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A Au nanofin array embedded in SiO2 was designed and fabricated to achieve an achromatic half waveplate with high transmittance at visible wavelengths. On the basis of the waveguide theory of nanogaps and the Fresnel reflection theory, nanofin array is calculated to have ideal properties for an achromatic half-waveplate in the visible band from 560 to 660 nm with the transmittance of around 50%. A Au nanofin array with a height of 830 nm and a period of 400 nm was fabricated through a sidewall-deposition process and overcoating with spin on glass. The polarization microscopy results showed that both transmittance greater than 50% and retardation of 165° at broadband wavelengths ranging from 600 to 800 nm were simultaneously achieved. It was also demonstrated that retardation had little dependence on the incident angle.
© 2016 Optical Society of America
1. Introduction
Tailored polarization distributions in light beams with microscale pixel size have recently gained importance in the fields of advanced optical technologies and integrated optical devices. In this context, the development of microscale polarization elements including polarizers, retarders and waveplates is required. Novel applications has been proposed by adopting such advanced polarization elements. For example, integration of distributed polarizer array on each pixel of an image sensor is proposed in order to improve holographic imaging quality [1].
Use of an optical metasurface is a promising way to control light polarization and phase with microscale pixel size. A metasurface is a patterned array of ultrathin (< 100 nm) metal nanostructures on a flat substrate. Many types of nanostructures including metal nanobricks [2–6], nanoslits [7] and V-shaped nanoantennas [8,9], have been proposed as optical resonators with anisotropic optical characteristics. They can induce large phase shifts in the wavelength ranging from the infrared (IR) to visible region, and they can be used as optical retarders or waveplates. Therefore, metasurfaces that comprise a patterned- or size-gradient array of such nanostructures have been applied to the production of light beams with arbitrary wavefronts.
Due to metasurfaces’ advantages in terms of light-modulation and design-flexibility in a plane with nanoscale resolution, many optical-element applications have been proposed using this technology. For example, computer-generated holograms that produce arbitrary wavefronts on the basis of optical retarder arrays have been demonstrated [10,11]. Laguerre-Gaussian beam converters, including optical voltex plates based on distributed arrays of V- or L-shaped antenna phase shifters at visible-to-infrared wavelengths, have been realized [12, 13]. We previously reported a radial polarization converter at visible wavelength with patterned half-waveplate based on a Au nanoslit array [14].
Expansion of the applicable region of metasurfaces is an emerging requirement, and broadening bandwidth, improving conversion efficiency, and increasing phase shift are all growing demands that can only be met by addressing certain challenging issues.
There is generally a tradeoff between conversion efficiency and phase shift due to competition between increased photon-electron interaction and the lossy nature of metal. Y. Zhao et al. reported a transmission-type broadband quarter waveplate in the visible-to-infrared region using integrated metal nanorods [15] and achieved an efficiency of above 50%. However, a further increase in retardation has yet to be reported. Although transmission-type retarders based on Y-or L-shaped antennas are reported to produce 2π phase shift [12], they have a disadvantage of low conversion efficiency, resulting in strong background; this implies that filtering is required. Reflection-type waveplates are reported to achieve both of high efficiency and half-wavelength retardation [5]. Optical setup becomes complicated under reflection arrangements.
To achieve both high conversion efficiency and large phase shift, the adoption of resonance phenomena are possble candidates including Fano resonance or electromagnetically induced transparency (EIT) [16]. However, this high-Q resonant nature specifies applicable wavelength.
As described above, transmission-type metasurface half waveplates with efficiency reaching 50% and broad applicable wavelengths have yet to be reported. To realize such a design, we have focused on the large birefringence induced on metal nanoslit array [14, 17] and nanofin array [18]. A metal nanofin array consists of a sub-wavelength periodic line and space pattern with thin metal walls (fins), and a height approximately 10 times higher than that of conventional metasurfaces, as shown in Fig. 1(a). It simultaneously achieved both 40% transmittance for TM polarization and 170° retardation at a wavelength of 633 nm [18]. However, strong dichroism was also observed, as the transmittance for TE polarization was under 10%. Furthermore, the wavelength-dispersion of retardation was not discussed. It was also evident that mechanical fracture toughness was insufficient for physical contact with bulk solids and use in a liquid.
Fig. 1 (a) Schemtaic of the conventional free-standing Au nanofin array. Tall, thin gold walls (fins) are arrayed along the x-axis. TM and TE polarizations are defined perpendicular and parallel to the nanofins, respectively. (b) Schemtaic of the Au nanofin array embedded in a dielectric medium. Slits between the nanofins and the top are filled with a dielectric medium with permittivity identical to that of the substrate.
