Efficient multiband and broadband cross polarization converters based on slotted L-shaped nanoantennas

Jun Ding; Bayaner Arigong; Han Ren; Mi Zhou; Jin Shao; Yuankun Lin; Hualiang Zhang

doi:10.1364/OE.22.029143

1. Introduction

Manipulation of the polarization state of electromagnetic (EM) waves and light is of practical importance in many optical systems as many phenomena are polarization sensitive in optics. Metamaterials (MMs) are the artificial structures assembled with subwavelength building blocks featuring unusual properties not found in nature or in their constituent materials [1]. Over the past decades, MMs as an alternative to manipulate the wave polarization state have attracted paramount attentions due to a variety of fascinating phenomena, such as negative refraction [2,3] and invisible cloaking [4,5], etc. Recently, various designs of polarizers and wave plates have been achieved through anisotropic and chiral metamaterials structural simplicity and easy fabrication. Researchers have found that the strong polarization dependence working from microwave and terahertz to optical frequency regimes, such as metallic nanoparticles [6–13], subwavelength metallic apertures [14–16], and three-dimensional chiral metamaterials [17,18]. Among these designs, L-shaped and V-shaped metallic nanoparticles and apertures are widely adopted due to the structural simplicity and easy fabrication. Researchers have found that the strong polarization dependence is highly related to the localized surface plasmon excitations arising from the nanoscale particle or slot in these metamaterials [16,19–22]. However, one major disadvantage of polarization converter based on MMs is their narrow operating bandwidth (frequency range, referred as band) owing to their reliance on the resonances. Although many techniques have been proposed to address the issue of narrow bandwidth, broadband and multiple-band polarization converters that can realize different polarization conversions are still highly desirable.

In this paper, we proposed highly efficient cross polarization converters (CPC) operating in the infrared (IR) range, which are composed of a single patterned top layer with planar slotted L-shaped nanoantennas, a silicon dioxide layer (the spacer layer), and a gold ground plane layer. The slotted L-shaped nanoantenna is realized by cutting an extra L-shaped or L-shaped-like slot in the solid metallic antenna. We numerically demonstrate that the CPC can convert the linearly polarized incident wave to its cross polarization with a high efficiency (>0.95) and multiband and wideband responses. From the field analysis, it is found that the resonant frequencies of the designed CPCs are resulted from the plasmon hybridizations of the slots and the metallic nanoantennas. In addition, the angular independence of the polarization conversion effect has been validated. The proposed CPCs feature both flexible properties (e.g., multiband operations) and high conversion efficiency, making them attractive for practical applications.

2. Design

Figure 1(a) schematically depicts the proposed CPC based on the slotted L-shaped nanoantenna structure and the θ indicates the incident angle of the incident wave. The CPC consists of an array of metallic L-shaped nanoantennas with L-shaped slots, and a silicon oxide layer backed by a thick gold ground plane to totally suppress the wave transmission, which is likely to convert a linear polarization completely to its orthogonal state in a reflection mode. Figures 1(b) and 1(c) show the unit cells of the two proposed structures with the geometrical parameters described in the caption, where p represents the periodicity of the unit cell, L and w represent the arm length and width of the metallic L-nanoantenna, respectively, while Li and wi (i = 1,2) are the arm length and arm width of the slots, respectively. Specifically, in the first type of design as shown in Fig. 1(b), L-shaped slot with uniform width is applied. In the second type of design as shown in Fig. 1(c), L-shaped slot with stepped junctions (i.e., L-shaped-like slot) is employed. If w1 = w2, the two types of proposed designs are identical. The thicknesses for the metallic L-antenna and the silicon oxide layer are t_Au and t_sub, respectively. The dielectric constant of the silicon oxide layer is 1.98, and the optical constant of bulk gold in the infrared regime is computed from a Drude model which fits the literature data from Palik [23]: $ε (f) = 1 - {[(f / f_{p} + i γ) f / f_{p}]}^{- 1}$ with $f_{p} = 1886.8$ THz and $γ = 0.0077$ .

Fig. 1 (a) Schematic model of the proposed CPC consisting of array of slotted L-shaped nanoantennas; (b) and (c) unit cells of the proposed designs with L-shaped and stepped L-shaped slots.

