1. Introduction

The continuous phase accumulation is an important property when light propagates through optical components, which has been used to design conventional optical components such as lenses, prisms and plates according to Fermat's principle. However, the resulting components are often too bulky for optical integration. Recently, abrupt phase shifts by arrays of optical resonators have been used to realize beam steering device [1,2], focusing elements [1,3] and optical vortex [4] in the subwavelength scale, which can be served as ultra-thin optical components for optical integration. As one of the most important optical components, wave plate has attracted much attention and various metamaterial wave plates have been proposed and realized [5–7]. However, in those designs with single resonant layer [5,8,9], abrupt phase shift introduced by plasmonic resonance is generally coupled with resonant amplitude, resulting in a narrow operation band or low efficiency for polarization conversion.

Recently, multiple-layered metamaterials have been proposed for fully engineering both the amplitude and phase of light, either in transmission [7,10–14] or reflection configurations [6,7,15,16]. By mimicking Huygens’ dipole light sources through coupled electric and magnetic resonators, the transmitted signals cannot only cover complete phase space but also keep high transmission amplitude [10,11]. However, achieving large magnetic response in optical wavelengths is generally difficult [17]. In this regard, wave plates operated in reflection configuration using the resonators array coupled with thick metal film have been proposed and demonstrated both in GHz [16], THz [7], and near-infrared [6]. However, the bandwidth of the designed wave plate is limited, especially in visible light spectrum.

The difficulty can be solved by composite metamterials which have been widely used to design broadband metamaterial perfect absorption [18,19] and broadband light extraction from white light-emitting device (LED) [20]. Contrast to that only the intensity of light is needed to control in above applications, herein we intend to construct broadband half-wave plate through harnessing both of the amplitude and the phase of light. To this end, we first design a half-wave plate with an operation band covering entire visible light spectrum (from 400 nm to 780 nm) through optimizing the parameters of patterned metal nanoarray/insulator/metal (P-MIM) structure. Then, by integrated two different patterned metal nanoarrays into the top layer of P-MIM, we realize a composite half-wave plate with an ultra-broad bandwidth exceeding an octave span from 400 nm to 830 nm. Finally, we investigate the polarization conversion efficiency of the composite half-wave plate and its temporal response to an ultra-short light pulse. As compared to the conventional crystal-based optical components and the plasmonic wave plate with single resonant layer, our proposed half-wave plate based on composite metal/insulator/metal structure has prominent merits of ultrathin thickness (< 300 nm) and compactness, with a broad bandwidth and high polarization conversion efficiency, making it more conveniently integrated into the advanced optoelectronic device.

2. Results and discussions

Figure 1(a) is the schematics of the unit cell of the patterned metal nanoarray/insulator/metal (P-MIM) structure to construct the half-wave plates. It consists of three layers, in which an insulating spacer layer is sandwiched between a two-dimensional periodic array of silver nanopatches and an opaque gold film. The geometrical parameters of the structure are chosen and determined by the known behaviors of plasmonic resonances combined with trial-and-error method. After systematical optimization, herein we use the parameters as follows. The periodicity of the pattern is kept at 152 nm along both x-axis and y-axis. The length of the nanopatch L_x can be varied in the simulation, while the width of the nanopatch is equal to its thickness and kept at 40 nm. The thickness of the spacer layer is 56 nm with a refractive index n = 1.3. The dielectric constants of gold and silver are from Johnson and Christy [21] and Palik [22], respectively. It is worth to point out that, in principle, the P-MIM structure can be treated as a cavity, and the interference theory similar to the analysis of Fabry-Perot cavity can be applied. For some special case such as the array of ellipsoid nanoparticles, an analytical solution has been reported [23]. However, for the nanopatch array in our case, the complex transmission and reflection coefficients of the interfaces can only be obtained by numerical simulations.

