Nanostructure array and apparatus using the same

Abstract

The experimental Q value was increased by approximately 100 times from the typical value, resulting in 1.0 × 10⁻⁶ 5 To provide a nanostructure array that achieves a Q value exceeding [a certain threshold]. [Solution] The system comprises an inorganic solid insulating layer 12 and a metasurface layer 14 made of a high refractive index dielectric material that confines light, which is laminated on the inorganic solid insulating layer 12. The metasurface layer 14 is configured as an array having pair rods or nanopillars as single units, which have a shallow-cut structure in which the etching depth h of the light confinement regions (16a, 16b) is in the range of 25 nm to 200 nm. The system has a thin film high refractive index dielectric layer located in the region opposite to the inorganic solid insulating layer and the bottom of the shallow-cut structure that forms the side wall of the waveguide. The light confinement region has a resonance wavelength of 1.0 × 10 in the quasi-bound state in a continuum. 3 Exceeding 1.0 × 10 6 It has the following Q-values.

Description

[Technical Field]

[0001] This invention relates to a nanostructure array using a quasi-bound state in the continuum (quasi-BIC). [Background technology]

[0002] The Q-factor, an indicator of how strongly light is confined in a nanophotonic material, is an important indicator in numerous applications, including optical devices, nonlinear amplification, sensors, non-Hermitian systems, and topological photonics. To experimentally increase the Q-factor, it is important to design nanophotonic materials to increase their radiative Q-factor. Photonic crystal resonators consisting of nanostructures with a period of approximately the same duration as the wavelength of light, and metasurfaces consisting of nanostructures with a period of shorter duration than the wavelength of light have been proposed. For example, Patent Document 1 proposes an optical resonator aimed at improving the Q-factor in optical devices. Non-Patent Document 1 reports on the dependence of propagation loss on waveguide width and polarization for strip waveguides and rib waveguides made of tantalum pentoxide.

[0003] In recent years, a unique optical resonance state called bound state in the continuum (BIC) in dielectric periodic nanostructures has attracted attention as a nanophotonic material that achieves high Q-factors. BIC is an optical localization state in a continuum with zero linewidth and infinite Q-factor, in which light is strongly confined within the periodic nanostructure. In particular, under quasi-BIC conditions that arise by slightly breaking the central symmetry of the unit cell, the radiated Q-factor becomes a finite value, and a radiated component with a sharp resonance peak can be experimentally observed by vertical excitation. Patent document 2 proposes a resonant nanophotonic biosensor using a metasurface with a high Q-factor.

[0004] Quasi-BICs are characterized by their high radiative Q-factor and electric field resonance enhancement effect, and are attracting attention as a new method that contributes to the high functionality of optical devices. On the other hand, metasurfaces using quasi-BICs have a large surface area relative to the volume of the nanostructure, and are susceptible to scattering losses due to fabrication errors, so the experimentally obtained Q-factor is typically around 1000. This Q-factor is 10-100 times larger than that of nanophotonic materials based on metal nanostructures, and although it has advantages in terms of application, there has been a need for methods to further increase the Q-factor. To date, there have been studies that have predicted the achievement of strong light confinement based on quasi-BIC by coating an electron beam resist onto a substrate and forming nanostructures in the resist itself, thereby obtaining a high experimental Q factor (see Non-Patent Literature 2). However, these studies have achieved ultra-high Q factors using periodic hole arrays similar to photonic crystals, and ultra-high Q factors have not yet been achieved in metasurfaces using typical quasi-BIC. Furthermore, in Non-Patent Documents 3 and 4, the inventors have proposed all-dielectric metasurfaces based on BIC, but the Q-factor obtained from experimentally fabricated all-dielectric metasurfaces was only about 1000. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2007-47604 [Patent Document 2] Special Publication No. 2023-545069 [Non-patent literature]

[0006] [Non-Patent Document 1] S. Lindecrantz, et al., "Estimation of propagation losses for narrow strip and rib waveguides," IEEE Photonics Technol. Lett 26(18), 1836-1839 (2014) [Non-Patent Document 2] L. Huang, et al., “Ultrahigh-Q guided mode resonances in an All-dielectric metasurface”, Nat Commun 14, 3433 (2023) [Non-Patent Document 3] Keisuke Watanabe and Masanobu Iwanaga, “Nanogap enhancement of the refractometric sensitivity at quasi-bound states in the continuum in all-dielectric metasurfaces”, Nanophotonics 2023; 12(1): 99-109 [Non-Patent Document 4] Keisuke Watanabe and Masanobu Iwanaga, “Optimum asymmetry for nanofabricated refractometric sensors at quasi-bound states in the continuum”, Appl. Phys. Lett. 124, 111705 (2024) [Overview of the project] [Problems that the invention aims to solve]

