1. Introduction

Artificial subwavelength structures have been extensively stimulated as they exhibit very many extraordinary phenomena, such as omnidirectional light absorption as a dark material [1,2]. Novel devices are leading developments toward the full manipulation of all features of an electromagnetic wave, except its polarization state. Numerous methods for producing specifically polarized waves have been developed over several decades. They include the use of a polarizer [3,4] to absorb an unnecessary polarization component from unpolarized light. Some new and sophisticated nanostructures [5–11] have been designed and fabricated as circular or linear polarization beam splitters that function for a designated wavelength and range of incident angles, to separate two orthogonal polarization states from unpolarized light. Complete manipulation of the polarization state depends on a lossless polarization conversion device that is effective for a broadband spectrum and wide range of angles. The traditional scheme for changing polarization state is to use a phase retarder [12], also called a wave plate, which produces a phase (optical path) difference between two electric field components of the light, to generate a specific polarization state. The effect of such a phase retardation plate depends strongly on the wavelength and angle of incidence. The most achromatic quarterwave plates appear to be rhomb-type devices [13]. In nature, the only known perfect achromatic wave plate exists in the eye of a stomatopod crustacean [14].

Recently, a single tilt columnar thin film with weak birefringence was experimentally demonstrated effective to convert the polarization state [15]. The single tilt columnar thin film can be deposited by oblique angle deposition (OAD) [16]: the substrate is tilted with respect to the deposition flux and the shadowing effect [16] produces a column-structured thin film that exhibits a biaxial optical property [17,18]. For some typical low refractive columnar thin films like magnesium fluoride (MgF₂) and silicon dioxide (SiO₂), the birefringent optical property is uniaxial-like [19,20]: two of the principal indexes are pretty close. A tilt columnar SiO₂ thin film with a column angle β = 30° with respect to surface normal and a thickness of 800 nm in a BK7 glass prism/anisotropic SiO₂ film/air system, exhibited enhanced polarization conversion reflection (of over 90%) in a strict range of incident angles that exceed the critical angle of the system when the plane of incidence is perpendicular to the deposition plane determined by the columns and the surface normal. However, the use of polarization converter based on an anisotropic MgF₂ thin film is limited to a strict incident angle range of only 0.5° [15]. The polarization conversion reflectance R_ps(R_sp) is defined as the ratio of intensity of the reflected s(p)-polarized ray to that of the incident p(s)-polarized ray. In order to satisfy the boundary condition for fields, the R_ps has to be equal to R_sp. The polarization conversion reflectance is raised due to the synthesized effects including interference, phase retardation, total reflection and cross-polarization in the anisotropic thin film. For example, when a p-polarized ray is incident onto the uniaxial optical thin film, the refracted waves are coupled into ordinary (o) waves and extraordinary (e) waves that undergo multi-reflection in the thin film. When the o-wave and e-wave are coupled into the reflected wave with s-polarized and p-polarized components, the phase difference between the o-wave and the e-wave caused by propagation, the reflection coefficient and the transmission coefficient at the interfaces cause the e-wave coupling to the p-polarized component and the o-wave coupling to p-polarization component to cause destructive interference, reducing the intensity of the reflected p-polarized ray. The diminishing of the intensity of the reflected p-polarized ray enhances the intensity of the reflected s-polarized ray to satisfy the total reflection condition: constructive interference occurs when the o-wave and e-wave combine to form the reflected s-polarized ray, causing polarization conversion.

The OAD technique has been widely employed to grow various nanostructures on large-area substrates by manipulating the substrate during deposition. Helical [5–8] and zig-zag [9–11] structured dielectric thin films are also deposited and utilized as circular and linear polarization beam splitters, respectively. Slanted S-shaped nano-columnar (SSNC) thin films are composed of various tilted columns to construct slanted S-shaped morphologies in the deposition plane. A SSNC film is fabricated by varying the deposition angle sinusoidally during deposition. Then, the SSNC film with spatially modulation tilted columns grows in the deposition plane. The SSNC films have spatially modulated refractive indices. By incorporating empirical equations for the principal refractive indices of titanium oxide (TiO₂) and zirconium oxide (ZrO₂) into the sinusoidal model, a SSNC film has been demonstrated as birefringent rugate filters [21]. Recent report indicates that a SSNC film can be designed and fabricated to support multiple surface plasmons [22] over a wide range of incident angle in the Krestchmann configuration. It is motivated to study the performance of polarization conversion versus angle of incidence and wavelength by arranging a SSNC film in a prism-coupling system.

