Research on Dual-Transmission Cross-Shaped Microcavity Metamaterials in the Mid-Infrared Region

Mid-infrared detection technology is widely used in military and civilian applications with its unique advantages. The filter is the core component of the mid-infrared detection system, realizing controllable modulation of its dual-band transmission peak is an important prerequisite for optimizing detector performance. In this paper, a cross-shaped microcavity structure metamaterial based on gold material is designed to achieve mid-infrared dual-band transmission. By changing the width of the microcavity and the width of the gap, the controllable modulation of the dual-band transmission peaks is achieved, corresponding to the dual-band ranges of 3.23 ~ 3.46 μm and 4.06 ~ 4.60 μm. The maximum transmission of the resonant transmission peaks λI and λII can reach 94.5% and 92.6%, respectively. The corresponding FOM is up to 17.70. This study provides a theoretical basis for the preparation of dual-band transmission filters in the mid-infrared band.


Introduction
Mid-infrared (MIR) light has attracted great research interest due to its various scientific and technological applications.Especially, 3 ~ 5-μm band has important application value in biomedical imaging [1,2], infrared detection [3], national defense security [4,5], gas molecular detection [6], and quantum communication [7], due to that the absorption bands of many gas molecule types as well as water molecules are in this region.Significant progress has been made in these areas of research, which can be attributed to advances in mid-infrared detectors and optical components.In particular, optical filters play an important role as critical optical components in a wide range of sensing, imaging, and detection applications.However, compared to the more mature near-infrared, the performance of mid-infrared filter elements still has great potential for improvement.
In recent years, optical filters based on the spectral modulation mechanism of metamaterial micro-nanostructures have attracted extensive attention for the advantages of low cost, small size, high integration, and flexible spatial variation [8][9][10][11].In addition, in order to meet the needs of target detection in complex environments, the design of midinfrared sensing devices with dual-band imaging capability is the current research trend [12][13][14].The main reason for this is that the mid-infrared dual-band detection technology can obtain information in two spectral channels simultaneously, reflecting the advantages of high resolution and strong antiinterference capability, resulting in a significant increase in detection accuracy.Therefore, it is of great theoretical and practical significance to study the dual-band resonance effect based on metamaterial structure to improve the sensitivity of mid-infrared sensor.In 2019, Ke Jin et al. designed a dualchannel ultra-narrowband mid-infrared filter structure with two transmission peaks of 2.08 μm and 2.35 μm under TM polarization, and the peak wavelength can be adjusted in a small range by changing the structure size [15].In 2020, Shilin Yu et al. proposed a chip-scale plasmonic band-stop filter that achieves dual-band transmission in the range of 0.7 ~ 1.4 μm, and the adjustment of the central wavelength can be achieved by changing parameters such as the width and depth of the bilateral trapezoid of the structure [16].Currently, there is still a great deal of discussion on metamaterial structures in the MIR dual-band.The study of the transmission performance of MIR dual-band and its related mechanism by analyzing the electromagnetic properties is important for the practical application and further development of MIR metamaterial devices.However, there are few studies on dual-band metamaterial filters in the range of 3 ~ 5 μm.
In this paper, finite-difference time domain (FDTD) simulation software was used to construct a cross-shaped dual-band transmission microcavity metamaterial that can be modulated in the MIR band (3.0 ~ 5.0 μm).The influence of the duty cycle of the cross-shaped microcavity structure on transmission characteristics is studied theoretically.The transmittance of the metamaterial was improved by adjusting the structural parameters, and the high-quality factor of the material was achieved.

