Open AccessArticle

Enhanced Optical Bistability of a Metasurface Based on Asymmetrically Optimized Mirror-Induced Magnetic Anapole States

Institute of Electromagnetics and Acoustics, Xiamen University, Xiamen 361005, China

Fujian Provincial Key Laboratory of Electromagnetic Wave Science and Detection Technology, Xiamen University, Xiamen 361005, China

Author to whom correspondence should be addressed.

Appl. Sci. 2024, 14(21), 9914; https://doi.org/10.3390/app14219914

Submission received: 28 September 2024 / Revised: 23 October 2024 / Accepted: 28 October 2024 / Published: 29 October 2024

(This article belongs to the Section Optics and Lasers)

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Figure 1
Schematic diagram of the proposed mirror-induced MAS-based metasurfaces. Optical bistability originates from the silicon with third-order susceptibility. (a) Before asymmetrical optimization. Geometric parameters: length of silicon strip L1 = L2 = 250 nm, width W1 = W2 = 230 nm, height H = 360 nm, Ag film thickness D = 200 nm, and period P = 1500 nm. (b) After asymmetrical optimization. Geometric parameters: L1 = 190 nm, W1 = 210 nm, H2 = 120 nm, and H1 + H2 = H, while others remain unchanged as in (a). "> Figure 2
Physical mechanism of the metasurface based on mirror-induced MAS before asymmetric optimization. (a) The main figure presents the multipolar decomposition of the SCS spectrum of the silicon nanoribbon in the SOA structure. The inset shows a schematic diagram of the traditional MAS. (b) The main figure shows the multipolar decomposition of the SCS spectrum of the silicon part in SOM and the corresponding overall. The left inset is a schematic diagram of the mirror-induced MAS, and the right inset shows the multipolar decomposition of the SCS spectrum of the silicon nanoribbon in SOM. "> Figure 3
(a,b) Normalized field distributions for the conventional MAS and the mirror-induced MAS, respectively. Black arrows denote their current orientations inside silicon. (c) Average EF of silicon for these two scenarios. "> Figure 4
Average EF of the electric field by asymmetrically optimizing the proposed mirror-induced MAS-based metasurface. (a) Dependence on L1 and height duty ratio H2/(H1 + H2). W1 = 210 nm. (b) Dependence on W1 and H2/(H1 + H2). L1 =190 nm. Except when specified, parameters are the same as those in <a href="#applsci-14-09914-f001" class="html-fig">Figure 1</a>a. "> Figure 5
(a) Optical bistability of mirror-induced MAS metasurfaces. (b) Reflection spectra. The insets are the field distribution. "> Figure 6
(a) Nonlinear reflection spectra with increased incident light input intensity in the asymmetric device structure. (b) Nonlinear reflection spectra with reduced incident light input intensity in the same structure. The two dashed lines represent the resonant wavelength λres and the input wavelength λin, respectively. "> Figure 7
Dependences of switch thresholds on the incident angle. ">

Versions Notes

Abstract

In the field of modern optical computing and communication, optical bistability plays a crucial role. With a weak third-order nonlinear coefficient, low switch thresholds of optical bistability from Si-based nanophotonic structures remain a challenge. In this work, a metasurface consisting of silicon nanostrip arrays placed on the optically thick silver film is proposed. The light–matter interaction is enhanced by mirror-inducing the magnetic anapole states (MASs) and asymmetrically optimizing its silicon nanostrip. Numerical results show that the average enhancement factor (EF) of an electric field can be greatly enhanced to be 1524.8. Moreover, the optical bistability of the proposed metasurface achieves the thresholds of I_ON-OFF and I_OFF-ON of 8.5 MW/cm² and 7.1 MW/cm², respectively, which is the lowest threshold when compared to the previous works based on silicon nanostructures. The angular dependance of the bistability performance is also investigated. This work facilitates the proposed hybrid metasurface in the fields of miniaturized all-optical switches and modulators, which are key components in optical computing and communication.