In this work, two-period SSNC tantalum oxide (Ta₂O₅) thin films with various structures sculptured with OAD are analyzed for their abilities in changing the polarization. The optimum sculpture parameters for a two-period SSNC Ta₂O₅ film are derived and applied in fabrication. It is demonstrated experimentally that a SSNC film can reach high polarization conversion efficiency over visible wavelengths and wide incident angles.

2. Anisotropic properties of the SSNC film

A SSNC film is fabricated by varying the deposition angle sinusoidally during deposition. To describe the principal indices of a SSNC film, the functional equations are built in the following process. The columnar Ta₂O₅ thin films are prepared at various deposition angles of $\alpha$ = 50°, 60°, 70°, and 80°. The principal indices [20] of these films are determined by fitting polarization conversion reflectance angular spectra R_ps. From Scanning–electron–microscope (SEM) image, column angle is obtained. The column angle β and principal indices (n₁, n₂, n₃) as functions of deposition angle $\alpha$ are derived [17]. Figure 1 plots the SSNC film is grown by varying deposition angle periodically to form a two-dimensional slanted S-shaped columnar structure. The surface coordinates are defined as (x, y, z) axes and the substrate surface is on the z = 0 plane. The column angle β as a function of the deposition angle α satisfies the relationship shown in Eq. (1).

 

Fig. 1 Scheme of the SSNC film grown by varying deposition angle periodically to form a two-dimensional slanted S-shaped columnar structure in the y-z deposition plane. The principal indices (n₁, n₂, n₃) are associated with orthogonal principal axes (1, 2, 3).

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In this case, SSNC films are assumed to be sculptured with continuous change of the deposition angle α oscillating between two angles ${\alpha }_{\min }$ and ${\alpha }_{\max }$. With designated tooling factor and deposition rate, the deposition angle is designed as a function of z, as shown in Eq. (5).

3. Polarization conversion from a two-period SSNC film

Berreman’s matrix calculation [23] can accurately derive four field eigenstates in the biaxial film by solving Maxwell’s equations and electromagnetic field boundary conditions. Transmittance and reflectance coefficients at the interfaces can be calculated in terms of ratios of power flux. Then, the reflectance and transmittance at the interfaces can illustrate energy transfer between four coupled waves. The polarization conversion reflectance is calculated for the SSNC film in a prism-coupling system: a BK7 glass prism/SSNC film/air configuration in which the SSNC film with two-period S-shaped structures and the deposition plane perpendicular to the plane of incidence, as given in Fig. 2 . The Berreman’s matrix calculation is applied to obtain the reflection coefficients and reflectance R_ps of the SSNC Ta₂O₅ film for the incident angle ranged from θ = 42° to θ = 70° and wavelengths ranged from λ = 400 nm to λ = 700 nm. The numerical calculation is implemented for thickness d varied every 100 nm from 600 nm to 900 nm. To achieve the polarization conversion reflectance with high conversion efficiency over the entire visible region and wide-angle range, the polarization conversion reflectance R_ps(λ, θ) is simulated to get its maximum performance that enhanced R_ps(λ, θ) can cover the whole visible wavelengths with maximum range of incidence.

 

Fig. 2 The SSNC film is arranged in the BK7 glass prism/SSNC film/air configuration in which the SSNC film with two-period S-shaped structures and the deposition plane perpendicular to the plane of incidence $\Phi$ = 90°.

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Figure 3 plots the reflectance R_ps(λ, θ) for the first type of the designed SSNC films. In figures, the marked square region for the reflectance R_ps(λ, θ) is defined as enhanced polarization conversion region (EPCR) to represent the possible wavelengths and incident angles area that the reflectance R_ps(λ, θ) is over 80% and continuously distributed. Three sets of the first type of SSNC films are simulated for the amplitudes A = 20°, 25°, and 30° at fixed initial deposition angle of ${\alpha }_0$ = 80°. For the two sets associated with amplitudes A = 20° and A = 25°, the wavelength widths of EPCR are gradually extended when the thickness increases from d = 600 nm to d = 800 nm, as shown in Figs. 3(a)-3(d) and 3(e)-3(h). At the thickness of d = 800 nm, the wavelength width of EPCR is extended to cover the entire visible wavelength region, as shown in Figs. 3(c) and 3(g). When the thickness increases to d = 900 nm, the wavelength width of EPCR is reduced to 244 nm (wavelength range: 456-700 nm), as shown in Figs. 3(d) and 3(h). For the amplitude of A = 30°, the wavelength width of EPCR for each case is unable to cover the whole visible regime, as shown in Fig. 3(i)-3(l). Notably, angle widths for all sets are about 8° but the angle widths of EPCR are located at (θ = 48°, θ = 56°), (θ = 51°, θ = 59°), and (θ = 53°, θ = 62°) for the amplitude A = 20°, A = 25°, and A = 30°, respectively.