Simulation Method and Model Design
In order to obtain the optimal bimodal resonance performance, we simulated the spectral properties of the periodic array structure on the gold surface using the FDTD method.
Figure 1a shows a schematic diagram of the cross-shaped microcavity metamaterial structure, which consists of a substrate layer and a top layer.SiO 2 was adopted as the substrate material because of its high transmittance in the midinfrared band of 3 ~ 5 μm, and the thickness of the substrate material was set to H = 1 μm.We should mention that, as the substrate thickness does not significantly affect the transmittance spectrum, we set the substrate thickness to 1 μm to reduce computation.In the top layer, a gold film with a thickness of 6 μm was placed on the substrate material, and a cross-shaped microcavity structure was etched on the Au film.This cross-shaped microcavity consists of a pair of symmetrical C-shaped walls.
In the simulation, we achieved transmission spectral modulation of the metamaterial by changing the relevant parameters of the structure.Transmission is defined as the ratio of the transmitted power P out at the structure exit to the incident power P in at the structure entrance, which is given by T = P out /P in [17].For this metamaterial design, we defined a set of structural parameters, as shown in Fig. 1b, including the overall height Y, wall length L of the C-shaped wall, and the width w of the microcavity.In which, Y is constant values of Y = 6 μm.In addition, they can be calculated by Y = h 1 + 2h 2 and L = l 1 + l 2 , where h 1 and l 1 represent the height and length of the pilaster, and h 2 and l 2 represent the height and length of the pilaster claw.And h 1 and h 2 are initially set to 4 μm and 1 μm, respectively.w is the critical parameter variable in the simulation, which can be adjusted by w = x + 2l 2 , where x is the gap width of the cross-shaped microcavity.In the FDTD software setup, periodic boundary conditions were set in the X-and Y-axis directions, and perfectly matched layer (PML) boundary condition was set in the Z-axis direction.The period size was set to P x = P y = 2 μm.A plane wave light source with a wavelength range of 3 ~ 5 μm transmitting along the negative direction of the Z-axis was utilized.The parameters of the gold material are based on the Drude model [18][19][20][21][22][23].To meet the calculation accuracy and improve the operation speed, the mesh size was set to Δx = Δy = Δz = 10 nm.

Simulation Process and Results
To further investigate the controlled modulation performance of the dual-band transmission peak, we perform theoretical simulation analysis study using the control variable method.

The Influence of Microcavity Width on Transmission Spectrum
Firstly, we simulated the variation rule of transmissivity with the width of the microcavity.In this simulation, we controlled the structure parameters P, H, Y, L, h 1 , and h 2 to be constant and set the gap width x to 0.4 μm.The microcavity width w was set as a parametric variable with a variation gradient of 0.2 μm.Thereby, we controlled the duty cycle of the structure by adjusting the variation value of w. Figure 2 plots the dual-band transmission spectrum at different w (0.6 ~ 1.8 μm). Figure 2 clearly confirms that the designed cross-shaped microcavity structure is capable of achieving two transmission peaks in the mid-infrared wavelength range, which is denoted as λ I and λ II .When the microcavity width value is 0.8 μm, the resonant transmission peak λ I reaches its maximum value, which has a peak value at 3.45 μm and a transmission value of 72.4%.At this moment, the resonant transmission peak λ II is 4.56 μm, and the transmission value is 72.9%.The resonant transmission peak λ II reaches its maximum value at the microcavity width value set to 0.6 μm, with a peak value of 4.50 μm and a transmission value of 73.7%.The corresponding resonant  2, it can be seen that when the microcavity width value is 0.8 μm, the full widths at half maximum (FWHMs) values of resonant transmission peaks λ I and λ II are 161.88nm and 328.14 nm, respectively, and when the microcavity width value is 0.6 μm, the FWHM values of resonant transmission peaks λ I and λ II are 183.77nm and 366.17 nm, respectively.Therefore, when the microcavity width is 0.8 μm, the resonant transmission peak FWHMs of this structure are smaller and the performance will be better.It can be seen that the spectral curves of the resonant transmission peak λ I exhibit the blue-shift phenomenon when the value of w is taken in the range of 0.6 ~ 1.4 μm.Generally, the effective refractive index will enlarge with the increase of duty cycle.This is because when the duty cycle is larger, the light transmission in the structure will be closer to free propagation.However, the duty cycle tends to decrease with the increase of w, resulting in a decrease in the effective refractive index of the structure.Thus, the blue-shift phenomenon is generated [21].Resonant transmission peak λ I is insensitive to changes in structure when w increases to 1.6 μm.With the continuous increase of the microcavity width (1.6 ~ 1.8 μm), the length of the transverse electron oscillation of the resonant transmission peak λ I mode within the microcavity increases, resulting in a slight red-shift phenomenon [21].For the resonant transmission peak λ II , it is characterized by an overall blue-shift with increasing w.The main reason for this is that the duty cycle of the structure decreases, resulting in a decrease in the effective refractive index as w increases.By varying the width of the cross-shaped microcavity, the resonant transmission peaks λ I and λ II can be modulated at 3.29 ~ 3.40 μm and 4.24 ~ 4.50 μm, respectively.
To analyze the transmission phenomenon, the electric field distribution in X-Z plane of the cross-shaped microcavity structure at the resonant transmission peak is shown in Fig. 3.In Fig. 3(a I ~ b II ), surface plasmons (SP) will be excited at the surface of the metallic structure when the incident light is irradiated vertically to the designed structure [22].Meanwhile, due to the presence of electrons converging at the upper and lower positions of the structure's gaps, localized surface plasmons (LSP) are generated at the corners of the metallic structure [23][24][25].Besides, it can be seen that longitudinal standing waves, i.e., Fabry-Perot resonance, are formed in the optical microcavity consisting of two C-shaped walls.And this optical microcavity is called Fabry-Perot resonant cavity [26].
As shown in Fig. 3(a I and b I ), the strong local electric field at the resonant transmission peak λ I is mainly concentrated in the gap width positions of the structure as well as in the interior.Due to the existence of edges and corners at the gap width positions, a large number of electrons are accumulated, and therefore, the LSP mode is excited.Moreover, the cross-shaped microcavity structure has a relatively shorter gap spacing, which eventually induces the near-field coupling between the structures [27][28][29].Corresponding to the gap width position above the cross-shaped microcavity structure, the intensity of the strong local electric field weakens with increasing w.In the interior of the cross-shaped microcavity structure, the electric field intensity induced by the Fabry-Perot resonance attenuates sharply with the increase of w.It is sufficiently demonstrated that the resonant transmission peak λ I is weakly influenced by the LSP.For the electric field distribution at the resonant transmission peak λ II (Fig. 3 (a II and b II ), we observe that the electric field intensity at the gap width position above and below remains almost constant as w increases.The variation of the electric field intensity is mainly concentrated in the interior of the structure, which is attributed to the active role played by the Fabry-Perot resonance.According to the transmission line theory [30], the reduction of the overall impedance of the structure would lead to an increase in transmittance at the non-resonant broadband [21].

