Active perfect absorber based on planar anisotropic chiral metamaterials

Xiu Yang; Min Li; Yidong Hou; Jinglei Du; Fuhua Gao

doi:10.1364/OE.27.006801

1. Introduction

Chiroptical effect derives from structure-dependent higher-order interactions between light and molecules, i.e. the electric dipole-magnetic dipole (dipolar) and electric dipole-electric quadrupole (quadrupolar) interactions, which result in a phase retardation difference (i.e. optical activity, OA) or an absorption difference (i.e. circular dichroism, CD) between the incident left and right circular lights (LCP and RCP). The chiroptical effect, together with its structure dependent properties, paves the way for the enantiomer biosensor and also manipulating the polarization states of light. However, the higher-order interaction between the light and the natural chiral molecules or medium is very weak, and this greatly restricts the practical applications of chiroptical effect from natural materials and stirs up a high motivation for finding a mechanism to obtain the enhanced chiroptical effect.

Recently, plasmonic chiral metamaterials (PCMs) composed by electric or magnetic resonators have attracted a great amount of attentions for their giant chiroptical effect, for example, their CD signal usually is about 1000 times larger than that from nature chiral medium [1–5]. Through engineering the structure morphology of the resonators or applying suitable measured configuration conditions, four type chiroptical effects have been demonstrated in PCMs, i.e. intrinsic chirality, intrinsic structural chirality, extrinsic chirality and extrinsic structural chirality [6–8]. These giant chiroptical effects from PCMs pave the way for controlling the polarization states of light, and also enable many fascinating physical effects, such as negative $r e f r a c t i o n$ index [3,9,10], repulsive Casimir effect [11–13] and unusual spin Hall effect of light [14,15]. In addition, the chiroptical effect from nature chiral mediums also can be enhanced greatly by incorporating plasmonic nanostructures to form a chiral medium @ plasmonic nanostructure complex system [16–18]. This enhanced chiroptical effect is very advantage for highly-sensitive enantiomer sensing.

Active chiral plasmonics are highly desired for practical applications, such as the highly integrated polarization sensitive devices and the stereo display [19,20]. However, almost all of the currently-developed PCMs own a fixed chiroptical effect [4,5,21–25] and few PCMs systems are demonstrated to own actively-tunable chiroptical effect under the influence of an external stimulus. The DNA-self-assemblied technology has been used to achieve the active chiroptical effect in visible region by changing the geometric reconfiguration of chiral building blocks [26,27]. In the THz region, the overall achiral geometry has been selectively activated to form either positive or negative $C D_{T}$ signal by the generation of charge carriers excited by laser [28,29]. Recently, the electrically- or optically-induced phase transformation enabled by the phase change material Ge₃Sb₂Te₆ (GST-326) has been demonstrated to reverse the $C D_{T}$ signal in the mid-infrared region with a tuning range of from 4.15 to 4.90 μm [20]. These approaches, however, usually require strict miro/nano-engineering technology, and their modulation effect is very limited, for example these approaches are only suitable for some fixed wave bands.

In this work, we firstly introduce the planar anisotropic chiral metamaterials (PACMs) in the metamaterial absorber to form a kind of active chiral metamaterial absorber (ACMA). Both of the theoretical and simulation results demonstrate that the circular conversion dichroism (CCD) from the PACMs leads to a differentiated microcavity-interference effect between LCP and RCP, and then the active chiroptical effect related to the equivalent optical length between the PACMs and the metal layer. The ACMA proposed here can be realized easily both in simulations and experiments, and the chiroptical resonance of ACMA can be turned in the whole plasmonic resonance band from ultraviolet light to radio wave. In simulations, we give a design of a high-performance ACMA based on the ‘Z’-shaped PACMs, and the active range for $C D_{R}$ signal is from 0 to 0.882, where the maximum reflection $C D_{R}$ approaches to the idea value of 1. In addition, the modification sensitivity and sensing performance for displacement and temperature also have been investigated.

2. Theoretical model for active chiral absorber

Generally, a simple chiral absorber is composed by one layer of PCMs and one metal reflection layer (as shown in Fig. 1), which are separated by one dielectric layer with the refractive index of $n (w)$ . When the thickness of the dielectric layer is larger than the half of the considered wavelength, the coupling effect between the PCMs layer and the metal layer can be ignored, and the PCMs layer can be considered as one layer of uniform chiral medium with a reflection coefficient of $\hat{r}$ and a transmission coefficient of $\hat{t}$ , which can be written as [30]

\hat{r} = [\begin{matrix} r_{+ +} & r_{+ -} \\ r_{- +} & r_{- -} \end{matrix}], \hat{t} = [\begin{matrix} t_{+ +} & t_{+ -} \\ t_{- +} & t_{- -} \end{matrix}],

where ‘-’ and ‘ + ’ denote the LCP and RCP, respectively. Then, the transmissivity

T_{i j},

the reflectivity

R_{i j},

and the phase retardation

φ_{t, i j}

(or

φ_{r, i j}

) can be calculated by

T_{i j} = {| t_{i j} |}^{2},

R_{i j} = {| r_{i j} |}^{2},

and

φ_{t, i j} = \arg (t_{i j})

(or

φ_{r, i j} = \arg (r_{i j})

), respectively.

