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Abstract
Laser-guided detector and infrared detection have attracted increasing attention in a wide range of research fields, including multispectral detection, radiative cooling, and thermal management. Previously reported absorbers presented shortcomings of lacking either tunability or compatibility. In this study, a metamaterial perfect absorber based on a Helmholtz resonator and fractal structure is proposed, which realizes tunable perfect absorptivity $\left(\alpha_{1.06 \mu \mathrm{m}}>0.99, \alpha_{10.6 \mu \mathrm{m}}>0.99\right)$ of guided-laser radar dual operating bands (1.06 µm and 10.6 µm) and a low infrared average emissivity (${\bar{\varepsilon }_{3 - 5{\mathrm{\mu} \mathrm{m}}}} = 0.03,\; {\bar{\varepsilon }_{8 - 14{\mathrm{\mu} \mathrm{m}}}} = 0.31$) in two atmospheric windows for compatible camouflage. The proposed perfect absorber provides a dynamically tunable absorptivity without structural changes and can be applied to optical communication, military stealth or protection, and electromagnetic detection.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterial (MM), phase change material (PCM), and, more recently, micro/nanostructures are used to manipulate electromagnetic (EM) waves [1,2,3,4]. These novel materials have properties that are not present in traditional materials and have, therefore, attracted significant research interest. Several meaningful applications have been reported in various fields, such as in the design of metalens [5,6], polarization converters [7,8], and perfect absorbers [9,10,11] for sensor imaging technology [12], stealth camouflage [13,14,15], and perfect absorption [16]. These technologies have widely used in various frequency bands, including microwave [9,9,17], millimeter-wave [18,19,20], terahertz [21,22], infrared [23,24], and visible light [25] bands. Among them, since 1.06/1.55 µm and 10.6 µm are the operating wavelengths of laser-guided detector and CO2 laser radar, we may call this wavelength as the “guided-laser radar” wavelength. In these applications, the design of highly absorbent MMs plays a key role in manipulating light at selected frequencies for EM stealth and perfect absorption. Currently, most MM absorbers are only able to work in a single band with a narrow bandwidth. Therefore, achieving dual- or multi-band high absorption and broadband absorption is a major challenge in the development of novel absorbers.
To achieve a high absorption response for dual bands, the most critical parameter of the absorber is the frequency ratio (Fu/Fl), where Fu and Fl are the higher and lower center frequencies of the absorption bands, respectively. If this ratio is excessively high, it is impossible to simultaneously cover two absorption bands with one broadband structure. In this case, special micro/nanostructures must be designed for MM absorbers to achieve a high absorption response for dual bands [26,27]. A Helmholtz resonator, traditionally an acoustic device used to select a single frequency, is extremely useful in electromagnetism [28,29,30]. For example, an EM two-dimensional Helmholtz resonator made of a metal slit box structure can achieve high absorption of a single frequency through a Helmholtz resonance similar to the LC (inductor L and capacitor C) resonance form.
A fractal structure is a unique self-similar structure, which can be introduced in MMs for EM manipulation [31,32,33,34]. Because of their space-filling and self-similar geometry, fractal structures are used in many fields to obtain the characteristics of broadband frequencies, as well as for miniaturization and integration, specifically for the decrease in size of network devices [35,36,37,38] and the Pythagorean-tree fractal meta-absorber [39]. In EM, their repeated patterns can generate multiple resonance reactions, thus providing a structural basis for the design of optical devices to achieve wideband absorption. This can be used to achieve wideband high absorption through monolayer metasurfaces.
As EM waves propagate without any medium, thermal radiation is the only possible method of heat transfer in a vacuum. Studies have reported that in the process of thermal radiation transmission when the size of a target object is close to or less than the characteristic wavelength of the corresponding band, the designed micro/nanostructures of MMs ensure that the target exhibits adequate thermal radiation spectral selectivity [40]. With advances in numerical simulations and manufacturing of micro/nanostructures over the last decade, the local plasmon resonance excited by nanogaps has been the subject of extensive research. Plasmonic micro/nanostructures have been used in various applications, such as solar steamships [41,42], metal-insulate-metal (MIM) structures, radiant coolers [43,44,45], and various military thermal camouflage technologies. In the polarization resolution spectrum, the high-amplitude absorption peaks of discrete wavelengths appear in nanogaps with different plasmonic modes. To achieve thermal camouflage or laser stealth, the emissivity of a structure must be tuned to the appropriate band. However, the excitation of these interstitial plasmonic modes and selective spectral camouflage are closely related to the shape, size, and period of the corresponding micro/nanostructures. When a micro/nanostructure is manufactured, its function, the band suitable for camouflage, and other applications are set and remain fixed. Therefore, in the same micro/nanostructure, it is necessary to realize the perfect absorption of multi-function dynamic tunability without changing specific parameters of the structure (thickness, width, period, and shape) for stealth camouflage.
