1. Introduction

Propagating surface plasmon polaritons (SPPs) through flat metal film have been considered as promising photon carriers in the fields of integrated optics and subwavelength imaging [1, 2]. Their high confinement, fast information speed, and strong field enhancement insure that SPPs are appropriate for various applications in nanophotonics such as active switches [3, 4], plasmonic holography [5], integrated optical interconnections, and optical isolations [6–9]. For these purposes, demands for tuning or multiplexing SPP signals with convenient routes are increasing. Especially, SPP phase manipulation without using bulk optics such as spatial light modulator (SLM) may have great potential for abovementioned applications.

Recently, manipulating the phase of light with ultra-thin films has been achieved with the use of metasurfaces [10, 11]. A metasurface is a kind of flat thin film layer arranged by subwavelength size of unit cells having own functions. Differently from the broad definition of metamaterial, the thickness of metasurface is shorter than optical wavelength which is more beneficial for compact design of optical phenomena. The metasurface can be designed with numerous purposes such as color filter [12], broadband optical waveplate [13], negative-refraction [14], and ultra-thin lens [15]. Especially, some research shows that it is possible to obtain broadband, high-efficiency holography by using the metasurface which consists of the nanorods with spatially-tuned tilted angle distribution. The phase profile transmitted through the metasurface can be arbitrarily designed by optimizing the distribution of nanorods, hence the structure can act as an ultra-thin phase-only holography [16].

On the other hand, there have been great efforts to achieve an arbitrary phase profile for propagating SPPs. Such attempts are quite important to make various types of plasmonic fields such as plasmonic Airy beams, hot spots, and vortices [17–19]. In the early works on these fields, spatially varying phase profiles of SPPs are often obtained by simply shifting the location of SPP sources in order to make phase delays. However, in these cases, the fields generated from the SPP sources are fixed to certain shape, i. e. there are no degree of freedom for multiplexing SPP signals.

Very recently, design principles of metasurface are applied for tuning of SPP signals. It is shown that certain arrangement of nanoslits can be used for directional launching of SPP, where its launching direction can be switched by optical polarization of incident light [20]. Multiple nanoslit arrays with rotating slit orientation have also been proposed for directional switching of propagating SPPs [21]. Similar concepts are also applied to focal length tuning of near-field plasmonic focus [22] and controlling the spin-direction and size of plasmonic vortex [23]. In addition, metasurface consists of mixed random antenna groups have been proposed for SPP wavefront shaping [24]. However, there is still no research for the generation of arbitrary SPP phase profile multiplexed by incident polarization state. Studies on the unit cell of nanoslit-based metasurface have been reported [22, 23].

In this paper, we present a method for the generation of polarization-multiplexed arbitrary phase profile by distributing the nanoslits with a simple design law. The proposed structure is composed of double arrays of nanoslit with spatially varying tilted angle distribution. Each nanoslit acts as a unit cell of the proposed structure. In order to make two different arbitrary phase distributions of excited SPPs for left-handed and right-handed circular polarizations (LCP and RCP), two different mechanisms for expressing the polarization-reversible and polarization-independent phase profiles are combined. For the phase terms independent of optical polarizations, lateral shift of nanoslit is directly applied similar to the previous works [18, 19]. On the other hand, polarization-reversible phase profile comes from the tilt angle of each nanoslit with respect to the envelope of the double nanoslit array. As a result, the proposed structure is possible to excite SPP signals with two different arbitrary phase profiles for LCP and RCP incidences. We verify such polarization-multiplexing characteristics by switching the location of plasmonic hot spots located at two arbitrary positions.

