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All issues Volume 12 (2025) EPJ Appl. Metamat., 12 (2025) 6 Full HTML
Open Access
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EPJ Appl. Metamat.
Volume 12, 2025
Article Number 6
Number of page(s) 9
DOI https://doi.org/10.1051/epjam/2025011
Published online 22 December 2025

© J. Dong et al., Published by EDP Sciences, 2025

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

In recent years, Epsilon-near-zero (ENZ) materials have emerged as a focal point in optoelectronic fields research [1–4]. These materials exhibit vanishing permittivity at spectific wavelengths, offering a novel method to transcend the limitations of conventional optics, such as directional radiation and enhancement of nonlinear optical response [5,6]. Currently, ENZ materials have been identified in natural substances, primarily due to plasma oscillations and phonon frequency resonance [7]. For instance, the ENZ wavelength of most metals is located in the ultraviolet (UV) range [8], while that of transition metal nitrides lies within the visible band (Vis) [9]. In contrast, doped semiconductors, such as indium tin oxide (ITO), exhibit an ENZ response in the near-infrared band (NIR) [10–12]. Additionally, due to phonon resonance effects, materials like silicon carbide (SiC) and fused silica (SiO₂) display ENZ properties in the mid-infrared band [13,14]. Obviously, the ENZ wavelength of a material is typically fixed, as its structure cannot be adjusted. This constraint limits the application of ENZ materials across various wavelength ranges, hindering the application of ENZ materials in the broadband spectrum. Hence, the concept of artificially constructing materials, named ENZ metamaterials, with tunable ENZ wavelengths has been proposed and is now being implemented, such as through the alternating stacking of metallic media and the construction of a Dirac cone at the center of the Brillouin zone [15,16].

Nonlinear optical responses differ from conventional optical responses in that they require strong light and typically exhibit very weak behavior, which limits their applications. Recent studies have shown that utilizing ENZ properties of materials can significantly enhance nonlinear optical absorption [17–19]. In 2016, M.Z Alam et al. first investigated the enhanced nonlinear optical response behavior at the ENZ wavelength of ITO [20]. They found that ITO displays a significant enhancement in nonlinear response at the ENZ wavelength under different angles and elucidated this ultrafast nonlinear phenomenon using a two-temperature model. Then, S. Suresh et al. designed an ENZ multilayer film and changed its ENZ wavelength to Vis-band. They similarly observed an enhanced nonlinear optical response at this ENZ wavelength [7]. Additionally, enhanced nonlinear optical responses can be achieved by integrating micro-nano structural designs with material ENZ mode coupling [21,22]. However, this approach can substantially increase fabrication complexity [23]. Despite the availability of various methods to enhance nonlinear optical responses, these effects are still too weak for practical applications. Therefore, the continuous improvement of nonlinear optical response such as saturated absorption (SA) and reverse saturation absorption (RSA) effects of materials has long been an important research objective [24–26].

Here, we designed a multilayer metamaterial composed of Ag, ITO and SiO2 via equivalent medium theory (EMT). It enables tuning of the ENZ wavelength into visible band while enhancing nonlinear absorption. Specifically, the as-deposited multilayer exhibits the strongest nonlinear absorption at the ENZ wavelength (725 nm, β = −3.3 ×  104 cm/GW). It exceeds that of reference material by more than an order of magnitude, indicating potential for applications in saturable absorption devices. A set of multilayers underwent annealing treatment (600 °C, 2 h). The results show that the SA peak shifts consistently with changes in the ENZ wavelength of the annealed samples. Finally, we propose a theoretical explanation for the saturable absorption behavior based on electronic transition and relaxation mechanism. The results demonstrate that such excellent behavior of multilayer metamaterial has great application potential in saturated absorbers, contributing to the advancement of nonlinear absorption devices.