Herein, we focus on a medium among the Au nanofin array to improve the dichroism and toughness. On the basis of the waveguide theory of nanogaps, the dispersions of retardation and transmittance on a nanofin array are calculated for both TE and TM polarizations. Using this theoretical calculation, a Au nanofin array embedded in a dielectric medium was designed and fabricated. Effective refractive index of metal nanograting varies by filling the gaps with dielectric. Enhanced transmittance of TE polarization through the Al nanograting by filling the gaps with SiO2 is reported at ultraviolet spectrum [19]. In this paper, the improvement of dichroism and transmittance on Au nanofin array was reported and dependence on the incident angle was experimentally evaluated. Consequently, the nanofin array showed angular independence on retardation.
2. Principle and design
Figure 1 shows a schematic of the Au nanofin array. Two kinds of dielectric media—vacuum (n = 1) and fused silica glass—were considered. These two media correspond to the structures shown in Fig. 1(a) and 1(b), respectively. Refractive index of fused silica glass comes from the literature, with consideration of dispersion [20]. Light propagation in the nanoslit between a nanofin array can be treated as per the waveguide theory of nanogaps [17, 18]. In theoretical discussion of this report, a single metal-insulator-metal (MIM) waveguide is employed to model the nanofin array. For TE polarization, the propagation constant kTE considering the metal skin depth is shown as [21]
where w, εd, and εm denote slit width and the permittivities of the dielectric and metal, respectively; k0 is the propagation constant of the incident light in vacuum.In contrast, propagation constant for TM polarization is estimated to be a long-range mode plasmon propagating in an MIM structure which is described as follows [22, 23]:
Note that size effect of Au permittivity is remarkable for TM polarization because fins are thin in the TM direction. In contrast, the metal nanofin can be treated as a bulk material for TE polarization. Therefore, the spectral permittivities calculated from the combined Forouhi-Bloomer and modified Drude models are cited for TM polarization [24], and the well-known bulk values from the literature are used for TE polarization [25]. From these equations and the effective medium approximation, complex refractive indices in the Au nanofin array for TE and TM polarizations NTE,TM = kTE,TM/k0 are also estimated.
Figures 2(a) and 2(b) show the real and imaginary parts of the calculated refractive index spectra for both TE (blue lines) and TM (red lines) polarizations, respectively. Solid and dashed lines correspond to free-standing- and glass-embedded-type nanofin arrays, respectively. Slit width (w) is set to be 310 nm. Slight maxima of Re(NTM) around a wavelength of 0.50 μm come from the interband transition of Au. At a shorter wavelength, Im(NTE,TM) increases, resulting in lower transmittance.
Fig. 2 Optical characteristics of the Au nanofin array. In the calculation, slit width (w), height (h), and period (p) are set to 310, 800, and 400 nm, respectively. (a) Real part of the calculated refractive index. (b) Imaginary part of the calculated refractive index. (c) Calculated retardation induced by the Au nanofin array. Solid lines show free-standing nanofin array and dashed lines show the results of SiO2-embedded one. (d) Calculated transmittances through Eq. (4). Solid lines show the resultant free-standing nanofin array and dashed lines show the results of the glass-embedded one. Blue and red lines indicate the TE and TM polarizations, respectively.
The Re(NTM) values for both embedded and free-standing types become greater than those of bare dielectric films (nair = 1, nglass ≈ 1.46, respectively): contrarily, that of Re(NTE) becomes lower. This difference in the refractive indices induces large birefringence.
The free-standing array shows a clear cut-off characteristic, with Im(NTE) drastically increasing and Re(NTE) becoming asymptotic to zero at a wavelength longer than 0.70 μm. When the wavelength is close to the cut-off, TE transmittance rapidly decreases, resulting in strong dichroism. For the embedded-type array, the cut-off wavelength increases due to the increase in refractive index, and the transmittance dispersion decreases. Therefore high transmittance over a wide range of the visible spectrum is expected. Furthermore, as the dispersions under TM and TE approach one another in the embedded-type array, achromatic retardation is expected.
