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We present an experimental study of Hetero-Chiral (HC) plasmonic lenses, comprised of constituents with opposite chirality, demonstrating linearly dichroic focusing. The lenses focus only light with a specific linear polarization and result in a dark focal spot for the orthogonal polarization state. We introduce the design concepts and quantitatively compare several members of the HC family, deriving necessary conditions for linear dichroism and several comparative engineering parameters. The HC lenses were experimentally investigated using aperture-less near field scanning microscope collecting the amplitude of the plasmonic near-field. Our results exhibit an excellent match to the simulation predictions. The demonstrated ability for linearly dichroic functional focusing could lead to novel sensing applications.
© 2016 Optical Society of America
A plasmonic lens is formed by predefined shaped boundaries engraved in a metal layer [1]. When excited by vertically impinging light beam, the boundaries serve as secondary sources for propagating Surface Plasmon Polaritons (SPPs) that are interfered to generate a focal point within the plane of the lens. The primary operation of such lenses is achieving constructive interference of the dominant, out-of-plane field component [2,3] at the focal point. This field component is desirable in various devices – e.g. satisfying the absorption selection rules of unipolar quantum wells based detectors [4–6]. Several such plasmonic lenses have already been suggested, focusing circularly [7] and linearly [8–10] as well as radially [11–14] polarized illumination. Moreover, a plasmonic lens can be designed to perform differently under variation of the illumination parameters and add functionality to the focusing. It was shown that structures with chiral symmetry like the Archimedes spiral (AS) [7,15–19] achieve circular dichroism, focusing circularly polarized illumination of matched handedness and resulting in anti focusing (dark spot) for the orthogonal polarization state. In contrast, much less effort had been exerted to linearly dichroic devices – namely devices focusing electromagnetic waves with a specific linear polarization – while blocking (not focusing) the orthogonally polarized illumination.
Here we study plasmonic lenses constructed by combinations of constituents with opposite chirality. We show both theoretically and experimentally that such Hetero-Chiral (HC) structures achieve linearly dichroic focusing. We study spirals as the chiral building blocks, present several features of this structural family and discuss the related physical insights. The demonstrated linearly dichroic functional focusing could lead to novel sensing and imaging applications.
Planar chiral symmetry is ascribed to objects lacking in-plane mirror symmetry. When it comes to electromagnetism, it is well known that chiral structures may exhibit circular dichroism and can discriminate the handedness of circularly polarized light. This property was studied, applied and demonstrated in various metamaterials [20–24]. From the plasmonic focusing perspective, it is widely accepted that an AS plasmonic lens with geometrical charge m = ± 1 distinguishes between right (RHC) and left (LHC) circularly polarized illumination [7,15–19]. When an AS lens with geometrical charge is illuminated by LHC it will focus the SPPs at the center of the lens creating a field distribution that can be approximated by EAS + 1(LHC)∝J0(kspp∙r), where J0(r) is the Bessel function of order 0, kspp is the plasmonic wavenumber and r is the radial coordinate. Conversely, under RHC illumination the same lens will produce a dark spot with a field distribution that can be approximated by EAS + 1(RHC)∝J2(kspp∙r)e+2j𝜃, with J2(r) the Bessel function of order 2 and θ is the azimuthal coordinate. The spiral with the opposite chirality, having geometrical charge will act in a complimentary manner resulting in EAS-1(RHC)∝J0(kspp∙r) and EAS-1(RHC)∝J2(kspp∙r)e-2j𝜃 with phase accumulation in the opposite azimuthal direction. We show that a co-centered combination of two ASs with opposite handedness (chirality) and unity geometrical charge results in a AS HC plasmonic lens (AS HC lens) (Fig. 1) with a linearly dichroic focal spot (Fig. 2).
Fig. 1 Construction schematic (a) and Scanning Electron Microscope (SEM) image (b) of the AS HC lens formed by two engaged Archimedes spirals.
Fig. 2 AS HC lens (a,c) Experimental results of the absolute value of the field within the lens under horizontal (a) and vertical (c) linearly polarized illumination (white arrows) and the corresponding FDTD simulation results (b,d). The insets show the enlarged focal region. The measured extinction ratio of the linear dichroism is 32.
In such a merger, the chiral symmetry of the constituents is broken, but the mirror symmetry is not completely restored. The resulting structure is mirror symmetric with respect to the horizontal axis but mirror asymmetric with respect to the vertical axis. This implies that the combined structure should distinguish between horizontal and vertical excitations – which is a necessary condition for linear dichroism. The other condition is that the linearly polarized excitation perpendicular to the asymmetry axis will actually be focused by the HC structure. This means assigning a π phase shift to counter propagating SPPs generated at the antipodal points of the lens boundary, in order to obtain constructive interference of the out-of-plane field at the focal point [11].