Fig. 1 Schematic diagram of light reflection from the chiral absorber. (a)-(b) The chiral absorber composed by卍- shaped PCMs (i.e. planar isotropic chiral metamaterials) and Z-shaped PCMs (i.e. planar anisotropic chiral metamaterials). A dielectric layer is placed between the PCMs layer and the metal layer to form a microcavity. The yellow and purple arrows denote the LCP and RCP lights, respectively. $d$ is the thickness between the PCMs layer and the metal layer.

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According to [6,31,32], we use the following equations to evaluate the circular reflection difference between LCP and RCP, i.e.

C D_{R} = (R_{+} - R_{-}) / (R_{+} + R_{-}), O A_{R} = [\arg (r_{+ -} + r {}_{+ +}) - \arg (r_{- -} + r {}_{- +})] / 2

where

R_{+} = R_{+ +} + R_{- +},

and

R_{-} = R_{- -} + R_{+ -}

.

When a beam of light illuminates on the chiral absorber along the +z direction (as shown in Fig. 1), a multiple reflection lights will be formed from the chiral absorber due to the Fabry-Perot (FP) cavity effect between the PCMs layer and the metal layer. The reflectivity can be calculated by:

\begin{array}{l} \hat{R} = {\vec{T}}_{1} * {\hat{R}}_{2} * {\overset{\leftarrow}{T}}_{1} * e^{2 k d i} + {\vec{T}}_{1} * {\hat{R}}_{2} * {\overset{\leftarrow}{T}}_{1} * e^{2 k d i} * (^{R_{1} * R_{2} * e^{2 k d i}) 1} + {\vec{T}}_{1} * {\hat{R}}_{2} * {\overset{\leftarrow}{T}}_{1} * e^{2 k d i} * (^{R_{1} * R_{2} * e^{2 k d i}) 2} + ... \\ = \frac{{\vec{T}}_{1} * {\hat{R}}_{2} * {\overset{\leftarrow}{T}}_{1} * e^{2 k d i}}{1 - (R_{1} * R_{2} * e^{2 k d i})}, \end{array}

where

d

is the thickness between the PCMs layer and the metal layer.

{\vec{T}}_{1}

and

{\overset{\leftarrow}{T}}_{1}

denote the transmission along the + z direction and the -z direction,

{\hat{R}}_{1}

and

{\hat{R}}_{2}

denote the reflection of the PCMs layer and the metal layer.

k

is the effective wave-vector in the dielectric layer, and

k = w * n (w) / c .

Thus, the reflectivity

\hat{R}

is highly depended on the thickness

d

and the refractive index

n (w)

of the dielectric layer, and the reflection and transmission coefficients of the PCMs layer. In order to simply the equation in Eq. (3), we consider two simple cases as discussed below.

Case 1: planar isotropic chiral medium. For a planar isotropic chiral medium, such as the 卍- type chiral nanostructure array with a square lattice, only the non-conversion CD will be observed from the structures. The reflection and transmission coefficients of this kind PCM layer can be written as

{\hat{T}}_{1, 2} = [\begin{matrix} t_{+ +} & 0 \\ 0 & t_{- -} \end{matrix}], {\hat{R}}_{1, 2} = [\begin{matrix} 0 & r_{+ -} \\ r_{- +} & 0 \end{matrix}],

where

r_{- +} = r_{+ -} = 0

. According to Eqs. (3) and (4), we have:

{\begin{cases} | \overset{\leftarrow}{R_{+}} | = \frac{{| \vec{t_{- -}} |}^{2} * {| r_{0} |}^{2} * {| \overset{\leftarrow}{t_{++}} |}^{2}}{1 + {| r_{0} |}^{4} - 2 {| r_{0} |}^{2} * \cos (2 k d + 2 φ_{r 0})} \\ | \overset{\leftarrow}{R_{-}} | = \frac{{| \vec{t_{+ +}} |}^{2} * {| r_{0} |}^{2} * {| \overset{\leftarrow}{t_{- -}} |}^{2}}{1 + {| r_{0} |}^{4} - 2 {| r_{0} |}^{2} * \cos (2 k d + 2 φ_{r 0})} \end{cases}

Thus, we have:

C D_{R} = 0.