Herein, Helmholtz resonance and fractal technology are combined along with a phase-changing material Ge2Sb2Te5 (GST) to couple metal nanogaps with micro/nano structures. We propose a multi-combination structure of a fractal structure (made of Au)-Al2O3-GST-Helmholtz resonance cavity (made of Si)-Au with the Helmholtz resonance cavity as the base and the metal fractal structure as the top layer. Unlike other absorbers that only allow for single-band absorption and tunability, we designed a perfect absorber with a fractal structure, Helmholtz resonator, and GST to improve performances. The characteristics of MMs and PCMs are used to overcome these shortcomings of traditional absorbers and provide an adequate foundation for future practical applications and integration. The proposed material design has the advantage of dual-frequency high absorption, compatible camouflage, dynamic tunability, and polarization insensitivity. It can be applied to military camouflage, energy conservation, environmental protection, and communication detection.
2. Structure and method
Figure 1 shows the unit cell geometric model and periodic structure of the proposed MM perfect absorber under working conditions. This multi-combined structural unit consists of five layers, as shown in Fig. 1(a). From top to bottom, these are the periodic metal (Au) fractal structures, Al2O3, GST, the Helmholtz resonator (Si) of the top metasurface, and Au metal wrapped around the bottom layer. The bottom structure is a two-dimensional Helmholtz resonator that extends indefinitely in the y-direction. The slits and boxes were filled with silicon and surrounded by gold. Perfect absorption was achieved via the resonance generated by the Helmholtz resonator that was filled with dielectric silicon. To investigate the EM response of the structure, after modeling and optimization using numerical simulations performed in COMSOL Multiphysics 5.6, a commercial Multiphysics simulation software, the optimal structural parameters obtained were as follows: TAu1 = 10 nm, TAl2O3 = 28 nm, TGST = 18 nm, TSi = 22 nm, and TAu2 = 300 nm. As indicated in Fig. 1(b), the period, Q, of the fractal structure of the top metal pattern layer is 1150 nm, the side length, L, of the first-order fractal structure is 160 nm, and the side lengths of the second- and third-order fractal structures are 2/3 L and 1/3 L, respectively. As shown in Fig. 1(c), the internal geometry of the slit and box of the Helmholtz resonator is Wa = 90 nm, Ta = 40 nm, Wh = 450 nm, and Th = 235 nm. T and W are the thickness and width of each material, respectively.
Fig. 1. Schematic of the proposed geometric model of a tunable perfect absorber. (a) Three-dimensional view of the unit cell structure. (b) Top view. (c) Side view. (d) Three-dimensional view of periodic multi-composite structures.
To evaluate the function of the proposed device, the finite element method (FEM) was used for analysis. In the simulation, three-dimensional structure was modeled, and TE-mode plane wave was used as excitation light. The linear-polarized wave generated by the port was incident to the cell structure and its reflected wave was received by the two-dimensional power monitor. The infinite array was modeled using periodic boundary conditions, and the unit cell of the proposed device is shown in Fig. 1(a). The simulation time is about 12 hours. Periodic boundary conditions were selected in the x and y-axis directions, and open boundary conditions were set in the z-axis direction, which greatly shortened the calculation time, and contributed to the full-wave simulation. The absorption rate $A\textrm{(}\lambda \textrm{)}$ of the absorber is calculated as follows:
where $R(\lambda )$ and $T(\lambda )$ are the reflectivity and transmittance, respectively. It follows from Eq. (1) that to increase the absorption rate, the reflectivity and transmittance should be reduced as much as possible. In the EM simulation, we consider the metal film to be the perfect electric conductor, with a transmittance of zero, so the absorption rate of the perfect absorber is $A(\lambda) = 1 - R(\lambda) $.The material parameters used in the structural design of the absorber unit were obtained from relevant studies: the dielectric constants of gold and silicon were taken from E. D. Palik et al. [46]; the refractive index and extinction coefficient of GST were taken from M. Wuttig et al. [47]; and the parameters of Al2O3 were derived from the research of M. R. Querry [48]. We discuss the description of fabrication steps in Supplement 1.
