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Abstract
In this paper, we propose a new type of metal-insulator-metal (MIM) hybrid cavity compound grating micro-structure array, which can achieve dual narrowband super-absorption in the near-infrared window. The thin plasmonic microstructure effectively modulates coupling and hybridization effects between surface plasmon polaritons of different transmission resonance cavities to form designable dual narrowband resonance states to achieve near-infrared operation proving manipulation of the optical characteristics in the near-infrared light field. Furthermore, we conduct an in-depth theoretical exploration of the structure's unique properties, such as its high-quality factor, low noise, super-absorption, precise control, and the physical mechanism of its excellent performance in ambient refractive index sensing and detection. This study provides developmental insights for the miniaturization, easy modulation, and multi-function development of surface plasmon superabsorbers while broadening their application in near-infrared environment refractive index detection. The proposed microstructure is also suitable for integration with optical elements.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Surface plasmons (SPs) are electromagnetic oscillations formed by the coupling of incident light field and free electrons and exist at the interface between a metal and a dielectric [1–4]. SP behavior has two main categories: surface plasmon polaritons (SPPs) that travel along the metal-dielectric interface and localized surface plasmons (LSPs) bound to the geometry of the nanostructure [5–7]. By parameter design and optimization such as the arrangement of the plasma structure, period, and material properties, the amplitude [8], polarization [9], and phase [9,10] of the acting light field can be modulated to achieve precise control of the optical response of the structure [11]. In addition, as their length scales are consistent with the trend of miniaturization of optical systems and related components, surface plasmon micro-nano structures have myriad application prospects [12–16], such as in biosensors [17], energy harvesting [18–21], nonlinear optics [22–24], surface-enhanced Raman scattering (SERS) [25,26], waveguides, [27,28] and photocatalysts [29], and other optical applications [30–32].
The light field superabsorber [18] has found important applications in photodetector [33,34], thermal radiation modulation [35], and sensing [36]. Surface plasmon superabsorbers have attracted wide attention because of their ability to control and collect light fields in the deep sub-wavelength range. These absorbers are made of proper materials and have appropriate geometric profiles. They can achieve nearly 100% narrowband or broadband absorption in the desired waveband and play an important role in the areas such as detection and sensing, energy harvesting, and near-field enhancement. The plasma super-absorption refractive index sensor has attracted wide attention due to its unique and excellent properties. In 2016, Hu et al. [37] proposed a new type of Al metamaterial absorber microfluidic sensor. Its figure of merit (FOM) for evaluating the refractive index sensitivity can be up to 3.5 THz/RIU, and the normalized FOM (FOM*) reached to about 0.31/RIU. In 2018, Guo et al. [38] proposed a wide-angle infrared metamaterial absorber and obtained the highest FOM values of 128, 117, and 105 in the air, water, and glucose environments, respectively. In 2020, Zelio Fusco et al. [39] obtained FOM values of as high as 150 nm/RIU to study nonperiodic sodium tungsten bronze (NaxWO3) metamaterials. Plasmon superabsorbers are difficult to study with consideration of both super-absorption characteristics and high FOM simultaneously. Their detection sensitivities on the scales of their spectral width still need further improvement. Therefore, there are still challenges in achieving high-quality factor resonance, low background noise, narrowband absorption, and high sensitivity based on superabsorbers in the plasmon modes [40–43]. In addition, the related studies tend to focus on sample preparation and the realization of specific physical properties. Studies on the physical mechanism of related mode coupling, especially in the near-infrared window, are lacking.
In this paper, we investigated the optical properties of the MIM hybrid cavity compound grating in the near-infrared region. Based on the cavity-coupled gap plasmon polaritons (CGpp) mode, the physical mechanism of high-quality, low-noise, and narrowband absorption is explained. Compared with the studies at the apex of this field, the new MIM hybrid cavity compound grating has obtained excellent FOM values. In addition, using the structural model's excellent ability to control the acting light fields, we can shift its response wavelength to ideal values and even adjust the optical characteristics such as spectral linewidth, absorption intensity, and the number of modes. The above-mentioned optical performance also provides a basis for plasma super-absorption refractive index sensors applied in the near-infrared band and has high potential for future applications.
