Circular polarization analyzer based on an Archimedean nano-pinholes array

Jingran Zhang; Zhongyi Guo; Keya Zhou; Lingling Ran; Lie Zhu; Wei Wang; Yongxuan Sun; Fei Shen; Jun Gao; Shutian Liu

doi:10.1364/OE.23.030523

1.Introduction

The interactions between the light and the metallic nanostructures exhibit various functionalities, such as plasmonic focusing [1–8 ], extraordinary optical transmission (EOT) [9–12 ] and so on. These particular effects can be attributed as the generated surface wave called the surface plasmon polaritons (SPPs) which are the surface wave propagating along the interface between the dielectric and metal. The excited SPPs demonstrate a strong light confinement near the surface of metal [13], which make it possible to implement optical field shaping, manipulation beyond the diffraction limit and a varieties of optical applications, such as high-density optical data storage [14, 15 ], and circular polarization analysis [16–20 ].

Recently, analyzing the concrete polarizations of the circularly polarized light is a significant issue in the concrete applications, such as polarimetric imaging technique. Currently, a graphene-coated spiral dielectric lens as polarization analyzer has been reported for its superior advantages of tunable operation wavelength in the mid-infrared [21], and a plasmonics lens can analysis concrete circular polarization states by controlling surface plasmons propagation [22]. Both of these proposals demonstrate some preponderances in high extinction ratio and a relative wide operating wavelength. However, the fabrications of a large number of rectangular nano-apertures with nano size and 1 nm thick graphene-coating are relatively complicated because of the limited fabricating capabilities. Hence, here, we have proposed a simple structure based on the metallic nano-pinholes array with a high extinction ratio and relatively simpler fabrication process.

In this paper, we have presented theoretical analysis and numerical simulation on the single-turn spirally arranged Archimedean pinholes array for the circular polarization analysis. The performances of the designed plasmonic structures with different parameters under the CPL illuminations have been investigated in detail by finite element method (FEM) simulations. Compared with many previous structures based on Archimedean spiral slits [16–19 ], our designed structures show the superior characteristics in enhanced electric field intensity, the high extinction ratio and relatively broad operating wavelength, which are helpful in the actual CPL detection. Thus the proposed structure will open up a vital path toward nano-photolithography, biosensor and the polarimetric imaging owning to its simple design.

2. Structural design

The schematic diagram of the proposed single-turn Archimedean pinholes structure under the incidences of CPL is illustrated in Fig. 1 . In our scheme, the 250nm gold film is deposited on the surface of the glass substrate, which can be realized by means of e-beam evaporation. The 25 nano-pinholes etched into gold film, are arranged along the Archimedean spiral formula of r = r₀-λ_spp *ϕ/2π, which can be realized very easily with focused ion beam (FIB). The computational zone is 8 μm *8 μm *4 μm and the center of this structure is located at origin of coordinates. The laser with free space wavelength of λ = 808nm is used as the incident source (the corresponding SPP wavelength is λ_spp = 787.5nm), and the radius of pinholes r is set as 150nm. The nano-pinholes are penetrated through gold thin film, which is chosen to prevent far field direct transmission through the gold film. The initial radius of spiral is indicated as r₀ shown in Fig. 1(b). Figures 1(a) and (b) show the lateral and top views of the proposed single-turn Archimedean pinholes structure respectively. As shown in Fig. 1(a), the incident light illuminates to the Archimedean pinholes structure from the glass side.

Fig. 1 The schematic diagram of the single-turn Archimedean pinholes array (25 pinholes): lateral view (a) and the top view (b).

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3. Theoretical background

To investigate the focusing performances of the Archimedean nano-pinholes array, firstly, we will discuss the theoretical characteristics of a single circular nano-pinhole under the incidences of CPL. For a single nano-pinhole, the surface plasmons generated at the two sides of the nano-pinhole will have a π-phase difference [6], whether that is illuminated by the azimuthally polarized component or the radially polarized component. Figure 2 shows a schematic for explaining the definitions of used parameters in the proposed structure. The left-handed circularly polarized (LCP) light can be expressed in cylindrical coordinates as:

E_{L C P} = \frac{1}{\sqrt{2}} (\vec{e_{x}} - i \vec{e_{y}}) = \frac{1}{\sqrt{2}} e^{i θ_{1}} (\vec{e_{ρ_{1}}} - i \vec{e_{θ_{1}}})