[0007] As mentioned above, metasurfaces using quasi-BICs, which in principle have a high radiant Q-factor, have the problem that their Q-factor is only about 1000 due to scattering losses caused by fabrication errors. Furthermore, when waveguides are fabricated directly on a silicon oxide layer, although they in principle have a high radiant Q-factor, scattering losses due to fabrication errors are large, limiting and reducing the experimentally observed Q-factor. Since this scattering loss is mainly caused by the roughness of the waveguide sidewalls, structures with a large surface area relative to the waveguide volume are particularly affected by this problem. The present invention solves the above problems of the prior art, increases the experimental Q value by about 100 times from a typical value, and realizes a nano-structured array with a high Q value exceeding 1.0×10 5 The purpose is to provide a nano-structured array with a high Q value exceeding 1.0×10

Means for Solving the Problem

[0008] The inventor of the present invention considered that in a metasurface structure using a quasi-BIC having a high radiative Q value in principle, if a structure that minimizes the influence of scattering loss can be realized, the radiative Q value can be increased by about 100 times from a typical value, and a high Q value exceeding 10 5 can be realized, and thus the present invention was conceived. That is, 〔1〕The nano-structured array of the present invention has, for example, as shown in FIG. 1, an inorganic solid insulating layer 12 and waveguides (16a, 16b) made of a high refractive index dielectric material that confines light laminated on the inorganic solid insulating layer 12. The waveguide is configured as an array having, as a single unit, paired rods or nanopillars having a shallow trench structure in which the etching depth h of the light confinement region is in the range of 25 nm or more and 200 nm or less. It has a thin film high refractive index dielectric layer 14 located in the facing region between the inorganic solid insulating layer and the bottom of the shallow trench structure forming the side wall of the waveguide. The light confinement region has a Q value exceeding 1.0×10 3 and less than 1.0×10 6 using a quasi-bound state in a continuum, which is a nano-structured array. Preferably, the upper limit value of the Q value may be 2.0×10 5 or less, and more preferably 5.0×10 5 or less.

[0009] 〔2〕In the nano-structured array〔1〕of the present invention, preferably, it further has a substrate on which the inorganic solid insulating layer is laminated. 〔3〕In the nano-structure array [2] of the present invention, preferably, the substrate may be any one of a silicon-on-insulator (SOI) wafer, a glass substrate with a low refractive index, a quartz substrate, a sapphire substrate, and a calcium fluoride substrate. 〔4〕In the nano-structure array [1] of the present invention, preferably, the light confinement region may be any one of a pair of rods with different longitudinal lengths (L±2ΔL), a pair of rods with different widths (W1 and W2), a pair of rods arranged with different inclination angles (θ) of the opposing pair of rods, a nano-structure with a circle or a square cut out by slightly shifting the position from the center, nano-pillars arranged facing each other with different sizes and ellipticities, or nano-pillars arranged in a crescent shape. 〔5〕In the nano-structure array [1] of the present invention, preferably, the high refractive index dielectric material may be selected from silicon, germanium, gallium arsenide, and silicon nitride.

[0010] 〔6〕In the nano-structure array [1] of the present invention, preferably, the resonance wavelength of the quasi-bound state in the continuum is at least one resonance wavelength included in the range of 400 nm or more and 2000 nm or less. 〔7〕In the nano-structure array [1] of the present invention, preferably, the etching depth of the light confinement region is in the range of 50 nm or more and 100 nm or less. 〔8〕In the nano-structure array [2] of the present invention, preferably, the thickness of the thin film high refractive index dielectric layer is in the range of 300 nm or more and 350 nm or less.

[0011] 〔9〕In the nano-structure array [1] of the present invention, preferably, the light confinement region has a quasi-BIC metasurface structure that minimizes the overlap between the local electric field in the light confinement region and the nano-structure sidewall. 〔10〕In the nano-structure array [1] of the present invention, preferably, the array may be selected from the group consisting of a one-dimensional array and a two-dimensional array.

[11] In the nanostructure array [1] of the present invention, preferably the inorganic solid insulating layer is selected from the group consisting of borosilicate glass, quartz glass, sapphire, and calcium fluoride.

[0012]

[12] Optical devices, medical sensors, optical communication sensors, nonlinear augmentation sensors, non-Hermitian photonics, or topological photonics having any of the nanostructure arrays [1] to

[11] of the present invention.

[0013] In this invention, a metasurface structure is obtained using a shallow trench structure with a thin film high refractive index dielectric layer interposed. In the shallow trench structure, the roughness of the sidewalls is reduced and the scattering loss is also reduced, so the experimentally obtainable Q value increases, which solves the problems that arise when directly fabricating waveguides on a conventional silicon oxide layer (limiting the Q value or being susceptible to manufacturing errors). Therefore, in this invention, the Q value is 1.0 × 10, which is about two orders of magnitude larger than the typical Q value of 1000 in conventional BIC metasurfaces. 5 An ultra-high Q-factor exceeding [a certain value] is achieved, making it applicable to various applications requiring strong light-matter interactions, including optical devices, nonlinear amplification, sensors, non-Hermitian systems, and topological photonics. Furthermore, silicon-based BIC metasurfaces can utilize existing high-precision, mass-production-capable fabrication processes using CMOS processes. In addition, due to their characteristic of using resonance based on the periodic structure of relatively large nanostructure arrays, BIC metasurfaces do not require precise alignment. [Brief explanation of the drawing]