A more quantitative interpretation for the linearly dichroic characteristics of the structure is manifested by the superposition principle. We can express the linear polarization basis in terms of the circular polarization basis: and. By construction, the field in the focal spot of the HC lens is the linear superposition of the focal fields of the constituent spirals of opposite chirality. When the HC lens is illuminated with the polarized light, the out-of-plane component of the focal field of the HC lens can be expressed as
The two bright focal spot contributions given by J0(kspp∙r) are in phase, resulting in a constructive SPP focus. Conversely, when the illumination is polarized the resulting focal field is given by,
Now the bright contributions from the constituent spirals cancel out leaving only the dark focal spot described by J2(kspp∙r). The modulation by the sin(2θ) azimuthal dependence leads to the four lobes in the absolute value of the field (Fig. 2(c) and 2(d)).
We studied all the proposed structures both experimentally and by using 3D finite difference time domain (FDTD) simulations. The results of the simulations are brought alongside the experimental results (Fig. 2, Fig. 4 , and Fig. 6 ) ). The representative structures of the HC family were fabricated by focused ion beam (FIB) carving of ~130nm wide slits in a 150nm thick gold film over a glass substrate (Fig. 1, Fig. 3, and Fig. 5. The samples were illuminated at the predefined polarization states using a semiconductor laser emitting at λ0 = 671nm. The width of the milled slits was chosen to maximize the SPP coupling efficiency [25]. The transmitted near field pattern was mapped using an aperture-less near field optical microscope (NSOM) with a metal tip – which predominantly measures the complex amplitude of the out of plane field component. The structures were designed to fit in a 10µm2 area giving good signal to noise ratio with reasonably short scan time and tolerable plasmon propagation delay. The experimental results (Figs. 2,4,6(a) and 6(c)) exhibit excellent match to the corresponding simulation results (Figs. 2,4,6(b) and 6(d)) – all demonstrating high extinction ratio linear dichroism.
Fig. 3 Construction schematic (a) and SEM image (b) of the Hollow HC lens formed by two engaged Archimedes spirals of m = 4 with erasure of the internal part.
Fig. 4 Hollow HC Lens (spiral order m = 4) NSOM measurements (a,c) and corresponding FDTD simulation results (b,d) under linearly polarized illumination (white arrows). The measured linear dichroism extinction ratio is 10.
Fig. 5 Construction schematic (a) and SEM image (b) of the Half-Moons lens formed by two engaged circular, non-Archimedean spirals.
Fig. 6 Half-Moons Lens NSOM measurements (a,c) and corresponding FDTD simulation results (b,d) under linearly polarized illumination (white arrows). The measured linear dichroism extinction ratio is 80.
The simulation and measurement results of the AS HC plasmonic lens are detailed in Fig. 2. Linearly dichroic focusing is measured with an extinction ratio (intensity ratio between the two polarizations at the focal point) of 32, limited mainly by the measurement spatial resolution. The experimental results exhibit a very good match to the predicted field pattern by the full wave simulations.
A more elaborated path for a linearly dichroic focusing lens is engaging two high order spirals (order ± m, m>1) and then removing, or erasing, the internal part of the structure boundaries (Fig. 3) resulting in a Hollow HC lens which resembles a distorted circle. Interestingly, this slight deformation from a perfect circle results in a strong linear dichroism at the focal spot of the structure (Fig. 4.). This is surprising, because the original high order spirals (e.g. m = 4 in Fig. 3(a)) do not exhibit a circular dichroism, but rather anti focal behavior for both polarization handedness (topological singularities of order m ± 1 for left/right polarization respectively [26]). For the same reason, the related engaged HC structure does not yield a focal point even for the proper linear polarization. Only the removal of the internal core eliminates the additional plasmonic secondary sources that interfere destructively at the focal point and enables the necessary conditions for linear dichroism.
A clear and distinctive focal point is generated for the appropriate linear polarization – for any order of hollow lens. The simulation and measurement results of the Hollow HC lens demonstrate a clear linearly dichroic focal spot with measured extinction ratio of 10 with a very good match to the predicted field pattern by the FDTD simulations (Fig. 4).
Expanding the family of linearly dichroic lenses based on a HC assembly is obtained by using as building blocks non-Archimedes spirals with opposite chirality (Fig. 5(a)). Here we selected a circular spiral, comprised of two half circle arcs with radii difference of λspp⁄2. Engaging the two spirals results in a structure resembling the AS HC lens (Fig. 1(a)). This engaged structure can also be viewed as two circles with λspp⁄2 radii difference, with the inner circle tangent to the outer. We can simplify this structure further by applying a step of erasing opposing halves of the outer and inner circles. This erasure retains the 2 ingredients required for a linearly dichroic lens, namely the specific symmetry and the π phase shift required for constructive focusing.