2. Configuration of the proposed structure and basic principle

In Fig. 1(a), schematic of the proposed scheme is briefly shown. As a point-like dipole source for SPP generation, nanoslits are carved on the thin metal film. Our purpose is to make an arbitrary SPP phase profile for each circularly polarized case (LCP or RCP), which is totally independent of each other, by appropriately distributing the nanoslits varying with their positions and tilted angles. For the general case of polarization-multiplexed SPP phase generation, we define the desired phase profile for LCP and RCP incidence at x = 0 as Φ_L(y) and Φ_R(y), respectively. Then, we separate the desired phase profile into symmetric and anti-symmetric terms which can be simply written as,

 

Fig. 1 (a) Distributed nanoslits structure proposed for polarization-multiplexed SPP phase generation. (b) Schematics for explaining two different mechanisms: Φ_s(y) is obtained from the shift of nanoslits, whereas Φ_a(y) is obtained by rotating the slit orientation.

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Figure 1(b) shows detail of distributed nanoslits for understanding the abovementioned two types of SPP phase generation mechanisms. A virtual straight line, indicating x = 0 plane for our configuration, is shown as a dotted black line in Fig. 1(b). On the left side of the virtual line, pairs of nanoslits are distributed with the uniform distance along the y-direction. The polarization-independent phase profile (Φ_s(y)) of excited SPPs is achieved by the lateral shifting of each nanoslit pair in order to produce the phase delay with respect to the virtual x = 0 plane, as shown in upper-left side of Fig. 1(b). Considering the effective wavelength of the SPP mode propagating on the metal surface, the distance shifted from the x = 0 plane can be determined as follows,

Next, the polarization-reversible phase profile can be achieved from the tilted angle distribution of the unit cells. For the simplicity, we show the nonzero Φ_a(y) case without considering the lateral shift of nanoslit positions in upper-right side of Fig. 1(b). Similar to the design mechanism of metasurfaces [12–15], the unit cell of SPP source consisting the proposed structure is a pair of nanoslit, having tilted angle distributions of θ_r(y) for the right-side ones and those of the left-side ones are perpendicular to θ_r(y), i. e. θ_l(y) = θ_r(y) + π/2. Here, the right-side tilted angle distribution is designed to be directly related to the Φ_a(y) as follows,

For circular polarization incidence, electric field vector rotates according to the phase of incident light. In addition, a subwavelength rectangular nanoslit with high aspect ratio can only excite SPPs for electric field component perpendicular to its longer axis [22]. Due to these characteristics, phase delay of excited SPPs can be introduced with respect to the angular distribution of nanoslits for each circular polarization case. In our recent work [22], we have shown that the complex amplitude of excited SPPs from the nanoslit array having tilted angle distribution of θ_r(y) is proportional to,

Finally, these two phase formation mechanisms are combined as depicted in lower side of Fig. 1(b). The Φ_s(y) is achieved by the lateral shift of the nanoslit pairs, whereas Φ_a(y) is achieved by rotating the orientation of the nanoslit pairs.

3. Analysis on plasmonic hot spot switching with distributed nanoslits

Although the proposed scheme can be applied to any type of SPP phase generation, we would like to show one of the simplest examples which can verify the polarization-multiplexing characteristics of the proposed scheme. The phase profile for LCP and RCP incidences are designed to make a single focus at arbitrary position of (x_L, y_L) and (x_R, y_R) respectively, as illustrated in Fig. 2(a). The reconstructed phase profiles of these foci at the x = 0 plane are defined as Φ_L(y) and Φ_R(y), respectively. As a specific example, Φ_L(y) and Φ_R(y) at the x = 0 plane are shown in Fig. 2(b) when the locations of foci are designed as (x_L, y_L) = (9 µm, –2 µm) and (x_R, y_R) = (18 µm, 10 µm), respectively.

 

Fig. 2 (a) Tuning the location of plasmonic focus by using the proposed distributed nanoslits with the change of optical handedness. (b) Recorded phase profiles for designed focus locations (x_L, y_L) = (9 µm, –2 µm) and (x_R, y_R) = (18 µm, 10 µm), respectively. Solid lines are theoretical phase profiles, and circular markers denote the sampled phase profiles which will be used for calculating geometrical profiles of the proposed structure.