3. Results and discussion
3.1 Perfect absorption for tunable, polarization-insensitive, and wide-angle absorption in dual-band guided-laser
Nowadays, light detection and ranging (LiDAR) has become an important tool in military detection and laser guidance, owing to the rapid development of laser technology. Due to advances in optical detection systems, the utilization of visible light (400−780 nm), infrared (3−5 µm and 8−14 µm), guided-laser (1.064 µm and 10.6 µm), and other compatible camouflage or stealth have become an important goal in military research [49,50,51,52]. In the defense field, improvements in the detection accuracy of guided-laser techniques used in weapon systems increased the probability of a particular target being destroyed. Therefore, it is of considerable strategic importance to protect targets from being locked using guided-laser stealth. These types of “laser detection” and “laser stealth” are analogous to a spear and shield, respectively. Currently, the laser operating band is concentrated at 1.06 and 10.6 µm. To achieve guided-laser stealth, it is necessary to reduce the reflectivity of the target surface in the laser operating band such that the detection laser does not receive the signal reflected by the target. This reduces the probability of the target being locked.
At present, the methods commonly used for experimental verification of LiDAR camouflage are mainly: emitting laser through CO2 laser device, extracting reflected light through ZnSe beam splitter, and then collecting data by power meter [52]. At the same time, taking the 1.06 µm laser emitter as an example, we can use the point cloud data [53,54] obtained from the laser to simulate the camouflage performance of the proposed photonic structure [55]. In order to further characterize the camouflage performance of this photonic structure in guided-laser radar more clearly, we have added detailed explanations and supplements in the Supplement 1.
Different from the principle of guided-laser camouflage, infrared camouflage aims to reduce the infrared emissivity of the object as much as possible so that the radiation intensity of the target and the background are similar, and the infrared detector can’t distinguish between the two. According to Kirchhoff’s law, $\alpha = \varepsilon $, under the condition of thermal equilibrium, the infrared absorptivity ($\alpha $) of the surface is equal to the infrared emissivity ($\varepsilon $) of the object [56,57]. However, increasing the absorption rate of the target surface in the 10.6 µm laser band will inevitably increase the absorption rate in the 8−14 µm infrared band. Therefore, targets with a high absorption/radiation at 8−14 µm are easily detected using an infrared detector, which conflicts with infrared stealth. This renders it challenging to achieve multi-band compatible stealth in the 10.6 µm laser band and the 8−14 µm infrared band [58]. In Fig. 3(a), the dotted box and the short arrow represent the spectrum of infrared band and light detection and ranging (LiDAR) band respectively (the orange dotted box is mid-wave infrared (MWIR: 3-5µm), the purple dotted box is long-wave infrared (LWIR: 8-14µm), and the short arrow is LiDAR operating band (1.06 and 10.6 µm)). And the Ideal design absorption curve (Target Spectral Absorption Figure) is shown in Fig. 3(b).
To study the stealth and camouflage effects of the proposed fractal structure and Helmholtz resonator in different states of phase-changing materials, we simulated the absorption spectra of this multi-combined structure in the crystalline and amorphous GST states using the simulation software, as shown in Fig. 2(a). First, an amorphous GST film was obtained by magnetron sputtering with three targets. At this time, the extinction coefficient of the aGST in the infrared band was nearly zero, which meant that it could be used as a transparent medium in the infrared band. This was then annealed at temperatures above 160 °C (433.15 K) to obtain the crystalline GST. After the cGST was formed, the refractive index and extinction coefficients increased significantly from 4.5 to 6.0 at 1.06 µm, and the extinction coefficient also increased from zero in the mid-infrared band. Because the GST is a nucleation material, which follows a process of gradual crystallization from the beginning to an amorphous state and then to its crystallization point due to an increase in temperature, after which, it gradually becomes crystalline. The stimulation of external factors first induces the aGST to form many small crystal nuclei inside it, and then these nuclei join to form a crystalline structure. The other materials in the device are physically stable due to their high temperature resistance properties. Meanwhile, we only consider the device performance before and after the complete phase transition, so our simulation results are plausible. Therefore, it is theoretically possible to estimate the proportion of crystalline molecules in the GST thin layer using corresponding spectral simulations that estimate the extent of the phase transition of the GST. We assume that the intermediate GST film is composed of amorphous and crystalline molecules in different proportions and that their dielectric constants at wavelength $\lambda $ are ${\varepsilon _{\textrm{aGST}}}(\lambda )$ and ${\varepsilon _{\textrm{cGST}}}(\lambda )$, respectively. Furthermore, we can use several related effective medium theories to estimate the effective dielectric constant ${\varepsilon _{\textrm{GST}}}(\lambda ,C)$ of the GST film in the intermediate state, where C is the crystallization fraction of the GST film, which ranges from 0 to 100% (aGST to cGST). In this study, the Lorentz-Lorenz relation—expressed in Eq. (2)—was used to approximate the effective dielectric constant of the intermediate phase state of the GST [59]. We discuss the influence of the proposed device at different crystallization fractions of GST in Supplement 1.
