Multifunctional and multi-output plasmonic meta-elements for integrated optical circuits

Based on a novel phase-sieve method by in-plane interference processes, a well-designed nonperiodic nanogroove array on gold surface is proposed as a multifunctional and multi-output plasmonic meta-element (MPM) for surface plasmon polariton waves. An MPM functions as a plasmonic lens (PL) as well as a plasmonic array illuminator (PAI), and another MPM acts as two PLs with an intersection angle of π/4 are fabricated and validated by leakage radiation microscopy measurements. Our proposed scheme with implemented functionalities could promote potential applications in high density integrated optical circuits. ©2014 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (240.3990) Micro-optical devices; (260.3910) Metal optics. References and links 1. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). 2. H. Raether, Surface plasmons on smooth and rough surfaces and on grating (Springer, 1988, Chap. 2). 3. A. V. Zayatsa, I. I. Smolyaninovb, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005). 4. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824– 830 (2003). 5. Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005). 6. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005). 7. J. Wang, J. Zhang, X. Wu, H. Luo, and Q. Gong, “Subwavelength-resolved bidirectional imaging between two and three dimensions using a surface plasmon launching lens,” Appl. Phys. Lett. 94(8), 081116 (2009). 8. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005). 9. W. Cai, W. Shin, S. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater. 22(45), 5120–5124 (2010). 10. J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. Ebbesen, C. Girard, M. U. Gonz’alez, and A.-L. Baudrion, “Near-field characterization of bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70(23), 235406 (2004). 11. A. Drezet, D. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Surface plasmon polariton microscope with parabolic reflectors,” Opt. Lett. 32(16), 2414–2416 (2007). 12. J.-C. Weeber, M. U. González, A.-L. Baudrion, and A. Dereux, “Surface plasmon routing along right angle bent metal strips,” Appl. Phys. Lett. 87(22), 221101 (2005). 13. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). 14. A. Drezet, A. L. Stepanov, H. Ditlbacher, A. Hohenau, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Surface plasmon propagation in an elliptical corral,” Appl. Phys. Lett. 86(7), 074104 (2005). 15. Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103(14), 141101 (2013). 16. L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy beam generated by in-plane diffraction,” Phys. Rev. Lett. 107(12), 126804 (2011). 17. L. Li, T. Li, S. Wang, S. Zhu, and X. Zhang, “Broad band focusing and demultiplexing of in-plane propagating surface plasmons,” Nano Lett. 11(10), 4357–4361 (2011). 18. T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011). #216375 $15.00 USD Received 9 Jul 2014; revised 27 Aug 2014; accepted 4 Sep 2014; published 11 Sep 2014 (C) 2014 OSA 22 September 2014 | Vol. 22, No. 19 | DOI:10.1364/OE.22.022753 | OPTICS EXPRESS 22753 19. L. Li, T. Li, S. M. Wang, and S. N. Zhu, “Collimated Plasmon beam: Nondiffracting versus linearly focused,” Phys. Rev. Lett. 110(4), 046807 (2013). 20. S.-H. Chang, S. K. Gray, and G. C. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13(8), 3150–3165 (2005). 21. A. Giannattasio, I. R. Hooper, and W. L. Barnes, “Dependence on surface profile in grating-assisted coupling of light to surface plasmon-polaritons,” Opt. Commun. 261(2), 291–295 (2006). 22. W. Zhang, C. Zhao, J. Wang, and J. Zhang, “An experimental study of the plasmonic Talbot effect,” Opt. Express 17(22), 19757–19762 (2009). 23. A. Drezet, A. Hohenau, A. L. Stepanov, H. Ditlbacher, B. Steinberger, N. Galler, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “How to erase surface plasmon fringes,” Appl. Phys. Lett. 89(9), 091117 (2006). 24. J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-Controlled Tunable Directional Coupling of Surface Plasmon Polaritons,” Science 340(6130), 331–334 (2013). 25. L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, ““Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Scie. Appl. 2(3), e70 (2013).