As shown in Eq. (1), the incident CPL can be decomposed as azimuthal and radial components. And the circular nano-pinholes can be assumed as the dipole sources under CPL illuminations, which are associated with the concrete directions of the radial component and the azimuthal component of the incident CPL, as indicated as red arrows in the Figs. 2(a) and 2(b) respectively. Such an approximation is often considered for analyzing the surface fields that are far away from the pinholes [23]. Owning to the propagating SPP waves on the metal surface with the polarization in the z direction substantially, here, we mainly focus on the calculations of longitudinal electric field E_z by integrating the dipole sources along the spiral route, therefore, the E_z at the observing point (ρ, θ, z) near the origin can be expressed as [24]:

E_{z} (ρ, θ, z) = e^{- κ_{a} z} \int A (φ (θ_{1})) e^{j Φ (φ (θ_{1}), θ_{1}) + j m θ_{1}} e^{j k_{s p p} | \vec{ρ -} \vec{ρ_{1}} |} d θ_{1}

where ρ, θ, z denote the radial, azimuthal, and the z-directional position of the observing point inside the spiral separately, ρ₁, θ₁ signify those of the dipole sources integrated along the azimuthal direction, and κ_a denotes the attenuation coefficient of SPP mode in the air. We must note here that the propagating loss of the SPP is neglected. The azimuthal distribution function of the dipole orientations with respect to the radial orientation and x-axis are indicated as φ(θ₁) and ϕ(θ₁). The relationship between the two functions is φ(θ₁) = ϕ(θ₁)−θ₁, which can be clearly visualized from Fig. 2(a). Α and √ can be used to express the amplitude and phase functions of the surface propagating wave to the origin (generated from the azimuthal (Fig. 2(a)) and radial (Fig. 2(b)) dipole sources associated with the azimuthal and radial polarization components) at every locations of dipole sources with the varying of ϕ(θ₁) [25]. And here, Α and √can be expressed as:

A = A_{0} \cos (φ (θ_{1}))

Φ = ϕ (θ_{1})

where Α₀ denotes the amplitude of the generated dipole sources. For the azimuthal polarization components of the CPL incidence shown in Fig. 2(a), φ(θ₁) = π/2 and ϕ(θ₁) = π/2 + θ₁. Therefore, the E_z electric filed intensity at the observing point is zero because A = 0, which matches well with the analysis of symmetrically arranged triangle arrays in the Re [26]. For the radial polarization components of the CPL incidence as shown in Fig. 2(b), φ(θ₁) = 0 and ϕ(θ₁) = θ₁. The Eq. (2) can be written as:

E_{z} (ρ, θ, z) = e^{- κ_{a} z} \int A_{0} e^{\pm j θ_{1} + j m θ_{1}} e^{j k_{s p p} (ρ_{0} - ρ \cos (θ - θ_{1}))} d θ_{1} \propto J_{m \pm 1} (k_{s p p} ρ)

where m defines the geometrical charge of the spiral structure [16]. Besides these two obvious dipole sources associated with the radial and azimuthal polarization components respectively, there are another two dipole sources associated with the coupling modes between the radial and azimuthal polarization components, as indicated by the green dashed arrows between the red arrows in Fig. 2(c). And owning to the π-phase difference between the four point sources, so the φ(θ₁) = 3*π/4, ϕ(θ₁) = θ₁ + 3*π/4 for LCP incident. Therefore, the Eq. (2) can be written as:

Fig. 2 A schematic for explaining the definitions of parameters used in the proposed structure. (a) the azimuthal polarization components, (b) the radial polarization components of LCP illumination, (c) the schematic for the two dipole sources associated with azimuthal and radial polarization components (red arrows) and the concrete coupling dipole sources between azimuthal and radial polarization components (green dashed arrows).

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\begin{matrix} E_{z} (ρ, θ, z) = 2 e^{- κ_{a} z} \int \sqrt{2} / 2 A_{0} e^{j (θ_{1} + 3 * \frac{π}{4}) + j m θ_{1}} e^{j k_{s p p} (ρ_{0} - ρ \cos (θ - θ_{1}))} d θ_{1} \\ = \sqrt{2} e^{- κ_{a} z} \int A_{0} e^{j θ_{1} + j m θ_{1} + j 3 * \frac{π}{4}} e^{j k_{s p p} (ρ_{0} - ρ \cos (θ - θ_{1}))} d θ_{1} \\ = \sqrt{2} e^{- κ_{a} z} e^{j 3 * \frac{π}{4}} \int A_{0} e^{j θ_{1} + j m θ_{1}} e^{j k_{s p p} (ρ_{0} - ρ \cos (θ - θ_{1}))} d θ_{1} \\ \propto J_{m + 1} (k_{s p p} ρ) \end{matrix}