2 Material and methods

The multilayer metamaterial structure is depicted in Figure 1a. Each later from top to bottom is SiO2, Ag and ITO, respectively. SiO2 functions as a protective layer on the top surface while also diluting the overall carrier concentration within the structure, thus enabling ENZ wavelength tuning. Ag and ITO play a crucial role in achieving strong nonlinear optical absorption, as the absorption of dielectric materials in the visible light spectrum is minimal [27]. Besides, ITO film is deposited on the substrate layer to prevent adverse effects on other layers due to high temperature deposition. Since each layer is much smaller than wavelength of laser, the equivalent permittivity (εeff) of the metamaterial can be calculated by EMT [28,29], that is,

εeff=ρεm+(1-ρ)εd(1)

where the ρ, εm and εd are fraction of material, permittivity of metal and dielectric, respectively. According to optical constant of each layer, the equivalent permittivity of different fraction of sandwich structure is shown in Figure 1b, where the ρ is the fraction of conductive materials (ITO and Ag). It can be seen that tunable ENZ area of multilayer is from Vis to NIR, which greatly broadens the application and it is impossible to achieve in single-layer film. Most importantly, increasing the conductive content induces a blue shift in the ENZ wavelength of structure, causing it to progressively exhibit more metallic-like properties. The optical constants of the single layer were measured using an ellipsometer (ME-L, Wuhan Eoptics Technology Co., Ltd, China) in Figures 1c and 1d. For non-magnetic materials, the relationship between permittivity and optical constants is as follows [30].

ε′=n2−k2(2)

ε″=2nk(3)

Where the ε′, ε″, n and k are the real part of permittivity, imaginary part of permittivity, refractive index and extinction coefficient. In Figure 1c, it can be seen that the dispersion of SiO2 is not pronounced, whilst its loss is extremely low (≈0). Through high-temperature processing, the ENZ wavelength of ITO undergoes a blue shift into the NIR in Figure 1d. However, the extent of tuning achievable by this method is limited and remains insufficient for specific desired wavelength bands. The ENZ wavelength of Ag is located in the UV region, resulting in a negative permittivity throughout the entire measured wavelengths (Fig. 1e). To ensure the accuracy of subsequent transmissive Z-scan measurement, it is essential that the sample possesses transmittance. Finally, we selected ρ = 0.3 (λENZ = 725 nm) multilayer to study the enhancement of nonlinear absorption responses. Simultaneously, we utilized S-parameter retrieval to determine the corresponding ENZ wavelength of multilayer metamaterial in Figure 1f, with the result falling within an acceptable margin of error [7]. The shaded region in the diagram represents the wide ENZ region (−1 < ε′ <1).

Then, we fabricated the multilayer metamaterials (ρ = 0.3) on quartz substrates via magnetron sputtering (ATTO10-R, Beijing Pator Co., Ltd, China). Meanwhile, one set was subjected to annealing treatment (600 °C, 2 h). The thin film is deposited onto clean quartz substrates (3 × 3 × 0.1 cm). Before deposition, the quartz substrates are thoroughly cleaned with alcohol, acetone, piranha solution (volume fraction, H2SO4:H2O2≈3:1) and DI water. Then, the targets (99.99%, Zhongnuo Advanced Material Technology Co., Ltd, China) and substrates are loaded sequentially into the deposition chamber. The details are shown in Table 1.

thumbnail Fig. 1

(a) Schematic diagram of metamaterial structures. (b) Metamaterial structures designed for calculating the wavelength of tunable ENZ using EMT. (c) The permittivity of SiO2. (d) The permittivity of ITO. (e) The permittivity of Ag. (f) Comparison of equivalent permittivity Results between the S-parameter and the EMT.
thumbnail Fig. 2

(a) The transparent multilayer metamaterial and (b) X-ray diffraction patten of annealed and unannealed multilayer metamaterials.
Table 1

Deposition parameters for the designed multilayer metamaterial.