Thus, the chiroptical effect will be completely eliminated when the planar isotropic chiral medium is used in the chiral absorber system as shown in Fig. 1(a), although a periodic modulation is observed in the reflection coefficient of the chiral absorber. This is suitable for all of the chiral mediums without CCD, include the planar isotropic chiral metamaterials mentioned here, the Faraday mediums and the nature chiral mediums, as discussed in [8,23,33].

Case 2: planar anisotropic chiral medium. For the planar anisotropic chiral medium, such as fish-shape [33], L –shape [30,34] and split ring chiral nanostructures [1,35], the CCD will be observed. In this case, we just consider the influence from the conversion parts in the transmission coefficients and the non-conversion parts in the reflection coefficients. And we have,

{\hat{T}}_{1, 2} = [\begin{matrix} 0 & t_{+ -} \\ t_{- +} & 0 \end{matrix}], {\hat{R}}_{1} = [\begin{matrix} r_{+ +} & 0 \\ 0 & r_{- -} \end{matrix}] a n d {\hat{R}}_{2} = [\begin{matrix} 0 & r_{+ -} \\ r_{- +} & 0 \end{matrix}],

where

r_{- +} = r_{+ -} = 0

for a metal layer. According to Eqs. (3) and (7), we can get the reflectivity for LCP and RCP as

{\begin{cases} | \overset{\leftarrow}{R_{+}} | = \frac{{| \vec{t_{- +}} |}^{2} * {| r_{0} |}^{2} * {| \overset{\leftarrow}{t_{- +}} |}^{2}}{1 + {| r_{- -} * r_{0} |}^{2} - 2 | r_{- -} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, - -})} \\ | \overset{\leftarrow}{R_{-}} | = \frac{{| \vec{t_{+ -}} |}^{2} * {| r_{0} |}^{2} * {| \overset{\leftarrow}{t_{+ -}} |}^{2}}{1 + {| r_{+ +} * r_{0} |}^{2} - 2 | r_{+ +} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, + +})} \end{cases} .

Based on Eqs. (2) and (8), we have:

C D_{R} = \frac{{| \vec{t_{- +}} |}^{2} * {| \overset{\leftarrow}{t_{- +}} |}^{2} * [1 + {| r_{+ +} * r_{0} |}^{2} - 2 | r_{+ +} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, + +})] - {| \vec{t_{+ -}} |}^{2} * {| \overset{\leftarrow}{t_{+ -}} |}^{2} * [1 + {| r_{- -} * r_{0} |}^{2} - 2 | r_{- -} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, - -})]}{{| \vec{t_{- +}} |}^{2} * {| \overset{\leftarrow}{t_{- +}} |}^{2} * [1 + {| r_{+ +} * r_{0} |}^{2} - 2 | r_{+ +} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, + +})] + {| \vec{t_{+ -}} |}^{2} * {| \overset{\leftarrow}{t_{+ -}} |}^{2} * [1 + {| r_{- -} * r_{0} |}^{2} - 2 | r_{- -} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, - -})]} .

According to the Lorentz symmetry principle, we have $\vec{t_{- +}} = \overset{\leftarrow}{t_{+ -}}$ and $\vec{t_{+ -}} = \overset{\leftarrow}{t_{- +}} .$ Thus, Eq. (9) can be simplified to

C D_{R} = \frac{{| r_{+ +} * r_{0} |}^{2} - {| r_{- -} * r_{0} |}^{2} - 2 | r_{+ +} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, + +}) + 2 | r_{- -} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, - -})}{2 + {| r_{+ +} * r_{0} |}^{2} + {| r_{- -} * r_{0} |}^{2} - 2 | r_{+ +} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, + +}) - 2 | r_{- -} * r_{0} | * \cos (2 k d + φ_{r 0} + φ_{r, - -})},

Equation (10) indicates that, the resulting

C D_{R}

is highly related to the thickness

d

and the reflection coefficient of the planar anisotropic chiral medium used here, include the reflectivity and the reflection phase. This is obviously different with that in Case 1 and provides an effective method for modulating or enhancing the chiroptical effect. As shown in Fig. 2(a), a periodic modification of the