And for the right-handed circularly polarized (RCP) incidence, the direction of azimuthal component is opposite to the case indicated in Fig. 2(a). The Eq. (3) should be revised as √ = −ϕ(θ₁), and φ(θ₁) = 3*π/4,ϕ(θ₁) = θ₁ + 3*π/4. Thus the corresponding Eq. (2) can be written as:

\begin{matrix} E_{z} (ρ, θ, z) = 2 e^{- κ_{a} z} \int \sqrt{2} / 2 A_{0} e^{- j (θ_{1} + 3 * \frac{π}{4}) + j m θ_{1}} e^{j k_{s p p} (ρ_{0} - ρ \cos (θ - θ_{1}))} d θ_{1} \\ = \sqrt{2} e^{- κ_{a} z} \int A_{0} e^{- j θ_{1} + j m θ_{1} - j 3 * \frac{π}{4}} e^{j k_{s p p} (ρ_{0} - ρ \cos (θ - θ_{1}))} d θ_{1} \\ = \sqrt{2} e^{- κ_{a} z} e^{- j 3 * \frac{π}{4}} \int A_{0} e^{- j θ_{1} + j m θ_{1}} e^{j k_{s p p} (ρ_{0} - ρ \cos (θ - θ_{1}))} d θ_{1} \\ \propto J_{m - 1} (k_{s p p} ρ) \end{matrix}

Thus, by superposing light fields generated from each dipole sources, the total transmitted longitudinal electric field of proposed structure can be enhanced obviously, and the power conversion efficiency of this spirally arranged nano-pinholes structure will also be improved efficiently compared with that of spiral nanoslit. According to the above analysis, there is geometrical charge of m = 1 for our proposed left-handed structure. Hence, the order of Bessel function can be obtained to be 2 under LCP incidence while to be 0 under RCP incidence which results in spatially separated fields under CPL incidence with different polarizations.

4. Reults and discussions

Because of the particular polarization-dependence, the Archimedean spiral plasmonic lens, has been extensively reported before [16–19 ]. Hence, due to its geometric phase effect, such designed left-handed structure can focus RCP (LCP) light into a confined focus spot (doughnut shaped field). The existing circular pinholes can improve the coupling efficiency of SPP mode and enhance the electric field intensity.

Firstly, we have investigated the longitudinal electric field intensity distributions at the wavelength of 808nm when the initial radius is set as r₀ = 2000nm, and the simulated results are shown in Fig. 3 for the RCP (Fig. 3(a)) and LCP (Fig. 3(b)) illuminations respectively. From the results, it can be observed that the generated longitudinal electric field intensity distributions are obviously different and can be applied to analysis the incident polarizations effectively, which agree well with the former theoretical analysis. Then the relationship between the circular polarization extinction ratio and the initial radius of spiral r₀ (from 1000nm to 2400nm by step of 200nm) has also been investigated for acquiring the optimized r₀. Because the dominant component of the SPPs wave is longitudinal component (polarized in the z direction), here, the circular polarization extinction ratio is calculated with the Ez solely. Figs. 4(a) and 4(b) illustrate the circular polarization extinction ratio (defined by the longitudinal intensity integral on the detector size (D = 200nm) of the focal spot field divided by the one of the donut shape field) as the function of r₀ and the position along z axis, for the proposed structure and the spiral slit structure respectively. The simulated results reveal that the optimal parameter for our Archimedean nano-pinholes array and the traditional spiral slit structure are different, and the extinction ratio can reach to its maximum value of 515 when r₀ is set as 1400nm for our structure, which is higher than that of the optimal value of 409for the traditional spiral slit.

Fig. 3 The longitudinal electric field intensity distributions at XOY plane under RCP (a) and LCP (b) illuminations.

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Fig. 4 The comparison of the optimal circular polarization extinction ratio as the function of r₀ and the position along z axis(from z = −1.45 μm to z = 0.25μm) for our proposed Archimedean nano-pinholes array (a),and the traditional spiral slit structure (b)

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The comparisons of performances between the single-turn Archimedean spiral slit with initial radius r₀ = 1400nm shown in Figs. 5(a)-5(c) and our proposed structure (Archimedean nano-pinholes array) with r₀ = 1400nm in Figs. 5(d)-5(f) have been given in the yoz plane visions under RCP (on middle column) and LCP (on right column) incidences respectively. The simulated results reveal that the electric field intensity of the single-turn Archimedean spiral slit shown in Figs. 5(b) and 5(c) are obviously weaker than that of the Archimedean nano-pinholes array shown in Figs. 5(e) and 5(f), which indicates that the designed Archimedean nano-pinholes array is more effective because of the enhanced coupling efficiency of SPPs. The weaker transmitted field intensity of the traditional spiral slit is due to only the contribution from the radial dipole sources associated with the radial component, while for the proposed Archimedean nano-pinholes array, as discussed above, the enhanced total transmitted field distribution is originating from superposing fields caused by all dipole sources (the radial dipole sources, the coupling between the radial and azimuthal dipole sources)