3 Results and discussion

Figure 2a shows the transparent multilayer metamaterial. Its visible transparency facilitates the measurement of its nonlinear absorption. To determine whether annealing induced chemical reactions within the multilayer metamaterials, X-ray diffraction (XRD, Bruker D8) analysis was conducted to examine the phase composition of the samples in Figure 2b. The XRD diffraction peaks of the multilayer film exhibit significantly enhanced intensity after annealing, indicating improved crystallinity and a well-defined polycrystalline cubic structure. The diffraction peaks of the embedded ITO layer align closely with the reference pattern from the standard PDF card #74-1990. The enhanced crystallinity following annealing results in a distinct characteristic peak of ITO emerging at approximately 56° [12]. Due to the low Ag content, the corresponding diffraction peaks are weak, with only a single discernible peak at approximately 38°, consistent with the (111) plane of Ag (PDF card #65-8428). No notable shift in peak position was observed after annealing. Additionally, no diffraction signals corresponding to Sn, SnO and SnO₂ were detected. These findings suggest that the Sn atoms are fully incorporated into the lattice sites without forming secondary phases. The primary effect of annealing is an enhancement in crystallinity, indicating that no significant chemical reactions or phase separations occurred during the thermal treatment.

The surface microstructure and cross-sectional thickness of the multilayer metamaterials were examined using a field emission scanning electron microscope (FESEM, Zeiss Sigma 300) in Figure 3. Due to the Ag layer being designed with a thickness of only 6 nm, island-like growth inevitably occurred [31]. Therefore, the Ag layer in the multilayer forms a densely packed but discontinuous film in Figures 3a and 3b. The Ag nanoparticles displayed irregular sizes and a non-uniform distribution. After annealing, both the size distribution and spatial arrangement became more uniform, with a reduction in the average particle diameter. This results in an increase in resistivity of multilayer, indicating enhanced dielectric behavior, causes a redshift of the ENZ wavelength, and similar results have also been reported [32]. In Figure 3c, it can be seen that the as-deposited multilayer demonstrates clear stratification with an overall thickness of approximately 64.8 nm, aligning well with the design value. Notably, due to the high conductivity of both Ag and ITO, the individual layers are not distinctly discernible. However, the combined thickness of these conductive layers is approximately 20 nm, which is consistent with the design. Due to the superior stability of SiO2, it effectively suppressed thermal diffusion within the multilayer film after annealing. As a result, delamination remained in the multilayer structure, with the overall thickness showing a slight increase, while the combined thickness of Ag and ITO decreased slightly (Fig. 3d) [33].

Then, we employed the Z-scan method to measure the nonlinear absorption response of multilayer. The nonlinear optical response of materials typically weakens with increasing nonlinear order, while factors such as material dimensions and morphology also significantly affect their nonlinear performance. Therefore, reliable and precise measurement techniques are essential for accurately characterizing the nonlinear optical properties of materials. Typical single beam Z-scan is a widely used technique for characterizing nonlinear optical responses [34]. In this method, a laser beam is focused through a lens, and the sample is translated symmetrically through the focal plane. During the scan, detector 1 monitors the relative intensity of the pre-focal near-field light, while detector 2 simultaneously records the relative intensity of the post-focal far-field light. Meanwhile, the type of nonlinear absorption in the multilayer can be directly observed. Figures 4a–4h illustrate the normalized “open aperture” (OA) transmittance of as-deposited and annealed samples. Given that the designed ENZ wavelength is 725 nm, the as-deposited samples were characterized within a spectral range of 700–775 nm. After annealing, a redshift in the ENZ wavelength was predicted, prompting an adjustment of the measurement range to 775–850 nm, and the laser power is 130 mW. After measurement, all experimental data were fitted for normalized transmittance using the conventional Z-scan method [34,35].