C D_{R}

signal as a function of the thickness

d

(i.e. the FP cavity length) is observed when the planar anisotropic chiral medium, where both of the intensity and phase are different between

t_{- +}

and

t_{+ -}

, and

r_{++}

and

r_{- -}

. It should be noted that both of the intensity and phase differences between

r_{++}

and

r_{- -}

are the key factors to modulate or enhance the

C D_{R}

signal. The intensity difference between

r_{++}

and

r_{- -}

can change the fluctuation intensity of

| R_{+} |

or

| R_{-} |,

and then the

C D_{R}

signal; While the phase difference between

r_{++}

and

r_{- -}

can change the fluctuation phase of

| R_{+} |

or

| R_{-} |,

and then the

C D_{R}

signal. As shown in Fig. 2(b), the fluctuation intensity of

| R_{+} |

is improved due to the larger intensity

r_{++}

when compared with that shown in Fig. 2(a), which results in a larger

C D_{R}

signal. Certainly, the fluctuation phase of

| R {}_{+} |

and

| R_{-} |

keeps unchanged in the meanwhile. Figure 2(c) shows that a phase difference between

r_{++}

and

r_{- -}

results in a fluctuation phase difference for

| R_{+} |

and

| R_{-} |

, which also results in an obvious

C D_{R}

signal, although the fluctuation intensity is the same between

| R_{+} |

and

| R_{-} |

. Certainly, no

C D_{R}

signal can be observed when the planar isotropic chiral medium is used, as shown in Fig. 2(d).

Fig. 2 The calculated $| R_{+} |$ (red curve in right), $| R_{-} |$ (black curve in right) and $C D_{R}$ (blue curve in left) as a function of the thickness d for chiral media with (a-c) and without CCD (d). The reflection and transmission coefficients used here are (a) ${\hat{T}}_{1} = (\begin{matrix} 0 & 0.5 * e^{i * p i / 4} \\ 0.7 * e^{i * p i / 5} & 0 \end{matrix})$ & ${\hat{R}}_{1} = (\begin{matrix} 0.2 * e^{i * p i / 4} & 0 \\ 0 & 0.2 * e^{i * p i * 3 / 4} \end{matrix})$ ; ${\hat{T}}_{1} = (\begin{matrix} 0 & 0.5 * e^{i * p i / 4} \\ 0.7 * e^{i * p i / 5} & 0 \end{matrix})$ & ${\hat{R}}_{1} = (\begin{matrix} 0.4 * e^{i * p i / 4} & 0 \\ 0 & 0.2 * e^{i * p i * 3 / 4} \end{matrix})$ ; ${\hat{T}}_{1} = (\begin{matrix} 0.5 * e^{i * p i / 4} & 0 \\ 0 & 0.7 * e^{i * p i / 5} \end{matrix})$ & ${\hat{R}}_{1} = (\begin{matrix} 0 & 0.2 * e^{i * p i / 4} \\ 0.2 * e^{i * p i * 3 / 4} & 0 \end{matrix})$ ; ${\hat{T}}_{1} = (\begin{matrix} 0.5 * e^{i * p i / 4} & 0 \\ 0 & 0.7 * e^{i * p i / 5} \end{matrix})$ & ${\hat{R}}_{1} = (\begin{matrix} 0 & 0.2 * e^{i * p i / 4} \\ 0.2 * e^{i * p i / 4} & 0 \end{matrix})$ . The reflection coefficients for the metal layer used here are ${\hat{R}}_{1} = (\begin{matrix} 0 & 1 * e^{i * p i} \\ 1 * 1 * e^{i * p i} & 0 \end{matrix})$ . The cavity length d and refractive index of dielectric material in cavity investigated here are 1000 nm and 1.49, respectively.

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3. Design and performance discusions of activechiral absorbers

In this section, we demonstrate the ACMA predicted theoretically in Section II by using the Finite Difference Time Domain method (FDTD), and provide a high-performance ACMA based on PACMs. As shown in Fig. 3, two types PCMs have been investigated, one is Z-shaped PCMs (Fig. 3(a)), i.e. PACMs, and the other is the 卍-shaped PCMs (Fig. 3(b)), i.e. planar isotropic chiral metamaterials. The lattice size of the chiral nanostructure array in x - and y- direction are $P_{x}$ and $P_{y}$ respectively. For Z- shaped nanostructure, the length and width for the wide and narrow parts are $L_{1}$ and $W_{1}$ , $L_{2}$ and $W_{2},$ respectively. For 卍- shaped nanostructure, the total side length, the arm length and width are $L_{1}$ , $L_{2}$ and $W$ respectively. The thickness for both of the Z- and 卍- shaped chiral nanostructures is 40 nm.

