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Abstract
The designs of single ellipse-shape metamaterials (SESM) and cross ellipse-shape metamaterials (CESM) in the infrared (IR) wavelength range are presented. They are composed of a tailored gold (Au) layer on a silicon (Si) substrate. The characterizations of the proposed devices can have their electromagnetic responses manipulated between single-band and dual-band resonances by changing different ratios of the macro-axis and minor-axis of the ESM. The electromagnetic behavior of the dual-band resonance exhibits the resonance with a broad bandwidth or narrow bandwidth. The corresponding free spectral range (FSR) could be tuned 90 nm in transverse electric (TE) mode and 224 nm in transverse magnetic (TM) mode for SESMs. For CESMs, the FSR could be tuned 153 nm in TE mode and 230 nm in TM mode. Depending on the design of symmetrical or asymmetrical ESM, we can design ESM-like nanostructures to realize the IR filter, polarization switch, band switch, and high-efficiency sensor applications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Infrared (IR) metamaterials are specific periodic structures or aperiodic structures whose feature sizes are approximately few micrometers to nanometers. Owing to metamaterials possess unique electromagnetic characteristics that are unable to be found in natural materials and have great research values [1–3], such as negative refraction [4,5], superlens [6,7], invisibility cloaking [8,9], artificial magnetism [10], and so on. These enormous attractions of metamaterial characteristics have been inspired many fascinating aspects in science. In view of these merits of metamaterials, there have been reported many literatures to demonstrate metamaterials used in widespread applications, such as filter [11,12], sensor [13–17], absorber [18–23], switch [24], reflector [25], and polarization converter [26,27]. According to the transportation optics theory, the electromagnetic wave could be manipulated the corresponding amplitude, wavelength, phase, direction, and polarization [12,28]. Therefore, by properly tailoring the geometrical dimension of metamaterial, it can be realized electro-optic devices spanning the wavelength ranges from microwave, IR, visible to ultraviolet.
In the past two decades, metamaterials were demonstrated by using subwavelength wires [29,30], fishnet structures [31,32], stacked metal-dielectric layers [21,33], hole arrays [34,35], and cross-shape metamaterials [28,36] owing to their distinct electromagnetic characteristics to realize filter, polarizer, and switch applications. Therefore, it is obvious that metamaterial plays an important role in opto-electronics, solid-state physics, and biomedical fields.
Although there have been reported many literatures of IR metamaterials using metallic disk, ring, U-shape, L-shape, and so on [37–40], there are few researches present the relationship of elliptic metamaterial with different ratio of minor-axis and macro-axis to electromagnetic response. In this study, we propose the designs of single ellipse-shape metamaterial (SESM) and cross ellipse-shape metamaterial (CESM) with different ratio of minor-axis and macro-axis of each design in infrared (IR) wavelength range. The electromagnetic behaviors of devices are performed by using Lumerical Solution’s finite difference time-domain (FDTD) based simulations to study the corresponding optical properties. The designs of SESM and CESM are composed of a textured gold (Au) layer on silicon (Si) substrate. The propagation direction of incident light is set to be perpendicular to the x-y plane in the numerical simulations. Periodic boundary conditions are also adopted in the x and y directions and perfectly matched layer (PML) boundaries conditions are assumed in the z direction. SESM and CESM exhibit extraordinary optical characteristics, such as switch functions of single-band to dual-band, narrow-band to broad-band resonances and tunable free spectral range (FSR). These superior characteristics are contributed to the arrangement of minor-axis and macro-axis of SESM and CESM. While the structures of SESM and CESM are responsible for the spectral response, unique electromagnetic behavior of incident light can be achieved by properly modifying the geometry of metamaterial. The merits of proposed SESM and CESM are simple structures, easy to manufacture, and low cost. Such strategy provides the great potential uses for next generation IR opto-electronic devices, such as various filter, polarizer, switch, sensor, and so on.
2. Designs and methods
Figure 1 shows the schematic drawings of proposed SESM and CESM. The composition is a tailored Au layer with 200 nm in thickness on Si substrate. We define the ratio of minor-axis (b) and macro-axis (a) of SESM or CESM as r = b/a. For the discussion of the influence of r value, a parameter is kept as constant while b parameter is variable. The periods of SESM and CESM are kept as constant as Px = Py = 3 µm. The coordinates of incident electromagnetic wave are indicated in Fig. 1(a) and (b) for SESM and CESM, where E, H, and k are the electric field, magnetic field, and Poynting vector of electromagnetic wave, respectively. The electromagnetic wave is normal incidence along z-axis.
Fig. 1. Schematic drawings of (a) single ellipse-shape metamaterial (SESM) and (b) cross ellipse-shape metamaterial (CESM), where Px, Py, and thickness of Au layer are kept as constant as 3 µm, 3 µm, 200 nm, respectively.