We used the significant difference between the two states to convert the absorption rate of the GST before and after phase transition. In the aGST state, two perfect absorption peaks of 99.110% and 99.475% were achieved at 1.06 and 10.6 µm, respectively. In the case of the cGST, the corresponding absorptivity decreased to 60.127% and 78.314%, thus realizing the tunable properties of the structure. Furthermore, the perfect absorber was polarization-insensitive to the incident light waves owing to the symmetry of the unit structure. Figure 2(b) and (c) depict the polarization insensitivities in the crystalline and amorphous states obtained through an analysis of the electric field. In the aGST state, there were two significant absorption bands at approximately 1.06 and 10.6 µm. In the cGST state, the absorption band at 1.06 µm exhibited an obvious redshift due to the significant change in the refractive index of the GST before and after phase transformation. However, the change in the polarization angle (from 0 to 90°) in both states did not affect the absorption rate, thus confirming the polarization insensitivity of the structure. In addition, we also evaluated the absorption characteristics of the proposed perfect absorber under changes in oblique incidence angle. Figure 3 depicts the absorption bands of the transverse electric (TE) and transverse magnetic (TM) waves in crystalline and amorphous states, respectively. In Fig. 4(a) and (b), it is obvious that the absorber still maintained the high absorption rates of 1.06 and 10.6 µm across a wide range of incident angles in the aGST state. Regardless of the wave type, the absorption rate reached approximately 90%, even at an oblique incident angle of 70°. We observed similar results for the cGST state, as shown in Fig. 4(c) and (d). Results obtained from a series of simulations were used to verify the effectiveness of the proposed design. The simulations verified that the design can achieve perfect absorption of tunable, polarization-insensitive, and wide-angle absorption of dual-band guided-laser radar wavelength.
Fig. 2. (a) Absorption spectra of the designed tunable perfect absorber in the aGST and cGST states. (b) Relationship between the absorption spectrum and polarization angles when the GST layer is amorphous. (c) Relationship between the absorption spectrum and polarization angles in the crystalline state.
Fig. 3. (a) Schematic diagram of atmospheric transmission spectrum of electromagnetic wave in infrared band, LiDAR absorption band and atmospheric window band. (b) Ideal design absorption curve (Target Spectral Absorption Figure).
Fig. 4. Relationship between the absorption spectra and incident angles of the designed tunable perfect absorber in different states and polarization modes. (a) TE mode in the aGST state. (b) TM mode in the aGST state. (c) TE mode in the cGST state (d) TM mode in the cGST state.
Based on the metal slit box structure of an EM two-dimensional Helmholtz resonator and the multiple resonance phenomenon caused by the high self-similarity of the fractal structure, we were able to achieve high absorption rates at specific wavelengths simultaneously in both the 1.06 µm and 10.6 µm bands. When the GST was amorphous, the perfect absorption at 1.06 and 10.6 µm reached 99.110% and 99.475%, respectively, thus achieving excellent and stable guided-laser radar camouflage at room temperature. Moreover, the GST layer in the structure could be controlled to convert between crystalline and amorphous states by changing the temperature to dynamically adjust the absorption rate of the corresponding band and achieve a tunable versatility of the structure. For example, with the transition of GST from an amorphous state to crystalline state, the absorption rates of 1.06 and 10.6 µm in the guided-laser band are reduced from 99.110% and 99.475% to 60.127% and 78.314%, respectively.
In addition to achieving perfect guided-laser radar stealth, the proposed device is also able to achieve low absorptivity/emissivity at two atmospheric window bands (3-5 and 8-14 µm). The absorptivity in the mid-wave infrared (MWIR) range is 0.0357, and in the long-wave infrared (LWIR) range is 0.3159. It is worth mentioning that the absorptivity in the LWIR range inevitably increases due to the high absorption above 0.99 achieved by the device at 10.6 µm. Except for at 10.6 ± 1 µm, the absorptivity of the device is 0.14 (in the range of 8-9.6 µm) and 0.15 (in the range of 11.6-14 µm), respectively. Following Kirchhoff’s law, the proposed perfect absorber exhibited an extremely low emissivity in the infrared band, which made it difficult for infrared detectors to find the absorber and thus provided an adequate infrared camouflage effect. It indicates that the proposed device achieves perfect laser stealth along with improved infrared stealth.