Fig. 3 The simulated transmission and reflection intensities of PCMs. (a) Schematic diagram of Z-shaped PCMs, i.e. planar anisotropic chiral structure. The structure parameters are set $W_{1} = 115$ nm, $W_{1} = 85$ nm, $L_{1} = 125$ nm, $L_{2} = 105$ nm, $P_{x} = 235$ nm and $P_{y} = 335$ nm. The thickness of the meta-molecules and dielectric spacer are 40 nm and 160 nm, respectively. (b) Schematic diagram of卍-shaped PCMs, i.e. planar isotropic structure. The structure parameters are set as $W = 50$ nm, $L_{1} = 250$ nm, $L_{2} = 125$ nm, and $P_{x} = P_{x} = 450$ nm. (c) and (d) The simulated transmission intensities for the optimized Z- and 卍-shaped PCMs, i.e. $T_{+ +}$ (blue), $T_{+ -}$ (green), $T_{- +}$ (red) and $T_{- -}$ (pink). (e) and (f) The simulated reflection intensities for the optimized Z- and 卍-shaped PCMs, i.e. $R_{+ +}$ (pink), $R_{+ -}$ (red), $R_{- +}$ (green) and $R_{- -}$ (blue).

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To obtain a good reflection coefficient, the PCMs are paced between two dielectric mediums as shown in Figs. 3(a) and 3(b), and the refractive index of the upper and lower dielectric medium are $n_{1}$ and $n_{2}$ , respectively. Silver (Ag) is used as the nanostructure material and the optical constants of Ag are taken from the previously measured values [36].

In order to extract the circular transmission and reflection coefficients, the transmission and reflection coefficients for linear polarization lights have been calculated firstly by analyzing the simulated datum from monitors in the reflection and transmission spaces, where the X- or Y- polarization light illuminates along –z direction, and a periodic boundary is used in both of the X- and Y- directions and a perfect matching layer is used in Z- direction. The linear transmission coefficients, i.e. $t_{x x}$ , $t_{x y}$ , $t_{y x}$ and $t_{y y},$ and the linear reflection coefficients, i.e. $r_{x x}$ , $r_{x y}$ , $r_{y x}$ and $r_{y y},$ are calculated by $t_{u v} = t_{u} / t_{v}$ and $r_{u v} = r_{u} / r_{v}$ , respectively. The subscript $u$ and $v$ denote the linear polarization state, $t_{v}$ and $r_{v}$ are the coefficients of incident lights, $t_{u}$ and $r_{u}$ are the coefficients of the zero-order diffraction lights in transmission and reflection spaces, respectively. Then, the circular transmission and reflection coefficients, i.e. $\hat{r}$ and $\hat{t}$ , can be calculated by

\hat{t} = (\begin{matrix} t_{+ +} & t_{+ -} \\ t_{- +} & t_{- -} \end{matrix}) = \frac{1}{2} * (\begin{matrix} t_{x x} + t_{y y} + {(- 1)}^{1 / 2} * (t_{x y} - t_{y x}) & t_{x x} - t_{y y} - i * (t_{x y} + t_{y x}) \\ t_{x x} - t_{y y} + {(- 1)}^{1 / 2} * (t_{x y} + t_{y x}) & t_{x x} + t_{y y} - i * (t_{x y} - t_{y x}) \end{matrix}) a n d \hat{r} = (\begin{matrix} r_{+ +} & r_{+ -} \\ r_{- +} & r_{- -} \end{matrix}) = \frac{1}{2} * (\begin{matrix} r_{x x} - r_{y y} + {(- 1)}^{1 / 2} * (r_{x y} + r_{y x}) & r_{x x} + r_{y y} - i * (r_{x y} - r_{y x}) \\ r_{x x} + r_{y y} + {(- 1)}^{1 / 2} * (r_{x y} - r_{y x}) & r_{x x} - r_{y y} - i * (r_{x y} + r_{y x}) \end{matrix}),

respectively.

Figures 3(c)–3(f) show the calculated transmission and reflection intensities for the optimized Z-and 卍- shaped PCMs, respectively. The reflection intensity is obtained for that light illuminates along +z direction. For the 卍- shaped PCMs, we see that no circular conversion part is observed in the transmission coefficient, i.e. $T_{+ -} = T_{- +} = 0,$ and the transmission $C D_{T}$ is originated from the difference between $T_{+ +}$ and $T_{- -}$ , which is very small near 900 nm. In the reflection coefficients, no conversion part is observed, i.e. $R_{+ +} = R_{- -} = 0$ , and the non-conversion part is equal to each other, i.e. $R_{+ -} = R_{- +}$ , indicating that no chiroptical effect is observed in the reflection. While for the Z-shaped PCMs, we see that the non-conversion parts in the transmission coefficient are equal to each other, i.e. $T_{+ +} = T_{- -},$ and the transmission $C D_{T}$ is originated from the differences in conversion parts, i.e. $T_{+ -} \neq T_{- +}$ . In the reflection coefficient, an obvious difference is observed in the conversion part near 1370 nm, i.e. $R_{+ +} \neq R_{- -}$ . These results coincide well with the theoretical prediction. In particular, the Z-shaped chiral nanostructures show a strong chiroptical effect, and the $C D_{R}$ value near 1370 nm is about 0.74, which is far larger than that from the 卍-shaped PCMs.