T(Z)=∑m∞[−βI0Leff(1+z2z02)]m(m+1)32(4)

Leff=1−e−αLα(5)

where the α, L, I0, z0 and Leff are linear absorption coefficient, thickness of sample, peak light intensity, Rayleigh diffraction length and effective thickness of multilayer, respectively. In Figure 4, it can be seen that all multilayers exhibit saturated absorption behavior. For as-deposited multilayers (Figs. 4a–4d), the normalized transmittance diffraction peak appeared at 725 nm, consistent with the designed ENZ wavelength, and the saturation absorption coefficient (β) is −3.3 × 104 cm/GW. In the annealed multilayer, the redshift of the ENZ wavelength results in a corresponding redshift in the theoretically predicted maximum saturable absorption, and it can be seen that the maximum saturation absorption coefficient (β = −2.7 × 104 cm/GW) is at 800 nm in Figures 4e and 4f.

Particularly, we compared the β results with nanoparticles, two-dimensional materials, a single film and similar sandwich structures, finding that the saturation absorption coefficient increased by more than an order of magnitude, as shown in Table 2. All multilayer metamaterials exhibit SA, which originates from photon absorption by free electrons in the ground state [35,36]. Only the single ITO film demonstrates very weak reverse saturable absorption behavior [12,37]. However, due to the significantly stronger saturable absorption of the single Ag film, the multilayer metamaterials ultimately exhibit SA. Furthermore, it is noteworthy that the saturable absorption of the annealed multilayer films is generally weaker than that of the as-deposited films. This reduction can be attributed to the suppression of ground-state free carrier bleaching, which is intrinsically linked to the carrier concentration in the structure. In Figures 3a and 3b, it can be observed that after annealing, the multilayer film exhibits a more uniform and finer grain size, thereby inhibiting the ground-state free carrier bleaching effect. Meanwhile, in our structure the Ag layer serves as the dominant contributor to nonlinear absorption. Nonlinear absorption measurements conducted on a single silver film confirm that annealing weakens its nonlinear absorption. Therefore, the observed reduction in saturable absorption across the annealed samples is consistent.

In the as-deposited multilayer, the standard absorption coefficient is as follows [41]:

α(I)=α01+(I/IS)+βI(6)

where the α0, I and Is are linear absorption, laser intensity and saturation intensity, respectively. The RSA observed in ITO originates from three-photon absorption, and SiO2 exhibits weak absorption. Therefore, the absorption coefficient is as follows:

α(I)Ag=α01+(I/ISAg)+βAgI(7)

α(I)ITO=α01+(I/ISITO)+γITOI(8)

where γITO is the RSA coefficient of ITO. Here, the difference in the nonlinear absorption coefficients can be expressed as:

ΔαAg=βI−α0(I/IS)1+(I/IS)(9)

ΔαITO=γI2−α0(I/IS)1+(I/IS)(10)

thus, the final absorption coefficient is:

Δα=βI−α0(I/ISAg)1+(I/ISAg)+γI2−α0(I/ISITO)1+(I/ISITO)(11)

it should be noted that β < 0 and γ > 0, the RSA observed in ITO arises from higher order nonlinear optical response, so |γ| << |β|, that means, Δα < 0, indicating SA behavior. Similarly, it also applies to the annealed multilayer metamaterials, confirming that all samples display SA behavior.

Finally, the mechanism underlying the overall saturable absorption response can be elucidated by analyzing the electronic excitation and relaxation processes in Figure 5. When the sample is irradiated with intense laser light, intra-band transitions initially take place in Ag, leading to SA. Simultaneously, photon excitation promotes free carriers in the ITO into the plasmonic band. Under continued optical pumping, these carriers are further excited into continuum state, giving rise to multiphoton absorption, corresponding to the RSA contribution of ITO, though its magnitude is significantly weaker than the SA from silver. Throughout the entire nonlinear absorption process, the SiO2 facilitates the relaxation of conduction band electrons back to the valence band, helping to establish a dynamic equilibrium in the overall nonlinear optical response [42,43].

thumbnail Fig. 3

(a) The surface image of as-deposited metamaterial. (b) The surface image of an annealed metamaterial. (c) The cross-sectional image of as-deposited metamaterial. (d) The cross-sectional image of an annealed metamaterial.
thumbnail Fig. 4

(a)–(d) Normalized transmittance near the ENZ wavelength for as-deposited multilayer metamaterials. (e)–(f) Normalized transmittance near the ENZ wavelength for annealed multilayer metamaterials.
Table 2

The SA of different materials.

thumbnail Fig. 5

Schematic diagram of electronic excitation and relaxation processes at energy levels in the multilayer metamaterials.