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Due to the size of each nanoslit, tilted angle profiles should be discretely sampled from the ideal phase profiles Φ_L(y) and Φ_R(y). The markers of Fig. 2(b) show the sampled phase information which will be applied to lateral shift and tilted angle of each nanoslit pair. The lower limit of sampling distance (Λ_y) is determined by the size of nanoslit. Here, we set the size of nanoslit as 300 nm by 75 nm, considering the fabrication limit and insuring sufficient aspect ratio. Therefore, to avoid the attachments of nearby nanoslits, sampling distance should be larger than at least 300 nm. On the other hand, the upper limit of Λ_y is determined by two conditions: one is the operating wavelength, and the other is a sampling limit determined by the Nyquist–Shannon sampling theorem. If Λ_y were larger than the operating wavelength, in-plane diffraction arises from the interference among radiated dipole SPP sources. In our previous work, it has been shown that such unwanted diffraction is rapidly reduced when interval between nanoslits is below the operating wavelength [22].

According to the Nyquist–Shannon sampling theorem, at least more than two samples should be sampled from the one period of the highest frequency component of the desired signal. Considering this limitation, we determine the sampling distance to be used in the experiment as 400 nm, which is much lower than operating wavelength (980 nm) and also satisfy the Nyquist–Shannon sampling theorem as can be checked by the markers of Fig. 2(b).

From the sampled phase information, geometrical profiles of the proposed structure such as d(y), θ_r(y), and θ_l(y) are determined by using the Eqs. (2) and (3). In Figs. 3(a) and 3(b), numerically calculated z-directional electric field (E_z) excited from distributed nanoslits for LCP and RCP incidences are shown, respectively. The total length of the distributed nanoslit array is 32 µm (81 pairs with 400 nm sampling distance) and w = 485 nm. It is clearly shown that the positions of plasmonic foci are located as intended, and can be switched from one to the other position according to the change of optical polarization. For other polarization states except for LCP and RCP, both foci are simultaneously observed since these states can be expressed as a superposition of LCP and RCP, which are orthogonal to each other. To show that, three cases of composite polarization states: (A_LCP, A_RCP) = ($\sqrt{3}/2$,$1/2$), ($1/\sqrt{2}$,$1/\sqrt{2}$), and ($1/2$,$\sqrt{3}/2$) are shown in Figs. 3(c)-3(e) respectively.

 

Fig. 3 Numerically calculated E_z field distribution from the proposed distributed nanoslits which are designed for (x_L, y_L) = (9 µm, –2 µm) and (x_R, y_R) = (18 µm, 10 µm). Incident polarization of each figure is set to (a) LCP, (b) RCP, (c) (A_LCP, A_RCP) = ($\sqrt{3}/2$,$1/2$), (d) (A_LCP, A_RCP) = ($1/\sqrt{2}$,$1/\sqrt{2}$), and (e) (A_LCP, A_RCP) = ($1/2$,$\sqrt{3}/2$), respectively.

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From now, we investigate the relative peak amplitude and full-width at half maximum (FWHM) characteristics of the hot spot generated from the proposed structure. At first, we observe the effect of the total length of the distributed nanoslit array with various values of focal length in Fig. 4(a). Here, the incident polarization is RCP and we only change the value of x_R from 5 µm to 20 µm, whereas other parameters are fixed to y_R = 0 µm, x_L = 15 µm, and y_L = 0 µm. In general, the FWHM of focused spot becomes smaller when total length of the array increases since wavevectors having higher spatial frequencies are included for longer total length. The saturation of FWHM occurs more rapidly for closer x_R, therefore relative peak amplitude of the focus is higher for closer x_R. However, for the case of too close x_R such as 5 µm, field generated from nanoslits far away from the focus cannot contribute to the formation of the focus. Therefore, relative peak amplitude is also saturated as shown in the blue dash-dotted line of Fig. 4(a). In Fig. 4(b), we show the effect of total length according to the lateral shift (y_R) of the focus. Other parameters are fixed to x_R = 15 µm, x_L = 15 µm, and y_L = 0 µm, respectively. Similar aspects are shown compared with Fig. 4(a). However, the broadening of FWHM is much smaller than the case of focal length tuning. Relative peak amplitudes are not significantly affected by the change of lateral shift of the focus. From these investigations, it is possible to figure out that the total length of the array chosen for our demonstration (32 µm) is appropriate for sufficiently narrow FWHM below 1 µm within the range of 5-20 µm focal lengths. In Fig. 4(c), focus characteristics with respect to the variance of sampling distance are shown. We find out that the average value of FWHM is not affected by the sampling distance, but the uniformity of FWHM is degraded for longer sampling distance. Degradation of peak amplitude originates from the decrease of the absolute number of nanoslit pairs.