From the calculated refractive indices, retardation and transmittance of the nanofin array were estimated, on the basis of the Fresnel reflection theory. A four-layers model consisting of a vacuum, a dielectric material (The same as that between nanofins), a nanofin array, and a glass substrates was used, and each layer is numbered from 0 to 3, respectively. The transmittance T of irradiation from the substrate side to the vacuum side was calculated from the equation , where the transmission coefficient t3210 is expressed as
and where is the complex conjugate of t3210. h1, h2 and λ are heights of dielectric and nanofin array layers, and vacuum wavelength, respectively. Heights h1 and h2 of the layers are 600 and 800 nm, respectively. tij and rij are the Fresnel transmission and reflection coefficients between each numbered interface calculated from the refractive indices. ATE,TM are the coupling efficiencies at the substrate/nanofin interface. For TE polarization, reflection occurs at the bottom of the fins, resulting in lower transmittance. Therefore, the coupling efficiency of the TE polarization is estimated to be ATE = 0.775, which is the aperture ratio of the nanofin array. For the TM polarization, the coupling efficiency is estimated to be ATM = 1 due to low reflectance at the substrate/nanofin interface.Figures 2(c) and 2(d) show the calculted retardation and transmittance spectra. Note that retardation of the glass-embedded-type array reaches 180° and is flat over the wide wavelength range from .056 to .066 μm as shown in Fig. 2(c). In contrast, a strong retardation dispersion is obtained by the free-standing-type array, though the amount of the retardation is greater than that in the embedded-type array. In Fig. 2(d), the TE transmittance of the free-standing-type evidently lowers, especially at the wavelength longer than 0.70 μm, which corresponds to cutoff. However, the TE transmittance of the glass-embedded array becomes higher and flater over the wavelength ranges from 0.60 to 0.80 μm. Furthermore, transmittance of the crossing point between TE and TM waves is increased by >50% in glass-embedded-type array. Thus, a small dichoroism is expected in a wide range of the visible spectrum around the crossing wavelength. In this range, transmittances reach 50%, which is higher than any previous report for metasurface half waveplates predicting that a Au nanofin array embedded in glass can realize a highly efficient, broadband half waveplate.
3. Fabrication
Figure 3 shows the fabrication process and result for a Au nanofin array embedded in glass. As a glass substrate, a 2×2cm2 fused silica with the thickness of 500 μm was used (Ishimoto Co., LTD.). In Fig. 3(a), Cr was patterned with a period of 800 nm using electron-beam lithography (F5112 + VD01, Advantest Co.) and a lift-off process, while for (b) silica glass substrate was etched by reactive ion etching (RIE, TEP-Xd-S1, Tateyama Machine Co., Ltd.) using SF6 gas with a Cr mask pattern. Figure 3(c), by removing the Cr mask, a glass convex-concave structure is obtained. Over the structure shown in Fig. 3(d), ∼130-nm-thick Au film was deposited through sputter-coating. The sticking layer was not deposited because of the fine adhesion of sputter-coated Au layer onto glass substrate; moreover, the structure will be embedded in a later process. Note that the Au film is deposited not only on the top and bottom of the glass convex-concave structure, but also on the side walls. The thickness of Au on the side wall is lower than that on the top. By adjusting the Cr-mask patterning width and sputtering thickness, a Au nanofin array with equal intervals can be formed. For the structure shown in Fig. 3(e) the sample was milled with Ar RIE (TEP-Xd-S1) and then the Au layers on the top and bottom of the glass mesa was removed, leaving the Au nanofin array on the mesa’s sidewalls. This process was based on the sidewall deposition process [26–28]. (f) The sample is coated with spin-on glass (SOG, ACCUGLASS®SPIN-ON GLASS 512B, Honeywell International Inc.) and annealed at 425°C for 1 h. Although the refractive index of SOG was reported to be ∼1.39 and differed from that of the glass substrate, this difference was not considered during theoretical calculation.
Fig. 3 Schematic drawing of the fabrication process. (a) Cr patterning with EB lithography and a lift-off process. (b) Silica glass RIE. (c) Cr mask removing. (d) Au sputtering. (e) Milling of the top and bottom of a Au film by Ar RIE. (f) Spin-on-glass coating and annealing. (g) Cross-sectional SEM image of the fabricated Au nanofin array. (h) Surface topography of the sample measured using AFM.