 

Fig. 1 (a) Schematic of the unit cell and simulation model for metamaterial half-wave plate. (b) Optical response of the half-wave plate for L_x = 112 nm. A gray-shaded area depicts the region of 170° < ΔΦ < 190°.

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The simulations are performed with the commercial software based on finite difference time domain method (FDTD Solutions, Lumerical Inc.). A polarized light in the wavelength range of 400-1000 nm is normally incident on the wave plate, and the amplitude and phase of the reflected light are monitored with a monitor [red point in Fig. 1(a)] 1500 nm far from the top surface of the wave plate. We have validated that the monitor is sufficiently far from the wave plate so that the electric field profiles in the corresponding xy plane are uniform (the nonuniformity is less than 1‰) and the effect of the plasmonic near field on the reflected light can be ignored safely. The obtained complex reflection coefficients can be expressed as r̃_x = A_xexp(iΦ_x) and r̃_y = A_yexp(iΦ_y), where A and Φ represent the reflection amplitude and phase, respectively; while the subscript x (y) is used for x (y) polarized incident light.

Figure 1(b) shows the amplitudes and phases of the reflection light from the wave-plate with L_x = 112 nm, in which A_x and A_y are plotted as solid and dashed blue lines, respectively. As seen, both A_x and A_y are larger than 0.85 for wavelength λ > 600 nm but decrease rapidly with decreasing wavelength as λ < 550 nm, which can be attributed to the high interband absorption of Au film. Obviously, the low reflection amplitudes at short wavelengths might be improved by choosing low loss plasmonic materials [24] or dielectric based metamaterial elements [25]. The amplitudes ratio A_x/A_y is in the range of 0.9-1.15, which satisfies the precondition that A_x/A_y should be within the range of 0.8-1.2 to construct wave plate [26].

The phase shifts Φ_x and Φ_y of the reflected light are shown in Fig. 1(b) with solid and dashed black lines, respectively. The phase difference between x and y polarized reflected lights, defined as ΔΦ = Φ_x – Φ_y, is shown in Fig. 1(b) with solid red line. The gray-shaded region in Fig. 1(b) demonstrates the phase difference in the range of 170°-190°, which is available and required for construction of half-wave plate [26]. Compared the curve of ΔΦ with the gray-shaded region, we find that our designed half-wave plate possesses a broadband response and can operate successfully across the whole visible light spectrum from 400 to 780 nm.

High reflection amplitude is required for the designed half-wave plate to achieve high polarization conversion efficiency. As seen in Fig. 1(b), a wide shallow dip around λ = 840 nm for A_x is observed. The behavior can be attributed to the gap surface plasmon resonances (GSP), which is corresponding to the confined magnetic fields below the nanopatch. It has been found that, when an electric current is excited in the nanopatch, an anti-parallel electric current can also be excited in the underlying metal film. According to the Ampere law, an enhanced magnetic field is consequently produced and confined in the gap between the nanopatch and the underlying metal film [23,27]. Figures 2(a) and 2(b) show the field maps of |H_y| in the xz plane for x-polarized incident light and |H_x| in the yz plane for y-polarized incident light, respectively, when the wavelength of the incident light is 840 nm. As seen in Fig. 2(a), the magnetic field confined below the nanopatch is enhanced about 3 times as compared to that of the incident light, implying the formation of GSP mode [23,27]. Note that GSP can also extend across the entire spacer layer due to the near-field interaction between the adjacent unit cells, implying weak confinement of GSP [23]. Because the light confined below the nanopatch is prone to be dissipated by ohmic losses, the GSP will lead to the reduction of the reflection amplitude and formation of shallow dip around 840 nm for A_x in Fig. 1(b). On the other hand, as seen in Fig. 2(b), the y-polarized incident light can readily pass through the nanopatch and be reflected by the bottom metal film, resulting in the uniform wave-front below and above the nanopatch as well as the high reflection amplitude [A_y = 0.967 at λ = 840 nm in Fig. 1(b)]. We should emphasize that, although the GSP exists in our case, it is still so weak due to the thick spacer layer and subwavelength period that the high reflection amplitude can be reached.

