Broad dual-band asymmetric transmission of circular polarized waves in near-infrared communication band

Deng Fei Tang; Chuan Wang; Wei Kang Pan; Min Hua Li; Jian Feng Dong

doi:10.1364/OE.25.011329

1. Introduction

Recently, owing to their novel electromagnetic properties, metamaterials (MMs) have been proposed to achieve polarization rotation. MMs have potential applications in intriguing photonics devices, such as linear-to-circular (LTC) polarization conversion devices [1–4], polarization converters (RPC) [5–7], diode-like devices [8]. In 2006, Fedotov et al. [9] firstly observed a novel electromagnetic phenomenon called “planar chiral circular conversion dichroism” (asymmetric transmission, AT). The magnitude of transmission wave is related to the direction of wave propagation that is similar to Faraday effect in some way, but requires no magnetic media. In comparison, Faraday effect does not have polarization limitation while AT effect has. Faraday effect does not hold reciprocity, but on the contrary AT effect satisfies the validity of the reciprocity lemma. Subsequently, asymmetric transmission has attracted enormous attention. Numerous MMs have been intensively investigated to realize AT effect. In 2011, Kang et al. [10] theoretically demonstrated that special structures breaking the symmetry in the principal propagation direction could realize the AT for linearly polarized light only. Besides, many research groups investigated high cross-polarization conversion [11] and broadband [12–14], dual-band [15,16] AT for linearly polarized waves. In terms of circularly polarized waves, many sophisticated MMs structures have obtained the AT effect but they suffer from either low magnitude [10,17,18] or narrow frequency band [19,20] which restrict their applications seriously. Gansel et al. [21] proposed a gold helix photonic metamaterial as broadband circular polarizer. However, the fabrication processes of helical metamaterials are complex and difficult. Many efforts have been devoted to increase the magnitude [22] and broaden the spectral band [23,24] of AT. During the past two years, dual-band [25–27] unidirectional circular polarizers are proposed, nevertheless, the AT parameters are not exceed 0.35. Recently, three-layered chiral MMs were particularly attractive to acquire larger AT parameter with single bandwidth at microwave [28] and near-infrared communication band [29,30]. In near-infrared communication band, to the best of our knowledge, there are no literatures about the realization of broad multi-band together with high magnitude AT effect.

In this paper, the rotated structure we proposed is motivated by two identical split-ring resonators with various twist angles proposed by Na Liu et al [31] that offers a way to engineer complex plasmonic nanostructures with a tailored electromagnetic response. Combining the handedness of G-shaped nanostructure that had already been demonstrated by V. K. Valev et al. [32], and Fabry-Perot like resonance cavities, we have achieved aforementioned properties and enable a dramatic improvement of AT effect. To begin with, we study the response of the cavity AB. Then we compare the electromagnetic responses of cavity AB and whole structure ABC to validate this enhanced effect that caused by cavities.

Noticeably, the structure we proposed can realize simultaneously asymmetric transmission of linearly and circularly polarized waves by introducing the rotation angle between two G-shape metallic layers. The geometric parameter l of the G-shape modulates the AT effect of circularly polarized waves and the gap size g modulates the AT effect of linearly polarized waves. These properties are not observed in previous works.

2. Model and method

The proposed structure is composed of three-layer metals which are illustrated in Fig. 1. Layer A consists of a G-shape nanostructure. Layer C is the mirror of G-shape and then rotated 180° along the z-axis. Layer B is composed of four tilting sub-wavelength nanowires and it is sandwiched in the layers A and C. These three layers are oriented at 45° with respect to the y axis and inserted in the dielectric substrate of silica with relative permittivity 2.25 as shown in Fig. 1(d). Figures 1(a) and 1(b) are the front view of the layer A, B and Fig. 1(c) is the back view of the layer C, respectively. Figure 1(e) is the perspective view of a whole unit cell. The Drude model is selected to describe the metal silver in this paper, the effective permittivity of silver in the infrared spectral region is given by [33]:

ε (ω) = 1 - \frac{ω_{p}^{2}}{ω (ω + i ω_{c})}

where

ω_{p}

is the plasma frequency,

ω_{c}

is the collision frequency. (

ω_{p} = 2 π \times 2.175 \times 10^{15} s^{- 1}

,

ω_{c} = 2 π \times 6.5 \times 10^{12} s^{- 1}

). We apply periodic boundary conditions in the x and y directions while opening condition along the z direction. The structure parameters of the MMs are as follows: ax = ay = 300 nm, w1 = 22 nm, w2 = 28 nm, l = 75 nm, g = 45 nm, d = 120 nm, L = 158 nm, s = 30 nm.