In the case of SESM, the r value is denoted as r0, while a and b are denoted as a0 and b0, respectively as shown in Fig. 1(a). In Fig. 1(b), r values of CESM are denoted as r1 and r2, which the minor-axes are b1 and b2 along x-axis and y-axis, while the macro-axes are a1 and a2 along y-axis and x-axis, respectively. The corresponding resonant wavelength of SESM and CESM can be obtained by [41]
3. Results and discussion
Figure 2(a) and (b) show the transmission spectra of SESM with different r0 value at transverse electric (TE) and transverse magnetic (TM) modes, respectively. By changing the minor-axis (b0) and kept the macro-axis (a0) as constant as 1.5 µm, the electromagnetic response is single-band dip resonance (ω0) at 3.104 µm for r0 = 1.0 at TE and TM modes. When r0 = 0.9, the resonance becomes polarization-dependence that has two resonances (ω1 = 3.114 µm and ω2 = 3.358 µm) at TE mode, while there is only one resonance (ω0 = 3.098 µm) at TM mode. By decreasing r0 = 0.7, the electromagnetic behaviors are two dip resonances at 3.117 µm and 3.266 µm for TE mode and two peak resonances at 3.023 µm and 3.400 µm for TM mode. At TE mode, the electromagnetic response is nearly identical for r0 = 0.7 and 0.6, there are two dip resonances. While r0 = 0.5 to 0.2, the electromagnetic response becomes two peak resonances, which are blue-shift 60 nm and 107 nm for ω1 and ω2, respectively as shown in Fig. 2(a). At TM mode, there are two peak resonances for r0 = 0.8 to 0.2, which are red-shift from 3.011 µm and 3.302 µm to 3.047 µm and 3.648 µm for ω1 and ω2, respectively as shown in Fig. 2(b). The corresponding tuning ranges are 36 nm and 346 nm. The tuning ranges of FSR of SESM with different r0 value from 0.9 to 0.2 at TE mode and 0.8 to 0.2 at TM mode are varied from 244 nm to 154 nm and 377 nm to 601 nm, respectively.
The relationship of resonance (ω2) and r0 is summarized in Fig. 3(a). To understand the physics mechanism of the narrow stop band becomes two pass bands, it can be explained by the full field distribution as the E-field and H-field distributions of SESM shown in Fig. 3(b). It shows the E-field and H-field distributions of r0 = 0.2, 0.5, 0.8, and 1.0, respectively. When r0 = 1.0, the SESM is a circle disk structure. The resonances are identical at TE mode and TM mode. When r0 is varied from 1.0 to 0.1, the resonance is blue-shift for TE mode and red-shift for TM mode. When r0 > 0.6, the pattern of Au layer occupies the most area of ESM structure. The electromagnetic behavior is a resonant dip (ω0) caused from the dipolar resonance. When 0.3 ≤ r0 ≤ 0.6, the area of Au pattern is not enough to make the coupling effect within ESM structure. The coupling efficiency of electromagnetic wave into ESM structure is weaker. Therefore, the transmission intensity becomes lower. When r0 < 0.3, the resonant peaks are generated from the interface of Au layer and Si substrate (ω1) and ESM structure (ω2), which can be explained the reason that ω1 is invariable while ω2 can be modulated by changing r0 value. According to full field distributions as shown in Fig. 3(b), the E-field energies are focused on the contour of SESM along x-direction while the H-field energies are focused on four corners of SESM to generate the ω2 resonance. By tailoring the geometrical dimension of ESM, ω2 is shift and ω1 is almost kept as constant.
Fig. 3. (a) The relationship of resonance (ω2) and r0 of SESM at TE and TM modes. (b) The E-field and H-field distributions of SESM with r0 = 0.2, 0.5, 0.8, and 1.0 are monitored at normal incident electromagnetic wave, respectively.
Figure 4 shows the transmission spectra of CESM with different r value at TE mode and TM mode. By changing the ratio (r = b1/a1 = b2/a2), two ellipse-shape nanostructures of CESM along x- and y-axis are varied simultaneously. It means the electromagnetic behaviors are identical at TE and TM modes. The electromagnetic responses of CESM with r = 1.0, 0.9, 0.8, 0.7, and 0.6 exhibit single-band resonant dip (ω0) at 3.104 µm for TE and TM modes. The electromagnetic responses are nearly identical for r = 1.0 to 0.6, which is only one resonant dip. This shows that CESM compensates the asymmetry of the former SESM in horizontal direction. While r is varied from 0.5 to 0.2, the resonant dip is gradually vanished while there appears first resonant peak (ω1) kept as constant at 3.002 µm and second resonant peak (ω2) is red-shift from 3.235 µm to 3.412 µm at TE and TM modes. The spectra are polarization-independence owing to the symmetrical structures of two ellipse-shape nanostructures of CESM. The tuning ranges of FSR of CESM with different r value from 0.5 to 0.2 are varied from 243 nm to 410 nm for TE and TM mode.
The relationship of resonance and r for CESM is summarized in Fig. 5(a). The E-field and H-field distributions of CESM are shown in Fig. 5(b). When r varies from 1.0 to 0.6, the resonance is kept at 3.104 µm. The bandwidth of transmission wavelength is broad. By changing r from 0.5 to 0.1, the resonance is red-shift with narrowband. The trend is different compared to that of Fig. 3. (a). It indicates the electromagnetic characteristics of CESM are between those of SESM at TE mode and TM mode. It is very reasonable because CESM is the combination of two SESM in horizontal and vertical directions. Figure 5. (b) shows the E-field and H-field distributions of r = 0.2, 0.5, 0.8, and 1.0, respectively. It can be seen that E-field and H-field energies are focused on two sides of the lateral ESM.