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The structure is modeled and simulated using the frequency domain solver of CST Microwave Studio 2014, which is based on the finite integral method. The unit cell boundaries are used in transverse directions and the Floquet ports in the z-direction (referring to Fig. 1(a)). In the analysis, we calculate the complex reflection coefficients for both cross- and co-polarized EM waves with a y-polarized incidence at the incident port due to the symmetry of the geometry. We can define the general reflection matrix R as follows, which describes the complex amplitudes of reflected waves,

R = (\begin{matrix} R_{x x} & R_{x y} \\ R_{y x} & R_{y y} \end{matrix})

where the arbitrary element

R_{l m}

represents the complex amplitude of the reflected wave, linearly polarized in the l direction for excitation in the m direction. Accordingly, we could express

R_{y y} = E_{y r} / E_{y i}

and

R_{x y} = E_{x r} / E_{y i}

to represent the reflection ratio of y-to-y and y-to-x polarization conversions, respectively. The subscript i and r indicate the incident and reflected EM wave, respectively. By defining

R_{l m} = | R_{l m} | e^{j φ_{l m}}

, we represent the reflection phase differences between _{$R_{x y}$} and _{$R_{y y}$} as

Δ φ = φ_{x y} - φ_{y y}

;

Δ φ

can take arbitrary value within

[- π, π]

depending on the operating frequency, indicating that all possible polarization states (i.e., circular, linear, and elliptic) are realizable for the reflected beam. To evaluate the performance of the proposed cross polarization converter, the polarization rotation azimuth angle φ and the polarization conversion ratio (PCR) can be obtained from the reflection coefficients under different polarizations. The φ can be calculated by using the following equation which is derived from the Stokes parameters [24]:

φ = \frac{1}{2} \tan^{- 1} [\frac{2 R \cos (Δ φ)}{1 - R^{2}}]

where

R = \frac{| R_{x y} |}{| R_{y y} |}

, and PCR can be defined as [8]

PCR = {| R_{x y} |}^{2} / [{| R_{y y} |}^{2} + {| R_{x y} |}^{2}] .

3. Results and discussions

To understand the properties of the proposed CPCs, typical polarized reflection spectra of $R_{x y}$ and $R_{y y}$ as a function of frequency for the L-shaped nanoantenna array, the L-shaped nanoslot array, and the slotted L-shaped nanoantenna array are plotted in Figs. 2(a)–2(c), respectively. The detailed geometrical parameters for the slotted L-shaped structure are described in the figure caption, while the parameters for the L-shaped nanoantenna in Fig. 2(a) and nanoslot in Fig. 2(b) are the same as the slotted L-shaped structure in Fig. 2(c). The unit cell structures for these three arrays are also displayed in the inset of each figure. For the L-shaped nanoantenna array (as shown in Fig. 2(a)), we can observe two prominent reflection dips in $R_{y y}$ , and the $R_{x y}$ maintains a high value (~0.9) in a rather broad frequency range. Thus, if proper parameters are selected, the two dips could be moved closer or farther to realize a broadband or dual-band cross-polarization converter [9]. In addition, the z-components of the H field distributions at the two dip frequencies are plotted in the inset of Fig. 2(a) as well. Two different modes at these two dip frequencies can be clearly identified. Meanwhile, for the L-shaped nanoslot array as shown in Fig. 2(b), four reflection dips (they are not prominent due to the relatively small dip depth) could be observed in $R_{y y}$ , and the z-components of the H field distributions at these four dip frequencies are plotted in the insets. Please note that only three different modes occur in this case, while the fourth one is identical to the second one. For the proposed slotted L-shaped nanoantenna array shown in Fig. 2(c), three prominent reflection dips could be observed in $R_{y y}$ . From the Hz field distributions shown in the insets of Fig. 2(c), we can find that the first two dips could be deemed as the hybridization of the modes from the L-shaped nanoantenna and nanoslot, i.e., mode Fig. 2(c).1 is the hybridization of mode Fig. 2(a).1 and mode Fig. 2(b).2, and mode Fig. 2(c).2 is the hybridization of mode Fig. 2(a).2 and mode Fig. 2(b).1. Furthermore, the mode Fig. 2(c).3 is a new induced mode, which is induced by the interaction between the slot and the metallic nanoantenna structure. Compared to the metallic nanoantenna structure, the proposed slotted nanoantenna structure has a third resonant frequency, which could be used to realize an extra operating band.