[0014] [Figure 1A] This is a conceptual diagram, shown in perspective, of a single unit of a pair-rod type shallow-cut BIC metasurface with different longitudinal lengths, illustrating one embodiment of the present invention. [Figure 1B] This is a conceptual diagram showing a yz cross-sectional view of a single unit of a pair-rod type shallow-cut BIC metasurface with different longitudinal lengths, illustrating one embodiment of the present invention. [Figure 2] Figure 1 shows a yz cross-sectional view of the electric field of a single unit of a pair-rod type shallow-cut BIC metasurface with different longitudinal lengths. [Figure 3A] The images show typical spectra and Q values ​​of shallow-cut BIC metasurfaces, with (a) showing etching depth t=82.7nm, (b) showing t=116.1nm, and (c) showing t=149.5nm. [Figure 3B] This shows a typical spectrum and Q-value of a shallow-hole BIC metasurface, specifically the case where the Q-value is 1.0 × 10⁵. [Figure 4] The measured Q values ​​(black plotted points) for BIC metasurfaces with different etching depths t are shown, along with the fitting curves obtained from Q-1 = Qr -1 + Qnr -1. [Figure 5A] This is a conceptual diagram of a single unit of a pair-rod type shallow-cut BIC metasurface with varying widths, illustrating one embodiment of the present invention, and showing a two-layer structure consisting of an insulating layer and a waveguide. [Figure 5B] This is a conceptual diagram of a single unit of a pair-rod type shallow-cut BIC metasurface with varying widths, illustrating one embodiment of the present invention, and showing a three-layer structure of substrate, insulating layer, and waveguide. [Figure 6] This diagram shows a conceptual representation of a single unit of a pair-rod type shallow-cut BIC metasurface arranged at different angles, illustrating one embodiment of the present invention. [Figure 7] This diagram shows a conceptual image of a single unit of a nanostructured shallow-cut BIC metasurface, in which a circle or square is cut out slightly off-center, illustrating one embodiment of the present invention. [Figure 8] This diagram shows a conceptual representation of a single unit of nanopillar-type shallow-excavated BIC metasurfaces arranged opposite each other with varying sizes and ellipticities, illustrating one embodiment of the present invention. [Figure 9] This diagram shows a conceptual image of a single unit of a crescent-shaped nanopillar type shallow-excavated BIC metasurface, illustrating one embodiment of the present invention. [Figure 10] This diagram shows a comparative conceptual diagram of BIC and quasi-BIC for a single unit of shallow-cut BIC metasurfaces of various shapes. [Modes for carrying out the invention]

[0015] In this invention, a dielectric nanostructure array based on the principle of BIC is used, in which shallow nanostructures are formed in a high refractive index dielectric layer. In this specification, the upper and lower limits are considered to be within a numerical range unless otherwise explicitly stated. That is, the upper limit to the lower limit means greater than or equal to the lower limit and less than or equal to the upper limit.

[0016] This invention proposes a structure that increases the Q factor of resonance modes and enhances the interaction between light and matter by introducing shallow-cut nanostructures into the unit cell of a metasurface made of a high refractive index dielectric material, such as silicon. While quasi-BIC modes are confined within the high refractive index silicon, the introduction of shallow-cut nanostructures allows electromagnetic fields to seep outside the silicon, i.e., into the air, for certain modes, thus interacting with the external medium. Metasurfaces with high Q factors exhibit small fluctuations in resonance wavelengths, enabling stable measurement of resonance peaks.

[0017] Therefore, a quasi-BIC metasurface structure with an optimized line of detection (LOD) in the refractive index sensor was determined through numerical calculations, and then a nanostructure array using this quasi-BIC metasurface structure was fabricated based on the results of these numerical calculations. This numerical calculation is based on the description in Non-Patent Document 4, and refers to the following documents specifically listed as references 22-26 in Non-Patent Document 4.I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express 16(2), 1020 (2008). S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569-572 (2003). K. Saurav and N. Le Thomas, “Probing the fundamental detection limit of photonic crystal cavities,” Optica 4(7), 757 (2017). 5X. Zhou, L. Zhang, and W. Pang, “Performance and noise analysis of optical microresonator-based biochemical sensors using intensity detection,” Opt. Express 24(16), 18197-18208 (2016). T. J. Seok, A. Jamshidi, M. Kim, S. Dhuey, A. Lakhani, H. Choo, P. J. Schuck, S. Cabrini, A. M. Schwartzberg, J. Bokor, E. Yablonovitch, and M. C. Wu, “Radiation engineering of optical antennas for maximum field enhancement,”Nano Lett. 11(7), 2606-2610 (2011).。

[0018] In a refractive index sensor, for the asymmetry imparted to the structure by the BIC metasurface, its Q value and SNR or the amplitude of the resonance mode are in a trade-off relationship, making it difficult to intuitively predict the conditions for the optimal structure. Therefore, the optimal structural conditions were predicted by considering the conditions that minimize the refractive index resolution to be detected.