Fig. 5. (a) The relationship of resonance and r for CESM. (b) The E-field and H-field distributions of CESM with r = 0.2, 0.5, 0.8, and 1.0 are monitored at normal incident electromagnetic wave, respectively.
To figure out the influence of the ratio of r1 and r2, r1 is kept as constant as 0.1 and r2 is varied from 0.1 to 1.0 as shown in Fig. 6. Figure 6(a) and (b) are the transmission spectra of CESM with different r2 by keeping r1 as constant as 0.1. The electromagnetic response is single-band and polarization-independent with a resonance dip (ω0) at 3.104 µm for r2 varied from 1.0 to 0.9 at TE and TM modes. When r2 is 0.8, the resonance becomes polarization-dependence that has two resonances at TE mode (ω1 = 3.005 µm and ω2 = 3.238 µm) and TM mode (ω1 = 3.011 µm and ω2 = 3.299 µm). At TE mode, the electromagnetic response is nearly identical for r2 is 0.7 and 0.6. When r2 is varied from 0.5 to 0.2, resonance dip (ω0) is vanished and there are two resonant peaks (ω1 and ω2) varied from 3.002 µm to 3.029 µm and from 3.193 µm to 3.373 µm for ω1 and ω2, respectively. The corresponding tuning ranges are 27 nm and 180 nm. At TM mode, there are two resonant peaks for r2 varying from 0.8 to 0.2. The tuning range of ω1 is 30 nm from 3.011 µm to 3.041 µm and that of ω2 is 260 nm from 3.299 µm to 3.559 µm. The tuning ranges of FSR are 153 nm from 191 nm to 344 nm and 230 nm from 288 nm to 518 nm for TE mode and TM mode, respectively.
Fig. 6. Transmission spectra of CESM with different r2 at (a) TE mode and (b) TM mode. The r1 is kept as constant as 0.1.
Figure 7. (a) shows the relationship of resonance and r2 of CESM by keeping r1 as constant as 0.1. The electromagnetic response of CESM with different r2 exhibits hysteresis behavior at TE and TM modes. Figure 7(b) shows the E-field and H-field distributions of r2 = 0.2, 0.5, 0.8, and 1.0, respectively. The E-field energy is focused on top and bottom sides of horizontal ESM (along x direction) while the H-field energy is focused on top and bottom sides of vertical ESM (along y direction). It is clearly explained the characteristics of electromagnetic response at TE mode mainly depends on the horizontal ESM while that at TM mode mainly depends on the vertical ESM.
Fig. 7. (a) The relationship of resonance and r2 for CESM. (b) The E-field and H-field distributions of CESM with r2 = 0.2, 0.5, 0.8, and 1.0 are monitored at normal incident electromagnetic wave, respectively. The r1 is kept as constant as 0.1.
To further understand the electromagnetic behaviors of ESM with different r2 by keeping r1 as constant, the relationships of resonance peak (ω2) and r2 of CESM under the conditions of r1 = 0.2, r1 = 0.3, r1 = 0.5, and r1 = 0.7 are shown in Fig. 8, respectively. The results exhibit the hysteresis behavior at TE and TM modes, which are identical to those in Fig. 7(a). The TM response is overall blue-shift by increasing r1 value and then saturated gradually and kept as stable at 3.230 µm. While the trend of TE response becomes approximately linearly by increasing r1 value. This can be explained by keeping a2 as constant and changing b2 to define the different r2 value along x direction of ESM as indicated in Fig. 1(b). The electromagnetic characteristics of CESM at TE mode mainly depends on the horizontal ESM while those of CESM at TM mode mainly depends on the vertical ESM.
Fig. 8. The relationships of resonance and r2 for CESM under the conditions of (a) r1 = 0.2, (b) r1 = 0.3, (c) r1 = 0.5, and (d) r1 = 0.7, respectively.
4. Conclusion
In conclusion, we present two types of ESM with different ratio of minor-axis and macro-axis and study the relative transmission characteristics in IR wavelength range. By varying r parameter, the electromagnetic responses of SESM and CESM can be manipulated between single-band and dual-band resonances, broad and narrow bandwidths, and tunable FSR. The tuning ranges of FSR are 90 nm from 244 nm to 154 nm at TE mode and 224 nm from 377 nm to 601 nm at TM mode for SESM. While those of CESM are 153 nm from 191 nm to 344 nm at TE mode and 230 nm from 288 nm to 518 nm TM mode. These results provide an alternative method for the optical switches between resonant peak/dip, board/narrow bandwidth, and single/dual resonance. Such strategy creates the great potential IR applications in related fields.
Funding
Sun Yat-sen University (SYSU) (76120-18831103).
Acknowledgment
The authors acknowledge the State Key Laboratory of Optoelectronic Materials and Technologies of Sun Yat-Sen University for the use of simulation codes.
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