2. Simulation model
We use the commercial software Lumerical FDTD Solutions to simulate the hybrid cavity compound structure to carry out the theoretical analysis of the coupled state of the plasmon field on the internal surface of the system. The structure model of the MIM hybrid cavity compound grating is shown in Fig. 1. The structure is composed of two alternately arranged Au/SiO2/Au nanowire modules. We define the two types of grating modules as Type-I and Type-II gratings. In Fig. 1, the difference in thickness of the lower metal of the two types of gratings, L1 and L2 represents the width of the two types of module structures. The period is represented by L = L1 + L2. The two types of gratings have the same dielectric layer thickness T. Considering the plasmon penetration depth effect on the coupled field of the system [8,44], the thickness of the upper gold film is set to 25 nm. In the simulation process, the incident light source placed 3µm above the structure with a wavelength range from 900 nm to 2100 nm propagates along the negative z-direction with the E field polarization in the x-direction. The compound microstructure is periodically arranged in the X direction for the spatial distribution and extends infinitely in the Y direction. Based on the symmetry of the structure, the asymmetric and symmetric boundary conditions align with the X- and Y-axes, respectively. It is more efficient than setting the simulation region mentioned above as periodic boundary conditions. The condition of the perfectly matched layers (PML) swaps on the Z-boundaries to eliminate echo interference. In the simulation and analytical calculation below, the dielectric properties of Au and SiO2 are obtained based on the Palik model. To ensure the accuracy of the calculation results, we used a discrete mesh with a size of 2.5 nm × 2.5 nm × 2.5 nm and performed repeated tests of the same designed structure more than 5 times.
Fig. 1. Schematic diagram of the hybrid cavity compound grating structure and the cross-sectional view of the structure.
3. Results and discussions
First, we explored the spectral characteristics at L = 2 µm, L2:L1 = 11/9, T = 150 nm, and t = 70 nm. Figure 2(a) shows the near-infrared dual narrowband absorption spectra. The two low-noise, high-Q absorption bands in the near-infrared region, are defined as A1 and A2. For A1 and A2, the central absorptance is 94.7% and 94.2%, the full width at half maxima (FWHM) of high reflection spectrum region are 13.37 nm and 20.21 nm, and the theoretical quality factors are as high as 86.3 and 80.7, respectively. In order to explore the physical mechanism of the two modes, we simulate the resonance states of the electric fields at the peak wavelengths of A1 and A2, as shown in Figs. 2(b) and 2(c). It can be seen that alternate light and dark transverse Gpp electromagnetic modes appear in the dielectric gap. The plasmons GppI and GppII reach a stable state through modulation by the coupling effect. This relationship is defined as the cavity-coupled gap plasmon polaritons (CGpp) mode. Meanwhile, the metal edge of the end face accumulates a large number of induced charges, which induces the localized surface plasmons resonance (LSPR) phenomenon under the action of the polarization field, and thus shows considerably high field enhancement characteristics. At the peak frequencies of A1 and A2, the highest relative energy intensity of the end face LSPR |ELSPR/E0|2 reached 1059 and 2308, respectively.
Fig. 2. (a) Under the characteristic structure parameters, the MIM hybrid cavity compound grating forms a double absorption band in the near-infrared domain. (b) and (c) The relative electric field distribution at the peak wavelengths of the A1 and A2 modes in (a), the color band represents the normalized electric field intensity.