[0019] The detection limit (LOD) in a refractive index sensor is given by the following equation. LOD = δλ / S (1) Here, δλ is the resonance peak wavelength fluctuation. To derive the parameters on which LOD depends, first, the relationship between the wavelength fluctuation δλ and the amplitude fluctuation δA is derived. Here, the reflection amplitude A(λ0, λ) of the resonance mode derived from the Temporal coupled-mode theory (TMCT) is considered.

Equation

Equation

Equation

Equation

[0020] Here, δA| δλ An approximation of / A << 1 is used. The actual amplitude variation includes other external noise sources, and is the sum of the contributions of relative intensity noise, shot noise, and Johnson noise, but here the wavelength variation δA| δλ To focus on the amplitude fluctuations caused by the noise source, we consider two factors δA| δλ and all other noise sources δA| O It is separated into two parts. This separation can be expressed by the following equation.

number

number

[0021] Next, numerical calculations were performed to predict the spectral characteristics of the BIC metasurface with the optimal structural conditions described above. The time-domain finite difference method (FDTD) was used to obtain the spectral characteristics. Here, Bloch boundary conditions were set in the x and y directions, and PML was set in the z direction, and an x-polarized plane wave was incident perpendicularly. The Q value was calculated using the frequency-domain finite element method, by applying Q = Re(f) / 2Im(f) to the complex natural frequency f. [Examples]

[0022] To experimentally verify the above theory, as Example 1, a silicon metasurface consisting of the rod pair shown in Figures 1A and 1B was fabricated. Figure 1 is a conceptual diagram of a single unit of a pair-rod type shallow-cut BIC metasurface with different longitudinal lengths, illustrating one embodiment of the present invention. Figure 1A is a perspective view, and Figure 1B is a cross-sectional view in the yz direction.

[0023] The manufacturing process followed the steps outlined below. The silicon metasurface was fabricated on a silicon-on-insulator (SOI) wafer with a silicon thickness of 400 nm and an embedded oxide film thickness of 2000 nm. The SOI wafer was first cleaned by organic cleaning and O2 plasma treatment, and then approximately 100 nm of positive electron beam resist ZEP520A (manufactured by Nippon Zeon) was spin-coated, followed by the antistatic agent ESPACER300Z (manufactured by Showa Denko). Subsequently, a nanopattern was formed using an electron beam (EB) lithography system at an acceleration voltage of 100 kV. After development, the resist pattern was transferred to the silicon layer using the BOSCH process consisting of SF6 and C4H8 gas. Residual resist was removed by O2 plasma treatment. The BOSCH process is a dry etching technology that achieves high-speed and high-aspect-ratio vertical deep etching of silicon by repeating three steps: (a) isotropic etching of Si, (b) deposition of a protective film, and (c) anisotropic etching of Si (removal of the protective film on the bottom surface). SF6 is mainly used for etching and C4F8 for the protective film, enabling highly anisotropic etching while maintaining a high selectivity ratio.

[0024] Next, we will describe the structure of a single unit of the fabricated pair-rod type shallow-drilled BIC metasurface. In the figure, the dielectric nanostructure array based on the BIC principle is also called a metasurface and has a three-layer structure consisting of a silicon substrate 10, silicon dioxide (SiO2) 12, and a metasurface 14. The silicon film thickness of the metasurface 14 is H+h and it has shallow waveguides 16a and 16b on its surface, with a depth of h. The depth h of this shallow cutting is preferably in the range of 25 nm to 200 nm, more preferably in the range of 50 nm to 100 nm, and most preferably in the range of 80 nm to 100 nm. These waveguides 16a and 16b are roughly rectangular paired rods with a longitudinal length L±2ΔL, width W, and height (depth) h. The silicon dioxide (SiO2) 12 is an insulating film.

[0025] Figure 2 shows the results of simulating the electric field distribution |E| at the resonance peak wavelength of the quasi-BIC mode using the FDTD method. This quasi-BIC mode is based on a higher-order mode, and it can be seen that the electric field is strongly localized within the silicon. This localized electric field is further enhanced by the resonance enhancement effect of the quasi-BIC, resulting in a strong electric field enhancement effect. The localized electric field slightly permeates into the external medium in the shallowly etched nanostructure, and the interaction between light and matter increases in this region.

[0026] To measure the spectral characteristics of the fabricated BIC metasurface, the reflected or transmitted spectrum was measured using a custom-made optical system consisting of a tunable-wavelength laser and an InGaAs photodiode. While confirming the position with an infrared camera, the laser beam was focused onto the metasurface through a 10x objective lens. This reflected or transmitted light was detected again on the InGaAs photodiode through the objective lens. Polarizing plates were positioned perpendicularly to both the incident and detection sides to suppress background noise. The spectrum was obtained by sweeping the wavelength of the tunable-wavelength laser from 1510 nm to 1630 nm. The Q-factor and peak wavelength of the resonance mode were determined by fitting the spectrum with a Fano function.