The Influence of Gap Width on Transmission Spectrum
Subsequently, we explored the improvement effect of the variation of the gap width on the transmission performance of the structure.In this simulation, we set the structural parameters P, H, Y, h 1 , and h 2 to fixed values and gave a value of 0.8 μm for the microcavity width w.The parameter variable was the gap width x, and the variation gradient was 0.1 μm.The dual-band transmission spectral curves at different gap widths x are shown in Fig. 4. With the increase of x, red-shift phenomenon occurs in both the resonant transmission peaks λ I and λ II .It is particularly evident that To analyze the reasons for the generation of transmission peaks, we simulated the electric field distribution at the corresponding wavelengths.As depicted in Fig. 5, the LSP is excited at the gap width position, and Fabry-Perot resonance is generated inside the cross-shaped microcavity.Accompanied by the increase of x, the overall electric field intensity of the structure tends to weaken.In which, the electric field intensity at the gap position corresponding to the resonant transmission peak λ I has the largest change in magnitude (Fig. 5(a I and b I )).It is mainly due to the increase in the distance between the cross-shaped walls, which causes the LSP resonance mode at both ends to weaken, thus presenting a weakening of the electric field intensity.And for the electric field inside the cross-shaped microcavity, it is slightly enhanced.This is because the increased distance permits lighter to enter the interior of the microcavity, triggering the Fabry-Perot resonance enhancement, and thereby the electric field intensity becomes stronger.For the resonant transmission peak λ II (Fig. 5(a II and c II )), the variation trend Fig. 3 Electric field distribution at the resonant transmission peaks at fixed x conditions Fig. 4 Transmission spectral curves at different gap widths at the gap width position is the same as that of λ I .However, the weakening of the electric field intensity inside the microcavity is more significant compared to λ I , which is due to the reduction of the impedance of the structure as a whole [30].