 

Fig. 3 The reflectance R_ps(λ, θ) for the first type of the designed SSNC films with the thickness d ranged from 600 nm to 900 nm. The sinusoidal variations with the fixed initial deposition angle ${\alpha }_0$ = 80° but different amplitudes: (a)-(d) A = 20°, (e)-(h) A = 25°, and (i)-(l) A = 30°. The marked square region represents the possible wavelengths and incident angles area that the reflectance R_ps(λ, θ) is over 80% and continuously distributed.

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The other three sets associated with the second type of SSNC films are simulated for initial deposition angles ${\alpha }_0$ = 70°, 75°, and 80° at fixed amplitude of A = 20°. Figures 4(i) -4(l) associated with (${\alpha }_0$ = 80°, A = 20°) are identical with Figs. 3(a)-3(d). For the set of ${\alpha }_0$ = 70°, the wavelength widths of EPCR for all cases are narrower than 100 nm and distributed at different wavelength regions, as shown in Fig. 4(a)-4(d). For the set associated with ${\alpha }_0$ = 75°, the wavelength widths of EPCR are gradually extended when the thickness increases from d = 600 nm to d = 800 nm, as shown in Fig. 4(e)-4(g). The angle widths of EPCR of the set (${\alpha }_0$ = 75°, A = 20°) are smaller than these of the set (${\alpha }_0$ = 80°, A = 20°).

 

Fig. 4 The reflectance R_ps(λ, θ) for the second type of the designed SSNC films with the thickness d ranged from 600 nm to 900 nm. The sinusoidal variations with the fixed amplitude A = 20° but different initial deposition angles: (a)-(d) ${\alpha }_0$ = 70°, (e)-(h) ${\alpha }_0$ = 75°, and (i)-(l) ${\alpha }_0$ = 80°. The marked square region represents the possible wavelengths and incident angles area that the reflectance R_ps(λ, θ) is over 80% and continuously distributed.

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According to the aforementioned analysis, a broadband and wide-angle polarization converter can be achieved by preparing a two-period SSNC film with the thickness around d = 800 nm to keep broadband polarization conversion in the visible region. More detailed simulations respect to SSNC films with thicknesses near d = 800 nm reveal that the optimum thickness range is ranged from d = 780 nm to d = 810 nm. The sculpture parameters (${\alpha }_0$, A) of the sinusoidal variation are chosen as (${\alpha }_0$ = 80°, A = 20°) and (${\alpha }_0$ = 80°, A = 25°) to ensure the angle width of EPCR larger than 8°.

4. Fabrication and measurement

Electron-beam evaporation was used to fabricate two-period SSNC films on glass substrates. The chamber pressure was pumped to $8\times {10}^{-4}$ Pa prior to each deposition. The SSNC film of Ta₂O₅ was deposited by varying the deposition angle per Eq. (5) but keeping the deposition rate fixed at 0.3 nm s⁻¹. Sample A and sample B were deposited by the sculpture parameters of (${\alpha }_0$ = 80°, A = 20°) and (${\alpha }_0$ = 80°, A = 25°), respectively. SEM images of both samples are shown in Fig. 5 , which clearly evinces the periodicity of the SSNC films along the z axis. From SEM images, the thickness is d = 725 nm for sample A and the thickness is d = 975 nm for sample B.

 

Fig. 5 Cross-sectional SEM images of SSNC films fabricated by OAD. (a) Sample A with the thickness of d = 725 nm. (b) Sample B with the thickness of d = 975 nm.