[0027] Furthermore, there are various options for the metasurface material as long as it is a high refractive index dielectric material that confines light, and the present invention can be applied to any material such as silicon, germanium, gallium arsenide, and silicon nitride. A high refractive index refers to a value of 2.0 or higher. For example, at the wavelength of a helium-neon laser, 632.8 nm, the refractive index is 3.882 for silicon, 5.477 for germanium, 3.857 for gallium arsenide, and 2.023 for silicon nitride. The layered structure of the substrate forming the nanostructure can be made of various materials, including not only SOI (Silicon on Insulator) wafers as shown in Figures 1A and 1B, but also low refractive index quartz substrates and calcium fluoride substrates. Here, SOI is a technology that improves the speed and low power consumption of CMOS LSIs. Furthermore, in the field of nanophotonics, low refractive index dielectric materials are used as insulating films, so inorganic solid insulating materials can be used. Examples of low refractive index materials include borosilicate glass, quartz glass, sapphire, and calcium fluoride. A low refractive index means that it is lower than the refractive index of a high refractive index dielectric material, for example, less than 2.0. At the wavelength of a helium-neon laser, 632.8 nm, the refractive index is 1.514 for borosilicate glass, 1.457 for quartz glass, 1.770 for sapphire, and 1.433 for calcium fluoride.

[0028] In the embodiment of the present invention, a higher-order mode with two antinodes of the electric field mode was used as shown in Figure 2. However, in principle, in addition to the fundamental mode with one antinode of the electric field mode, even higher-order modes can also be used. Therefore, the resonance wavelength of a quasi-BIC is typically set in the 1000nm to 1675nm range used in optical fiber communication, but the wavelength range may be further extended to the near-infrared wavelength range of 780nm to 2500nm. The optical communication wavelength band refers to the wavelength range used when performing optical communication. Optical communication is a communication method that transmits signals using light, and optical fibers are used as the transmission path. Therefore, because transmission losses in optical fibers must be taken into consideration, optical communication uses a very narrow wavelength range of 1000 nm to 1675 nm within the range of electromagnetic waves.

[0029] Furthermore, this wavelength band is subdivided into the following bands, from shortest to longest wavelength: T-band (Thousand-band) for 1000-1260 nm, O-band (Original-band) for 1260-1360 nm, E-band (Extended-band) for 1360-1460 nm, S-band (Short-wavelength-band) for 1460-1530 nm, C-band (Conventional-band) for 1530-1565 nm, L-band (Long-wavelength-band) for 1565-1625 nm, and U-band (Ultralong-wavelength-band) for 1625-1675 nm.

[0030] The C-band has high light transmittance, and with the development of ultra-long-distance transmission, erbium-doped optical fiber amplifiers (EDFAs), and wavelength division multiplexing (WDM) technology, this wavelength band has been widely used. However, with the development of advanced information technology and IT, the amount of information to be transmitted has become enormous, and this wavelength band alone is becoming saturated. Research is underway to utilize other wavelength bands that can be used for optical communication. The O-band is called the Original-band because it has been used since the dawn of optical communication, and it is characterized by low signal dispersion (low signal distortion). However, there are many technical challenges in optical fiber amplifiers that can handle O-band and S-band wavelengths, and few have been put into practical use. Due to the high transmission loss in optical fibers, long-distance transmission is difficult in the T-band, E-band, and U-band wavelength ranges, resulting in less active product development, and technologies using these wavelength ranges in optical information communication have not been put into practical use. However, it is certain that the amount of information will become even more enormous in the future, and it is quite possible that the wavelength ranges currently in use will become saturated. Therefore, research is being conducted on useful applications of optical communication in medium- and short-distance transmission using these wavelength ranges. The E-band includes the water absorption wavelength of 1450nm, resulting in high attenuation.

[0031] In this configuration, the effect of scattering loss is minimized by creating a shallow-etched structure with a nanostructure etching depth of 25 nm to 200 nm, thereby minimizing the overlap between the localized electric field in the light confinement region and the sidewalls of the nanostructure. This significantly increases the experimental Q value. In contrast, light confined within a typical nanostructure has the problem that its localized electric field overlaps with the sidewalls of the surrounding nanostructure. This causes the light to be scattered by surface roughness of the nanostructure sidewalls that occurs during fabrication, resulting in a decrease in the experimental Q-factor.