Fig. 1 Schematic diagram of the unit cell: (a),(b) the front view of the layers A, B; (c) the back view of the layer C; (d) left view of one unit cell; (e) perspective view of the structure.

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For linearly polarized light, the T-matrix connects the generally complex amplitudes of the incident field to the complex amplitudes of the transmitted field [20]:

(\begin{matrix} T_{x} \\ T_{y} \end{matrix}) = (\begin{matrix} T x x & T x y \\ T y x & T y y \end{matrix}) (\begin{matrix} I x \\ I y \end{matrix}) = (\begin{matrix} A & B \\ C & D \end{matrix}) (\begin{matrix} I x \\ I y \end{matrix}) = {\hat{T}}_{l i n}^{f} (\begin{matrix} I x \\ I y \end{matrix})

Here we replace

T_{i j}

by A, B, C, D for convenience. Applying the reciprocity theorem:

{\hat{T}}_{l i n}^{b} = (\begin{matrix} A & - C \\ - B & D \end{matrix})

where

I_{x}

and

I_{y}

are complex amplitudes of the plane wave that propagates in positive z-direction,

T_{i j}

stand for the co-polarization and cross-polarization transmission coefficients, indicating the amplitude of the electric field of i-polarized transmitted wave induced by j-polarized incident wave. The superscripts f (forward) and b (backward) denote propagation directions. For circularly polarized light, it can be obtained by a change of the base vectors from linear to circular states:

T_{c i r}^{f} = (\begin{matrix} T_{+ +} & T_{+ -} \\ T_{- +} & T_{- -} \end{matrix}) = \frac{1}{2} (\begin{matrix} (A + D) + i (B - C) & (A - D) - i (B + C) \\ (A - D) + i (B + C) & (A + D) - i (B - C) \end{matrix})

The subscript + and − represent right-handed polarization (RCP) and left-handed polarization (LCP) waves. Connecting the amplitudes of circularly polarized incident light with those of circularly polarized transmitted light:

(\begin{matrix} T_{+} \\ T_{-} \end{matrix}) = T_{c i r c}^{f} (\begin{matrix} I_{+} \\ I_{-} \end{matrix}) = (\begin{matrix} T_{+ +} & T_{+ -} \\ T_{- +} & T_{- -} \end{matrix}) (\begin{matrix} I_{+} \\ I_{-} \end{matrix})

T_{c i r c}^{b} = (\begin{matrix} T_{+ +} & T_{- +} \\ T_{+ -} & T_{- -} \end{matrix})

The AT effects are usually characterized by the AT parameters. For the linearly and circularly polarized waves, they are defined by:

Δ_{l i n}^{(x)} = {| T_{y x} |}^{2} - {| T_{x y} |}^{2} = - Δ_{l i n}^{(y)}

Δ_{c i r c}^{(+)} = {| T_{- +} |}^{2} - {| T_{+ -} |}^{2} = - Δ_{c i r c}^{(-)}

Obviously, for an arbitrary base the co-polarization transmission coefficients of the T-matrix for different propagation directions are not identical and will contribute to asymmetric transmission. Symmetry breaking could cause a difference between cross-polarization transmission coefficients of the T-matrix and will also cause the asymmetric transmission.

3. Results and discussion

As the first step, we study the response of the cavity AB. Figure 2(a) shows co- and cross-polarized reflection properties for circularly polarized waves. At the resonant frequency 178 THz, the co-polarized reflection $R_{- -}$ achieves a maximum value of 0.96, revealing that the incident LCP wave is nearly all reflected by the cavity AB. For RCP wave, the co-polarized reflection $R_{+ +}$ is 0.5, and the cross-polarization transmission $T_{- +}$ reaches a maximum value of 0.65 as depicted in Fig. 2 (b). In essence, RCP wave is almost transformed to elliptical polarization (EP) wave while passes through layer A [30]. The cavity AB provides the reflection and transmission for the different components of EP wave, reflects the majority of the component that is polarized along the nanowire direction and selects the perpendicular one [34]. Then transmitted RCP wave can be converted to the LCP wave by the cavity AB, which can be evidenced by $T_{- +}$ . Conversely, at the resonant frequency 235 THz, $R_{+ +}$ achieves a maximum value of 0.97, $T_{+ -}$ reaches a maximum value of 0.67, thus the transmitted LCP wave can be converted to the RCP wave. However, both of $R_{- +}$ and $R_{+ -}$ are below 0.2, and the asymmetric parameters as shown in Fig. 2(c) are below 0.6 for circular polarized waves.

Fig. 2 (a) The reflection properties of RCP and LCP waves for cavity AB; (b) The transmission properties of RCP and LCP waves for cavity AB; (c) AT parameter of RCP and LCP waves for cavity AB; (d) The cross-polarized reflection of circularly polarized waves for cavity BC.