To reflect the better performance of compatible camouflage and versatility of the proposed device, we compared our device with other devices [57,60,52,61,62,55,63] which realize some single functions. As shown in Table 1, the proposed device in our work has some functions including dual-band guided-laser radar perfect stealth, infrared stealth, and dynamic tunability. The other devices have the function of guided-laser radar stealth or IR stealth. However, the previous works could only achieve a unique function or could not achieve better compatible stealth at the same time. Such as in recent reports [60,61,62], these devices are unable to meet the dual-band guided-laser radar stealth while achieving decent IR stealth. Moreover, compared with previous work [57,52], our proposed device can achieve a higher absorption in the dual-band guided-laser radar range with a lower emissivity in the MWIR range. It means that the better dual-band guided-laser radar and IR compatible stealth has been realized. Furthermore, owing to the use of the non-volatile PCM GST, our device is dynamically tunable (absorption rate adjustment range is 0.99 to 0.60 at 1.06 µm and 0.99 to 0.78 at 10.6 µm). It is worth noting that our device has excellent wide-angle insensitivity and polarization insensitivity compared to the device composed of thin films. This implies that our device not only enables laser stealth but can also transform into a laser protection device if needed. This is a novel advancement on previous works and is necessary for practical military applications.
Table 1. Comparison of the function of the proposed device with other previously published devices
3.2 Influence of the top fractal structure and bottom Helmholtz resonator on absorption peaks
Due to the self-similarity in MM fractal structures, multiple resonance reactions generated by MMs are often used to achieve broadband absorption in EM devices. We used the repetition characteristic of a monolayer metasurface fractal structure to achieve multiple repeated absorptions in a specific band and an ultra-high absorption rate at a certain frequency. This introduced multi-order fractal structures into the absorber. To study the influence of fractal structures of different orders on the absorption rate, the absorption characteristics of first- to third-order fractal structures were analyzed, as shown in Fig. 4. It is clear from the absorption spectra in Fig. 5(a) that the top layer of the absorber only had a first-order fractal structure composed of squares with a side length L. The absorption rates of the absorber were 99.104% (at 1.06 µm) and 94.363% (at 10.6 µm) in the amorphous state, and 58.575% (at 1.06 µm) and 86.603% (at 10.6 µm) in the crystalline state, respectively. Simulation results show that in the aGST state, the peak of the first absorption was at 1.06 µm, and the absorption rate exceeded 99%. However, the peak of the second absorption was at 10.45 µm, resulting in an absorption rate of only 94.363% at 10.6 µm. We found that increasing the order of the fractal structure to shift the absorption peak to the desired target position may cause a redshift of the second absorption peak. Based on the previous first-order fractal structure, we connected four identical squares with 2/3 L × 2/3 L dimensions at the four vertex edges of the main square. Figure 5(b) shows the absorption response of the second-order fractal structure. This resulted in absorption rates of 99.212% (at 1.06 µm) and 97.919% (at 10.6 µm) in the amorphous state, and 59.100% (at 1.06 µm) and 82.574% (at 10.6 µm) in the crystalline state. Similarly, we analyzed the numerical simulation data and found that the first absorption peak remained at the target location of 1.06 µm, while the absorption rate increased slightly owing to the enhancement of multiple resonances. The second absorption peak was slightly redshifted, with the central wavelength at 10.53 µm, and the absorption rate at 10.6 µm also increased to 97.919%. In this state, the absorber exhibited an enhanced absorption capacity. However, the second absorption peak still did not appear at the ideal target position. For the third-order case, the top edges of all squares appearing in the second fractal stage were connected with three small square blocks of equal size, with 1/3 L × 1/3 L dimensions, forming a third-order fractal geometry. The absorption performance of the absorber in this final stage is shown in Fig. 5(c). The absorption rates for this stage were 99.110% (at 1.06 µm) and 99.475% (at 10.6 µm) in the amorphous state, and 60.124% (at 1.06 µm) and 78.314% (at 10.6 µm) in the crystalline state. Although the absorption rate at 1.06 µm decreased by 0.1%, the absorption rate at 10.6 µm was enhanced by nearly 2%. Figure 6 shows the distribution of the electric field energy under the various fractal structures described using numerical simulations.
Fig. 5. Absorption results for the proposed perfect absorber with (a) first-order, (b) second-order, and (c) third-order fractal structures.
Fig. 6. Top view of the electric field distribution at 1.06 and 10.6 µm of the proposed perfect absorber. (a), (b), (c), and (d) are the first-order fractal cases; (e), (f), (g), and (h) are the second-order fractal cases; and (i), (j), (k), and (l) are the third-order fractal cases.