Fig. 5 The longitudinal electric field intensity distributions at yoz plane under circular-polarization illuminations. (a)(b)(c) for the single-turn Archimedean spiral slit, (d)(e)(f) for 25 Archimedean nano-pinholes array with r₀ = 1400nm.

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The simulated results show such designed left-handed plasmonic lens can focus RCP light into a confined focus spot and defocuses the LCP light into doughnut shaped field, which match well with the theoretical analysis. Thus it can be used as a circular polarization analyzer with a high extinction ratio. Here, the field distributions can be detected by using a near-field scanning optical microscopy (NSOM) using a metal-coated fiber probe with aperture, enabling the measurement of both longitudinal and transverse E-field components [27]. And such a probe is selectively sensitive to different E-field components [28]. The spiral plasmonic lens consisting 20 etched nano-pinholes in the gold film has also been simulated with r₀ = 1400nm. The results display a relative weak longitudinal electric field intensity at z = −0.8μm compared with 25 nano-pinholes structure, which is owning to the low coupling efficiency of SPP waves of a small number of nano-pinholes. Then, the extinction ratio as the function of wavelength and the position along z axis is simulated as shown in Fig. 6 for the plasmonic lens with 25 spirally arranged nano-pinholes. From the simulated result, it is observed that the extinction ratio can maintain at relative high values from 650nm to 900nm at different detecting locations.

Fig. 6 The circular polarization extinction ratio as the functions of the incident wavelength and the position along Z axis (from z = −1.45μm to z = 0μm).

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Under RCP/LCP incidences with the wavelength of 715nm shown in Figs. 7(a) and 7(b) and the wavelength of 1000nm shown in Figs. 7(c) and 7(d), the transmitted electric field distributions have also been investigated for the Archimedean nano-pinholes array with r₀ = 1400nm. Though this plasmonic lens is designed at the wavelength of 808nm, such structure can still have an obvious focusing effect under RCP illumination and defocusing effect under LCP illumination at a wavelength of 715nm or 1000nm. These phenomena can be attributed to the extra dipole sources of pinholes compared with Archimedean spiral slits [29] and spirally arranged triangular apertures [30], in which the propagating SPPs waves to the center have imperfect constructive interference or imperfect destructive interference at other operating wavelengths. Compared with former investigations of pure spiral slit plasmonic lenses, owning to the enhanced SPPs wave from the radial and azimuthal excitations, the existing imperfect interferences still have an obviously enhanced electric field intensity.

Fig. 7 The electric field distributions at yoz plane. The left column ((a)(c)) is under RCP illuminations and the right column ((b)(d)) is under LCP illuminations;(a)(b)The incident wavelength is 715nm, (c)(d) The incident wavelength is 1000nm.

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5. Conclusion

In this paper, we have proposed a circular polarization analyzer based on the Archimedean nano-pinholes array with a higher extinction ratio and a relative broad operating wavelength from 650nm to 900nm. And we have given the working principle of designed structure for its superior performance as a circular polarization analyzer. For left-handed spiral structure, the RCP incidence will be focused into a confined focusing spot, while the LCP incidence will be defocused into a doughnut shaped pattern. The circular-polarization extinction ratio can reach around 500 when the detector size is 200nm at a flexible distance from the metal surface. And the longitudinal electric field distributions at the wavelengths of 715nm and 1000nm have also been simulated, which show the designed Archimedean nano-pinholes array has a broader operating wavelength as a circular polarization analyzer. Hence, such spiral plasmonic lenses integrated with metal wire grids can be used to extract full Stokes parameters in polarimetric imaging. An array of such proposed structures can find applications in parallel near-field imaging and sensing.

Acknowledgments

The authors gratefully acknowledge the financial supports for this work from the National Natural Science Foundation of China (NSFC) under Grant No. 61575060, and the Fundamental Research Funds for the Central Universities (2015HGCH0010).

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Circular polarization analyzer based on an Archimedean nano-pinholes array

Abstract

1.Introduction

2. Structural design

3. Theoretical background

4. Reults and discussions

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Equations (7)

Optics Express