1. Introduction

There is considerable interest at present in the development of nanoscale optical devices with potential applications as compact elements in imaging, data storage and as display components. In particular, there is a growing awareness of the potential of plasmonic devices to control the polarization states of transmitted or reflected light [1–11]. There have been previous investigations into a range of devices that have exploited the phase differences between orthogonal detuned dipoles [2–4, 9–12]. These have consisted of arrays of nanoparticles [2–4, 12] or arrays of apertures [9–11]. Recently, one of us proposed the use of an array of asymmetric cross-shaped apertures exhibiting localized plasmonic aperture resonances as a means to produce an ultra-compact quarter-wave plate (QWP) [11]. This proposal was supported by simulations. Polarization devices based on localized surface plasmons (LSPs) are of interest due to the greater robustness to the angle of incidence compared to surface plasmon polaritons (SPPs) and potentially greater transmission than SPP based structures [11, 13]. Here we experimentally demonstrate a device based on the principles outlined in Reference 11 and investigate its polarization and transmission properties.

2. Analytic model and numerical calculations

A schematic of the device under consideration is shown in Fig. 1(a). An infinite square array (period, P) of cross-shaped apertures of arm lengths, L, and widths, W are located in a silver film of thickness, T. The intensity transmission, calculated using the Finite Element Method (FEM), implemented in COMSOL Multiphysics 4.3a [14] is shown in Fig. 1(b). The transmission, normalized to that in the absence of metal, is shown as a function of wavelength for a device with a square array of symmetric apertures with a fixed arm-width of 40 nm and variable arm-length in a Ag film of thickness 40 nm is shown in Fig. 1(b). The period of the array is 300 nm and the refractive index of the substrate is taken to be 1.52. Optical constants of bulk Ag were taken from Johnson and Christie [15]. A clear resonance is seen in Fig. 2(a), where transmission of 700 nm light through the array as a function of antenna length is shown. This resonance is associated with the excitation of surface charges on the inner walls of the aperture leading it to behave as an electric dipole [16]. If a design wavelength of λ is selected and a Lorentzian dipole behavior assumed, the amplitude transmission, t_λ, is given by:

 

Fig. 1 (a). Schematic diagram of the unit cell of a plasmonic quarter-wave plate. The geometric parameters are film thickness, T = 40 nm, slot width, W = 40 nm, unit cell periodicity P = 300 nm and L_x, L_y, the slot lengths, are varied. A 2 nm Ge adhesion layer is also shown in green. (b) Transmission spectra for an array of 120 nm by 140 nm cross apertures, with a period of 300nm in a 40 nm Ag film calculated using the FEM for three polarization angles; 0° (blue line) 45° (black) and 90° (red). At a wavelength of 700 nm the intensity transmission is independent of the angle of linear polarization; this is the operating wavelength of the QWP.

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Fig. 2 (a). Computed transmission, T_λ(L), of 700 nm light through a rectangular aperture in a 40 nm Ag film on a SiO₂ substrate as a function of aperture length, L. The full-width half-maximum, Δ_λ, is 28 nm and is indicated by the dashed lines. (b) An SEM image of the fabricated plasmonic QWP. The cross apertures were milled using a focused ion beam. Each element is 300 nm from its neighbor.

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3. Fabrication

An aperture array was fabricated in 40 nm thick layers of Ag deposited using an Intlvac Nanochrome II electron beam deposition system onto a glass microscope slide on a 2 nm adhesion layer of Ge. The aperture array was defined using Focused Ion Beam (FIB) milling with a FEI Helios NanoLab 600 Dual Beam system using 30 keV Ga ions. An array with a periodicity of 300 nm and total dimension 160 µm × 160 µm was produced. Typical writing time is of the order of 110 minutes. The beam current used was 28 pA and the dwell time was set to 3.8 ms. A single serpentine scan of the beam was employed over the target area. A scanning electron microscope (SEM) image of the device is shown in Fig. 2(b). From the SEM, it is apparent that the modeled square profile cross-apertures are significantly rounded and the fabricated crosses have vertical arm-length (132.5 ± 7) nm and horizontal arm-length (145 ± 6) nm.