4 Conclusion

In conclusion, the changed ENZ multilayer metamaterial (ITO/Ag/SiO2) was prepared via magnetron sputtering and its nonlinear optical absorption was measured by Z-scan method. The results show that all multilayer metamaterials exhibit saturated absorption because of ground state free electron bleaching. The as-deposited multilayer shows maximum SA behavior at the ENZ wavelength (725 nm, β = −3.3 × 104 cm/GW), which is superior to nanoparticles, 2D materials, etc. For annealed multilayer, it exhibits a redshift in its ENZ wavelength, accompanied by a corresponding shift in the peak of SA coefficient (800 nm, β = −2.7 × 104 cm/GW), demonstrating the ENZ properties of the material can effectively enhance the nonlinear response. Finally, the mechanism underlying SA is explained through the processes of electronic excitation and relaxation. Such materials exhibiting strong SA can be applied in saturation absorbers, thereby advancing the field of laser technology.

Funding

The authors acknowledge funding from the Natural Science Foundation of Shanghai (Grant Nos. 25ZR1402254, 25ZR1404003), Industry-University-Research Collaboration Fund of Shanghai Academy of Spaceflight Technology (Grant No. USCAST2023-8), and the Startup Fund for Young Faculty at Shanghai Jiao Tong University (Grant No. 24 × 010502884).

Conflicts of interest

The authors declare no conflicts of interest.

Data availability statement

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Author contribution statement

Jiannan Dong: Original Draft Preparation. Zongling Lang: Methodology. Zhongyang Wang: Writing − Review & Editing, Formal Analysis, Supervision. Shuqiang Xiong: Supervision. Hao Luan: Investigation. Yihang Chen: Supervision. Tongxiang Fan: Supervision.

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Cite this article as: Jiannan Dong, Zongling Lang, Zhongyang Wang, Shuqiang Xiong, Hao Luan, Yihang Chen, Tongxiang Fan, Epsilon-near-zero ITO/Ag/SiO2 metamaterial for large nonlinear absorption, EPJ Appl. Metamat. 12, 6 (2025), https://doi.org/10.1051/epjam/2025011

All Tables

Table 1

Deposition parameters for the designed multilayer metamaterial.

In the text
Table 2

The SA of different materials.

In the text

All Figures

thumbnail Fig. 1

(a) Schematic diagram of metamaterial structures. (b) Metamaterial structures designed for calculating the wavelength of tunable ENZ using EMT. (c) The permittivity of SiO2. (d) The permittivity of ITO. (e) The permittivity of Ag. (f) Comparison of equivalent permittivity Results between the S-parameter and the EMT.
In the text
thumbnail Fig. 2

(a) The transparent multilayer metamaterial and (b) X-ray diffraction patten of annealed and unannealed multilayer metamaterials.
In the text
thumbnail Fig. 3

(a) The surface image of as-deposited metamaterial. (b) The surface image of an annealed metamaterial. (c) The cross-sectional image of as-deposited metamaterial. (d) The cross-sectional image of an annealed metamaterial.
In the text
thumbnail Fig. 4

(a)–(d) Normalized transmittance near the ENZ wavelength for as-deposited multilayer metamaterials. (e)–(f) Normalized transmittance near the ENZ wavelength for annealed multilayer metamaterials.
In the text
thumbnail Fig. 5

Schematic diagram of electronic excitation and relaxation processes at energy levels in the multilayer metamaterials.
In the text

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