Then, to more accurately predict the near-infrared resonance characteristics of the CGpp mode, we first combine the free Gpp dispersion models in the ideal state to quantitatively describe the mode:
where ω/c is the transmission wave number of the incident beam, ɛd(ω) and ɛm(ω) represent the dielectric functions of SiO2 and Au, respectively, β is the X-direction transmission wave vector of the Gpp coupled-wave in the cavity, and kd and km are the Z-direction wave vector components of Gpp in the dielectric and metal spaces, respectively. The asymmetry of the two gratings’ boundary materials causes different end face phase values, making GppI and GppII different in energy intensity and arrangement. Under ideal conditions, we can ignore these effects for the time being. The Bragg grating condition can give the excitation of the Gpp mode according to where θ represents the incident angle of the light field, g = 2π/L is the reciprocal lattice vector derived from the grating, and the integer n is the harmonic diffraction order.At vertical illumination, because there is no plane projection of the light field wavenumber, the initial value of Gpp of the response wavelength is entirely provided by the specific order of the reciprocal harmonics; thus, the two should be in the same position in the wave vector space. To prove this viewpoint, we calculate and plot the dispersion relationship between Au/SiO2/Au gap plasmons and the 1st–3rd Bragg diffraction harmonics at L = 2 µm and for a 150 nm-thick SiO2. The results are shown in Fig. 3. The dispersion curves of SPP at the Au/air interface are used as a reference. Through the calculation, the Gpp dispersion curve of the MIM cavity intersects the 3rd Bragg first and then 2nd Bragg wavenumber spectra at the wavelengths of 1.124 µm and 1.663 µm, respectively. They are very close to the center wavelengths of the two absorption bands of 1.155 µm and 1.630 µm, which proves our above hypothesis. Meanwhile, an SPP resonance mode at 1.007 µm is generated at the Au/air interface. Because the above calculation result corresponds to an ideal state, it is slightly different from the actual results.
Fig. 3. The dispersion relationship between the Gpp mode of the MIM cavity and different Bragg orders at L = 2 µm and T = 150 nm. The dispersion curve of the SPP at an Au/air interface is also given.
Next, we will combine the FP cavity transverse resonance waveguide theory to evaluate the effect of the end face phase on the modulation of response wavelengths in the absorption spectrum. The operating relationships in type-I and type-II MIM cavities are
where ψ1 and ψ2 represent the additional phase shift produced by the equivalent boundary of GppI and GppII surface waves at both ends, respectively; m1 and m2 correspond to the orders of the standing waves formed at the resonance length of the FP cavity. The interrelation between GppI and GppII was strengthened due to the coupling effect of CGpp. Furthermore, the boundary of the end face has been blurred to a large extent, making m1 and m2 change towards a non-integer value. For this reason, we carry out the analysis based on the field distribution characteristics of the entire hybrid cavity and introduce the equivalent refractive index Neff = cβ/ω=λr/λCGpp. The corresponding resonance wavelength is expressed as [45] where λr is the center wavelength of the absorption spectrum, the integer M is the total number of standing waves, and ψ represents the equivalent end face phase shift of the coupled wave. The transmission wavenumber β is solved using Eqs. (1)–(3) for λr equal to 1.155 µm and 1.631 µm, and the corresponding equivalent refractive indices Neff are 1.684 and 1.664, respectively. Because the ratio of ψ/2π in the denominator of Eq. (7) is relatively small, if the effect is temporarily ignored, the reduced resonance orders of the A1 and A2 absorption bands can be obtained as 6 and 4. Finally, from Eq. (7), the value of ψ/2π at the peak wavelengths of A1 and A2 is 0.168 and −0.081, respectively.Next, we explored the modulation effects of structural parameters on infrared absorption characteristics. As shown in Fig. 4(a), at fixed L2/L1 = 11/9, through simulation calculation, the valley wavelength curves in the reflection spectrum of each mode with the period L from 1.8 µm to 2.3 µm are drawn. It can be seen that they have inherited the characteristics of the original narrowband waveform with an absorptance above 91%. Figure 4(b) shows that the reflection valleys move to the long-wave region as the period increases. The corresponding wavenumber β continues to decrease, thereby ensuring that the primary resonance order M of the bound energy distribution is not affected. In addition, the FWHMs of the absorption states of A1 and A2 in different periods are below 15 nm and 23.9 nm, respectively. In addition, we calculated the equivalent end face phase ψ/2π of each period, as shown in Fig. 4(c). It can be seen that the end face phases of the two absorption modes A1 and A2 are distributed on both sides of the positive and negative space, which also explains the redshift in the analytical values obtained from Eqs. (1)–(4).
