Engineering

Rong Lin; Jin Yao; Zhihui Wang; Che Ting Chan; Din Ping Tsai

doi:10.1016/j.eng.2024.11.021

Engineering ›› 2025, Vol. 45 ›› Issue (2) :17 -27. DOI: 10.1016/j.eng.2024.11.021

Research Subwavelength Optics—Review

review-article

Engineering

Rong Lin ^a^,^#
, Jin Yao ^a^,^#^,^*
, Zhihui Wang ^a^,^#
, Che Ting Chan ^b^,^*
, Din Ping Tsai ^a^,^c^,^d^,^*

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Abstract

Meta-devices have significantly revitalized the study of nonlinear optical phenomena. At the nanoscale, the detrimental effects of phase mismatching between fundamental and harmonic waves can be substantially reduced. This review analyzes the theoretical frameworks of how plasmonic and dielectric materials induce nonlinear optical properties. Plasmonic and dielectric nonlinear meta-devices that can excite strong resonant modes for efficiency enhancement are explored. We outline different strategies designed to shape the radiation pattern in order to increase the collection capability of nonlinear signals emitted from meta-devices. In addition, we discuss how nonlinear phase manipulation in meta-devices can integrate the benefits of efficiency enhancement and radiation shaping, not only boosting the energy density of the nonlinear signal but also facilitating a wide range of applications. Finally, potential research directions within this field are discussed.

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Keywords

Nonlinear optics / Nanophotonics / Meta-devices / Metasurfaces / Plasmonic / Dielectric

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Rong Lin, Jin Yao, Zhihui Wang, Che Ting Chan, Din Ping Tsai. Engineering. Engineering, 2025, 45(2): 17-27 DOI:10.1016/j.eng.2024.11.021

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1. Introduction

Nonlinear optics fundamentally arise from nonlinear interactions between light and matter. In 1961, the observation of a second harmonic signal under laser illumination demonstrated that certain media could exhibit nonlinear responses when subjected to high electric field intensities [1]. This landmark discovery facilitated the rapid advancement of the field of nonlinear optics. Since then, various nonlinear optical processes have been studied, including four-wave mixing (FWM) [2], [3], optical rectification [4], third-harmonic generation (THG) [5], nonlinear photoluminescence [6], optical parametric amplification (OPA) [7], spontaneous parametric down-conversion (SPDC) [8], and electro-optic effects [9]. The field of nonlinear optics has gained fresh momentum with the development of nanotechnology [10], [11], [12]. At the nanoscale, the detrimental effects of phase mismatching between fundamental and harmonic waves on nonlinear responses are minimized due to the extremely short propagation distances of light. In addition, advanced nanofabrication techniques [13], [14], [15] have enabled the excitation of second-order nonlinear processes in plasmonic materials by artificially breaking the inversion symmetry through geometric modifications at surfaces or interfaces.

Plasmonic materials may not outperform traditional nonlinear crystals in terms of nonlinear susceptibility. Nevertheless, plasmonic meta-devices [16], [17], [18], [19], [20], [21], [22], whether individual particles or arrays, can confine and enhance the field near the surface to improve the nonlinear response, facilitated by local or nonlocal resonance modes [23], [24], [25], [26], [27], [28], [29], [30], including surface plasmon-polaritons (SPPs), localized surface plasmon resonance (LSPR), Fano resonance, and surface lattice resonance (SLR). It is crucial to acknowledge that plasmonic meta-devices have several intrinsic limitations, such as thermal heating, high reflectivity, the absorption of nonlinear emission, and finite penetration depth. Dielectric nanostructures have progressively demonstrated their potential to overcome these challenges. Many dielectric materials [31], [32] inherently possess non-inversion symmetric crystal structures, facilitating second-order nonlinear processes. Notably, the volume of light confinement in dielectric meta-devices [33], [34], [35], [36] can extend beneath the surface. By combining various resonant modes [37], [38], [39], [40] such as Mie resonance, lattice resonance, guided-mode resonance, and bound states in the continuum (BICs), the nonlinear efficiency can be further increased.

