiang , J. Zhou , B. Zhang . Generation of optical vortices with polarization-insensitive metasurfaces [J]. IEEE Photonics Journal , 2020 . 12 ( 4 ): 1 - 10 .

[18] F. Ding , Y. Chen , Y. Yang , S. I. Bozhevolnyi . Gap-surface plasmon metasurfaces for structured beams generation [C]// 2019 PhotonIcs &amp; Electro-magnetics Research Symposium Spring (PIERS-Spring) , 2019 . 1276 - 1280 .

[19] F. Zhang , M. Pu , Y. Guo , X. Ma , X. Li , P. Gao , X. Luo . Synthetic vector optical fields with spatial and temporal tunability [J]. SCIENCE CHINA Physics, Mechanics &amp; Astronomy , 2022 . 65 ( 5 ): 254211 -

[20] M. Pu , X. Li , X. Ma , Y. Wang , Z. Zhao , C. Wang , C. Hu , P. Gao , C. Huang , H. Ren , X. Li , F. Qin , J. Yang , M. Gu , M. Hong , X. Luo . Catenary optics for achromatic generation of perfect optical angular momentum [J]. Science Advances , 2015 . 1 ( 9 ): e1500396 -

[21] F. Zhang , M. Pu , X. Li , X. Ma , Y. Guo , P. Gao , H. Yu , M. Gu , X. Luo . Extreme-angle silicon infrared optics enabled by streamlined surfaces [J]. Advanced Materials , 2021 . 33 ( 11 ): e2008157 -

[22] S. Bharadwaj , T. Van Mechelen , Z. Jacob . Picophotonics: Anomalous atomistic waves in silicon [J]. Physical Review Applied , 2022 . 18 ( 4 ): 044065 -

[23] T. Liu , C. Chi , J. Ou , J. Xu , E. A. Chan , K. F. MacDonald , N. I. Zheludev . Picophotonic localization metrology beyond thermal fluctuations [J]. Nature Materials , 2023 . 22 ( 7 ): 844 - 847 .

[24] H. Zang , Z. Xi , Z. Zhang , Y. Lu , P. Wang . Ultrasensitive and long-range transverse displacement metrology with polarization-encoded metasurface [J]. Science Advances , 2022 . 8 ( 41 ): eadd1973 -

[25] V. D'Ambrosio , N. Spagnolo , L. Del Re , S. Slussarenko , Y. Li , L. C. Kwek , L. Marrucci , S. P. Walborn , L. Aolita , F. Sciarrino . Photonic polarization gears for ultra-sensitive angular measurements [J]. Nature Communications , 2013 . 4 ( 1 ): 2432 -

[26] H. Zang , Z. Zhang , Z. Huang , Y. Lu , P. Wang . High-precision two-dimensional displacement metrology based on matrix metasurface [J]. Science Advances , 2024 . 10 ( 2 ): eadk2265 -

[27] R. Barboza , A. Babazadeh , L. Marrucci , F. Cardano , C. De Lisio , V. D'Ambrosio . Ultra-sensitive measurement of transverse displacements with linear photonic gears [J]. Nature Communications , 2022 . 13 ( 1 ): 1080 -

[28] J. Park , A. Ndao , W. Cai , L. Hsu , A. Kodigala , T. Lepetit , Y. Lo , B. Kanté . Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing [J]. Nature Physics , 2020 . 16 ( 4 ): 462 - 468 .

[29] Z. Xi , L. Wei , A. J. L. Adam , H. P. Urbach , L. Du . Accurate feeding of nanoantenna by singular optics for nanoscale translational and rotational displacement sensing [J]. Physical Review Letters , 2016 . 117 ( 11 ): 113903 -

[30] S. Lin , Y. He , D. Feng , M. Piliarik , X. Chen . Optical fingerprint of flat substrate surface and marker-free lateral displacement detection with angstrom-level precision [J]. Physical Review Letters , 2022 . 129 ( 21 ): 213201 -

[31] Z. Xi , S. Konijnenberg , H. P. Urbach . Information-efficient metagrating for transverse-position metrology [J]. Physical Review Applied , 2020 . 14 ( 1 ): 014026 -

[32] A. Bag , M. Neugebauer , U. Mick , S. Christiansen , S. A. Schulz , P. Banzer . Towards fully integrated photonic displacement sensors [J]. Nature Communications , 2020 . 11 ( 1 ): 1 - 7 .