Fig. 4. (a) With L2:L1 = 11/9, modulation effect of different structural periods on the reflection spectrum. (b) In the above process, the corresponding relationship between the center wavelengths and FWHM of modes A1 and A2 and the period L. (c) The trend of the equivalent end face phase ψ/2π of the resonance states of A1 and A2 at different periods.
Due to the forced resonance of non-integer-level standing waves in the FP cavity, the end-face effect will become more significant [44]. Then with a fixed period, continuously changing the ratio of the lengths of the two gratings may affect the resonance state of the equivalent boundary coupled field, which may cause the center wavelength of each absorption state to drift continuously. To confirm this conjecture, we studied the response of the absorption spectra of A1 and A2 as L2 changes from 0.5 µm to 1.5 µm (that is, L2/L1 change from 1/3 to 3) at L = 2 µm. As shown in Fig. 5(a), δ1 and δ2 agree almost perfectly with the λCGpp/2 in the hybrid cavity in the absorption state of A1 and A2, corresponding to the distance between the left and right equivalent boundaries of the type II grating moving from a specific electric field (or magnetic field) standing wave node to an antinode.
Fig. 5. (a) At L = 2 µm, the absorption performance of the MIM hybrid cavity compound grating is significantly affected by a change in L2. (b) The Structure reflection spectrum is obtained when L2 is 0.87 µm and 1.39 µm, respectively, and the double absorption bands degenerating into single absorption bands.
In addition, we found that when L2 is 1.39 µm and 0.87 µm, the two absorption energy bands are split in sequence, causing the original bimodal absorption spectrum to degenerate into a single absorption mode and the corresponding peak absorptance to be slightly reduced, as shown in Fig. 5(b). The occurrence of the single-peak absorption spectrum allows for design flexibility and maneuverability. To elucidate the physical mechanism of the splitting of the absorption bands A1 and A2 when modulated by the grating duty ratio, we respectively calculated the relative magnetic field Hy distribution of the adjacent resonance states on both sides of the energy bandgap (i.e., the characteristic locations 1–4 in Fig. 5(a)), as shown in Fig. 6(a)–(d). The primary wave position and resonance order of the CGpp coupled wave corresponding to the absorption bands of A1 and A2 have almost no change, verifying the accuracy of our calculation of the resonance orders. However, the phase of the wave vector where Hy is extremely strong has changed by π. This means that when L2 increases to the critical position, the Gpp harmonics in some MIM resonant cavities begin to vibrate in the opposite direction and interfere with adjacent cavities that maintain the original resonant state until the macroscopically coupled waves in the system complete the mode conversion and are reunified. When reaching the extremum of Hy≈0, the main absorption peak will disappear from the spectrum, and the energy band is split.
Fig. 6. (a) and (b) Normalized Hy field distribution at characteristic resonance states 1 and 2 in the A1 mode, respectively. (c) and (d) Normalized Hy field distribution at feature characteristic points 3 and 4 in the A2 mode. Each color band represents the relative intensity.
To find out the cause for the decrease in the absorptance of the single-peak response spectrum, we calculated the relative electric field distribution at the center wavelength. The results are shown in Fig. 7. We can see that when L2 = 1.39 µm, the spatial distribution of LSPR in mode A1 is very similar to the situation in Fig. 2(b), but the highest relative energy intensity |ELSPR/E0=|2 is only 402, which is similar to the dual absorption band mode A1. Thus, the energy intensities of the modes are quite different, which is also the direct cause of the decrease in absorptance. In contrast, when the L2 changes to 0.87 µm, the highest energy intensity of the LSPR field in mode A2, |ELSPR/E0|2 = 1909, appears to be closer to the LSPR field in Fig. 2(c). However, the strong LSPR-bound field that should be located at the lateral metal edges of the two types of grating dielectric channels (the lower right marked area in Fig. 7(b)) almost disappears. As a result, the resonance intensity of the CGpp coupled wave in the cavity is significantly affected, and the absorption capacity of the structure is greatly reduced.