Aside from enhancing the nonlinear response from the perspective of excitation, another effective strategy is increasing the collection efficiency [41], [42], [43] of nonlinear signals by shaping the radiation pattern. This approach mitigates the destructive interference among adjacent nanostructures and increases the unidirectionality of the nonlinear response in meta-devices. In addition, the order of the nonlinear process and the rotational symmetry group of the nanostructures dictate the phase of the nonlinear wave. Thus, phase manipulation in nonlinear meta-devices can integrate the benefits of both resonance modes and radiation shaping, further boosting the energy density of the nonlinear signal. This method enables more dimensional manipulation in nonlinear processes, paving the way for various applications such as beam shaping [44], [45], imaging [46], [47], holography [48], [49], chiral sensing [50], vortex beam generation [51], and edge detection [52].

In this review, we discuss recent advancements in nonlinear optics, ranging from plasmonic to dielectric meta-devices. The structure of this review is organized as illustrated in Fig. 1 [53], [54], [55], [56], [57], [58], [59], [60], [61]. In Section 2, we review the theoretical frameworks used to investigate the nonlinear optical properties of meta-devices. This section also covers the nonlinear characteristics of commonly used materials. In Section 3, we discuss the contribution of various resonance modes to nonlinear efficiency enhancement in meta-devices. In Section 4, we present different strategies to shape the radiation pattern in order to increase the collection efficiency of nonlinear signals produced by meta-devices. Section 5 outlines the various possibilities introduced by nonlinear phase modulation. Section 6 provides a conclusion and discusses potential future research directions.

2. Nonlinear excitation: Natural and artificial

The optical response of a material is fundamentally characterized by the excitation of its polarization P . To accurately describe the nonlinear response of a material, it is essential to consider its polarization P as an expansion of the electric field E. This expansion can be expressed as a power series, described as follows:

(1)

P = ε_{0} χ^{(1)} \cdot E + ε_{0} χ^{(2)} : E E + ε_{0} χ^{(3)} ⋮ E E E + . . .

(2)

P^{(1)} = ε_{0} χ^{(1)} \cdot E

(3)

P^{(2)} = ε_{0} χ^{(2)} : E E

(4)

P^{(3)} = ε_{0} χ^{(3)} ⋮ E E E

where

ε_{0}

represents the vacuum permittivity and

χ^{(i)}

corresponds to the ith-order nonlinear susceptibility tensors. Here, we use

P^{(1)}

P^{(2)}

, and

P^{(3)}

to denote various orders of excitation in Eq. (1). The first term

P^{(1)}

describes the linear response of the material to E. The second term

P^{(2)}

describes the second-order nonlinear processes, including second harmonic generation (SHG), difference-frequency generation (DFG), sum-frequency generation (SFG), and optical rectification. Each of these processes involves interactions that are quadratic in E, leading to new frequencies or altered propagation characteristics. The third term

P^{(3)}

relates to third-order nonlinear processes such as THG and FWM. These nonlinear processes respond to the cubic power of E.

It should be emphasized that nonlinear processes are intrinsically related to the crystal structure of the applied material. To be specific, the second-order susceptibility

χ^{(2)}

is zero in materials that exhibit inversion symmetry. In contrast, the third-order susceptibility

χ^{(3)}

is unaffected by such symmetry characteristics.

2.1. Plasmonic natural nonlinearity

Although most metallic elements, such as gold and other noble metals, have crystal structures with inversion symmetry that hinder the second-order nonlinear response, they inherently exhibit natural nonlinearity due to their third-order susceptibility [62], [63],

χ^{(3)}

, which is unaffected by symmetry characteristics. Here, we briefly illustrate this from a mathematical perspective. According to the characteristics of inversion symmetry, two kinds of transformations can be derived. The electric field

E

transforms as

E \to - E

. Consequently, the third-order polarization

P^{(3)}

, as stated in Eq. (4), transforms as follows:

(5)

P^{(3)} \to ε_{0} χ^{(3)} ⋮ (- E) (- E) (- E) = - ε_{0} χ^{(3)} ⋮ E E E

The third-order polarization

P^{(3)}

should also transform:

(6)

P^{(3)} \to - P^{(3)} = - ε_{0} χ^{(3)} ⋮ E E E

It is evident that the results of these two transformations are consistent. This invariance under inversion symmetry indicates that the third-order polarization remains unchanged in sign. Therefore, the third-order susceptibility

χ^{(3)}

can be nonzero in plasmonic systems, permitting a third-order nonlinear response. This third-order nonlinearity is often more pronounced than second-order nonlinearities and has several practical applications, including plasmonic logic gates [64] and nanoscale broadband light sources [65].