Introduction
The aggressive pursuit of ever-increasing high levels of integration on optical circuits has been a hallmark of the industry and the academe.Unfortunately, the minimum lateral size of dielectric photonic components is limited to about half a wavelength of light by the fundamental laws of diffraction [1].New opportunities for confining light to rather small dimensions are provided by utilizing surface plasmon polaritons (SPPs), which are hybrid modes of photons and electronic charge-density oscillations at a metal/dielectric interface [2][3][4].Various planar plasmonic devices have been successfully fabricated to control the propagation of plasmonic fields because of their unique two-dimensional (2D) confinement of electromagnetic field at the metal surface.These devices include plasmonic lenses [5][6][7], waveguides [8][9][10], reflectors [10][11][12], interferometers [13,14], metasurfaces [15] and so on.To date, most of these devices are single-functional elements; thus, a new class of multifunctional plasmonic devices, which could be a key ingredient in achieving compact and high-speed optical system, must be developed.More recently, spatially-defined phase modulation methods for manipulating SPP propagations from a nonperiodic array were carried out and have achieved great success [16][17][18][19].However, these approaches all have a common severe limitation, in which the SPP wavefront emerging in a specific direction is designed to target a single particular application.Thereafter, a question arises about the use of a nonperiodic array to mold SPP wavefront in multiple directions for multifunction/multioutput purpose.If this case is possible, what kind of wavefront could be constructed?
In this study, we propose a multifunctional and multi-output plasmonic meta-element (MPM) on gold films, which can control SPP wavefronts in two or four predefined directions with different functions.The MPMs were composed of uniform subwavelength grooves on the metal surface, the positions of which were determined via a novel phase-sieve method.Two MPMs were fabricated and validated.One functioned as a vertically oriented plasmonic lens (PL) as well as a horizontally oriented plasmonic array illuminator (PAI) and the other functioned as two PLs with an intersection angle of π/4.As such, multichannel and multifunction manipulations of SPPs can be directly achieved in a single component by using these devices.

Principle
The schematic of an MPM is shown in Fig. 1(a).A typical MPM is a set of subwavelength grooves on a gold film with a substrate, of which positions and sizes are carefully designed via a newly developed phase-sieve method that will be presented later.When the MPM is illuminated from the air side, the excited SPPs at the grooves are launched in the ± x and ± y directions depending on the polarization of the incident light and subsequently propagate to form the desired field patterns in the 2D plane of the metal/air interface, thereby making the MPM a multi-output device.To design an MPM, the whole area of the MPM is pixelated into a rectangular grid of M × N regular rectangular cells, as shown in Fig. 1(b).The position of the center of the rectangle (m, n) is written as r m,n = ma 1 a 1 + na 2 a 2 , where a i (i = 1, 2) is the primitive lattice vector basis (a 1 and a 2 along the + x and + y directions, respectively), a i is the lattice period, m and n are the column and row indexes, respectively.A portion of the cells is selected and fabricated into the same-sized grooves by using a focus ion beam milling system.When the MPM is normally illuminated with a plane wave, every point on the grooves functions as a point dipole source of SPPs (with an infinitesimal area of dS and a location of r s ) that radiates with the same initial phase.According to the Huygens-Fresnel principle, the resulting electric field of the SPPs can be obtained by adding up the contributions from all the point sources within the grooves.The electric field at point r that originates from groove (m, n) is expressed in the complex phasor form when |r-r m,n | is larger than several SPP wavelengths [20]: where A(r s ) is the field amplitude of the SPP point source, k SPP is the propagation constant of the SPPs at the air/gold interface, k z is the wave vector along the z direction, and φ s is the azimuthal angle between the polarization direction of the incident beam and the vector r-r s as defined in Fig. 1(b).The integration is over the whole groove area.Since the physical process of coupling free-space light to SPPs is not included in the model of dipole source of SPPs, therefore the limitation of Eq. ( 1) is that it is inapplicable to deal with any problems related to the coupling efficiency and phase.As a result, it would be mandatory to resort to full-wave simulations when the coupling effect should be considered.The total electric field at r is the sum of the contributions of all individual grooves: where T m,n is the transmission coefficient accounting for the scattering loss that the SPPs experience by crossing over other grooves.For simplicity, we assume , where t is the transmission over a single groove and p m,n is the number of the grooves to cross.Note that the resultant SPP intensity distribution given in Eqs. ( 1) and (2) depends on the polarization of the incident light as well as the positions of the grooves.Hence, the question of manipulating SPP wavefronts in multiple directions becomes that of identifying the groove positions to simultaneously satisfy the prescribed field patterns in different directions.For an MPM of M × N rectangles, 2 M × N groove position combinations are possible.In principle, a numerical method, e.g., simulated annealing algorithm, would be valid for such a global optimization problem.In this paper, a simple and feasible design algorithm named phase-sieve method, which is free of intricate numerical calculations, is used and developed as follows: i) A collection of grooves is chosen to generate the designed wavefront propagating in the fixed direction according to the designed function.The position indexes of the grooves is composed of a set {(m, n)} 1 .ii) The second set of grooves {(m, n)} 2 is chosen to implement the second function in another direction.iii) The groove set {(m, n)} of the MPM is then derived by the intersection {(m, n)} 1 ∩{(m, n)} 2 .The "intersection" operation is defined to generate a groove set which is formed of elements that belong to both {(m, n)} 1 and {(m, n)} 2 .The red double-headed arrow represents the polarization direction of the incident beam, φ s is the azimuthal angle between the polarization direction and the vector r-r s .