 

Fig. 2 Magnetic fields distribution of (a) |H_y| in the xz plane for x-polarized incident light, and (b) |H_x| in the yz plane for y-polarized incident light with the wavelength of 840 nm.

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We also investigate the effect of L_x on the reflection amplitudes and the phases. The results are illustrated in Fig. 3. As seen in Figs. 3(a) and 3(b), when L_x increases from 100 to 130 nm, both A_x and Φ_x vary substantially in the wavelength range from 600 nm to 1000 nm but change little in the wavelength range from 400 nm to 600 nm. The former behavior can be contributed to the spectral shifts of the GSP as discussed in the abovementioned paragraph [27], while the later one is due to that the incident light is mostly reflected by the nanopatch. On the contrary, as shown in Figs. 3(c) and 3(d), both A_y and Φ_y are nearly insensitive to L_x. This is because the plasmonic resonance along the y-axis cannot be tuned by varying L_x. Therefore, we can conclude that, as L_x varies, ΔΦ will vary in the similar tendency as Φ_x in the wavelength range of 700-1000 nm but has trivial change in the wavelength range of 400-600 nm.

 

Fig. 3 The simulated contour maps of (a) A_x, (b) Φ_x, (c) A_y, (d) Φ_y and (e) ΔΦ for the half-wave plate with various nanopatch lengths L_x. The units of the scale bars are degrees in (b), (d) and (e).

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Based on the results of Fig. 3(b) and Fig. 3(d), we can further get the contour map of the phase difference ΔΦ with variation of L_x, as shown in Fig. 3(e). To characterize the response of wave plate more clearly, we also plot two black contour lines when ΔΦ equals 170° and 190°, where the enclosed area by two contour lines is available for the operation of half-wave plate [25]. The area can be further divided into two regions: region I (wavelengths in the 400-600 nm range) and region II (wavelengths in the 600-1000 nm range), in which ΔΦ changes drastically in region II but varies little in region I as L_x increases. The causes of the different behaviors for the different regions have been clarified in the preceding text. As seen from Fig. 3(e), when L_x is in the range of 105-112 nm, the two regions will be merged, resulting in an availably broad operation band for the half-wave plate.

To further extend the operation bandwidth of half-wave plate, we try to replace the single nanopatch of the top layer of as-designed half-wave plate by an array of composite super unit cell consisting two nanopatches with different L_x. This is because, at fixed wavelength, the phase difference introduced by longer nanopatch is always larger than that introduced by shorter one, as shown in Fig. 3(e). The unit cell of the composite half-wave plate structure is shown in Fig. 4(a). Herein, L_x1 = 112 nm, L_x2 = 120 nm, the thickness of the spacer is 60 nm, the periodicity is 304 nm (152 nm) along the x-axis (y-axis), and the distance between two nanopatches is 152 nm. Similar to the result of Fig. 2(a), two GSP, along either length of the nanopatches of the super unit cell, can be excited in this case. Using the aforementioned method, the simulation results of Φ_x (solid black line), Φ_y (dashed black line) and ΔΦ (red line) of the structure are plotted in Fig. 4(b). As seen, with this composite super unit cell design, an ultra-broad bandwidth ranging from 400 to 830 nm can be achieved, which exceeds an octave.

 

Fig. 4 (a) Schematic of the composite super unit cell structure, consisting of two nanopatches with L_x1 = 112 nm and L_x2 = 120 nm, respectively. (b) Reflection amplitudes (blue lines), reflection phases (black lines) and phase difference ΔΦ (red line) obtained by simulations. Reflection phases obtained by average response theory are plotted as olive lines.