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Adding the nanowire and another rotated mirror of G-shape layer forms a functional independent Fabry-Perot like resonance cavity [30, 34] which enhances one of $T_{- +}$ or $T_{+ -}$ while weakens another one. We validate this concept by performing the cross-polarized reflection of BC. Then broadband (from 140 to 240 THz) and high (exceeding 50%) cross-polarized conversion in reflection is shown in Fig. 2(d), representing a high-performance circular polarization converter in reflection for this cavity. Subsequently, we show the transmission characteristics of the ABC structure in Fig. 3. As is depicted in Figs. 3(a) and 3(b), with the increases of frequency, $T_{- +}$ reaches a maximum value of 0.96, and $R_{- -}$ reaches to 0.96 at 174 THz. Meanwhile, $T_{+ -}$ is suppressed below 0.01. Both the co-polarization transmission $T_{- -}$ and $T_{+ +}$ are reduced to a minimum value of about 0.2. Thus RCP wave is almost fully transformed to LCP wave at this resonant frequency. On the other hand, $T_{+ -}$ and $R_{+ +}$ reach maximum value of 0.97. Apparently, the structure can transform LCP wave to RCP wave completely at 235 THz. $Δ_{c i r}^{+}$ and $Δ_{c i r}^{-}$ reach the maximum values of 0.9 and 0.86 which are plotted in Fig. 3(c). It is obvious that the AT parameter is significantly high in the multi-layered ABC structure compared with bi-layered AB as shown in Fig. 2(c), and the asymmetric parameter is over 0.6 in broad dual bands from 160 to 183 THz and from 220 to 245 THz. However, cross-polarization transmission $T_{y x}$ is nearly overlap with $T_{x y}$ in Fig. 3(d), there is no AT effect for x or y-polarized waves which is calculated by Eq. (7). Finally, this novel structure achieves the high-performance polarization conversion for RCP and LCP waves. Apparently, it has potential application as a dual-band circular polarizer.

Fig. 3 (a) The transmission properties of whole structure for circularly polarized waves; (b) The reflection properties of whole structure for RCP and LCP waves; (c) AT parameter of whole structure for linearly and circularly polarized waves; (d) The transmission properties of whole structure for linearly polarized waves.

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To provide deeper insight, the E-filed distributions for incident RCP/LCP waves under different phase 0 and $π / 2$ at resonance frequency 174 THz are simulated. The directions of electric fields are denoted by the black arrow as shown in Fig. 4. Clearly, in Figs. 4(a)-4(d), it is apparent that electric fields direction has a 90° polarization rotation of incident RCP wave, indicating RCP wave is transformed into LCP output wave. While the LCP wave illuminates the structure normally, the electric fields direction of the output transmitted wave has not been changed as shown in Figs. 4(e)-4(h), implying that LCP incident wave cannot be converted into RCP wave at this resonant frequency. By contrast, the whole E-filed distributions are in good agreement with the above numerical T-matrix results. At 235 THz, obviously, the structure can change the handedness of LCP incident wave (not shown here). It is very opposite to the lower frequency case.

Fig. 4 (a)-(d) Four snapshots of the E-filed distributions of front surface in the structure; (e)-(h) Four snapshots of the E-filed distributions of back surface in the structure.

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4. Effects of different parameters on AT

It will be significant to study the different G-shape rotation angle dependence of the transmission property. Figure 5(a) shows the rotation angle which is applied to the layer C only. Figures 5(b) and 5(c) exhibit the calculated AT spectra and co- and cross-polarization transmission coefficients for different rotation angles. To avoid redundant, the AT parameters of rotation angle θ varies from 90° to 180° are not shown here since it sustains an opposite behavior contrast to 0° to 90°.

Fig. 5 (a) Rising rotation angle θ; (b) and (c) are AT parameter under different parameter θ.

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Especially, in Figs. 5(b) and 5(c), the obtained data show a clear simultaneously asymmetric transmission of circularly and linearly polarized waves which are rigorously introduced by the G-shape rotation angle θ. This is superior to previous works [26]. Clearly, the rising rotation angle θ fades the anisotropic in the structure. The difference between the co-polarization transmission $T_{x x}$ and $T_{y y}$ of linearly polarized wave becomes not remarkable from 0° to 90°, attenuating the AT effect of circularly polarized waves as shown in Fig. 5(b). It is evident that the whole structure exhibits inversion symmetry in the propagation z direction [35]. It is properly accounted, as soon as the θ changed, the symmetry is broken, the deviations of off-diagonal elements $T_{x y}$ and $T_{y x}$ become noticeable. As a result, the AT effect is observed for linearly polarized wave which is depicted in Fig. 5(c).