The Influence of Pitch Height on Transmission Spectrum
Subsequently, we investigated the effect of pitch height variation on improving the transmission properties of the structure.In this simulation, we set the structural parameters P, H, Y, and w to fixed values and gave a value of 0.7 μm for the gap width x.The parameter variable was the microcavity height h 1 with a variation gradient of 1 μm. Figure 6 shows the two-band transmission spectral profiles for different microcavity heights h 1 .As h 1 increases, the resonant transmission peak λ I undergoes a series of redshifts, blueshifts, and redshifts, while the resonant transmission peak λ II undergoes a blueshift followed by a redshift, both with over 80% transmission.The results show that the resonant transmission peaks λ I and λ II can be modulated to 3.40 ~ 3.47 μm and 4.45 ~ 4.63 μm, respectively, by changing the gap width of the cross-shaped microcavity structure.
At the peak of the resonant transmission λ I , the LSP of the prismatic excitation at the upper and lower surfaces of the structure remains essentially constant as h 1 increases, as can be seen from Fig. 7(a I ~ e I ).From Fig. 7(a I ~ c I ), the Fig. 5 Electric field distribution at the resonant transmission peaks at fixed w conditions Fig. 6 Transmission spectral curves at different h 1 conditions LSP of the angular excitation inside the structure gradually increases as h 1 changes from 1 to 3 μm, while the Fabry-Perot resonance intensity inside the structure remains essentially constant.From Fig. 7(c I ~ d I ), it can be seen that as h 1 changes from 3 to 4 μm, the LSP of the prismatic excitation inside the structure decreases, and the intensity of the Fabry-Perot resonance inside the microcavity of the structure also decreases.As h 1 changes from 4 to 5 μm, it can be seen from Fig. 7(d I ~ e I ) that the LSP excited by the angles inside the structure further weakens, but the intensity of the Fabry-Perot resonance generated within the structure increases.This leads to a redshift, blueshift, and redshift again of the resonant transmission peak λ I .At the peak of resonant transmission λ II , the change in the electric field of the structure is more pronounced as h 1 increases, as seen in Fig. 7(a II ~ e II ).As h 1 changes from 1 to 3 μm, it is clear from Fig. 7(a II ~ c II ) that the LSP of the prismatic excitation inside the structure does not change much; however, the strength of the Fabry-Perot resonance of the structure is weakened, resulting in a blue shift of the peak resonant transmission λ II .As h 1 changes from 3 to 5 μm, the enhancement of the LSP and Fabry-Perot resonance in the structure can be seen by Fig. 7(c II ~ e II ), leading to an increase in the intensity of the electric field in the structure and a red shift of the resonant transmission peak λ II .

The Influence of Combined Action on Transmission Spectrum
Finally, we investigated the enhancement effect on the transmission performance of the structure by simultaneously varying the microcavity width and gap width, for which the optimal structure parameters are obtained.During the simulation, the structure parameters such as P, H, Y, h 1 , and h 2 are kept as fixed values.The duty cycle of the whole structure is adjusted by changing x and w synchronously.We established the initial values of x and w in the software, which are 0.2 μm and 0.3 μm, respectively.Then, they will be varied in the ratio of 1:1, and the gradient of variation is 0.2 μm in both.
Figure 8 illustrates the transmission spectral curves of the structure for different x and w conditions.In the case of increasing both microcavity width and gap width, the resonant transmission peaks λ I and λ II undergo blue shift in the whole.Also, there is a visible enhancement of transmittance here.The spectral widths of λ I and λ II are broadened as well, and the degree of broadening is gradually increased.In addition, the transmittance at the non-resonant peak is tremendously improved.From the conclusions in Figs. 2, 4, 6, and 8, we believe that the cross-shaped microcavity structure is strongly influenced by the width of the microcavity.This is mainly attributed to the increase in the microcavity width, which will lead to an increase in the electron oscillation length and consequently to the blue shift phenomenon.The maximum resonant transmission peaks are achieved for the designed structure when x and w are increased to 1.3 and 1.4 μm, respectively.The corresponding central wavelengths of the resonant transmission peaks λ I and λ II are 3.24 μm and 4.07 μm, with transmittance up to 94.5% and 92.6%, respectively.By simultaneously changing the microcavity width and gap width, the resonant transmission peaks λ I and λ II can be modulated at 3.23 ~ 3.46 μm and 4.06 ~ 4.60 μm, respectively.
The simulated electric field distribution at the corresponding wavelengths is shown in Fig. 9.As the microcavity width and the gap width continuously enlarge, the LSP effect is still excited at the gap width position (Fig. 9(a I and a II )), However, the electric field intensity at this position decreases dramatically when x and w increase to 1.4 μm and 1.8 μm (Fig. 9(b I and b II )).The main reason is that the duty cycle of the structure is reduced to the extent that the near-field coupling between the gap widths is difficult to maintain.Thus, the plasmon resonance between the gap widths disappears, contributing to a significant attenuation of the localized electric field intensity.Similarly, the Fabry-Perot resonance intensity inside the microcavity is significantly reduced due to the excessive length of electron oscillation caused by the large width of the microcavity.In particular, in terms of transmittance, the overall trend is improving.Furthermore, the near-field coupling between the structures is enhanced.All of these benefits from the structure's reduced duty cycle, which makes the overall structure's impedance extremely weak [27][28][29].
To investigate the absorption and reflection of the structure, the parameters in Fig. 8 were studied at x = 1.3 μm and w = 1.4 μm, as shown in Fig. 10.Combined with the electric field distribution in Fig. 9, it can be seen that the absorbance and transmittance of the structure are equally influenced by the LSP and Fabry-Perot resonance strengths in the structure.Due to the excessive gap in the structure, more light sources pass through the slit, resulting in an enhanced transmittance of the structure and a reduction in the overall absorption and reflection of the structure.In addition, it can be seen that the transmission is just about 90% at two peaks and mainly of the rest energy is absorbed by the structure.
In order to further investigate the resonant modes of the cross-shaped microcavity structure, the quality factor (Q-factor) of the filter was introduced.Q-factor can be calculated by Q = λres/FWHM λres [31], and the results are shown in Fig. 11a.Apparently, the Q-factor of the crossshaped microcavity structure gradually decreases with the increase of the width of the microcavity and the width of the gap, and yet the overall transmission performance of the cross-shaped microcavity structure is increased.However, when x = 1.3 μm and w = 1.4 μm, the Q factor will show a trend of z enhancement, and the Q factors at resonant transmission peaks λ I and λ II are 12.11 and 19.11, respectively, and the transmission performance of the cross-shaped microcavity structure will be further improved.
To quantify Q-factor and transmission, the product of Q-factor (Q) and transmission (T) is defined as the figure of merit, which is given by FOM = Q × T [31].As shown in