Fig. 2 Reflection spectra for (a) L-shaped nanoantenna; (b) L-shaped nanoslot; and (c) slotted L-shaped nanoantenna (the z-components of H field (Hz) distributions at reflection dips for each structure are shown in the insets); (d) PCR and rotation azimuth angle φ for the slotted L-shaped nanoantenna structure. (p = 1500, t_sub = 300, t_Au = 50, L = 930, w = 460, L1 = 610, w1 = 25, unit: nm)

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Fig. 3 Simulated $R_{y y}$ and $R_{x y}$ with different (a) length of the solid L-shaped metallic antenna (L); (b) width of the solid L-shaped metallic antenna (w); (c) length of the L-shaped slot (L1); (d) width of the L-shaped slot (w1). (The other parameters are the same as the structure labeled in Figs. 2(c) and 2(d))

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Figure 2(d) shows the calculated PCR and rotation azimuth angle φ for the proposed slotted L-shaped nanoantenna structure shown in Fig. 2(c). As can be seen from Fig. 2(d), the PCR is higher than 0.95 illustrated by the dash-dot-dot line within three bands (i.e., frequency ranges), which indicates nearly total conversion of the cross-polarization of the reflected wave. Note that the PCR nearly achieves unity at the three peaks, (i.e., 69.1 THz, 96.5 THz, and 157.6 THz) corresponding to the resonant frequencies. At all the three resonant frequencies, the rotation azimuth angles approximately equal 90°, which confirms the converter with 90° polarization rotation. Thus, a triple-band cross-polarization converter can be achieved. It is worth mentioning that at frequencies 61.87 THz, 116.05 THz, 148.5 THz and 163.3 THz, the PCR achieves 0.5, and φ approximately achieves ± 45°, which means the incident linearly polarized wave is converted to a circularly polarized one by the designed device.

To better understand the effects of the geometric parameters to the proposed triple-band CPC with L-shaped slot, we conduct parametric studies by varying one physical parameter of the structure in Fig. 2(c) while fixing others. Figures 3(a) and 3(b) demonstrate the simulated reflection spectra ( $R_{y y}$ and $R_{x y}$ ) with different lengths and widths of the metallic antenna (i.e. the solid L-shaped patch), respectively. And Figs. 3 (c) and 3(d) display the simulated reflection spectra with different lengths and widths of the L-shaped slot, respectively. Here L, w, L1, and w1 are as labeled in Fig. 1(b). Note that the shadow part in each figure indicates the third resonance range. As can be seen in Fig. 3(a), the first and second resonant frequencies both decrease as the length L increases (which are consistent with the observations in [9]) and the change in the first resonant frequency is larger than the second one; while the center of third resonant frequency does not change too much, only the reflection ratio $R_{y y}$ becomes smaller and achieves almost 0 with L = 930 nm, which means nearly total cross polarization conversion. In Fig. 3(b), as the width w increases, we observe that the first resonant frequency almost remains the same, and both the second and third resonant frequencies slightly decrease, and the operating bandwidth for the third resonant frequency becomes wider. In Fig. 3(c), as the length of the slot L1 increases, all three resonant frequencies almost keep the same, although the reflection ratio $R_{y y}$ ( $R_{x y}$ ) becomes smaller (larger), which indicates a better polarization conversion. In Fig. 3(d), as the width of the slot w1 increases, the first and third resonance frequencies almost keep the same, while the second resonant frequency slightly increase. The results shown in Fig. 3 have clearly demonstrated that, although the resonances of the slotted L-shaped structure might be complicated, the resonant frequencies can be manipulated by adjusting its geometric parameters.

It is found that each operating band for the proposed triple-band CPCs presented above is still narrow due to the reliance on resonances, many methods have been applied to achieve broadband functions [9,10,25]. Here, the method utilized in [10] is adopted to realize a wideband CPC by adjusting the substrate thickness because the dispersion of the metallic structures could be cancelled out by the thickness-dependent dielectric layer. Figure 4(a) shows the simulated reflections $R_{y y}$ and $R_{x y}$ of the structure in Fig. 2(c) with different thicknesses of the silicon oxide layer t_sub. As the thickness increases, the second resonant frequency moves toward the first resonant frequency, along with the decrease (increase) of $R_{y y}$ ( $R_{x y}$ ) between the two resonant frequencies, and although the third resonant frequency almost keeps the same, the $R_{y y}$ decreases dramatically. The PCRs for three different t_sub are plotted in Fig. 3(b), from which we can notice that as the first two resonant frequencies move close enough, the original first two bands merge into a wider one as t_sub increases. However, for the original third band (now the second band), as t_sub increases, the conversion efficiency decreases significantly (i.e., the PCR < 0.85). In order to realize the broadband property in the first band (by combining the first two bands of the proposed triple-band CPC) and keep the high efficiency in the second band (the third band of the proposed triple-band CPC), we proposed a new design by replacing the L-shaped slot with the stepped one, inspired by the wideband property of the stepped structure [26]. Figure 4(c) demonstrates the simulated $R_{y y}$ and $R_{x y}$ with different L1 (Note: L1 + L2 is fixed during the sweeping of L1) of the stepped slot as shown in Fig. 1(c) with the detailed parameters described in the figure caption. As L1 increases, the first two resonant frequencies remain unchanged, while the third resonance frequency decreases without affecting the bandwidth too much. The w1 has the similar effect, which is not shown here. Figure 4(d) shows the PCR and rotation azimuth angle φ for the stepped design with L1 = 400 nm. Compared to the non-stepped one in Fig. 4(b), not only the bandwidth of the first band is increased (i.e., from 63.5 THz to 93.2 THz), but also the bandwidth of the second band is increased for the CPC with stepped L-shaped slot. More importantly, within the second band (i.e., from 144.4 THz to 154.8 THz), the conversion efficiency is much higher.