Fig. 7. When period L = 2 µm and L2 are (a) 1.39 µm and (b) 0.87 µm, respectively, the relative electric-field distributions of the MIM hybrid-cavity compound grating in A1 and A2, the color bars stand the normalized electric-field intensity.
According to Eqs. (1)–(3), the thickness of the dielectric layer T is the key to the positions of resonance wavelengths. Two clear absorption bands can be obtained in the short cavity with small T (90 nm–280 nm). As T increases, the peak wavelengths of the absorption modes of A1 and A2 have significant blue shifts, as shown in Fig. 8(a). When thickness T reaches the long cavity region (T > 300 nm), which is close to half of the wavelength of the gap plasmon, the coupling effect of the optical field and the hybrid cavity excites a polarization charge sufficient to support the FP longitudinal mode on the metal surface. In addition, according to the Ez field distribution state and the symmetry and anti-symmetry properties of the Ez component of the Gpp mode, the coupling effect leads the hybrid spectra to form crossing and anti-crossing behaviors [46], significantly changing the dispersion characteristics of the different resonance states, as shown in Fig. 8(b). This coupling has different levels of effect on the peak wavelength and absorption intensity of the response states of A1 and A2. Side-peak interference also appears in the original low-noise near-infrared background.
Fig. 8. Relationship between the structure absorption spectrum and the wavelength at L = 2 µm, t = 70 nm, L2/L1 = 11/9, and T located in short cavity region (90 nm–270 nm) (a), and long cavity region (280 nm–600 nm) (b).
In addition, the height difference t of the lower gold layer of the two types of gratings is also an important parameter of the absorption spectrum of the modulation structure. Figures 9(a) and (b) respectively show the Z-direction relative electric field distribution function of the absorption spectrum at t = 70 nm in Fig. 2(a), and in the peak absorption states of A1 and A2 at the end face X = −0.55 µm. Note that the distribution curve at the other end surface X = 0.55 µm is the same. Each sharp peak position in the figures corresponds to the excited LSPR local field mode. It can be seen that the high-energy enhancement characteristics of LSPR significantly increase the vibration amplitude of the bound field in the nearby area through the coupling effect and improve the light field collection efficiency of the hybrid cavity structure.
Fig. 9. (a) and (b), When t = 70 nm, the relative electric-field functions in the Z direction of the end face position at the center wavelengths of A1 and A2 modes, respectively
However, as t changes, the intensity changes of different LSPR modes become very complicated, and it is difficult to quantify the specific effect of each LSPR bound state on the structure absorptance. Here, we propose the concept related to the end face equivalent electric field and use it to evaluate the field confinement ability of LSPR and to predict the trend of the structure absorptance as
where Ω is the spatial length from the upper surface of the metal layer on the top of the I-type grating in a periodic unit to the reference height Z = 0. Eeff can evaluate the LSPR field enhancement efficiency per unit length in the end face position and establish a correlation with the structural absorptance. Based on the structural parameters in Fig. 2(a), we studied the relationship between the peak absorptance of the modes A1 and A2 and the end face equivalent electric field Eeff as t changes from 50 nm to 90 nm, as shown in Fig. 10(a) and (b). In mode A1, both the structural absorbance and Eeff reach their highest values at t = 70 nm. Both parameters also show a high degree of consistency in the change trends; this positive correlation feature is also reflected in mode A2. Therefore, we describe the positive feedback contribution of LSPR to the structure absorptance through the end face equivalent electric field model. Considering that when t = 70 nm, both A1 and A2 have ideal absorbance and Eeff values, this value is used as the initial parameter value of the structure.Fig. 10. (a) and (b), During the change of t from 50 nm to 90 nm, the changing trend of the absorption and Eeff of A1 and A2 states.