By increasing the order of the fractal structure, the nearly uniform energy was enhanced because of the multiple-resonances phenomenon caused by the high level of self-similarity. Therefore, in the aGST state, a third-order fractal structure is the optimal choice. The two absorption peaks were in the wavelength bands of 1.06 and 10.6 µm, and the corresponding absorption rate was above 99%. The fractal structure can realize the response and regulation of broadband wavelength, which effectively broadens the response band of our designed devices. With the change from first-order to third-order fractals, the absorptivity was perfect in the amorphous state, however, it was reduced in the crystalline state, and the difference between the two states increased. This shows the tunability of the proposed system. Specifically, as shown in Table 2, the proposed perfect absorber based on a third-order fractal structure provided better guided-laser absorption capacity and wider tunability than the first-order and second-order fractal structures.
Table 2. The effect of each order of fractal structure on the absorptivity at the two wavelength peaks
We explored the physical mechanisms underlying the two absorption peaks. To intuitively observe the effect of the absorber’s structural change on the absorption peaks of 1.06 and 10.6 µm, another sample absorber was designed. The only difference between the absorbers was that, in the new absorber, the original Helmholtz resonator at the bottom was replaced by a metal layer entirely made of gold, as shown in Fig. 7. Using the absorption spectrum in Fig. 6 and our calculations, we found that the first absorption peak of the sample absorber was at 1.04 µm and that the absorption rate at 1.06 µm was 91.819%. Concurrently, the absorption rate of the sample absorber at 10.6 µm was almost zero and there was no absorption peak. Analyzing the electric field distribution of the absorber revealed that surface plasmon resonance (SPR) was generated at the interface between the metal and the medium, as shown in Fig. 8. There was an obvious coupling between the metal fractal and Al2O3 top layers and between the Au layer at the bottom and the Si layer at the top; opposite charges appeared adjacent, resulting in strong energy distribution. Additionally, it can be seen from Figs. 8(a) and (b) that at 1.06 µm, the electric field energy in the Helmholtz resonating cavity and slit was extremely weak in both the crystalline and amorphous states and had almost no effect on the absorption peak. This indicates that the existence of the first absorption peak was independent of the Helmholtz resonator. However, as shown in Fig. 6, the type of fractal structure of the top layer of the perfect absorber affected the distribution of its electric field energy, and the size of each layer in the perfect absorber also affected the precise position of the wave peak. Following, we analyzed the generation of the second absorption peak. In Fig. 6, the absorption peak at 10.6 µm appeared in the presence of the Helmholtz resonator. In the analysis of the electric field distribution and numerical calculations at 10.6 µm, the Helmholtz theorem may be applied because the cavity slit is a periodic boundary that extends indefinitely in both the x and y-directions.
Fig. 7. Absorption spectra of a sample absorber without a Helmholtz resonator structure (red line) and proposed absorber with a Helmholtz resonator structure (blue line) at normal incidence.
Fig. 8. Cross-sectional view of the electric field distribution at 1.06 and 10.6 µm of the proposed perfect absorber. (a) and (c) are amorphous states. (b) and (d) are crystalline states.
The equations of this two-dimensional (2D) EM problem (Eq. (4)) are derived from the linear equations of acoustic Helmholtz resonators (see Eq. (3)) [64–66]. The relationship between the gas velocity ${\textbf u}$ and the pressure field p in an acoustic Helmholtz resonator satisfies Eq. (3), where $\mathrm{\chi }$ is the isentropic compressibility of the fluid and ${\rho _0}$ is the density. In Eq. (4), $\epsilon $ and $\mu $ represent the flux and permittivity, whereas ${\textbf E}$ and ${\textbf H}$ are the electric and magnetic field strengths, respectively. An acoustic design cannot be applied directly to electromagnetism because sound waves are scalar in nature, while EM waves are directional vectors, which prevent their propagation through deep subwavelength pores. However, in our simulation model, the fixed pores are replaced by infinite slits extending along the y-direction, and the 2D EM problem, which is transfixed in the y-direction, becomes a scalar. The magnetic field moves along the y-direction, and the electric field moves in the z-x plane, so that the acoustic and EM conditions of a particular polarized wave may be simulated. Due to their similar forms, Eq. (3) and (4) have similar boundary conditions—on the side walls of such resonators, the acoustic velocity ${\textbf u}$ is zero and in terms of electromagnetism, ${\textbf E} \times {\textbf y}$ is zero for perfect metals [67]. Therefore, we can compare the 2D EM field and its constitutive parameters with those of 2D acoustics, as shown in Table 3 [68].
Table 3. Similarity between two-dimensional EM and acoustic fields
By analyzing the electric and magnetic fields of the proposed perfect absorber, it was found that the strength of the magnetic field is nearly equal throughout the Helmholtz resonator, which indicates that the structure of the interior of a Helmholtz resonator could be used as an equivalent inductor and that its strength is proportional to cavity width Wh and thickness Th. These results are shown in Fig. 9(a).