The resulting structure, denoted here as Half-Moons, is mirror-symmetric about the horizontal plane and mirror-asymmetric about the vertical plane. This structure indeed exhibits tight linearly dichroic focusing with high efficiency. Since relative shift of the half circles along the horizontal axis retains the required conditions for linear dichroism - we searched for their optimal relative positioning. We found that moving the half circles to be concentric, yields the best performance. From pure phase consideration this focal point is the ideal point of a geometrical π phase shift between the out-of-plane field components of the counter propagating SPP fields emanated from the boundaries to assure constructive interference. A related structure to the latter was studied in [10]. It is important to note that being composed of two half circles, none of which is chiral, this structure might be regarded as not belonging to the hetero-chiral family. However by construction, it is formed according to same symmetry rules discussed for the previous structure. Furthermore, the Half-Moons lens is actually comprised of 2 hetero chiral segments; each is made of half of the red semicircle and half of the blue semicircle, mirror symmetric with respect to the horizontal axis (Fig. 5 (a)). This lens is thus a legitimate member in the hetero-chiral family.
We calculated the theoretical efficiency improvement (focal point intensity ratio) between the shifted and the eventual Half-Moons structures to be 17%. The simulation and measurement results of the Half Moons lens (Fig. 6) exhibit strong linearly dichroic focusing with a measured extinction ratio of 80 and with an excellent match to the predicted field pattern by the FDTD simulations.
The possibility of having such a variety of configurations for achieving linear dichroism should assist us in optimizing the structures according to specific applications. One important optimization criterion is efficiency, the percentage of impinging optical power that is eventually focused by the lens. To make a proper comparison we engineered all the structures to have an almost identical slit area by assigning the same length and width. We also added for reference the Archimedes and non-Archimedes (circular) spiral lenses which focus linearly polarized light but do not exhibit linear dichroism. The comparison was performed using 3D FDTD simulations and presented in Fig. 7.
Fig. 7 Relative focal spot intensity efficiency (blue) and relative focal point intensity/device area (red) for impinging light with horizontal polarization. All structures have the same slit width and similar length. From left to right: non-Archimedean HC lens, AS HC lens, Half Moons lens, Hollow HC m = 4, circular spiral, Archimedes spiral.
The Half-Moons lens slightly outperforms the other structures in terms of efficiency. However although the HC structures comprised of engaged circular or ASs are slightly less efficient, they are packed in an area which is roughly four times smaller than the area taken by the other structures. Thus they are by far the most area efficient structures as demonstrated in Fig. 7 (red). A notable result is that the non-Archimedean (circular) structures outperform their Archimedean counterparts. This has a fundamental reason; the m = 1 AS lens is ideal for focusing the corresponding circularly polarized illumination because of the following: I. The distance of opposite points on the boundary from the focal point is shifted by half a wavelength to assure same phase of the out-of-plane field at the focal point for instantaneous excitation. II. As the circularly polarized polarization vector rotates in time within the light oscillation period, the light excites different portions of the lens boundaries at different times. Due to the azimuthally varying distance of the AS boundary to the focal spot, the geometrical phase is smaller for the SPPs with a more progressive time excitation such that all excited SPP waves arrive to the focal spot at the same time. The AS geometrical phase essentially compensates for the temporal phase of the circular polarization. While (I) is essential also for focusing linearly polarized illumination, (II) is counter-productive. For linearly polarized illumination, lacking the temporal azimuthal phase, all points of the structure boundaries are excited simultaneously and the spiral geometrical phase results in an imperfect constructive interference at the focus, reducing the focal efficiency. Therefore, geometries contributing less geometrical phase, like the non-Archimedean structures, would prevail. In particular, the circular geometry of the Half-Moons lens, where each segment is equidistant to the focus and does not introduce geometrical phase, is thus the preferred configuration for focusing linear polarization.
To summarize, we presented the symmetry based Hetero-Chirality approach and derived necessary conditions to achieve plasmonic lenses that exhibit linearly dichroic functional focusing. Several structures comprised of constituents with opposite chirality were suggested and studied both theoretically and experimentally. All the structures were shown to have a significant linearly dichroic focal spot. Finally, the performance of the different structures was quantitatively compared by detailed FDTD simulations. The possibility of having a variety of solutions for achieving linear dichroism allows selecting the optimal configuration according to the specific application and in combination with detectors may serve in novel sensing and imaging applications such as spatially resolved polarization detectors.
Acknowledgments
This research was supported partially by ICore, the Israeli Excellence Center ‘Circle of Light’.
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