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We have calculated the response of the composite half-wave plate straightforwardly by averaging complex reflection coefficients of the constitute elements, that is, r̃ = Aexp(i<Φ>) = (r̃₁ + r̃₂)/2, where r̃₁ and r̃₂ are the complex reflection coefficients of the structure with L_x1 = L_x2 = 112 nm and L_x1 = L_x2 = 120 nm, respectively. Note that both r̃₁ and r̃₂ can be obtained using the numerical method as described in the aforementioned section. The calculated <Φ_x> (solid olive line) and <Φ_y> (dashed olive line) for the composite super unit cell structure by average response theory are shown in Fig. 4(b). Compared to the simulation results (black lines), we find that the average response approach can produce excellent agreement with the simulation results in the 500-1000 nm range, although a small deviation of several degrees exists in the range of 400-500 nm. This discrepancy is due to the fact that the wavelength of the incident light is comparable to the period of the array, resulting in the failure of the effective medium theory. Anyway, the result in Fig. 4(b) demonstrates that the average response theory, which is essentially a simplified effective medium theory, can simplify and speed up the design process for the broadband wave plates as well as other phase-response based optical components.

The wave plate is frequently used to rotate the polarization state of light. In this regard, we investigate the polarization conversion efficiency of the composite half-wave plate. As shown in the inset of Fig. 5(a), a linear polarized light is normally incident on the wave plate and the reflected light is recorded. In general, an incident light with polarization angle of 45° is often chosen because the transmission/reflection coefficients for orthogonal electric field components are assumed to be the same. However, in our case, due to the different reflection amplitudes for x and y-polarized light (that is, A_x ≠ A_y) as shown in Fig. 4(b), an appropriate polarization angle other than other than 45° should be chosen to compensate this difference. Therefore, the polarization angle of the incident light is set to be 42°. The reflected light is then decomposed into two orthogonal components: E_∥ and E_⊥, which are parallel and perpendicular to the incident electric field (amplitude E_in), respectively. The polarization conversion efficiency is defined asη = E_⊥/E_in. As seen in Fig. 5(a), the polarization conversion efficiency is around 90% in the range of 580-900 nm. It is worth noting that, due to the high ohmic losses of the Au film, the polarization conversion efficiency drops rapidly when λ < 550 nm. The problem might be solved using low loss metamaterials [24].

 

Fig. 5 (a) Polarization conversion efficiency and (b) temporal response to an ultra-short pulse of light for the composite super unit cell wave plate. Inset of Fig. 5(a) shows the schematic of the incident and reflected light. The reflection signal in (b) has been offset vertically for clarity.

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One of the advantages of a broadband optical device is its ability to deal with truly broadband light, such as an ultra-short pulse of light. In this context, we study the temporal response of the composite half-wave plate. Figure 5(b) shows the electric amplitudes of an incident pulse light (black line) and reflected light from the wave plate (red line). The incident light is centered at 500 THz (λ = 600 nm) with a 2.7 fs pulse width (bandwidth of 163 THz). One can see that the pulse width does not distort significantly after reflection. According to the interference theory for MIM structure [28], the merit behavior of pulse width reserved after reflection can be attributed to the subwavelength nature of the spacer layer and low quality factor of the structure, both of which can result in slight time delay in the MIM.

3. Conclusion

We design and realize a broadband half-wave plate capable to cover entire visible light and near infrared spectrum with patterned Ag nanoarray/insulator/Au film structure. Moreover, we demonstrate that the bandwidth of the wave plate can be further improved to surpass an octave by arranging two nanopatches with different lengths into a composite super unit cell. It is found that the designed wave plate can achieve high polarization rotation efficiency and reserved the pulse width. Additionally, we argue that the average response theory can be used to simplify and speed up the design process for the broadband wave plates. The work provides a useful guide for designing, evaluating and optimizing broadband high efficiency phase-response based optical components using P-MIM structure. Our designed half-wave plate possesses advantages of high polarization conversion efficiency over a broad bandwidth, ultra-fast response and compactness, making it more convenient for the applications in integrated optics.