Fig. 9. Cross-sectional view of the distribution of (a) the magnetic field and (b) the electric field of the proposed perfect absorber with the highest absorption rate of 10.6 µm.
It is evident from the electric field distribution in Fig. 9(b) and Fig. 8(c) and (d) at 10.6 µm, that most of the electric field energy exists in the regions near the dielectric layer and the slit of the Helmholtz resonator, and only a small portion is distributed between the fractal metal layers. These regions can be analogous to an equivalent capacitance model whose strength is related to the slit width Wa and thickness Ta. Therefore, the EM response of this structure conforms with the LC resonance model. We used the Helmholtz resonance analogy discussed earlier for analyzing LC resonance, using the above theoretical analysis combined with numerical simulations of Figs. 7 and 8, to explain the wavelength and the Helmholtz cavity coupling between the proposed absorber, thus realizing absorption resonance at a wavelength of 10.6 µm. The width and thickness of the cavity and slit were adjusted to the specific position of the absorption resonance wavelength (i.e., the second absorption peak).
3.3 Influence of dimensional parameters on absorption peaks of the proposed multi-composite structure
The previous discussion indicates that the analogy of the Helmholtz resonator in acoustics to electromagnetism indicates that the entire Helmholtz resonator spring-particle system is equivalent to the LC resonator. As shown in the distributions of the electric and magnetic fields in Fig. 8, the electric field is constant throughout the volume of the slit. In contrast, the magnetic field is nearly uniform and homogenous everywhere inside the cavity. This means that the cavity acts as an inductor, and the slit acts as a capacitor and collects the incident light wave and allows it to leak in and out of the cavity, which then absorbs the light wave into the box. This confirms that the structure may be equivalent to an LC resonator and exhibits the following relationship to the capacitance of the slit:
In Eq. (7), the resonance wavelength depends not only on the slit aspect ratio of the Helmholtz resonator but also on the cavity area. In addition, we can set ${T_{\textrm{eff}}} \approx {T_\textrm{a}} + {W_\textrm{a}}$ in this model. This adds an effective thickness edge effect to the slit in the capacitor to optimize the model. Therefore, the final expression to calculate the resonance wavelength while considering the edge effect [68] is as follows:
The dielectric constant in the Helmholtz resonator is uniform and is set to ${\varepsilon _\textrm{s}} = 1$. In Eq. (8), the width Wh and thickness Th of the cavity, and the width Wa and thickness Ta of the slit has an important influence on the absorption resonance wavelength.
As indicated in Fig. 10, the offset and change in the second absorption peak was calculated by changing the values of these parameters through a numerical simulation. In Fig. 10(a), as the width of the slit increases (shown as the black, blue, and red lines in the figure), the second absorption peak shows a clear blueshift, and the peaks of the absorption are obtained from the simulation data for wavelengths of 11.16 to 10.6 and 10.04 µm, respectively. This is because the larger the slit width, the smaller the equivalent capacitance, which is also verified by the blueshift of the absorption spectrum. In contrast, in Fig. 10(c), a slight increase in the thickness of the slit is equivalent to a slight increase in the capacitance of the model, resulting in a slight redshift of the absorption peak. This frequency response verifies the formula contained in Eq. (5). Figure 10(b) shows the clear displacement of the absorption peak when the cavity width changes between 400 and 500 nm, indicating that cavity width has a significant influence on the resonance wavelength. With an increasing Helmholtz resonator width, the corresponding absorption resonance wavelength gradually redshifts from 10.08 to 10.59 and 11.02 µm. This is because the EM response of the structure conforms to the equivalent LC resonance model; that is, increasing the area of the cavity will increase inductance, leading to a redshift of the absorption peak. A similar phenomenon can be observed in Fig. 10(d), where an increase in the cavity thickness also leads to a larger inductance. These results confirm that the proposed Helmholtz resonance cavity in the absorber is equivalent to the LC resonance model and explains the generation and drift of the second absorption peak.
Fig. 10. Absorption spectra of the perfect absorber with different structural parameters for the Helmholtz resonator. (a) Slit width, (b) cavity width, (c) slit thickness, and (d) cavity thickness.