When one layer of Ag film is placed under the chiral nanostructure array, a chiral absorber is well formed. Two types of chiral absorber have been investigated, one is composed by Z-shaped PCMs as shown Fig. 4(a), and the other is composed by 卍-shaped PCMs as shown in Fig. 4(b). The Ag film is set to semi-infinite in simulations, and the distance between the chiral nanostructure and the Ag film is $d$ . For the chiral absorber composed by the Z-shaped PCMs, a huge difference is observed between $R_{+ +}$ and $R_{- -},$ when $d$ with a proper value of 160 nm is used (Fig. 4(c)), especially near the wavelength of about 1370 nm. This huge difference, together with the near zero value of $R_{+ -}$ and $R_{- +},$ lead to a giant reflection $C D_{R}$ signal of about 0.852, and indicates the giant enhanced effect for chiroptical effect by using the well-designed chiral absorber. Certainly, the chiroptical effect from this designed chiral absorber can be periodically modified by changing the cavity length $d$ . As shown in Fig. 4(e), a periodic fluctuation is observed in the $C D_{R}$ signal when the cavity length $d$ is changed from 0 nm to 1000 nm. The maximum $C D_{R}$ signal can reach to about 0.882, while the minimum $C D_{R}$ signal can reach to about 0. This giant modification depth is very useful for practical applications. The modification period $P_{d}$ is about 460 nm for the considered wavelength of about 1367 nm and the medium with the refractive index of 1.49 placed between the PCMs layer and the metal layer. While for the chiral absorber composed by the 卍- shaped PCMs, no $C D_{R}$ signal is observed in the reflection light as shown in Figs. 3(d) and 3(f), although a periodic fluctuation is also observed in the reflection lights of LCP and RCP when changing the cavity length $d .$ These results meet well with the theoretical predication as discussed in Section II.

Fig. 4 The simulated chiroptical effect of chiral absorber. (a) Schematic diagram of chiral absorber comprised by PCMs with CCD, i.e. the Z-shaped nanostructure. (b) Schematic diagram of chiral absorber comprised by PCMs without CCD, i.e. the 卍-shaped nanostructure. The corresponding structural parameters are the same as that shown in Figs. 3(a) and 3(b). A metal backing plate of sufficient thickness is required to ensure total reflection of light. (c) and (d) The simulated the reflection intensity of the chiral absorber composed by the Z- and 卍-shaped PCMs with the cavity length $d = 100$ nm, i.e. $| R_{+ +} |$ (pink), $| R_{- +} |$ (green), $| R_{+ -} |$ (red) and $| R_{- -} |$ (blue). (e) and (f) The simulated reflection intensity, i.e. $R_{+}$ (green) and $R_{-}$ (blue), and the reflection $C D_{R}$ of chiral absorber composed by the Z- and 卍-shaped PCMs as a function of the cavity length $d .$ The wavelengths considered here in Figs. 4(c) and 4(d) are 1367 nm and 1406 nm, respectively.

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Figures 4(c) and 4(d) also indicate that the chiral absorber composed by the Z- shaped PCMs is a kind of abnormal mirrors. The polarization state, i.e. LCP or RCP, is well kept in the reflection light, especially in the waveband of from 1200 nm to 1450 nm, where intensity of the normal reflection parts, i.e. non-conversion part $R_{+ -}$ and $R_{- +}$ are near zero. But for the chiral absorber composed by the 卍-shaped PCMs, only the non-zero normal reflection part are observed, i.e. $R_{+ -} = R_{- +} > 0$ , while the abnormal reflection part is equal to zero in the whole investigated waveband from 900 nm to 1800 nm. In addition, the chiral absorber composed by the Z-shaped PCMs can completely absorb the incident LCP (or RCP) and reflect the incident RCP (or LCP). The polarization state (LCP or RCP) of lights absorbed or reflected by the design chiral absorber can be switched by applying left- or right-hand Z-shaped PCMs. These excellent performances indicate the huge application prospect of the chiral absorber composed by the Z- shaped PCMs. To better show the active optical performance, we plot the reflectivity spectra and the reflection $C D_{R}$ spectra by changing the cavity length $d$ as shown in Fig. 5. The reflection intensity of LCP and RCP and the reflection $C D_{R}$ spectra have been effectively modified periodically in the whole waveband. The modification period increases with the increase of the cavity length. The green dotted lines in Figs. 5(a) and 5(b) denote the maximum reflection intensity and $M$ is an integer denoting the resonance orders of the FP cavity ( $M = 1, 2, 3, 4...$ ).