Keywords:

magnetic anapole; mirror effect; metasurface; optical bistability

1. Introduction

Metasurfaces are types of artificial surfaces with subwavelength meta-atoms, organized 2D spatially to achieve the light manipulation of amplitude, phase, and polarization, as well as light enhancement [1,2]. Among them, the all-dielectric metasurface based on Mie resonances can efficiently localize and enhance the light in the nanostructures and find wide applications in nonlinear optics [3], optical switching [4], sensing [5,6], and nanomaterial imaging [7]. The resonant excitation of magnetic dipolar (MD) resonance can realize low-power ultrafast (65 fs) all-optical switching, whose two-photon absorption is enhanced by a factor of 80 with respect to the unstructured film [8], while electric dipolar (ED) resonance [9] and anapoles [10,11] can not only enhance the second-harmonic generation efficiency of nanostructures, but also increase the third-harmonic generation efficiency of nanostructures to as high as 1% [12,13].

Beyond the capabilities of metasurfaces, optical bistability is another crucial aspect in the field of optics. Optical bistability is a process in which there are two possible optical output states for a single light input. It allows for rapid switching between these states through the flexible adjustment of the input light [14], and offers wide-ranging applications in all-optical switching, optical computers, transistors, memory devices, etc. [15,16,17]. A common method to realize optical bistability is to pump the dielectrics with intensity-dependent permittivities, which is known as the Kerr effect. It relies on the third-order nonlinear optical process, which is intrinsically weak. The nanophotonic structures can not only contribute to device miniaturization and the integration of multiple functions on a chip, but also strongly localize and enhance optical fields within the Kerr dielectric to improve the bistability performance. The grating nanostructures with guided mode resonances [18,19] and quasi-bound states in the continuum [20], the photonic crystals [21], and the film-coupled plasmonic metasurfaces [22,23] and metamaterials [24] were utilized to reduce the all-optical bistability switch threshold, as well as to enlarge the on/off ratio. The Kerr medium used in these works was mostly polymers that have high third-order nonlinear coefficients, e.g., polyDCHD-HS with χ⁽³⁾ up to 4.4 × 10⁻¹⁷ m²/V² [25]. However, they had disadvantages including a low refractive index and low endurance, which make them not suitable for the switch devices that work in a high-intensity input laser and have a high repetition rate. On the other hand, silicon has a high laser damage threshold and is complementary metal oxide semiconductor (CMOS)-compatible for large-scale production at a low cost [8,13]. However, its third-order nonlinear coefficient is at least two orders of magnitude lower than that of polyDCHD-HS, and switching thresholds of >75 MW/cm² can be found for Si-based optical bistabilities [26,27,28].

As the counterpart of electric anapole, the magnetic anapole state (MAS) in resonant dielectric nanostructures is also a nonradiative resonance originating from the destructive interference between Cartesian magnetic dipole [MD(C)] and magnetic toroidal dipole (MTD) moments [29]. However, it finds rare practical applications [30] due to its relatively weak field enhancement and localization. The traditional dielectric structure has a single structure and a slow response speed, which limits the data processing speed of optical bistable devices [31]. The Kerr effect has a fast response speed, but the nonlinearity coefficient of Kerr materials is small, and high light intensity is required to realize the optical bistable function [24]. Therefore, in terms of achieving optical bistability, the further research and development of novel materials and device structures is needed to overcome the above challenges and limitations.

In this work, our objective is to optimize the metal-dielectric hybrid metasurface structure. This mainly involves improving the average electric field enhancement factor and enhancing bistability performance. Specifically, we propose a metal-dielectric hybrid metasurface for enhanced optical bistability, achieving the switch thresholds of I_ON-OFF and I_OFF-ON of as low as 8.5 MW/cm² and 7.1 MW/cm², respectively. The MAS resonances supported by the metasurface are manipulated by the PEC mirror effect and asymmetrical optimization, and the electric field is significantly enhanced and localized within the Si nanostrip, which is exactly the Kerr medium. This paper is organized as follows. In Materials and Methods, the enhancement of the proposed metasurface is demonstrated, and the materials, mechanism, and process are elucidated. In Section 3, the bistable performance of the proposed metasurface and the influence of the incident angle of light on the threshold are investigated and discussed. Finally, conclusions are drawn in Section 4.