Figure 3(g) shows the cross-section scanning electron microscope (SEM) image of fabricated nanofin array. A vertically formed Au nanofin array structure was successfully embedded in the glass with equal intervals. Note that there are voids in the SOG filling that were possibly caused by insufficient spin coating or shrinkage under annealing. The period, height and width of the Au nanofins are 400, 830 and 60 nm, respectively. The average thickness of the top SOG coating is 580 nm. Some Au nanofins slightly tapered due to tapered RIE in the step Fig. 3(b). These results decreased the effective slit width, which is assumed to affect to coupling efficiency of the TE transmittance. The average minimum width between nanofins is wmin = 300 nm. The surface roughness of the SOG coating was measured using an atomic force microscope (AFM, JEOL JSPM-5200, Japan Electron Optics Laboratory (JEOL) Co.). Figure 3(h) shows the surface topography. Despite the coating on an 830-nm-high mesa structure with nanofins, the arithmetic average roughness Ra was 3.7 nm, which is less than 0.5% of the mesa height. The roughness is also much lesser than incident visible wavelength, which does not affect the optical characteristics.
4. Measurement and discussion
Figure 4(a) shows the measurement setup based on polarization microscopy. The nanofin array sample was set at an orientation of ϕ =45°, and sandwiched between a polarizer and analyzer with orientations of ψ and θ, respectively. Transmitted light is expanded with an objective lens (TU Plan Fluor 20× / 0.45A Pol, Nikon Co.) and guided to the USB spectrometer (USB2000, Ocean Optics Inc.) through a bundle optical fiber(P200-2-UV/VIS, Ocean Optics inc.) with a 200-μm core diameter.
Fig. 4 (a) Schematic of the measurement setup based on polarization microscopy. (b) Theoretical and measured transmittance spectra. Red and blue lines show the transmittances under TM and TE polarization, respectively. Solid and dashed lines correspond to the measured and theoretical values derived from Eq. (4). Thick and thin lines show the averages and standard deviations of measurement(n = 5). (c) Transmittance as the function of the analyzer angle θ with the constant polarizer angle ψ = 90° at a wavelength of 633 nm. Black and gray plots correspond to transmittances measured with and without the sample and red line shows the direction of the sample. (d) Retardation spectra. The thick solid line shows the measured retardation, whereas the thin lines show the standard deviations(n = 5). The dashed line shows the theoretically calculated retardation.
First, transmittance spectra were measured. The analyzer was removed from the setup and the orientation of polarizer was set to be parallel (TE, ψ = 45°) and perpendicular (TM, ψ = 135°) to the nanofin array. The transmission spectra of the nanofin array are measured using a quartz-glass substrate as a reference. Figure 4(b) shows the measured transmittance spectra (solid lines) of the nanofin array, together with theoretical calculations (dashed lines). The blue and red lines correspond to the TE and TM polarizations, respectively. The theoretical values are derived with the dimensions of the fabricated sample being p = 400 nm, h1 = 580 nm, h2 = 830 nm, and w = 340 nm. Coupling efficiency of TE polarization was set to be effective aperture ratio ATE = wmin/p = 0.75. The transmittance of the TM polarization (red lines) exceeds 50% at the spectral range from 0.60 to 0.80 μm. At this range, TE transmittance also reaches approximately 50%. Furthermore, at a wavelength of approximately 0.60 μm, transmittances of the TE and TM polarizations are identical, which is an ideal condition for a waveplate. Compared to our previous research [18], transmittance of the TE polarization has significantly improved. The measured transmittance spectra agree well with theoretical estimates for both TE and TM polarizations.
The transmitted light’s polarization state was investigated with a polarizer and analyzer. The orientation of the polarizer was set to be ψ = 90° and the analyzer orientation θ was rotated and the intensity change of each θ was measured. Figure 4(c) shows the intensity normalized to the maximum of incident linear polarization (270°, gray marker) as a function of θ at the wavelength of 633 nm. The orientation of the nanofin array was set at ϕ =45° (red line). Black and gray markers correspond to intensities with and without (i.e. with only a glass substrate) the sample, respectively. Black solid and gray dashed curves correspond to sinusoidal fitting to the datum. It is observed that the polarization direction of the transmitted light is converted to linear polarization along 0°, which is symmetric to the incident linear polarization (90°) with respect to the nanofin axis. Ellipticity is defined as (Imin/Imax)1/2, where Imax and Imin are the maximum and minimum of sinusoidal fitting, respectively. The ellipticity of the transmitted light was calculated to be 0.105. Thus, this sample is confirmed to act as a half waveplate.