Fig. 4 (a) Simulated R_yy and R_xy and (b) PCRs for the proposed slotted L-shaped CPC in Fig. 2(c) with different substrate thickness t_sub; (c) Simulated R_yy and R_xy for the proposed CPC with stepped slots as shown in Fig. 1(c) (p = 1500, L = 930, w = 460, w1 = 120, L2 = 210, w2 = 40, unit: nm); (d) PCR and rotation azimuth angle φ for the proposed CPC with stepped L-shaped slots (L1 = 400 nm).

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Furthermore, the effect of the incident angle θ for the broadband CPC with stepped L-shaped slot shown in Fig. 4(d) is investigated theoretically. The reflectivity spectra of ${| R_{y y} |}^{2}$ and ${| R_{x y} |}^{2}$ over the frequency range [50,165] THz have been plotted in Figs. 5(a) and (b) as a function of incidence angle from 15° to 45°, respectively. The ${| R_{x y} |}^{2}$ ( ${| R_{y y} |}^{2}$ ) keeps a high (low) value as shown in Fig. 5(b) (Fig. 5(a)) in the first broad working band, which indicates that the first two resonant frequencies of the triple-band CPC (as shown in Figs. 1(b) and 4(b)) appear to be independent of θ. However, as can be seen from Fig. 5(b), for the second band, the value of ${| R_{x y} |}^{2}$ is large for low θ and varies a lot as θ increases, which means the resonance is dependent of θ. These observations can be confirmed from the PCRs for three different incidence angles, i.e., θ = 15°, 45°, and 75° plotted in Fig. 5(c), from which we can notice that each band is split into multiple sub-bands, and more sub-bands appear as the incidence angle increases. Nevertheless, the center resonant frequency for the first broad band almost keeps the same. In Fig. 5(d), the mean PCR over different incident angles is plotted. Since the PCR in the second broad band (i.e., frequency range [144.4, 154.8] THz) is split into many sub-bands and the center of the resonant frequency is also shifted a lot, only the mean PCR for the first band (i.e., frequency range [63.5, 93.2] THz) is calculated and displayed in this figure. As can be seen from Fig. 5(d), the mean PCR in this range remains higher than 0.8 up to 47°. These results show that the proposed CPC with L-shaped slots appears to be independent of the incidence angle at the first two resonant frequencies of the triple-band CPC and the first broad band of the broadband CPC, which could be the result of the hybridization of the localized resonant modes from the slot and the metallic nanoantenna.

Fig. 5 Reflectivity for (a) ${| R_{y y} |}^{2}$ and (b) ${| R_{x y} |}^{2}$ as a function of the incidence angle; (c) the PCR for different incidence angles; (d) the mean PCR in the frequency range [63.5, 93.2] THz.

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4. Conclusions

In conclusion, we have numerically demonstrated multiband/broadband cross polarization converters based on metamaterial structures with a very high efficiency (PCR>0.95) in IR regime. The first type of proposed slotted L-shaped CPCs can convert a linearly polarized wave to its cross polarized wave at three different resonant frequencies, which are the results of the mode hybridizations between the slot and the metallic nanoantenna. Moreover, the second resonant frequency could gradually move toward the first one by increasing the substrate thickness, thus, the first two sub-bands can merge into a broad one. However, the efficiency within the original third band decreases significantly. This issue could be addressed by replacing the L-shaped slot with a stepped one, which widens both bands and achieves much higher conversion efficiency in the second broad band. Furthermore, we have also demonstrated that the first broad band (or the first two resonant frequencies) of the converters is independent of the incidence angle (up to 47°), which could be resulted from the localized mode hybridization of the resonances between the slot and the solid metallic structure. The proposed multiband/broadband cross polarization converters may have great potential for the design of efficient wave manipulation components in microwave, terahertz, and optical regimes.

Acknowledgments

This work is supported by research grants from the U.S. National Science Foundation under Grant Nos. ECCS-1128099, CMMI-1266251, and CMMI-1109971.

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Efficient multiband and broadband cross polarization converters based on slotted L-shaped nanoantennas

Abstract

1. Introduction

2. Design

3. Results and discussions

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (5)

Equations (3)

Optics Express