Fig. 5 The simulated reflectivity $| R_{+} |$ (a), $| R_{-} |$ (b), and $C D_{R}$ (c) from the chiral absorber composed by the Z-shaped PCMs. as a function of the wavelength and the cavity length. The structure parameters of the Z-shaped PCMs used here are the same with that shown in Fig. 3. Green dotted lines represent the FP cavity mode. $M$ is an integer denoting the resonance orders of the FP cavity.

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4. Active and sensor performances of the active chiral absorber

The modification range and sensitivity are the two key indexes for an active chiral absorber. The modification rang, for example the maximum and minimum reflection $C D_{R}$ values, is depended on the PACMs that used in the chiral absorber. For the chiral absorber composed by Z-shaped PCMs, the modification range of $C D_{R}$ signal is from about 0 to 0.882 as indicated in Section III, which is very close to the maximum $C D_{R}$ signal in theory, i.e. $C D_{R - \max} = 1$ . To quantificationally describe the modification sensitivity, we define the modification sensitivity as $M_{L} = \partial C D_{R} / \partial L_{e o p}$ , where $L_{e o p}$ is the effective optical path for light transmitting in the chiral absorber. According to the $C D_{R}$ signal from the designed active chiral absorber shown in Fig. 4(e), we extract the modification sensitivity $M_{L}$ at 1370 nm with the effective optical path $L_{e o p}$ in one period (i.e. 1370 nm), as shown in Fig. 6(a). Thus, the modification sensitivity $M_{L}$ shown in Fig. 6(a) can be periodically extended to large optical path band as $M_{L K} = M_{L + 1370 n m * K}$ , where $K$ is a positive integer. The maximum and minimum modification sensitivity $M_{L}$ can reach to about 0.0069 nm⁻¹ and −0.0036 nm⁻¹ when $L_{e o p} = 1133$ nm and 1376 nm, respectively. To control the chiroptical effect of chiral absorber effectively, the modification sensitivity $M_{L}$ of large absolute value as denoted by the light orange regions in Fig. 6(a) is highly desired. It should be noted that the plasmonic resonance properties can be highly remained when changing the cavity length to obtain a desired effective optical length $L_{e o p}$ , which is very advantage for practical applications when compared the previous work, where the plasmonic resonance is also tuned at the same time [37–39].

Fig. 6 The active and sensor performances of the designed active chiral absorber. (a) The modification sensitivity $M_{L}$ as a function of the effective optical path $L_{e o p}$ in one period of from 715 nm to 2085 nm. The light orange regions denote the modification sensitivity $M_{L}$ with the absolute value of larger than 0.0035 nm⁻¹. (b) and (c) The modification sensitivity $M_{n}$ and $M_{d}$ as a function of the refractive index $n$ and the cavity length $d,$ respectively. The modification sensitivity $M_{n}$ and $M_{d}$ is highly related to the cavity length $d$ or the refractive index $n$ . (d) The measured refractive index of ${VO}_{2}$ varied as a function of the temperature from 15 °C to 85 °C [42]. (e) and (f) The modification sensitivity $M_{T}$ in the slow-varying region and the quick-varying region with the cavity length $d = 100$ um, which are denoted by the purple and blue dashed lines shown in Fig. 6(d). The temperature of the purple region is changed from 40 °C to 46 °C and the reflection index $n$ is changed from 2.295 to 2.30185, while the maximum modification sensitivity $M_{T}$ can reach about 1.36825 °C⁻¹ in Fig. 6(e). The temperature of the blue region is changed from 67 °C to 67.06171 °C and reflection index $n$ is chenged from 2.567 to 2.57385, while the maximum modification sensitivity $M_{T}$ can reach about 151.8759 °C⁻¹ in Fig. 6(f).