As discussed previously, the structure and size of the absorber affect the precise position of its wave peak. Therefore, we fine-tuned the position of the absorption peak by controlling the side length and period of the top fractal structure, as shown in Fig. 9. It can be seen from the change in the absorption spectrum that the frequency shift of the absorption peak is very weak (less than 0.1 µm). Figure 11(a) shows the simulation results for the side length, L, of the first-order fractal structure from 140 to 180 nm, and the absorption peak at 1.06 µm barely changed, while the second absorption peak only changed from 10.55 to 10.62 µm. Similarly, Fig. 11(b) shows the fine-tuning effect of the period of the fractal structure on the absorption peak. When Q increased from 1050 to 1250 nm, the first absorption peak was maintained at approximately 1.06 µm, while the second absorption peak shifted from 10.62 to 10.54 µm. It implies that the side length and period size change of the top layer fractal structure differs from the key roles of slit capacitance and cavity inductance in complex models. The main purpose of altering the fractal structure was to achieve accurate control of the target absorption peak. These simulation results are consistent with the previously discussed electric field distribution. The electric field intensity near the top fractal structure was significantly weaker than that between the slit and the cavity. Therefore, to ensure that the absorption bands were just inside the target bands of 1.06 and 10.6 µm, the optimal parameters are L = 160 nm and Q = 1150 nm.
Fig. 11. Response of the absorption spectra to the (a) side length and (b) period of the top fractal structure.
As indicated in Fig. 12, we also evaluated the influence of the thickness of each layer on the absorption capacity of the proposed absorber in the case of a multi-combination structure. It can be seen from Fig. 12(a) and (b) that the absorptivity of the absorber at 10.6 µm changed significantly after the thicknesses of Si and the GST were changed, and the absorptivity was more than 99% when TSi and TGST were equal to 22 and 18 nm. However, if the thickness was increased or decreased, the absorption rate in the target band was only approximately 80%, indicating that the thicknesses of the two layers affect the strength of the SPR. In addition, with the change in silicon layer thickness, the absorption rates of 17 nm and 27 nm at 10.6 µm decreased to 98.87% and 97.72%, respectively. When the GST thicknesses were 13 and 23 nm, the corresponding absorptivity was 96.48% and 97.91%. In contrast, Fig. 12(c) shows that changing the Al2O3 layer thickness has no significant effect on the two absorption peaks. Figure 11 and Fig. 12 of the revised manuscript show the relationship between the size change of the photonic structure and the change of absorptivity. We have considered the common errors of existing CMOS processes, and we have discussed the performance after a size change of 10 nm or 100 nm. Through analysis, the proposed photonic structure is verified to have good manufacturing robustness. Owing to the introduction of more combinations of structures of the control, and through top-level fractal structure optimization and adjustment of the parameters of the materials in each layer, we proposed a Helmholtz resonator that provides better applicability and fine-tuning capability. This is expected to be achieved by changing the fractal structure of the top to provide high bandwidth, spectrum, and a wider range of applications.
Fig. 12. Absorption response of the proposed perfect absorber to a change in the thickness of (a) silicon layer, (b) GST layer, and (c) alumina layer.
4. Conclusion
In this study, we propose a dynamically tunable metamaterial perfect absorber using a combination of Helmholtz resonance and a fractal technique to successfully obtain dual-band guided-laser radar perfect stealth combined with infrared stealth. The results show that the proposed device provides a perfect absorptivity (${\alpha _{1.06{\mathrm{\mu} \mathrm{m}}}}$>0.99, ${\alpha _{10.6{\mathrm{\mu} \mathrm{m}}}}$>0.99) in the two target bands, has a large frequency ratio, and maintains an absorption efficiency of approximately 90% at an oblique incidence angle up to 70°. In addition to achieving perfect guided-laser radar stealth, the proposed device is also able to achieve low absorptivity/emissivity at two atmospheric window bands (3-5 µm and 8-14 µm). The absorptivity is 0.03 in the MWIR range and achieves 0.31 in the LWIR range. Due to the symmetry of the structure and the introduction of the phase change material, the GST, the proposed perfect absorber exhibits desirable characteristics, such as polarization insensitivity and dynamic tunability. Additionally, based on SPR and Helmholtz resonance analysis, which is analogous to the LC resonance theory, a precise resonant peak control is achieved by adjusting the fractal structure and size of the Helmholtz resonance cavity. Therefore, this absorber has clear advantages (it is tunable and has better control) when compared to traditional metal MM absorbers. Moreover, the proposed design method can be extended to include perfect absorption of high bandwidths in other frequency ranges. This is useful in a wide variety of potential applications, such as optical communication, military camouflage, and spectral detection.
Funding
National Key Research and Development Program of China (2022YFF0706005); National Natural Science Foundation of China (61805278, 12272407, 62275269, 62275271, 62305387) Guangdong Guangxi joint Science Key Foundation (2021GXNSFDA076001); Guangxi Key projects of science and technology (Grants No.2020AA21077007).
Disclosures
The authors declare no conflicts of interest.
Data availability
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.
Supplemental document
See Supplement 1 for supporting content.
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