Conclusion
In summary, we have designed a cross-shaped microcavity metamaterial structure operating in the mid-infrared band (3 ~ 5 μm).With this structure, the effect of the variation of the cross-shaped microcavity structure parameters on the enhanced transmission is studied.By adjusting the microcavity width and gap width to control the duty cycle of the structure, the resonant transmission peaks λ I and λ II can be modulated in a small range.The corresponding tuning ranges are 3.23 ~ 3.46 μm and 4.06 ~ 4.60 μm, respectively.Under the excitation of the external optical field, the localized plasmon resonance phenomenon will be generated at the gap between the upper and lower surfaces of the C-shaped symmetric structure, leading to a significant near-field enhancement effect.In addition, selective super-transmission will be achieved in band 3 ~ 5 μm by means of the mode hybridization effect.Under the influence of microcavity width and gap width, with the smaller duty cycle of the cross-shaped microcavity structure, the electric field intensity excited in the structure is weakened, but the transmission intensity is enhanced, and its cross-shaped microcavity structure can lead to a maximum FOM of 17.70.It should be noted that the fabrication of this sample is indeed a very challenging work.while some similarly challenged samples have already been achieved in recent articles [32].We believe that with the continuous development of micro-nano manufacturing technology, this structure can be fabricated.This research implemented a dual-band transmission modulation filter with a relatively simple structure and controlled modulation that can support mid-infrared band incidence.We are eager for this study to provide a design reference for the preparation of filter elements for mid-infrared detectors.

Fig. 1
Fig. 1 Schematic diagram of structure.a Cross-shaped microcavity structure three view.b Unit Structure X-Z plane view

Fig. 7 1 Fig. 8
Fig. 7 Electric field distribution for the resonant transmission peak under different h 1

Fig. 9
Fig. 9 Electric field distribution at the resonant transmission peaks at fixed x and w conditions

Fig. 8 ,
Fig. 8, the FOM of the resonant transmission peak λ I of the cross-shaped microcavity structure obtains a maximum value of the 13.28 at x = 0.3 μm and w = 0.4 μm, while the FOM of the resonant transmission peak λ II is 8.96.The FOM of the resonant transmission peak λ II of the cross-shaped microcavity structure obtains a maximum value of the 17.70 when x and w increase to 1.3 μm and 1.4 μm, respectively.At this point, the resonant transmission peak λ I reaches the 11.45.The numerical simulation results obtained after careful consideration of the trade-offs confirm that the cross-shaped microcavity structure designed to have a unique gap configuration and high figure of merit.It can be expected to be applied in biotechnology, medical diagnosis, and other fields.

Fig. 11
Fig. 11 From the data in Fig. 6: a Q factor, b FOM