From the measured datum of intensity as shown Fig. 4(b) and 4(c), retardation was calculated for each measured wavelength. As the optics shown in Fig. 4(a) were set to be ψ = 90° and ϕ = 45°, the Stokes vector of the transmitted light is described by the following Mueller matrix analysis:
where LP, X and Sunp, are the Muller matrices of the linear polarizer the sample, and the Stokes vector of the non-polarized light source, respectively. Here, X describes the nanofin sample modelled as a combination of a partial polarizer and optical retarder. The intensity of the transmitted light S0 is given by where p1 and p2 are the amplitude transmittances for electric field of TE and TM waves, respectively. Δ is the retardation between the TE and TM polarizations induced by the sample. The solid line in Fig. 4(d) shows the measured retardation spectra derived through Eq. (6). The sinusoidal rise and fall was obtained with a period of approximately 20 nm, which was possibly due to interference on the measurement setup. Other than this sinusoldal variation, retardation is likely to be flat at approximately 165° at wavelengths ranging from 0.60 to 0.80 μm. The dashed line shows the theoretical retardation calculated using fabricated sample dimensions. The measured retardation agrees well with theoretical estimates. Thus, retardation reaching half-wavelength is demonstrated together with high transmittance at a broad bandwidth in the visible range.Waveplates are required to have little dependence on the incident angle, whereas a metal grating can cause strong angular dependence and result in a resonant transmission peak due to the surface plasmon [29]. To clarify the characteristic of the Au nanofin array, the incident angular-dependences of transmittance and retardation were measured. Since the diameter of an aperture stop is 4.0 mm and the distance between the sample and the aperture is 55 mm, the angular aperture of this measurement was estimated to be 4.2°.
Figure 5 shows the transmittances and retardations with variation in the tilt angle of the sample, as shown in each inset. Figures 5(a), 5(b) and 5(c), 5(d) show the transmittance and retardation spectra, respectively, and Fig. 5(a), 5(c) and 5(b), 5(d) show the results tiled around the x- and y-axes, respectively.
Fig. 5 Measured spectra of transmittance and retardation under various incident angles. Transmittance spectra when the substrate was tilted around the x- (a) and y-axes (b). Retardation spectra when the substrate was tilted around the x- (c) and y-axes (d).
As shown in Fig. 5(a), a slight variation of transmittance spectra was measured for both TE and TM polarizations with tilting around x-axis. However, in Fig. 5(b), the TM transmittance shows a dip at a wavelength of 0.72 μm as the tilt around the y-axis increases, whereas TE transmittance was almost constant. A possible reason for this dip is assumed to be the destructive interference of the plasmon modes. As shown in Fig. 5(c) and 5(d), retardation spectra has little dependence on tilt angle around both the x- and y-axes. Constant retardation regardless of incident angle is ideal nature for waveplate. This nature was due to the zero-order characteristic of the sample. The result shows that the Au nanofin array realizes a broadband and robust waveplate.
5. Conclusion
A Au nanofin array embedded in glass was proposed and demonstrated as a broadband half waveplate with transmittance higher than 50% in the visible spectrum. Theoretical estimation was performed on the basis of the waveguide theory of nanogaps. Two types of Au nanofin—free-standing and embedded in glass—were compared. From the calculation result, the Au nanofin array embedded in glass was believed to have the ideal characteristics of low dichroism and broadband retardtaion. A specimen of structure was fabricated through a sidewall deposition process and SOG coating. Transmitted light was measured through polarization microscopy. A constant retardation of 165° was obtained at the broad spectral range over 200 nm. Simultaneously, a transmittance higher than 50% under both TE and TM polarization was shown at wavelengths from 600 to 800 nm.
The incident angle dependence of the transmittance and retardation of the Au nanofin array were measured. Low dependence was measured for both transmittance and retardation in the incident angle range of from 0 to 15°, except for the transmittance of a TM wave under about y-axis rotation at the wavelength of 720 nm. This structure can be patterned in area of several μm with lithographic process. Complicated distribution of polarization or phase such as that of a Laguerre-Gaussian beam in a micro-scale plane is expected to be realized. The flatness of the surface enables patterning of other structures on the microscale waveplate and subsequently lends itself to the production of vertically integrated optical devices.
With these characteristics, the device designed herein enables highly efficient illumination with tailored polarization or phase, even if the area is small, or submerged in liquid for in vivo observation of biological samples. Applications to integrated plasmonic devices are also expected.
Acknowledgments
This work was supported by Grant-in-aid No. 15J11917 for scientific research from the Japan Society for the Promotions of Science (JSPS). This work was also supported by the VLSI Design and Education Center (VDEC) at the University of Tokyo.
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