[0032] Figure 3A shows representative spectra of shallow-etched BIC metasurfaces compared at different etching depths, where (a) is with an asymmetry parameter α=3%, (b) is with α=4%, and (c) is with α=5%. Here, the asymmetry parameter α is the asymmetry parameter α (α=2ΔL / L) added to the unit structure of the BIC metasurface. Here, L is the reference length of the pair rod, and ΔL is the asymmetric length of the other pair rod constituting the single unit structure. The length of one pair rod constituting the single unit structure is L+2ΔL, and the length of the other pair rod is L-2ΔL. In shallow-cut BIC metasurfaces, the amount of radiation loss can be controlled according to the asymmetry parameter α, but here, for each etching depth, the radiation Q value Q r and non-radiative Q value Q nrStructural parameters near the critical coupling conditions where the two values ​​coincide were selected and compared. The experimental Q value increased as the etching depth decreased, and in Figure 3(a), the resonance wavelength was 1561.3 nm and Q = 4.5 × 10⁻⁶. 4 In (b), the resonant wavelength is 1548.0 nm and Q = 1.9 × 10⁻⁶. 4 In (c), the resonant wavelength is 1524.3 nm and Q = 4.2 × 10⁻¹⁰ 3 This was the case. This is thought to be because, when the etching depth is shallow, the surface area relative to the volume of the structure is small, and the scattering loss of the nanostructure sidewalls is reduced. Figure 3B shows a typical spectrum and Q-value of a shallow-drilled BIC metasurface, with a Q-value of 1.0 × 10⁻¹⁰ when the asymmetry parameter α = 1%. 5 This illustrates the case.

[0033] Figure 4 shows the measurement results of Q values ​​for BIC metasurfaces with different etching depths, with the asymmetric parameter α on the horizontal axis. The curves that overlap the plotted points are the fitting curves obtained from the following equation. Q -1 =Q r -1 +Q nr -1 (6) (However, Q r Q is the calculated radiation Q value. nr (This is the experimentally determined non-radiative Q value.) To obtain a large Q-factor, it is necessary to reduce α, but the upper limit of the Q-factor increases as the etching depth decreases, and the experimental Q-factor also increased. The maximum Q-factor obtainable by nanofabrication is 1 × 10⁻⁶ when using silicon. 5 〜1×10 6 It is known that this is the case, and a Q value that roughly corresponds to its upper limit was experimentally obtained.

[0034] In another embodiment of the present invention, a dielectric nanostructure array based on the principle of BIC is used, in which waveguides with a height h (25 nm to 200 nm) of about 1 / 64 to 1 / 8 of the resonant wavelength λ (in the range of 400 nm to 2000 nm, for example 1600 nm) are formed in a high refractive index dielectric layer in which light is confined. [Examples]

[0035] Figure 5A is a conceptual diagram of a single unit of a pair-rod type shallow-cut BIC metasurface with varying widths, illustrating one embodiment of the present invention, and showing a two-layer structure of an insulating layer and a waveguide. In the figure, the dielectric nanostructure array based on the BIC principle, also called a metasurface, has a two-layer structure of silicon dioxide and silicon, and includes silicon dioxide (SiO2) 12, a thin film silicon layer (Si) 14 as silicon, and waveguides 16a and 16b made of silicon (Si). The height h of these waveguides is preferably in the range of 25 nm to 200 nm, more preferably in the range of 50 nm to 100 nm, and most preferably in the range of 80 nm to 100 nm. These waveguides 16a and 16b are roughly rectangular paired rods, with longitudinal length L, width (W1 and W2), and height (depth) h. The silicon dioxide (SiO2) 12 is an insulating film. The film thickness of the thin film silicon layer (Si) 14 is preferably in the range of 200 nm to 375 nm, more preferably in the range of 300 nm to 350 nm, and most preferably in the range of 300 nm to 320 nm.

[0036] Figure 5B is a conceptual diagram of a single unit of a pair-rod type shallow-cut BIC metasurface with varying widths, illustrating another embodiment of the present invention, showing a three-layer structure of substrate, insulating layer, and waveguide. In the figure, the dielectric nanostructure array based on the BIC principle, also called a metasurface, has a three-layer structure comprising a silicon substrate 10, silicon dioxide (SiO2) 12, a thin-film silicon layer (Si) 14, and waveguides 16a and 16b made of silicon (Si). The height h of these waveguides is preferably in the range of 25 nm to 200 nm, more preferably in the range of 50 nm to 100 nm, and most preferably in the range of 80 nm to 100 nm. These waveguides 16a and 16b are roughly rectangular paired rods, with longitudinal length L, width (W1 and W2), and height (depth) h. The silicon dioxide (SiO2) 12 is an insulating film. The film thickness of the thin-film silicon layer (Si) 14 is preferably in the range of 200 nm to 375 nm, more preferably in the range of 300 nm to 350 nm, and most preferably in the range of 300 nm to 320 nm. [Examples]