2. Materials and Methods

Figure 1 depicts the schematic of the proposed mirror-induced MAS-based metasurfaces, which consist of silicon nanostrip arrays placed on the optically thick silver film. The dielectric material hydrogenated amorphous silicon is used due to its high refractive index and accessible third-order nonlinearity [32], while the noble metal Ag is selected due to its low loss at the near-infrared [33]. An x-polarized plane wave normally illuminates onto the metasurfaces. Commercial software COMSOL Multiphysics (v.4.4) based on the finite element method is employed for both the linear and nonlinear simulations. For a single nano device, a perfect matching layer is used in the x, y, and z directions to truncate the space [34], and the periodic device uses a P_x = P_y = 1500 nm periodic structure, while the perfect matching layer is still used in the z direction to truncate the space. The practical fabrication can be readily accomplished by the combination of evaporation, lithography, and lift-off procedures [35,36].

In order to elucidate the physical mechanism of the resonance inside the high-refractive-index silicon nanostrip, we start with the scattering of one single-unit cell extracted from the arrayed metasurface in Figure 1a, and analyze its features induced by the PEC mirror effect [37]. Figure 2a and Figure 2b show the multipolar decompositions [38] of the scattering cross-section (SCS) spectra for a high-refractive-index silicon nanostrip placed on the air (silicon on air, SOA) and silver film (silicon on metal, SOM), respectively. It should be noted that the height of the nanostrip in the SOA configuration is 2H, which is two times higher than that of the SOM configuration. For SOA in Figure 2a, a suppression of MD (red solid line) scattering appeared at the wavelength λ = 1090 nm, which resulted from the destructive interference of the Cartesian MD [denoted as MD(C), magenta dashed line] and MTD (yellow dotted line) moments. Consequently, the dominant resonance at this wavelength can be determined as an MAS. This can be further validated by the field and current distributions presented in Figure 3a. It can be seen from the upper panel of Figure 3a that four electric hotspots emerge within the silicon nanostrip, together with four unidirectional currents in the corresponding regions, as denoted by the black arrows. These four currents can thus form three circulating current loops, leading to three magnetic hotspots, as shown in the lower panel of Figure 3a. The features of these current and magnetic hotspot distributions are schematically illustrated in the inset of Figure 2a, which vividly demonstrates the characteristic of an MAS [34,39].

Next, by observing the centrosymmetry of the currents in the silicon nanostrip depicted in the insets of Figure 2a and Figure 3a, the PEC mirror effect can be readily introduced by cutting off the lower half of the nanostrip and placing the remaining part onto a Ag film, thus forming the SOM structure with a nanostrip height of H. Figure 2b shows the multipolar decomposition of the silicon part, and the corresponding overall multipolar decomposition is presented. Notably, an obvious resonance peak can be observed at λ = 1145.7 nm, where the ED peak and the MD peak are the predominant peaks. However, the introduction of the silver metal film makes it infeasible to accurately calculate the SCS spectrum and its multipole decomposition of the whole system. Under such circumstances, the silicon component and some metal reflectors near the silicon component can be considered for approximate calculation. The selected physical solution domain is located at the interface between the silicon component and the silver film, and the size of the calculation region selected below the interface is 1500 nm × 1500 nm × 1000 nm. The right inset of Figure 2b shows the multipolar decomposition of the silicon nanostrip within the SOM, and the left inset shows the schematic diagram of the mirror-induced MAS. Although the geometric parameters are the same, the structure of the SOM differs from that of the SOA. Consequently, the resonance of the total SCS scattering (indicated by the black dashed line) becomes narrower, and the resonance wavelength shifts to λ = 1145.7 nm. The ED peak (blue solid line) dominates the scattering and is hybridized with EQ (green dotted line) and MD(C). Nevertheless, at this point, the magnetic dipole (MD) peak (red solid line) is strongly suppressed, corresponding to two currents and one and a half magnetic hotspots inside the SOM nanostrip, as shown in the uncovered part of the inset of Figure 2b. When two currents are placed on the surface of the silver film, the PEC mirror effect generates virtual images that are centrosymmetric with the original images, enabling the real image and the virtual image to jointly form a mirror-induced MAS.