4. Device characterization

The device was characterized in a bench-top polarimetry system shown in Fig. 3(a). Light from a multi-mode fiber-coupled tungsten-halogen bulb (Ocean Optics HL-2000-FHSA) was collimated and focused onto samples using a 0.4 NA Olympus Plan N microscope objective. The state of polarization of the input field was controlled using a linear polarizer (Thorlabs LPVIS050-MP) and a broad-spectrum quarter-wave plate (Thorlabs AQWP05M-600). The light transmitted through the device was analyzed with an identical linear polarizer and a quarter-wave plate. Figure 3(c) shows the measured transmitted intensity spectra.

 

Fig. 3 (a). A schematic diagram of the bench top polarimetry set up. The incident beam passes through a collimator, a linear polarizer (LP) and an achromatic quarter wave-plate (QWP) and is then focused onto the array with an objective lens (OL). The analyzer consists of the same optical elements, in reverse order. (b) The principle axis of the array forms an angle, $\alpha$with the $x$-axis. The angle of polarization,$\theta ,$is measured from the$x$-axis. (c) The measured intensity of linearly polarized light transmitted through the plasmonic QWP for 0° (blue line) 45° (black line) and 90° (red line) angle of polarization. At a wavelength of 702 nm the transmission is polarization independent.

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The polarization independent point is at a wavelength of 702 nm, in excellent agreement with the design wavelength of 700 nm. The model, however, underestimates fabrication errors and the loss assumed when using the optical properties of bulk Ag [15]. This has led to a reduction in the relative amplitude of the transmission of light polarized at 0°, which can be seen by comparing Figs. 1(b) and 3(c). Full polarization tomography (FPT) was then performed on the fabricated array. The maximum likelihood estimation method was used to calculate a Mueller matrix for the plasmonic QWP [17]. A set of 42 polarization measurements were performed, to measure the intensity of light, polarized at 0°, 45°, 90°, 135° with respect to the x-axis, left- and right-hand circular polarization states, transmitted in those same polarization states (36 measurements for all combinations of the 6 initial states and the 6 final states as well as 6 normalization measurements performed without the analyzer). The measured Mueller matrix is shown in (7) and resembles the Mueller matrix of a classical depolarizing QWP [18],

It is possible to extract several optical properties of the sample from the Mueller matrix in (7). For instance, the phase retardance can be calculated, in this case it is 87.1°, which is very close to the desired phase retardance, ${\text{Γ}}_{\lambda }={90}^{\circ },$for a QWP [18, 19]. The diattenuation, D, the differential transmission of orthogonal polarization states (which has a value between 0 and 1), can also be derived from the Mueller matrix. For this structure D = 0.084, which indicates a negligible dependence on polarization angle for the transmitted intensities at the operating wavelength [19].

Importantly, the principle axis of this plasmonic quarter-wave plate can also be extracted. The principle axis in fact lies 9.8° clockwise from the x-axis. It is expected that the principle axis of the plasmonic quarter-wave plate is coincident with the long arm of the crosses in the array. Hence, the horizontal arms of the crosses in the array are not parallel to the horizontal measurement axis as intended, but, in fact, form an angle of 9.8° with the horizontal measurement axis. The Mueller matrix, however, is robust to issues such as this. Rotating the sample by α is equivalent to performing a unitary basis transformation on$ℳ.$The Mueller matrix for the rotated sample, ${ℳ}^{\text{'}}(\alpha )$ is given by [21],

5. Conclusion

We have demonstrated a simple Lorentzian model can be used to design an ultrathin plasmonic quarter-wave plate operational at optical wavelengths. One such design was fabricated in a 40 nm thin Ag film using focused ion beam lithography and full polarization tomography measurements were performed on this device. This research could be useful in future telecommunications technologies, new imaging systems and for biosensing applications.