 

Fig. 4 Characteristics of the maximum peak amplitude and FWHM of the focus depend on the total length of the nanoslit array varying with (a) focal length and (b) lateral shift of the focus. (c) Characteristics of the maximum peak amplitude and FWHM depend on the sampling distance and focal length. Incident polarization is set to RCP. Solid lines are related to FWHM and dash-dotted lines are related to the normalized peak amplitude.

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At last, we need to confirm the independency between the phase profiles of RCP and LCP incidences. We checked it by observing the variance of FWHM and relative peak intensity of the focus at (x_R, y_R) according to the location of (x_L, y_L). In this case, we fixed the location of (x_R, y_R) = (15 µm, 0 µm), with the RCP incidence, whereas the locations of x_L and y_L are varied from 5 to 20 µm and from 0 to 12 µm, respectively. For ideal polarization multiplexing, there must be no difference for the focus characteristics of RCP incidence. However, there may be some degradation because the variation of geometrical profiles such as d(y), θ_r(y), and θ_l(y) caused by the location of (x_L, y_L) can affect the characteristics of the focus. The peak-to-peak variances of maximum peak amplitude and FWHM within the abovementioned region are less than 6.8% and 10.5% of their mean value. Since the variation flow of maximum peak amplitude and FWHM are quite irregular, we do not depict them with plots.

As a numerical calculation method, we used dipole sources laid on metal surface in order to express the nanoslits. The directions of dipole sources are set perpendicular to the longer axis of nanoslit with appropriate phase delay representing the polarization state. The scattered field from each dipole source is calculated by using the Green’s dyadic function [25]. Although the nanoslits are approximated as dipole sources, the method has an advantage for calculating diffraction pattern from large-size, complicate nanoslit array compared to full electromagnetic simulation methods such as finite-difference time-domain (FDTD) method. The details of calculation method can be found in our recent publication [22].

4. Experimental configuration and results

For experimental fabrication of the proposed structure, 200 nm thick of silver film is evaporated on SiO₂ substrate by using e-beam evaporator. In order to improve the uniformity of film, another SiO₂ substrate is attached by a transparent adhesion solution and the Ag layer is lifted off. Then, nanoslits are patterned by using the focused ion beam (FIB) machine (FEI, Quanta 200 3D). In Fig. 5(a), the scanning electron microscope (SEM) image of the proposed distributed nanoslits is shown. In the inset of Fig. 5(a), magnified SEM image of the proposed structure is depicted. Although the designed phase profiles for LCP and RCP illuminations are simple Fresnel lens patterns as shown in Fig. 2(b), it is quite difficult to figure out the original phase profile from the resultant structure since the summation and subtraction of these profiles (${\Phi }_{\text{s}}(y)$ and ${\Phi }_{\text{a}}(y)$) have complicate profiles.

 

Fig. 5 (a) SEM image of the fabricated distributed nanoslit structure. Inset shown in the lower-left side is an expanded SEM image of the proposed structure. SPP signals generated from the proposed structure measured by NSOM are shown for (b) LCP and (c) RCP incidences, respectively.