Figure 3b provides further verification. The field and current distributions inside the SOM nanostrip have similar patterns to half of those in the SOA [34]. The mirror effect significantly contributes to the electromagnetic enhancement and localization within the dielectric of the nano resonator [37]. As can be seen from Figure 3b, |E_max/E_inc| = 11.7 and |H_max/H_inc| = 68.7, which are nearly three times larger than the corresponding values in Figure 3a. Additionally, the electromagnetic field is more concentrated within the specific dielectric. This can be quantified by the average enhancement factor (average EF) of the electric field, which can be estimated using the following formula [12,13]:

| E_{a v g} / E_{i n c} |^{2} = \frac{∭ | E |^{2} d V}{| E_{i n c} |^{2} V}

(1)

where E_avg represents the average electric field intensity, E signifies the local electric field intensity within the dielectric with volume V, and E_inc denotes the incident light intensity. From Figure 3c, it can be seen that the average EF within the silicon of SOM is calculated to be 151.8 at the resonant wavelength, while that of SOA is 7.1. This factor is usually used to quantize the ability to enhance the performance of nonlinear harmonic generation and optical switch. The large average EF of the proposed mirror-induced MAS-based metasurfaces indicates its potential for optical bistability.

In order to apply efficient optical bistability, we further optimize the geometry. As can be observed from Figure 3b, one and a half magnetic hotspots occupy different positions inside the silicon nanostrip. This provides the possibility for further optimization by adjusting their geometry parameters. First of all, we set the period of the proposed metasurfaces in Figure 1 to be P = 1500 nm. This is because the period array on metal surfaces tends to excite propagating surface plasmon resonance (PSPR), and the choice of period can keep the PSPR away from the mirror-induced MAS to avoid the coupling effect [9]. Then, the average EFs are investigated by dividing the height of the silicon nanostrip into two parts and letting L₁ ≠ L₂, W₁ ≠ W₂, as shown in Figure 1b. The average EFs as functions of length L₁ and height duty ratio H₂/(H₁ + H₂) are given in Figure 4a, with W₁ = 210 nm and W₂ = 230 nm. It can be seen that, for every H₂/(H₁ + H₂), the average EFs have an optimal value within the L₁ range, and the highest value is 1524.8 happening at L₁ = 190 nm and H₂/(H₁ + H₂) = 1/3. Figure 4b gives those as functions of width W₁ and H₂/(H₁ + H₂), with L₁ = 190 nm, L₂ = 250 nm. Although other W₁ or L₁ were performed, a higher average EF could not be found, so the results are not presented here form simplicity. From all asymmetrical optimizations, the highest average EF can be found to be 1524.8 happening at L₁ = 190 nm, W₁ = 210 nm, and H₂/(H₁ + H₂) = 1/3. This might result from the coupling between the one magnetic hotspot and the half ones when they occupy different volumes, and the enhancement is a significant boost of about 10 times when compared to that of the symmetry situation in Figure 1a. When the mirror-induced MAS and asymmetric optimization of the silicon nanobar is performed, it can significantly enhance and localize the electric field within the silicon nanobar, thereby effectively improving the optical bistability performance. In contrast, in this specific system, electric anapole states (EAS) cannot produce the same ideal structural and performance optimization effects due to their different interaction mechanisms with the structure.

3. Results and Discussion

With the significant enhancement and localization of the electric field in the silicon nanostructures, enhanced optical bistability could be achieved. As per the hysteresis phenomenon between the input and output lights, optical bistability relies on the Kerr nonlinear medium inside a resonator. The relative permittivity of the Kerr nonlinear medium under strong irradiation has a nonlinear relationship with respect to the electric field, which is determined as follows:

ε_{r} = ε_{L} + χ^{(3)} | E |^{2} .

(2)

where ε_L is the linear relative permittivity, E is the electric field inside the nonlinear medium, and χ⁽³⁾ is the third-order nonlinear coefficient of the Kerr medium. For the proposed mirror-induced MAS-based metasurfaces, the nonlinear medium is silicon, with the nonlinearity of silver being neglected due to its inferior intrinsic nonlinearity and weak distribution of local fields. Rather than traditional silicon, we choose hydrogenated amorphous silicon with a χ⁽³⁾ of 2.84348 × 10⁻¹⁹ m²/V². From Equation (2), it can be seen that the ε_r is estimated by E, while E is determined by the ε_r of the resonator. Equation (2) gives rise to a self-consistent problem, which requires the iterative numerical solution of E (local electric field) using COMSOL [23,24]. The numerical implementation of bistability starts from the outside of the hysteresis loop. In each step of the self-consistent calculation, the electric field distribution from the previous step is used as the initial value. This guarantees convergence to the correct branch of the hysteresis loop. The upper hysteresis branch is obtained by gradually increasing the intensity of incident light. The lower hysteresis branch is obtained by reducing the intensity of incident light from a high level. When the input intensity enters the hysteresis loop region from either direction, the iteration process slows down, indicating a significant nonlinear process within the bistability region. For optical bistability generated from resonances, the incident operational wavelength λ_in must be chosen to satisfy the critical condition as follows [40]:

| (λ_{r e s} - λ_{i n}) / (w_{F W} / 2) | > \sqrt{3}

(3)

where λ_res is the resonant wavelength and w_FW is the full width half maximum (FWHM) of the resonance. Since the proposed metasurface has a strong resonance, and thus a narrow FWHM, the incident operational wavelength λ_in should be carefully selected to ensure a good compromise between the wide distance of bistability thresholds and the large ON/OFF ratios. We have already chosen λ_in = λ_res + 1.5w_FW.

Figure 5a demonstrates the hysteresis loops of the mirror-induced MAS-based metasurfaces as a function of the incident intensity. For this, generated from the proposed metasurface after asymmetrical optimization, it can be seen that, when the incident intensity increases, the reflectance maintains high values steadily, which is considered as the ON state. As the incident intensity rises to reach the threshold of I_ON-OFF = 8.5 MW/cm², the bistable switch transforms from ON state to OFF state, and the reflectance drops to a small value of R = 0.14 from R = 0.79. The ON/OFF ratio is calculated to be 5.6. This phenomenon occurs because the constant λ_in reads a different reflectance when the resonance moves by the intensity-dependent permittivity of the Kerr material [26], as depicted in Equation (2). Next, the lower hysteresis branch is obtained by decreasing the intensity of incident light from a high level. As it decreases to the threshold I_OFF-ON = 7.1 MW/cm² from the right-hand side of Figure 5a, the reflectance dramatically jumps to a high value of R = 0.85 from R = 0.06, which shows a great OFF/ON ratio of 14.2.

Figure 6a shows the variation in the nonlinear reflection spectra with the incident wavelength when the incident light intensity is increased. The red curve in it corresponds to the upper branch of the two red curves in Figure 5a. We chose five different intensities of incident light to comprehensively observe the change process of bistability. The observation results show that, when the incident light intensity is lower than 3 MW/cm², the resonant position of the spectrum has a slight redshift, but the overall line shape is still symmetric, as shown by the cyan curve and the green curve in Figure 6. It can be seen that the Kerr effect has almost no influence at a lower incident light intensity. As the incident light intensity gradually increases, the resonant wavelength gradually redshifts. At this time, due to the influence of the Kerr effect, the line shape of the spectrum also becomes asymmetric, and it shows a sharper characteristic on the long-wave side, and the corresponding reflectivity also gradually increases. When the incident light intensity increases to I_ON-OFF = 8.5 MW/cm², the resonant wavelength is close to the incident wavelength. Consistent with the behavior of the upper branch of the red curve in Figure 5a, the reflectivity drops sharply from the initial 0.79 to 0.14. The yellow dotted line and the black dotted line correspond to the resonant wavelength and the incident wavelength, respectively. This also proves that the I_ON-OFF obtained in Figure 5a is correct. Next, using the Kerr effect again, we continue to verify the correctness of I_OFF-ON from the spectra of the variation in reflectivity, with the incident wavelength obtained when reducing the incident light intensity.