[33] W. Shang , F. Xiao , W. Zhu , L. Han , M. Premaratne , T. Mei , J. Zhao . Unidirectional scattering exploited transverse displacement sensor with tunable measuring range [J]. Optics Express , 2019 . 27 ( 4 ): 4944 - 4955 .

[34] A. Bag , M. Neugebauer , P. Woźniak , G. Leuchs , P. Banzer . Transverse kerker scattering for angstrom localization of nanoparticles [J]. Physical Review Letters , 2018 . 121 ( 19 ): 193902 -

[35] L. Wei , A. V. Zayats , F. J. Rodríguez-Fortuño . Interferometric Evanescent Wave Excitation of a Nanoantenna for Ultrasensitive Displacement and Phase Metrology [J]. Physical Review Letters , 2018 . 121 ( 19 ): 193901 -

[36] N. Tischler , J. Stark , X. Zambrana-Puyalto , I. Fernandez-Corbaton , X. Vidal , G. Molina-Terriza , M. L. Juan . All-Optical Self-Referenced Transverse Position Sensing with Subnanometer Precision [J]. ACS Photonics , 2018 . 5 ( 9 ): 3628 - 3633 .

[37] J. Dorfmüller , R. Vogelgesang , W. Khunsin , C. Rockstuhl , C. Etrich , K. Kern . Plasmonic nanowire antennas: Experiment, simulation, and theory [J]. Nano Letters , 2010 . 10 ( 9 ): 3596 - 3603 .

[38] S. Roy , K. Ushakova , Q. van den Berg , S. F. Pereira , H. P. Urbach . Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate [J]. Physical Review Letters , 2015 . 114 ( 10 ): 103903 -

[39] M. Neugebauer , P. Woźniak , A. Bag , G. Leuchs , P. Banzer . Polarization-controlled directional scattering for nanoscopic position sensing [J]. Nature Communications , 2016 . 7 ( 1 ): 11286 -

[40] G. H. Yuan N. I. Zheludev . Detecting nanometric displacements with optical ruler metrology [J]. Science , 2019 . 364 ( 6442 ): 771 - 775 .

[41] M. Ghahremani , A. McClung , B. Mirzapourbeinekalaye , A. Arbabi . 3D alignment of distant patterns with deep-subwavelength precision using metasurfaces [J]. Nature Communications , 2024 . 15 ( 1 ): 8864 -

[42] Lithography, IEEE International Roadmap for Devices and Systems [EB/OL]. 2022 -

[43] W. Wan . Analysis of alignment method for NSR2205114 lithography equipment [J]. Plant Maintenance Engineering , 2018 . 11 ): 99 - 100 .

[44] R. H. M. Schmidt . Ultra-precision engineering in lithographic exposure equipment for the semiconductor industry [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences , 2012 . 370 ( 1973 ): 3950 - 3972 .

[45] C. Bender . Making Sense of Non-Hermitian Hamiltonians [J]. Reports on Progress in Physics , 2007 . 70 ( 6 ): 947 - 1018 .

[46] J. Wiersig . Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle detection [J]. Physical Review Letters , 2014 . 112 ( 20 ): 203901 -

[47] M. De Carlo , F. De Leonardis , R. Soref , L. Colatorti , V. Passaro . Non-Hermitian sensing in photonics and electronics: A review [J]. Sensor , 2022 . 22 ( 11 ): 3977 -

[48] С. М. Bender S. Boettcher . Real spectra in non-Hermitian Hamiltonians having PT symmetry [J]. Physical Review Letters , 1998 . 80 ( 24 ): 5243 - 5246 .