2.2. Plasmonic artificial nonlinearity

To excite second-order nonlinear processes in plasmonic meta-devices, it is essential to artificially break the inversion symmetry. This can be achieved by geometric modifications at the surfaces or interfaces of the material. More specifically, effective strategies include the construction of heterostructures or interfaces, the assembly of nanoparticle combinations, and the design of non-centrosymmetric nanostructures.

It should be noted that

P^{(2)}

consists of two components in the media with inversion symmetry: the surface component and the bulk component. The surface component (

P_{s u r f}^{(2)}

), which arises within only a few atomic layers at the surface of the material, can be expressed as follows [66]:

(7)

P_{s u r f}^{(2)} (2 ω, r) = ε_{0} χ_{s u r f}^{(2)} : E (ω, r) E (ω, r) δ (r - r_{s u r f})

where

ω

is the fundamental frequency,

χ_{s u r f}^{(2)}

is the surface second-order susceptibility, r is the position vector in space,

r_{s u r f}

represents the surface position, and the Dirac delta function δ dictates the surface characteristic of the nonlinear polarization.

To be specific, the surface second-order susceptibility

χ_{s u r f}^{(2)}

typically exhibits only three independent components due to the presence of an isotropic mirror-symmetry plane at the surface of the media. The three components are

χ_{nnn}^{(2) s u r f} (ω_{1}, ω_{2}, ω_{3})

χ_{ntt}^{(2) s u r f} (ω_{1}, ω_{2}, ω_{3})

, and

χ_{tnt}^{(2) s u r f} (ω_{1}, ω_{2}, ω_{3}) = χ_{ttn}^{(2) s u r f} (ω_{1}, ω_{2}, ω_{3})

. Here, the symbols

n

and

t

represent the directions normal and tangential to the surface, respectively, and the component values depend on the frequencies of the interacting waves. It should be noted that the three mentioned components are dominant components only in polycrystalline metal films; in crystalline noble metals, anisotropic components [67], [68], [69] become appreciable.

The bulk component (

P_{b u l k}^{(2)}

), which is generated inside the material, can be described as follows:

(8)

\begin{matrix} P_{b u l k}^{(2)} (2 ω, r) = γ \nabla [E (ω, r) \cdot E (ω, r)] + δ^{'} [E (ω, r) \cdot \nabla] E (ω, r) \\ + β [\nabla \cdot E (ω, r)] E (ω, r) + ϛ E (ω, r) \nabla \cdot E (ω, r) \end{matrix}

where the parameters

γ

δ^{'}

β

, and

ϛ

define the material [70].

It is notable that, in analyses of the bulk component, the second and third terms are typically neglected due to the homogeneous characteristics of the material. Consequently, the behavior of the bulk component is primarily dependent on the values of the parameters

γ

and

ϛ

. A notable specific case arises with noble metals, where the parameter

ϛ

tends to have a negligible value, simplifying the analysis and characterization of the bulk component [71].

2.3. Dielectric natural nonlinearity

Dielectric materials possessing naturally non-centrosymmetric crystal structures can be selected to fabricate meta-devices for second-order nonlinearity. Common dielectric materials utilized for second-order nonlinear processes include zinc oxide (ZnO), gallium phosphide (GaP), gallium arsenide (GaAs), aluminum gallium arsenide (AlGaAs), lithium niobate (LiNbO₃), and molybdenum disulfide (MoS₂). In contrast to second-order nonlinearity, third-order nonlinearity does not require specific crystallographic symmetry, so silicon (Si) and titanium dioxide (TiO₂) are suitable choices and are often used in their amorphous forms when fabricating meta-devices.

It is essential to note that the value of nonlinear susceptibility is not the only parameter that should be considered. Absorption at both the fundamental and harmonic frequencies, fabrication challenges, and material tunability also play crucial roles. Vabishchevich and Kivshar [72] provide a detailed exploration of various dielectric materials utilized in nonlinear meta-devices. Therefore, further elaboration on these materials will not be presented here.

3. Nonlinear efficiency enhancement

A key issue in nonlinear meta-devices is the nonlinear efficiency, which is determined by the local electromagnetic field inside nonlinear materials or on their surfaces. By involving strong resonant responses to concentrate and enhance the field, nonlinear meta-devices can substantially boost the nonlinear efficiency at the subwavelength scale without the phase-matching requirement in bulk crystals [73]. Various resonance modes have been excited to enhance the nonlinear efficiency, such as LSPRs [74], SPPs [75], and SLRs [76] in plasmonic metasurfaces, as well as Mie-type resonances [77], Fano-resonances [55], and BICs [78], [79], [80] in dielectric counterparts.