Remarkably, it should be noted that the geometric parameters l and g of the G-shape are crucial. The geometric parameter l modulates the AT effect of circularly polarized waves and gap size g modulates the AT effect of linearly polarized waves as shown in Figs. 6(a) and 6(b).

Fig. 6 AT parameter of (a) changing length of l; (b) decreasing split gap size; (c) different nanowire numbers.

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By decreasing of l from 75 to 27 nm, the asymmetry of an individual element G-shape causes a weakened anisotropy effect, resulting in the decreased $Δ_{c i r}$ . Interestingly, the bandwidth of each case is insusceptible of the changes. $Δ_{l i n}$ approximate to zero which are indicated by the highlighted blue lines which are depicted in Fig. 6(a). There shows no AT for linearly polarized waves under different geometric parameters l since $T_{x y}$ and $T_{y x}$ are essentially same that do not presented here. Indeed, when the length of l is continual altered to 26 nm, the G-shaped spiral element is transformed to SRR. It is necessary to explore the influence of SRRs split gap g. We apply periodic boundary conditions in the x and y directions, forming an array of single nonmagnetic metallic split ring which can be used to implement a magnetic resonance [36]. As a consequence of a broadened split gap size, it lowered the effective capacitance of the arms, leading the decreased inductance-capacitance (LC) resonance of SRRs as explicitly evidenced by the gradually improved $Δ_{l i n}$ as characterized in Fig. 6(b). Additionally, there appear two regular resonance regions. Around lower resonance region from 140 to 175 THz, $Δ_{l i n}$ only undergoes a slight shrinking. It can be traced to the excitation of circular currents which originates from LC plasmon resonance. That is an independent process and insensitive to the changing gap size. For another resonance region from 175 to 275 THz, that is ascribed to the split gap plasmon resonance which suffers greater impact on the gap changes [37]. Curiously, in Fig. 6(b), these transmission properties are only suitable for linearly polarized incident waves. No similar situation occurs for circularly polarized waves. For simplicity, same blue solid lines are represented the $Δ_{c i r}$ under different gaps, due to all of them are nearly to zero. Finally, nanowire is crucial importance in the whole structure. Here we take into account the transmission property of different nanowire numbers too. It changes the distribution of the magnitude of electric field in the cavities AB and BC, resulting in the improved magnitude of $Δ_{c i r}$ as shown in Fig. 6(c).

It is noteworthy that misalignments always occur in the fabrication and influence the performance of devices. According to the simulated results, the transmission curves of this structure are insensitive to the transversal and longitudinal misalignments between layers (not shown here). Therefore it will reduce the difficulty of fabrication.

5. Multi-band properties for circularly and linearly polarized waves

By varying the geometric parameters, this structure potentially exhibits broad multi-band properties for circularly and linearly polarized waves which are presented in Fig. 7. By adding the number of turns in a single G-shaped spiral unit cell, optimizing the structure parameters, we acquire another AT bandwidth from 275 to 330 THz for circularly polarized wave that is illustrated in Fig. 7(a). When we change the rotation angle of layer A, now it is oriented at − 45° with respect to the y axis, and layer C, now it is oriented at − 90° with respect to the y axis, simultaneously, the AT effect of circularly polarized waves is reduced below 0.1. Remarkably, multi-band AT of linearly polarized waves is observed in that case which is sketched in Fig. 7(b).

Fig. 7 Multi-band properties for (a) circularly polarized waves and (b) linearly polarized waves.

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6. Conclusions

In conclusion, by combining the G-shaped structure and nanowire together, we have demonstrated that a three-layer MM exhibits a perfect broad dual-band polarization conversion in near-infrared communication band for the circularly polarized wave. Making full use of the Fabry-Perot like resonance cavities, the maximum AT parameter reaches to 0.9/0.86 for RCP/LCP wave at 174/235 THz and is over 0.6 in broad dual bands from 160 to 183 THz and from 220 to 245 THz. We have calculated the complex T-matrices, and explained the physical mechanism of AT effect in detail. Particularly, the geometric parameters of the G-shape are the essential contribution, they determine the AT effect of circularly and linearly polarized waves appearance or evanishment. Additionally, the proposed structure has great potential application in high performance multi-band circular and linear polarizers.

Funding

National Natural Science Foundation of China (NSFC) (61475079, 61501269), Ningbo Nature Science Foundation (2014A610144), and K.C. Wong Magna Fund in Ningbo University.

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Broad dual-band asymmetric transmission of circular polarized waves in near-infrared communication band

Abstract

1. Introduction

2. Model and method

3. Results and discussion

4. Effects of different parameters on AT

5. Multi-band properties for circularly and linearly polarized waves

6. Conclusions

Funding

References and links

Cited By

Figures (7)

Equations (8)

Optics Express