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According to the theoretical model in Section II, $L_{e o p}$ is depended on both of the refractive index $n$ in cavity and the cavity length $d,$ i.e. $L_{e o p} = 2 n * d$ . In other word, the modification sensitivity $M_{L}$ can be further rewritten by $M_{n} = \partial C D_{R} / \partial n = 2 d * M_{L}$ or $M_{d} = \partial C D_{R} / \partial d = 2 n * M_{L} .$ Thus, the chiroptical effect can be modified by changing the refractive index $n$ or the cavity length $d$ . In particular, the modification sensitivity $M_{n}$ or $M_{d}$ is not only highly related to PCMs, but also to the cavity length $d$ or the refractive index $n .$ Thus, applying $d$ or $n$ of large values will absolutely lead to high modification sensitivity $M_{n}$ or $M_{d}$ . Figure 6(b) shows the modification sensitivity $M_{n}$ varied as function of the refractive index $n$ , where $d = 1500$ nm and the modification period is $Δ n = 0.457$ . The maximum modification sensitivity $M_{n}$ is 20.52378, which has been linearly enlarged 4 times to 82.0951 when $d = 6000$ nm (as shown in Fig. 6(b)). In fact, a cavity length of 100 um or even larger values is reasonable for practical applications. In this case, we can achieve a very small modification period of $Δ n = 0.00457$ and a large modification sensitivity of up to $M_{n} = 1368.252$ for $d = 100$ . This modification sensitivity is far larger than that from the previous reported ACMA, where the maximum modification sensitivity is about $M_{n} = 250$ [20]. Certainly, we also can apply $n$ of large values to enlarge the modification sensitivity $M_{d}$ , as shown in Fig. 6(c). However, the refractive index $n$ of nature materials is usually located in the range of 1 to 4. And this limits the improvement of $M_{d}$ .

In practical applications, the phase-change materials, such as VO₂ [40] and Silicone [41], are usually used to achieve the active modification of chiroptical effect from PCMs. The refractive index of phase-change materials is highly related to the extrinsic excitation conditions, such as the temperature, stress and the illumination conditions. Here, we use the common phase-change materials ${VO}_{2}$ as an example to discuss the modification sensitivity of the designed ACMA in this work. Figure 6(d) shows the refractive index of ${VO}_{2}$ [34] as a function of the temperature, where a linear relationship is observed between $n$ and $T$ in different regions and we can get $n = 0.001 T$ in the slow-varying region and $n = 0.111 T$ in the quick-varying region, although a retardation phenomenon is observed in the heating (atabout 67 °C) and cooling processes (at about 57 °C). When $d = 100$ um, we can get the modification period of $Δ T_{p e r i o d} = 6$ °Cand the maximum modification sensitivity of $M_{T} = 1.36825$ °C⁻¹ in the slow-varying region, while in the quick-varying region, we have_{$Δ T_{p e r i o d} = 0.06171$} and $M_{T} = 151.8759$ °C⁻¹ as shown in Figs. 6(e) and 6(f). These indicate that we can achieve a very large $C D_{R}$ modification range of from 0 to 0.885 through a weak temperature change (from $67 ℃$ to $67.06171 ℃$ ). In addition to the excellent active modification performance, this kind of ACMA also can be used as a high-sensitive sensor to detect the temperature. It should be noted that the commercial CD spectrometer usually owns an instrumental sensitivity of about 3.5 * 10⁻⁷. In this case, the sensing accuracy of the designed ACMA here can reach to about 3.067*10⁻⁸ °C in the temperature range of from 65 to 70 °C, which is far larger than that from the current commercial temperature sensors.

5. Conclusions

In this work, we demonstrate a kind of ACMA based on the PACMs both in theory and simulations. In theory, we give a clear analytical solution for the ACMA composed by PCMs with and without CCD effect, which indicates that the CCD effect from PACMs is the key factor to achieve the active chiroptical effect. In simulations, we investigate two types ACMA, and one is composed by the Z- shaped PCMs, and the other is composed by the卍- shaped PCMs. The simulation results indicate that for the ACMA composed by the 卍- shaped PCMs, no reflection $C D_{R}$ signal is observed no matter what the cavity length $d$ is. While for the the ACMA composed by the Z- shaped PCMs, a great active chiroptical effect is observed by changing the cavity length $d .$ And the maximum and minimum reflection $C D_{R}$ can reach to about 0.882 and 0, respectively, resulting a very large adjustable range of from 0 to 0.882. The calculated modulation sensitivity, defined as $M_{n} = \partial C D_{R} / \partial n$ and $M_{d} = \partial C D_{R} / \partial d,$ can reach to about 1368.252 for $d = 100$ um and 0.06157 nm⁻¹ for $n = 4.5,$ respectively. In addition, we also discuss the sensing performance of the ACMA composed by the Z- shaped PCMs when using as a temperature sensor, and the minimum sensing precision can reach to about 3.067 * 10⁻⁸ °C. These results indicate the great application prospect of the ACMA as active chiral metamaterials, temperature sensor and so on.

Funding

National Natural Science Foundation of China (NSFC) (11604227); International Visiting Program for Excellent Young Scholars of SCU (20181504).

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Active perfect absorber based on planar anisotropic chiral metamaterials

Abstract

1. Introduction

2. Theoretical model for active chiral absorber

3. Design and performance discusions of activechiral absorbers

4. Active and sensor performances of the active chiral absorber

5. Conclusions

Funding

References

Cited By

Figures (6)

Equations (11)

Optics Express