Plasmonic nanostructures are good candidates for external field enhancement, which is beneficial for enlarging the optical nonlinearity from their surface nonlinearity and in integrated nonlinear materials [81], [82], [83]. While previous studies have mostly utilized plasmonic nanostructures alone to enhance nonlinearity, recent discoveries have shown that composite nanostructures can further amplify this effect. Deng et al. [84] developed a hybrid metasurface integrating plasmonic meta-atoms with an epsilon-near-zero (ENZ) nanofilm, achieving a 10⁴-fold increase in the SHG, as shown in Fig. 2(a). This improvement was due to changes in the vectorial characteristics of the incident light near the gold meta-atoms and enhanced interaction with the ENZ film. Nonlocal effects in the metasurface played a key role in boosting optical interactions and enabling various nonlinear effects [85], [86].

In addition to inducing coupling between different material layers to improve field enhancement, introducing a nonlocal effect that can induce a collective response can achieve similar results. Sharma et al. [87] showcased substantial electric and all-optical modulation of SHG in a nonlinear nonlocal metasurface featuring a twisted nematic liquid-crystal (LC) layer, as described in Fig. 2(b). The LC layer induced strong nonlocal SHG through SLR. At resonance, the SHG enhancement exhibited over 25 dB electrical switching amplitude and an all-optically induced phase transition affecting the SHG.

It is noteworthy that the inherent loss in metal materials constrains the operational band of these nonlinear nanostructures. The fundamental working frequency of the samples discussed above is located in the near-infrared range, while the resulting SHG appears in the visible spectrum. Short-wavelength light, especially vacuum ultraviolet (VUV), has the potential for technological applications; however, it is difficult to generate in metal material due to the large material loss and robust fabrication requirements [88]. Dielectric metasurfaces and nanoresonators are suitable for nonlinear efficiency enhancement due to their high-Q resonances, which originate from a high refractive index and large nonlinear coefficient [89], [90], [91], [92], [93]. ZnO stands out as a good choice. Previous research has demonstrated that ZnO can generate near-ultraviolet light and possesses a near-zero extinction coefficient at the fundamental wavelength. Semmlinger et al. [94] developed an all-dielectric metasurface specifically for nonlinear light generation in the VUV range. By utilizing ZnO nanoresonators that exhibited Mie-type resonance at a 394 nm pump wavelength, they were able to generate a second harmonic wave at 197 nm, as depicted in Fig. 2(c) [94]. The nonlinear metasurface achieved an effective coefficient roughly three times higher than that of a prism-coupled potassium fluoroboratoberyllate (KBBF) crystal.

Apart from utilizing the fundamental second or third harmonic, high harmonics can be considered to generate ultraviolet light. Zalogina et al. [95] demonstrated high harmonic generation (HHG) by producing up to a seventh harmonic from a single subwavelength resonator made of AlGaAs material (Fig. 2(d)). The researchers activated a resonant optical mode linked to quasi-BICs using an azimuthally polarized tightly focused beam at λ = 3.7 μm pump wavelength. The resonator, with a volume of around 0.1λ³, demonstrated the feasibility of miniaturizing solid-state high-harmonic sources to subwavelength dimensions. Although only the seventh harmonic was experimentally observed in the study, a theoretical analysis indicated the presence of the ninth harmonic near 400 nm. We believe that this finding can inspire short-wavelength generation.

Apart from short-wavelength light generation, nonlinear chiral meta-photonics and quantum nonlinear effects have recently received wide attention. Nonlinear chiroptical effects are significantly more pronounced than their linear counterparts because of the high sensitivity of the optical harmonics generated by chiral light to molecular and structural asymmetry [96], [97]. High sensitivity is closely related to high-quality resonances, of which BICs are a typical example. Shi et al. [98] introduced a chiral metasurface design that supported BICs. Fig. 2(e) [98] demonstrates the experimental chiroptical responses with an ultra-high quality factor (Q-factor) and circular dichroism (CD) of 0.9. This design realized a strong enhancement in the near field, near-unitary nonlinear CD, and circular eigen-polarization within the same planar chiral metasurface.