Finally, to evaluate the application potential of the structure model in plasma superabsorber refractive index sensor, we calculated FOM and FOM* of the structure to measure its sensitivity [47–49] by
where S(λ) is the wavelength change per unit refractive index, and Γ is the spectral linewidth. Figure 11(a) shows the change in response of the reflection spectrum of the hybrid cavity structure after the dielectric changes from air (n = 1) to water (n = 1.321) with L = 2 µm and L2/L1 = 11/9. In this process, mode A2 completes the center wavelength shift while maintaining the narrowband waveform. The peak absorptance is always higher than 93%, and the corresponding sensitivity FOM* can reach 28.7. They appear near the valleys of the air environment reflection curve, as shown in Fig. 11(b). It is worth noting that when the environment refractive index is 1 and 1.321, a very narrow dark mode in the spectrum shifts from the wavelength of 1.007 µm to 1.332 µm, the corresponding Q factor is as high as 234.2 and 302.7, respectively, and the refractive index sensitivity S(λ) reaches 1012.5 nm/RIU. Since its spectral width Γ is only 4.3 nm, the figure of merit function FOM can reach about 235.5, which exceeds the scale of a hundred. At the same time, this peak also corresponds to the SPP resonance mode of the Au/air interface in Fig. 3.Fig. 11. (a) Simulated reflection spectra of the structure in different environmental media (air and water). (b) FOM* of the A2 mode sensitivity is a function of wavelength, and the reflection spectrum of the structure in the air atmosphere is also given.
Although the resonance state mentioned above has a low peak absorptance, it can also be identified and extracted under a low-noise background due to its large wavelength span in different materials. However, the existence of mode A1 creates difficulties to the above operations. Fortunately, when the structural ratio satisfies L2/L = 0.435, mode A1 disappears due to the coupling and interference of adjacent Gpp harmonics in the system so that only mode A2 exists in the reflection spectrum. Figure 12 shows the reflection curves of the structure in the air and water environment at L = 2 µm. Thus, the dark mode resonance state maintains a high refractive index sensitivity while eliminating the effect of side peak noise, effectively improving the spectral signal contrast and increasing the structure’s potential in sensing and detection applications.
Fig. 12. Simulated reflection spectrum of the hybrid cavity structure in air and water environments at L = 2 µm and L2/L = 0.435.
It is a challenge to fabricate this device because the suggested structure size is around 1µm, close to the fabrication limit of traditional lithography process. We recommend that the bottom 100 nm Au film be deposited through magnetron sputtering on Si substrate. The Au grating be fabricated firstly by using the lift-off lithography process, and subsequently SiO2 and Au films be deposited through magnetron sputtering or thermal evaporation. Since the optical properties of this structure are sensitive to the structure parameters, a fabrication method with a higher precision such as laser direct writing and e-beam lithography is required. Besides lithography, film fabrication with less oblique angle deposition is suggested to avoid sidewall deposition.
4. Conclusion
In general, our MIM hybrid cavity compound grating array, through the Gpp coupled effect provided by different grating modules inside the structure, successfully achieves dual narrowband super-absorption characteristics in the near-infrared region with the corresponding peak absorptances exceeding 94% and the quality factors being all above 80. We have proposed the macro CGpp harmonic theory to explain the physical mechanism of the formation of each absorption band and have evaluated the specific role of the equivalent end face phase in the wavelength shift. In addition, we have systematically studied the effects of different structural feature dimensions on the near-infrared absorption response. Finally, we have confirmed the excellent potential of the structural model as a high-performance sensor: in different environments, its unit refractive index sensitivity can reach 1012.5 nm/RIU, and its figure of merit is as high as 235.5. It provides theoretical information for developing plasma super-absorption refractive index sensors in terms of miniaturization, ease of modulation, and multi-functionality. At the same time, it can serve as a guide in biological environment sensing, coupled waveguides, and surface mode enhancement.
Funding
National Natural Science Foundation of China (11803034, 61705226).
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 maybe obtained from the authors upon reasonable request.
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