Contrary to Figure 6a, Figure 6b shows the variation in the nonlinear reflection spectra with the incident wavelength when the incident light intensity is reduced. The red curve therein corresponds to the lower branch of the two red curves in Figure 5a. Here, five different intensities of incident light are also chosen for observation. The observation results show that, under the condition of a lower incident light intensity, the nonlinear reflection spectra in Figure 6a,b have high similarity and are similar to the linear spectrum. With the influence of the Kerr effect, the decrease in the incident light intensity leads to a gradual blue shift of the resonant wavelength, and the line shape of the spectrum gradually changes from asymmetric to symmetric, and also shows a sharp characteristic on the long-wave side. When the input intensity is reduced to the threshold I_OFF-ON = 7.1 MW/cm², the reflectivity jumps sharply from 0.06 to 0.85, which is consistent with the behavior of the lower branch in Figure 5a. Figure 6 shows the evolution process of optical bistability induced by the nonlinear Kerr effect, and is consistent with the results calculated in Figure 5. In addition, by connecting Figure 6a,b corresponding to different fixed incident light intensities in series for observation, the bistability of reflectivity and wavelength can also be obtained.

For the sake of comparison, the hysteresis loop generated from the proposed before-optimization metasurface is also presented. It can be seen that it has higher thresholds, but the distance distinguishing the thresholds of ON/OFF and OFF/ON is wider. Figure 5b also gives the linear reflection spectra of the proposed metasurfaces, with the inset of field distribution. With the characteristic of field distribution almost unchanging, the FWHM is narrower after the geometry parameter is optimized. It reveals that the Q factor is higher and the resonance is stronger. Optical bistability from the metasurface relies on the resonance within the Kerr material. Stronger resonance leads to the enhancement and localization of the electric field, and thus lower bistability thresholds. However, it also means a narrower FWHM on the spectrum, and thus narrower distance-distinguishing thresholds of ON/OFF and OFF/ON.

The threshold is the key parameter to characterize the performance of a bistable switch. Here, Table 1 compares the proposed metasurface with previous works. It can be seen that, although the χ⁽³⁾ used in this work is weak, the optical bistability thresholds supported by the proposed metasurface after asymmetrical optimization have the lowest thresholds for both I_ON-OFF and I_OFF-ON, and they have at least one order of lowering when comparing to the configuration of photonic crystal using the bound states in the continuum (BIC) resonance [28]. Furthermore, the angular dependence of the bistability performance is investigated in Figure 7. In order to excite the nonlinear bistable hysteresis loop, high-incident-intensity light is needed, which is usually obtained by focusing a laser beam. The inclined portion of the focused laser beam would degenerate the threshold. From Figure 5, it is evident that both the thresholds of I_ON-OFF and I_OFF-ON barely change under incident angle θ < 10°. The reason might lie in the same magnetic field direction between the incident x-polarization light and the excited mirror-induced MAS in the proposed metasurface. As the incident angle increases further, the height–length ratio becomes not suitable for the original magnetic hotspots, and both thresholds experience an exponential rise. The insensitive dependence on incident angle within the range of 0~10° facilitates the practical application of the miniaturized bistable switch.

4. Conclusions

In summary, we have demonstrated that, by mirror-inducing the magnetic anapole state (MAS) and asymmetrically optimizing its silicon nanostrip in the proposed metal-dielectric hybrid metasurface, the average enhancement factor (EF) of the electric field can be greatly enhanced, as well as optical bistability performance. The results indicate that, with appropriate asymmetric geometries, a significant enhancement of the relevant property (EF in this case) is achieved. Moreover, the optical bistability of the proposed metasurface is investigated, achieving the thresholds of I_ON-OFF and I_OFF-ON of 8.5 MW/cm² and 7.1 MW/cm², respectively, which are the lowest thresholds when compared to the previous works based on silicon nanostructures. Together with the ON/OFF ratios of >5.6 and the insensitive dependence on the incident angle of <10°, the proposed metasurface paves the way for applying miniaturized bistability to all-optical switches and modulators, logic and memory devices, and on-chip optical communications.

Author Contributions

Conceptualization, R.X. and G.C.; methodology, R.X. and G.C.; software, R.X., S.T., Y.W. and G.C.; validation, R.X., S.T., Y.W. and G.C.; formal analysis, R.X. and G.C.; investigation, R.X., S.T., Y.W. and G.C.; resources, R.X. and G.C.; data curation, R.X. and G.C.; writing—original draft preparation, R.X., S.T. and G.C.; writing—review and editing, R.X., S.T. and G.C.; visualization, R.X. and G.C.; supervision, R.X., S.T., Y.W. and G.C.; project administration, R.X. and G.C.; funding acquisition, G.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the National Natural Science Foundation of China under Grant 92163134 and 62271429.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Schematic diagram of the proposed mirror-induced MAS-based metasurfaces. Optical bistability originates from the silicon with third-order susceptibility. (a) Before asymmetrical optimization. Geometric parameters: length of silicon strip L₁ = L₂ = 250 nm, width W₁ = W₂ = 230 nm, height H = 360 nm, Ag film thickness D = 200 nm, and period P = 1500 nm. (b) After asymmetrical optimization. Geometric parameters: L₁ = 190 nm, W₁ = 210 nm, H₂ = 120 nm, and H₁ + H₂ = H, while others remain unchanged as in (a).