Quantum-entangled photon pairs can be generated by the SPDC process in nonlinear metasurfaces [99], [100], [101], [102], which is the reverse of the classical nonlinear generation of parametric waves. In terms of quantum effects, Santiago-Cruz et al. [103] utilized the SPDC process to generate entangled photons in GaAs metasurfaces exciting high-Q-factor quasi-BIC resonances, as exhibited in Fig. 2(f). These metasurfaces enhanced the quantum vacuum field, significantly boosting the nondegenerate entangled photon emission at several narrow bands and over a large spectral range. Pumping single or multiple resonances at different wavelengths allowed for the generation of multifrequency quantum states, including cluster states. This method shows great promise for the development of high-dimensional quantum-entangled optical devices.

4. Nonlinear radiation shaping

It should be noted that the harmonic wave generated by a nonlinear meta-device will diffract into different diffraction orders, resulting in energy dispersion [104], [105], [106]. By shaping the radiation pattern, a nonlinear meta-device can produce directional radiation of the nonlinear light, contributing to the collection of nonlinear light energy and enhancing the nonlinear utilization efficiency [107], [108], [109], [110].

The harmonic far-field radiation pattern is affected by the local field distributions inside the meta-atom. Altering the pump polarization state leads to variations in the local field distributions. This will generate different nonlinear displacement currents [116], [117], [118], [119], thereby stimulating different nonlinear modes. Carletti et al. [111] demonstrated that control of the second harmonic radiation direction can be achieved by changing the polarization state of the pump beam, as illustrated in Fig. 3(a). When the pump light is x-polarized, 45° polarized, y-polarized, and circularly polarized, the cylindrical AlGaAs metasurface has different second harmonic far-field radiation modes, and the nonlinear mode of 45° polarization can be regarded as the superposition of the modes excited by x-polarized and y-polarized pump light. Under these circumstances, the radiation pattern can be modified to reduce the angular spread of the harmonic signal. This ensures that even an objective lens with a low numerical aperture can effectively collect all the generated nonlinear light.

The property of unidirectionality can also be engineered by designing a material with a specialized nonlinear tensor. Research conducted by Xu et al. [112] indicated that GaAs nonlinear metasurfaces with different crystal orientations exhibit differences in the relative directions of their crystal axis and pump light polarization. Therefore, different nonlinear multipole interference can occur. Since a (110)-GaAs nanoantenna only undergoes multipole interference [120], [121] with an odd azimuth index, this type of metasurface has large forward or backward radiation intensity. Switching between forward and backward radiation can be realized by adjusting the pump polarization, as shown in Fig. 3(b) [112]. Another strategy for nonlinear radiation pattern shaping involves redirecting the harmonics that propagate in directions deviating from the normal to the nanostructure’s surface back toward the normal direction. Ghirardini et al. [113] utilized asymmetric holographic gratings to adjust the second harmonic radiation direction of an AlGaAs cylinder nanoantenna. The two semicircular gratings were spatially misaligned relative to each other, which redirected the second harmonic radiated by the nanocylinder along the grazing angle to the normal, as depicted in Fig. 3(c) [113]. In addition to introducing in-plane asymmetric gratings, Gigli et al. [56] used an axially asymmetric nanochair resonator to excite nonlinear modes with the normal radiation direction, as shown in Fig. 3(d). Due to the interaction of the fundamental and nonlinear resonances within the nanochair resonator, the axially asymmetric resonator has a relatively stronger central emission lobe, compared with a cylindrical resonator.

Altering the plane in which the structure resides can also impact the radiation pattern. Tsai et al. [114] studied the second harmonic optical manipulation of vertical split ring resonator (VSRR) and planar split ring resonator (PSRR) metasurfaces. Changing the arrangement of the split ring resonator can shape the radiation pattern of the metasurface. The second harmonic of the VSRR metasurface had six radiation directions, while the second harmonic of the PSRR metasurface mainly radiated in the forward or backward direction, and the radiation in the direction perpendicular to the incident light was relatively weak, as exhibited in Fig. 3(e) [114]. In addition, Okhlopkov et al. [115] simultaneously excited the high-Q collective Mie resonance and quasi-BIC mode of a Si metasurface and generated a new hybrid resonance mode that supported higher diffraction efficiency and was sensitive to the angle of the incident pump light. High-efficiency directional radiation was only generated at the specific incident angle of the pump light (22°), as shown in Fig. 3(f) [115].