[0037] Figure 6 shows a conceptual diagram of a single unit of a pair-rod type shallow-cut BIC metasurface arranged at different angles, illustrating one embodiment of the present invention. The single unit of the shallow-cut BIC metasurface in this embodiment has a two-layer structure of silicon dioxide and silicon, and as shown in Figure 5A, it has silicon dioxide (SiO2) 12, a thin film silicon layer (Si) 14 as silicon, and waveguides 16a and 16b made of silicon (Si). The inclination angles of the paired rod shapes, positioned at different angles, are θ=0° (left), θ=10° (center), and θ=20° (right), respectively. The dashed rectangles indicate the contours of the unit cells of each metasurface. The white scale bar represents 1 μm. [Examples]

[0038] Figure 7 shows a conceptual diagram of a single unit of a nanostructured shallow-cut BIC metasurface, which has circles or squares cut out slightly off-center, illustrating one embodiment of the present invention. Figure 7(a) shows the trapping modes in an array of dielectric nanodiscs with asymmetric holes, Figure 7(b) shows sharp trapping mode resonances in plasmonic and dielectric split ring structures, Figure 7(c) shows symmetry-broken fanometasurfaces that enhance nonlinear effects, and Figure 7(d) shows the trapping light and metamaterial-induced transparency in an array of square split ring resonators. [Examples]

[0039] Figure 8 shows a conceptual diagram of a single unit of nanopillar-type shallow-excavated BIC metasurfaces arranged opposite each other with varying sizes and ellipticities, illustrating one embodiment of the present invention. Figure 8 shows a diatomic dielectric metasurface supporting a high-quality coefficient quasi-BIC resonance. (a) is a scanning electron microscope (SEM) image of the fabricated dielectric metasurface, which was coated with a thin layer of Electra, a carbon-based conductive polymer, to prevent charging during SEM imaging. (b) is a top view of a metaunit composed of elliptical (major and minor axes of 180 nm and 100 nm, respectively) and cylindrical (radius of 90 nm) amorphous Si resonators, and (c) is a side view.

[0040] Figure 8(a) shows a scanning electron microscope (SEM) image of a resonator fabricated by nanostructuring 100 nm thick amorphous silicon (a-Si) on a fused silica substrate using a top-down manufacturing method with CMOS-compatible technology. Silicon was chosen as the constituent material due to its biocompatibility, established surface biofunctionalization methods, and access to mature CMOS manufacturing facilities. Furthermore, silicon possesses desirable optical properties, such as a high refractive index and relatively low loss in the near-infrared region below 850 nm. The metasurface operates in an aqueous medium and resonates in the visible and near-infrared spectral range (600 nm to 850 nm). Operating in this range offers several unique advantages, including the widespread availability of high-performance, cost-effective silicon-based CMOS and CCD cameras. The fabrication used a design with the geometric parameters shown in Figure 8(b), which corresponds to an ellipticity of 0.44. [Examples]

[0041] Figure 9 shows a conceptual diagram of a single unit of a crescent-shaped nanopillar type shallow-excavated BIC metasurface, illustrating one embodiment of the present invention. Figure 9(a) shows a sketch of a unit cell with crescent-shaped metaatoms on a fused silica (SiO2) substrate. Figure 9(b) shows a lateral HR-SEM image of the fabricated silicon crescent-shaped metasurface, a close-up image of the resonator, and the simulated near-field distribution (inset).

[0042] The all-dielectric silicon crescent meta-surface is fabricated on a fused silica substrate by a standard top-down approach involving a series of steps: positive-type resist electron beam lithography and reactive ion etching. Figure 9(a) schematically shows a crescent meta-atom, defining a unit cell of the meta-surface with periodicity in the x-direction (Px) and y-direction (Py). The footprint of the crescent meta-atom is represented by two circles, as shown in Figure 9(a), where the first circle with radius R2 trims the area of ​​the second circle with radius R1 (Figure 9(a)). The result is the proposed crescent shape. The width (W) of this crescent shape is kept constant at a value of R1 / 3. The exact values ​​of W, Px, and Py are kept the same throughout this process. The values ​​of the aperture angle θ shown in Figure 9(a) are adjusted to correct for the asymmetry of the crescent meta-atom. Therefore, changing the radius of R2 simultaneously changes θ. The thickness of the amorphous silicon film deposited by plasma-enhanced chemical vapor deposition (PECVD) controls the height (h) of the crescent-shaped metaatom. Figure 9(b) shows a high-resolution scanning electron microscope (HR-SEM) side view of a fabricated all-dielectric crescent-shaped meta surface with high structural fidelity and homogeneity.

[0043] Figure 10 shows a comparative conceptual diagram of BIC and quasi-BIC for a single unit of shallow-cut BIC metasurfaces of various shapes. Metasurfaces based on quasi-BIC can have various structures, including not only pair rods of different longitudinal lengths as shown in Figure 1, but also pair rods of varying widths as shown in Figure 5, pair rods arranged at different angles as shown in Figure 6, nanostructures with circles or squares cut out slightly off-center as shown in Figure 7, nanopillars of varying sizes and ellipticities arranged opposite each other as shown in Figure 8, and crescent shapes as shown in Figure 9, among many other variations. The present invention can be applied to any BIC metasurface.