Figure 2. Physical mechanism of the metasurface based on mirror-induced MAS before asymmetric optimization. (a) The main figure presents the multipolar decomposition of the SCS spectrum of the silicon nanoribbon in the SOA structure. The inset shows a schematic diagram of the traditional MAS. (b) The main figure shows the multipolar decomposition of the SCS spectrum of the silicon part in SOM and the corresponding overall. The left inset is a schematic diagram of the mirror-induced MAS, and the right inset shows the multipolar decomposition of the SCS spectrum of the silicon nanoribbon in SOM.

Figure 3. (a,b) Normalized field distributions for the conventional MAS and the mirror-induced MAS, respectively. Black arrows denote their current orientations inside silicon. (c) Average EF of silicon for these two scenarios.

Figure 4. Average EF of the electric field by asymmetrically optimizing the proposed mirror-induced MAS-based metasurface. (a) Dependence on L₁ and height duty ratio H₂/(H₁ + H₂). W₁ = 210 nm. (b) Dependence on W₁ and H₂/(H₁ + H₂). L₁ =190 nm. Except when specified, parameters are the same as those in Figure 1a.

Figure 5. (a) Optical bistability of mirror-induced MAS metasurfaces. (b) Reflection spectra. The insets are the field distribution.

Figure 6. (a) Nonlinear reflection spectra with increased incident light input intensity in the asymmetric device structure. (b) Nonlinear reflection spectra with reduced incident light input intensity in the same structure. The two dashed lines represent the resonant wavelength λ_res and the input wavelength λ_in, respectively.

Figure 7. Dependences of switch thresholds on the incident angle.

Table 1. Comparison of optical bistability thresholds from nanostructures. The Kerr material is silicon.

Structure	Type of Resonance	The χ⁽³⁾ of Si (m²/V²)	I_ON-OFF (MW/cm²)	I_OFF-ON
Ring [26]	Fabry-Perot resonance	6 × 10⁻¹⁸	7.5 × 10³	6 × 10³
Grating [27]	Guided-mode resonance	6 × 10⁻¹⁸	350	200
Photonic Crystal [28]	BIC resonance	2.84348 × 10⁻¹⁹	150	75
This work (Symmetry)	MAS resonance	2.84348 × 10⁻¹⁹	25.0	19.6
This work (Asymmetry)	MAS resonance	2.84348 × 10⁻¹⁹	8.5	7.1

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Xu, R.; Tian, S.; Wen, Y.; Cai, G. Enhanced Optical Bistability of a Metasurface Based on Asymmetrically Optimized Mirror-Induced Magnetic Anapole States. Appl. Sci. 2024, 14, 9914. https://doi.org/10.3390/app14219914

AMA Style

Xu R, Tian S, Wen Y, Cai G. Enhanced Optical Bistability of a Metasurface Based on Asymmetrically Optimized Mirror-Induced Magnetic Anapole States. Applied Sciences. 2024; 14(21):9914. https://doi.org/10.3390/app14219914

Chicago/Turabian Style

Xu, Rui, Sen Tian, Yujia Wen, and Guoxiong Cai. 2024. "Enhanced Optical Bistability of a Metasurface Based on Asymmetrically Optimized Mirror-Induced Magnetic Anapole States" Applied Sciences 14, no. 21: 9914. https://doi.org/10.3390/app14219914

APA Style

Xu, R., Tian, S., Wen, Y., & Cai, G. (2024). Enhanced Optical Bistability of a Metasurface Based on Asymmetrically Optimized Mirror-Induced Magnetic Anapole States. Applied Sciences, 14(21), 9914. https://doi.org/10.3390/app14219914

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