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Figure 6 shows the measured R_ps(λ, θ) with the marked EPCRs for sample A. The measurement in experiment is difficult to distinguish R_ps(λ, θ) from R_sp(λ, θ). The angle of incidence associated with enhanced polarization conversion reflectance (above 80%) has a wide-angle range from θ = 42° to θ = 70° at a wavelength of λ = 550 nm. The wavelength bandwidth for enhanced polarization conversion reflectance (above 80%) has a broadband region from 400 nm to 700 nm at the angle of incidence of θ = 46°. There are two EPCRs in Fig. 6: (1) wavelengths from λ = 400 nm to λ = 684 nm and incident angles from θ = 43° to θ = 52° (2) wavelengths from λ = 540 nm to λ = 594 nm and incident angles from θ = 43° to θ = 64°. Compared with theoretical calculation in Fig. 3(a)-(d) and measured data presented in Fig. 6, the EPCR of our experimental sample shifts about five degrees: from (θ = 48°, θ = 56°) to (θ = 43°, θ = 52°). The discrepancy between theoretical estimation and experimental result can be resolved in the following way. The early part of the growth of a SSNC film is the initial film-forming stage that the shadowing effect and competition effect dominate the film growth from nucleation to columns forming [24]. Competition goes away and columns of stable cross sections grow after is roughly 35 nm in thickness. Because the shadowing effect is not obvious at initial deposition stage, the principal indices of the initial grown layer with thickness around 35 nm is difficult to follow the relationship Eq. (2)-(4). By setting the initial grown 35 nm thick film with constant principal indices (n₁ = 1.543, n₂ = 1.355, n₃ = 1.423) associated with deposition angle α = 80°, the calculated EPCR is then well matched with the measured EPCR.

 

Fig. 6 The measured reflectance R_ps(λ, θ) for sample A. There are two marked EPCRs: (1) λ = 400 nm to 684 nm and θ = 43° to 52°. (2) λ = 540 nm to 594 nm and θ = 43° to 64°.

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Figure 7 shows the measured R_ps(λ, θ) with the marked EPCR for sample B. The EPCR has a broadband polarization conversion at incident angles: wavelengths from λ = 500 nm to λ = 700 nm and incident angles from θ = 51° to θ = 58°. The EPCR of our experimental sample shifts obviously toward infrared wavelength range because the thickness is 975 nm larger than 900 nm. According to the aforementioned analysis for sample A, the discrepancy of sample B between theoretical estimation and experimental result is due to the same reason for sample A. By considering the initial growth thickness separately and recalculating the reflectance R_ps(λ, θ) for sample B, the recalculated EPCR is in agreement with the measured results.

 

Fig. 7 The measured reflectance R_ps(λ, θ) for sample B. The marked EPCR has λ = 500 nm to 700 nm and θ = 51° to 58°.

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The mechanism of the polarization conversion can be understood by tracing waves propagation through the film. The phase difference between eigenwaves comes from transmission, reflection and propagation in the film can be calculated. The total phase difference between reflected eigenwaves in the film would lead to constructive coupling effect for s-polarized reflected wave to achieve enhanced polarization conversion from incident p-polarization to reflected s-polarization. The analysis had been described in our previous study [25]. It is estimated that the phase difference presents a small variation over the visible regime.

5. Conclusion

In conclusion, this study demonstrates that the polarization state of light can be effectively converted using a SSNC Ta₂O₅ thin film over a broad range of wavelengths and wide range of angles of incidence. The SSNC films with spatially modulated refractive indices have been designed by changing the deposition angle variation and the thickness. The optimum sculpture parameters for EPCR are: ${\alpha }_0$ = 80°, A = 20°, d = 800 nm for two periods. The fabricated SSNC film is arranged in BK7 prism/SSNC film/air configuration to have above 80% conversion efficiency in the visible range at incident angles from θ = 43° to θ = 52°. The EPCR performance of a three-period SSNC film also can be derived by applying the simulation method mentioned in Sec. 3. The results are similar to these of a two-period SSNC film. Through modulating sculpture parameters (${\alpha }_0$, A) and the thickness d, the maximal EPCR can cover the whole visible regime and angle width around 10°.

A near-perfect polarizer can be formed by combining a polarization beam splitter and the polarization converter that is proposed herein, to align the polarization state from unpolarized light. The broadband and wide-angle polarization converter can be applied to recycle the wasted polarization light from a beam splitter to increase the efficiency of luminosity in projectors [25] or liquid crystal displays [26]. This work also serves as a reference for the future design and fabrication of SSNC films to convert among any two orthogonal polarization states, such as right-handed and left-handed circular states, with a wide range of angles of incidence and achromatic conversion power. This device can provide a more efficient way to control and manipulate the polarization of light.