5. Nonlinear phase modulation

To further manipulate the far-field radiation pattern of nonlinear meta-devices, nonlinear phase modulation can be introduced, which integrates the advantages of nonlinear efficiency enhancement and radiation shaping. A nonlinear geometric phase, propagation phase, and resonant phase have been reported for flexible wavefront shaping [36], [122], [123], [124], [125], [126], [127], [128]. Introducing phase manipulation into metasurfaces designed for efficiency enhancement can further increase the nonlinear power density. Tseng et al. [129] demonstrated a meta-lens that could both generate and focus second-harmonic VUV light. Constructed from 150 nm-thick ZnO nanoresonators with C3 symmetry, this meta-lens leveraged the nonlinear geometric phase to convert 394 nm light into a 197 nm focused beam, creating a 1.7 μm diameter spot whose power density enhancement was increased by 21-fold compared with that at the meta-lens surface, as shown in Fig. 4(a) [129].

In addition to enhancing the nonlinear power density, a meta-lens can facilitate harmonic imaging. Schlickriede et al. [130] investigated imaging objects through a dielectric nonlinear meta-lens utilizing Mie-type nanoresonators to generate a nonlinear propagation phase, as shown in Fig. 4(b). The researchers illuminated objects with infrared light and captured the images at the harmonic wavelength in the visible spectrum. By revisiting classical lens theory, they proposed and verified a generalized Gaussian lens equation tailored for nonlinear imaging through both experimental and analytical methodologies. Their experiments also demonstrated higher-order spatial correlations facilitated by the nonlinear meta-lens, revealing additional image features.

Holographic display is another important method for presenting images. Gao et al. [116] introduced a new mechanism for nonlinear holographic metasurfaces using a silicon metasurface with C-shaped meta-atoms, as illustrated in Fig. 4(c). These nanoantennas enhance the fundamental resonance at the pump laser wavelength, while the THG signals are redirected to the air gap region through higher-order resonance. This method significantly reduced the absorption loss at harmonic wavelengths, achieving an enhancement factor of up to 230. By incorporating abrupt nonlinear resonant phase changes, the researchers experimentally generated efficient cyan and blue THG holograms with the metasurface. This research demonstrates the potential for controlling the resonant phase and reducing the loss in nonlinear all-dielectric metasurfaces.

Various extended functionalities and applications have also been developed, such as terahertz (THz) wave generation and multiplexing functionalities [72], [131], [132], [133]. As shown in Fig. 4(d), McDonnell et al. [134] introduced broadband terahertz emission in nonlinear metasurfaces with geometric phases. The terahertz emitter allowed for an experimental demonstration of the tunable linear polarization of broadband single-cycle terahertz pulses, spatial separation of spin states and terahertz frequencies, and the generation of few-cycle pulses characterized by temporal polarization dispersion. The researchers also utilized spin control of terahertz waves to perform CD spectroscopy of amino acids. Wang et al. [135] proposed generating spin-unlocked orbital angular momentum (OAM) using nonlinear chiroptical metasurfaces based on geometric phases, as shown in Fig. 4(e). Their design included two types of plasmonic meta-atoms with opposite handedness, resulting in an enhanced spin-dependent CD effect. By encoding specific phase singularities and phase gradients into distinct channels, they demonstrated the experimental capability of spin-unlocked beam steering in SHG. This advancement paves the way for flexible manipulation of OAM light.

Nonlinear phase control requires both a high resonant enhancement with a high Q-factor and stable nonlinear phase control to ensure the high performance of nonlinear meta-devices [136]. The combination of high Q-factor resonance and phase control is challenging because phase control is generally a local response of individual meta-atoms, while high Q-factor resonance typically requires strong nonlocal interactions between multiple meta-atoms [137], [138], [139]. Hail et al. [140] demonstrated significant enhancement and precise spatial control of THG using a local high-Q-factor metasurface based on higher-order Mie-type resonances, as shown in Fig. 4(f). Their findings revealed a THG efficiency of 3.25 × 10^–5, accompanied by efficient focusing of the nonlinear meta-lens and a consistent, angle-independent nonlinear response with an incident angle of ±11°. This capability for local phase control and efficient harmonic generation addresses the challenge of balancing local phase control with nonlocal resonance excitation, offering promising potential for advanced nonlinear phase modulation devices.