[0044] In the above embodiments, in Example 1 shown in Figures 1 to 4, the case of rod-shaped waveguides formed by shallow etching on a thin-film silicon layer 14 which is a metasurface was shown as the light confinement regions 16a and 16b. However, the present invention is not limited to this. In the present invention, in Examples 2 to 6 shown in Figures 5 to 10, a thin-film silicon layer is provided on an insulating layer, and a waveguide is provided on the thin-film silicon layer, and waveguides of various shapes with a height corresponding to the etching depth of the shallow etching structure may also be provided.

[0045] Furthermore, in the case of refractive index sensing applications, Equation 5 shows that the detection limit LOD is minimized under conditions that satisfy the critical coupling condition, and in the case of the structure of Example 1 shown in Figures 1 to 4, it is indeed shown that the performance of the refractive index sensor is maximized when the asymmetry parameter α is around 2% to 5%. Here, the asymmetry parameter α of the pair rods or nanopillars constituting the waveguide is defined by the asymmetry parameter α (α = 2ΔL / L) using the asymmetric length (ΔL) of the other pair rod constituting the single-unit structure with respect to the reference length (L) of the pair rod. Changing the asymmetry parameter α changes the length of the upper and lower pair rods, but it does not change the depth of the shallow trench structure. However, in structures that increase the interaction between light and matter, it is known that the conditions for the asymmetric parameter α that satisfy the critical coupling condition vary greatly depending on the thickness and material of the light confinement layer and insulating layer. Therefore, in Example 1 shown in Figures 1 to 4, the maximum Q value was obtained when h was 82.7 nm for the fabricated silicon metasurface, but the conditions for the optimal etching depth h may also change if the shape and material of the single-unit structure change. [Industrial applicability]

[0046] The nanostructure array of the present invention is applicable to a variety of applications requiring strong light-matter interactions, and has industrial potential for use in optical devices, nonlinear amplification, sensors, non-Hermitian systems, and topological photonics. [Explanation of symbols]

[0047] 10 Silicon substrate 12. Inorganic solid insulating layer (SiO2) 14. Thin-film silicon layer (thin-film high-refractive-index dielectric layer) 16a, 16b Waveguides (regions of light confinement)

Claims

1. Inorganic solid insulating layer, This comprises a waveguide made of a high refractive index dielectric material that confines light, which is laminated on top of this inorganic solid insulating layer. The waveguide is configured as an array having a pair rod or nanopillar as a single unit, which is configured to have a shallow-etched structure in which the etching depth of the light confinement region is in the range of 25 nm to 200 nm. The inorganic solid insulating layer and the shallow trench structure forming the side wall of the waveguide are located in the region opposite each other, and the thin film high refractive index dielectric layer is located therein. The aforementioned light confinement region has a resonance wavelength of 1.0 × 10 in the quasi-bound state of the continuum. ３ Exceeding 1.0 × 10 ６ The following Q values ​​are observed: Nanostructure arrays using quasi-bound states in a continuum.

2. Furthermore, the substrate having the inorganic solid insulating layer laminated on it, The nanostructure array according to claim 1.

3. The nanostructure array according to claim 2, wherein the substrate is one of an SOI (Silicone on Insulator) wafer, a quartz substrate, or a calcium fluoride substrate.

4. The aforementioned light confinement region is, Pair of rods with different lengths in the longitudinal direction, Pair rods with different widths, Pair rods arranged with different inclination angles for opposing pair rods, Nanostructures in which circles or squares are cut out, slightly off-center. Nanopillars arranged opposite each other, with varying sizes and degrees of ellipticity. Nanopillars arranged in a crescent shape, The nanostructure array according to claim 1, which is any one of the above.

5. The nanostructure array according to claim 1, wherein the high refractive index dielectric material is selected from silicon, germanium, gallium arsenide, and silicon nitride.

6. The nanostructure array according to claim 1, wherein the resonance wavelength of the quasi-bound state in the continuum is at least one resonance wavelength included in the range of 400 nm to 2000 nm.

7. The nanostructure array according to claim 1, wherein the etching depth of the light confinement region is in the range of 50 nm to 100 nm.

8. The nanostructure array according to claim 1, wherein the thickness of the thin film high refractive index dielectric layer is in the range of 300 nm to 350 nm.

9. The nanostructure array according to claim 1, wherein the light confinement region has a quasi-BIC metasurface structure that minimizes the superposition between the localized electric field in the light confinement region and the sidewall portion of the waveguide.

10. The nanostructure array according to claim 1, wherein the array is selected from the group consisting of one-dimensional arrays and two-dimensional arrays.

11. The nanostructure array according to claim 1, wherein the inorganic solid insulating layer is selected from the group consisting of borosilicate glass, quartz glass, sapphire, and calcium fluoride.

12. An optical device, a medical sensor, a sensor for optical communication, a nonlinear augmentation sensor, a non-Hermitian photonic, or a topological photonic having the apparatus described in any one of claims 1 to 11.

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