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For experimental configuration, a 980 nm wavelength laser source illuminates the backside of the sample, after passing through the half- and quarter-wave retarders which are used for manipulating the desired incident polarization states. The transmitted SPPs from the distributed nanoslits are measured by fiber tip-based near-field scanning optical microscope (NSOM) (Nanonics, Multiview 4000) attached to atomic force microscope (AFM). The SPP signals are coupled through the metal-coated NSOM tip with a diameter of 250 nm, which is made by tapering the multimode fiber. Detection of the fiber-coupled signal is measured by an avalanche photodiode operating at near-infrared region (Agilent 81634B). The NSOM images of the distributed nanoslits designed for (x_L, y_L) = (9 µm, –2 µm) and (x_R, y_R) = (18 µm, 10 µm) are shown in Figs. 5(b) and 5(c), respectively. Green lines of Figs. 5(b) and 5(c) indicate the x = 0 and y = 0 lines, whereas the crossing points of white dotted lines are desired focal positions for LCP and RCP incidences. It is clearly shown that the locations of experimentally formed foci are well-matched to the designed values in both polarization states. A very weak SPP focus shown at (x_L, y_L) even for the RCP illumination may be caused by the imperfect fabrication of each nanoslit and non-ideal incidence of optical polarization state. However, the maximum intensity of unwanted focus at (x_L, y_L) is lower than 8.6% of that of the desired focus at (x_R, y_R) for RCP incidence.

Although we mainly focus on the polarization-multiplexed mechanism of SPP phase generation, the power efficiency of the proposed structure is also very important parameter for practical use. In our case, the full numerical simulation which can verify the numerical power throughput is quite difficult due to the very large number and complex angle profile of the nanoslit. Instead, we can approximately suppose the power throughput from our previously reported work that used similar nanoslit-distributed structure [22]. In that work, field coupling efficiency, defined as a maximum intensity value of the focus divided by that of the input signal, was 6.5%. Compared to the double array of nanoslit with zero tilted angles, which does not have any polarization-multiplexed characteristics, our structure theoretically has half amplitude due to the orthogonal phase delay between two arrays. However, we expect that the proposed structure can deserve such degradation of power efficiency due to the degree of freedom for multiplexing of SPP signal.

In experiments, total laser source of 200 mW is used and only few nW scale of SPP signal is measured at the focus. Of course, only very small amount of incident beam can pass the nanoslits from the input beam, and the coupling efficiency of our NSOM instrument is also very low in order not to perturb the distribution of SPP signal. Thermal loss of SPP during the propagation is also a degrading factor of power efficiency. Indeed, such low power efficiency is a critical issue in metasurface designing, especially for coupling of SPP signal. However, we think that it is possible to enhance the power throughput by using the multiple arrays of the proposed nanoslit distribution distanced by the integer multiplications of effective SPP wavelength as proposed in [20, 21]. However, the slit distribution should be more carefully designed for our case in order to make a narrow focus at the desired position.

At last, we would like to briefly mention the future expansion of the proposed scheme into more general case. For example, although our scheme can only provide two distinct phase profile for two orthogonal polarizations, LCP and RCP, we expect that it is possible to smoothly change the plasmonic focus in certain position to the other position by the changing of incident polarization if we design multiple pair of nanoslits as a unit cell. Moreover, by tuning the size of each nanoslit pair, the amplitude excited from the nanoslit pair can be tuned. We hope that the amplitude can be multiplexed as well as the phase of excited SPPs with the precise tuning of the nanoslit size.

5. Conclusion

We propose a method for SPP generation which can be generally applied to an arbitrary profile of polarization-multiplexed SPP phase for RCP and LCP incidences. A double-lined distributed nanoslit array is used for two independent types of SPP phase generation; one is a polarization independent profile achieved by shifting the location of nanoslit, and the other is a phase profile reversed by optical handedness governed by tilting the orientation of nanoslit. As an example of polarization-multiplexed SPP generation, we numerically and experimentally show that the location of plasmonic focus can be independently designed for LCP and RCP incidences. It is demonstrated that the characteristics of one spot are almost not affected by the position of the other spot. Although we only show the example of single focus generation in this manuscript, the proposed method can be applied to polarization multiplexing of any type of SPP phase profiles, such as in-plane plasmonic beaming, plasmonic vortex, and caustics. We expect that the proposed scheme can be applied for the manipulation of SPP field without using the conventional SLMs. It can be also used for reducing the size of SLMs, enhancing the polarization sensitivity of plasmonic holography, or in-plane plasmonic metasurfaces.