[49] H. Y. Fan J. Luo . Research progress of non-Hermitian electromagnetic metasurfaces [J]. Acta Phys. Sin. , 2022 . 71 ( 24 ): 247802 -

[50] H. A. Haus W. Huang . Coupled-mode theory [J]. Proceedings of the IEEE , 1991 . 79 ( 10 ): 1505 - 1518 .

[51] L. Feng , R. El-Ganainy , L. Ge . Non-Hermitian photonics based on parity-time symmetry [J]. Nature Photonics , 2017 . 11 ( 12 ): 752 - 762 .

[52] R. El-Ganainy , K. G. Makris , M. Khajavikhan , Z. H. Musslimani , S. Rotter , D. N. Christodoulides . Non-Hermitian physics and PT symmetry [J]. Nature Physics , 2018 . 14 ( 1 ): 11 - 19 .

[53] Y. Huang , Y. Shen , C. Min , S. Fan , G. Veronis . Unidirectional reflectionless light propagation at exceptional points [J]. Nanophotonics , 2017 . 6 ( 5 ): 175 - 177 .

[54] J. Luo Y. Lai . Hermitian and non-Hermitian Dirac-like cones in photonic and phononic structures [J]. Frontiers in Physics , 2022 . 10 . 845624 -

[55] M. Kerker , D. S. Wang , C. L. Giles . Electro-magnetic scattering by magnetic spheres [J]. Journal of the Optical Society of America , 1983 . 73 ( 6 ): 765 - 767 .

[56] M. V. Berry N. Moiseyev . Superoscillations and supershifts in phase space: Wigner and Husimi function interpretations [J]. Journal of Physics A: Mathematical and Theoretical , 2014 . 47 ( 31 ): 315203 -

[57] N. I. Zheludev G. Yuan . Optical superoscillation technologies beyond the diffraction limit [J]. Nature Reviews Physics , 2021 . 4 ( 1 ): 16 - 32 .

[58] E. T. F. Rogers N. I. Zheludev . Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging [J]. Journal of Optics , 2013 . 15 ( 9 ): 094008 -

[59] J. Lindberg . Mathematical concepts of optical superresolution [J]. Journal of Optics , 2012 . 14 ( 8 ): 083001 -

[60] F. M. Huang N. I. Zheludev . Super-resolution without evanescent waves [J]. Nano Letters , 2009 . 9 ( 3 ): 1249 - 1254 .

[61] F. Qin , K. Huang , J. Wu , J. Jiao , X. Luo , C. Qiu , M. Hong . Shaping a subwavelength needle with ultra-long focal length by focusing azimuthally polarized light [J]. Scientific Reports , 2015 . 5 ( 1 ): 9977 -

[62] A. Okamoto , H. Kuniyasu , T. Hattori . Detection of 30-40-nm particles on bulk-silicon and SOI wafers using deep UV laser scattering [J]. IEEE Transactions on Semiconductor Manufacturing , 2006 . 19 ( 4 ): 372 - 380 .

[63] Jacques van der Donck , Rob Snel , Jetske Stortelder , Alfred Abutan , Sjoerd Oostrom , Sander van Reek , Bert van der Zwan , Peter van der Walle . Particle detection on flat surfaces [C]// Proceedings Volume 7969, Extreme Ultraviolet (EUV) Lithography II , 2011 . 79691S -

[64] J. Pospsil S. Nespurek . Photostabilization of coatings. Mechanisms and performance [J]. Progress in Polymer Science , 2000 . 25 ( 9 ): 1261 - 1335 .

Funding

National Natural Science Foundation of China(62222511)

National Key Research and Development Program of China(2023YFF0613000)

Natural Science Foundation of Zhejiang Province China(LR22F050006)

STI 2030-Major Projects(2021ZD0200401)