6. Summary and perspectives

In this paper, we have provided a comprehensive review of recent developments in the field of nonlinear meta-devices. The fundamental requirement for exciting second-order nonlinear responses is an absence of inversion symmetry. This can be achieved either by artificially inducing symmetry breaking in plasmonic meta-devices or by selecting dielectric materials that inherently possess a non-inversion symmetric crystal structure. One of the primary benefits of meta-devices is their ability to support strong resonant modes. These modes significantly concentrate and enhance the electromagnetic field, thereby augmenting the nonlinear efficiency. Furthermore, far-field radiation shaping is emerging as an effective strategy to enhance the collection ability of nonlinear signals. Nonlinear phase control offers the dual advantages of efficiency enhancement and radiation shaping, which are beneficial to nonlinear imaging and sensing, among other applications.

It should be emphasized that the nanostructure designs applied in current research are always simple. However, integrated-resonant units (IRUs) [141], which can combine various meta-atoms and resonant modes to induce coupling within a single building block, have been shown to offer greater functionality and superior performance—including high efficiency, flexible phase manipulation, and a broad operational band—compared with individual meta-atoms. While most work on IRUs has been concentrated on the field of linear meta-devices, there is considerable potential for extending their application into nonlinear research. We believe this concept could significantly enhance nonlinear responses and open up new possibilities for nonlinear applications, such as tunable [142] and selective meta-devices. Moreover, it is worth noting that much of the work on nonlinear meta-devices has neglected the role of linear response. Developing meta-devices capable of operating under both linear and nonlinear conditions will enhance the overall functionality.

While our discussion has covered various applications of nonlinear meta-devices, there are still some specific directions that warrant development. To date, research has predominantly focused on second- and third-order nonlinear responses, while HHG deserves greater attention [58], [143], [144], [145]. HHG can extend the harmonic excitation from visible to deep ultraviolet and even X-ray regions. Additionally, the ability of a single meta-device to generate multiple harmonic waves introduces the potential for nonlinear wavelength-multiplexing functionalities. It must be acknowledged that the efficiency of HHG remains suboptimal. The primary challenge lies in enhancing the field confinement at high harmonic frequencies. Furthermore, since the HHG process is typically accompanied by lower-order processes, the issues of selecting specific harmonic frequencies and suppressing crosstalk must be addressed.

The capacity to manipulate multiple dimensions remains a critical metric in nonlinear meta-devices. Nonreciprocity has emerged as a promising strategy [146], [147], [148], [149]. For example, Kruk et al. [90] leveraged a dielectric meta-device to achieve asymmetric imaging in a third-order nonlinear process, and Boroviks et al. [59] developed plasmonic meta-devices to induce asymmetric SHG. In addition to enhancing the capability in the spatial domain, the time scale should not be neglected. Nonlinear time-varying meta-devices have been achieved for ultrafast modulation of the polarization of harmonic waves, including linearly polarized [60] and circularly polarized [150] switching.

Furthermore, the scope of research is broadening from classical to quantum optics [151], [152]. Numerous studies [153], [154], [155] have demonstrated the feasibility of generating entangled photon pairs via SPDC in nonlinear meta-devices. This approach not only miniaturizes the scale of quantum systems but also facilitates the generation of high-dimensional quantum sources [61], which might improve the performance of quantum imaging [156], sensing [157], and computing [158]. We envision that nonlinear meta-devices will continue to reveal their vast potential across a range of applications.

Acknowledgments

This work was supported by the University Grants Committee/Research Grants Council of the Hong Kong Special Administrative Region, China (AoE/P-502/20, C1015-21E, C5031-22G, CityU15303521, CityU11305223, CityU11310522, CityU11300123, and G-CityU 101/22), the City University of Hong Kong (9380131 and 7005867), and the National Natural Science Foundation of China (62375232).

Compliance with ethics guidelines

Rong Lin, Jin Yao, Zhihui Wang, Che Ting Chan, and Din Ping Tsai declare that they have no conflict of interest or financial conflicts to disclose.

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1. Introduction

2. Nonlinear excitation: Natural and artificial

2.1. Plasmonic natural nonlinearity

2.2. Plasmonic artificial nonlinearity

2.3. Dielectric natural nonlinearity

3. Nonlinear efficiency enhancement

4. Nonlinear radiation shaping

5. Nonlinear phase modulation

6. Summary and perspectives

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