MPM functions as a PL and a PAI
To demonstrate this method, we initially implemented an MPM that functions as a PAI along the x-direction and a PL along the y-direction in the working wavelengths λ 0 = 830 and 873 nm (SPP wavelength λ SPP = 814 and 858 nm), respectively.In general, a 1 and a 2 should be 0.5λ SPP to obtain a high coupling efficiency [21].The designed MPM has a rectangle grid (M × N = 61 × 61) with a 1 = 410 and a 2 = 429 nm, thereby making the total pattern size to be 25 µm × 26 µm.The reason that a 1 is not equal to 0.5λ SPP will be discussed later.

Design method
To determine the groove set {(m, n)} 1 of the PL, the grooves in the nth row (n = 0, ± 1, ± 2,…, ± (N-1)/2) are arranged to contribute to a focal spot at R n = (0, f n ), where f n should be larger than (N-1)a 2 /2 to keep the focus outside the MPM area.When illuminated by a ypolarized beam the selected {(m, n)} 1 should satisfy Eq. (3) to ensure the launched SPPs from the nth row could constructively interfere at R n , ( where l = 0, 1, 2,…, and ε = 0 or 1 for n that is odd or even, respectively, r m,n ± 0.5a 1 a 1 are the midpoints of the lateral sides of the groove (m, n) and d n = f n -na 2 is the distance from R n to the nth row.Equation (3) indicates that the grooves in each row form a Fresnel zone plate-like structure with a focal length d n .Besides (0, f n ), another focus exists at (0, 2na 2 -f n ) for each row because of symmetry.In general, we define two types of PLs depending on f n : monofocal PLs and bifocal PLs.In the former case, f n is maintained constant, i.e., f n = f.Since the period of the grid along the y axis is a 2 = 0.5λ SPP , the SPPs launched from all the N rows constructively interfere to give rise to a focus at (0, f).In the latter case, f n = f + na 2 , which results in 2N foci for the N-row grooves (N foci on the positive y-axis and N on the negative yaxis).As a consequence of coherent superposition, two focal spots with a large focal depth appeared on the two sides of the PL, which are symmetrical with respect to the x-axis.For the given parameters of M, N, a i (i = 1, 2) and k SPP , the focal positions can be estimated by (0, ± f') = (0, ± (0.89f + 14.3) µm), which was obtained by linear fitting the numerical values as shown in Fig. 2. Here, we adopted a bifocal PL design with f = 40 µm, which resulted in two foci at (0, ± 50 µm).The resultant pattern of {(m, n)} 1 is shown in Fig. 3(a).A PAI is capable of transforming a uniform plane light wave into regular arrays of plasmon spots, which is designed according to the plasmon Talbot effect [22]. Figure 3(b) shows the designed pattern of the groove set {(m, n)} 2 of the PAI, of which the unit cell consists of three a 1 × a 2 grooves.The groove set {(m, n)} 2 has a period of 2a 1 in the xdirection and 3a 2 in the y-direction.For an x-polarized incident beam, any two adjacent columns of the PAI will launch a regular array of focal spots with a spacing of 3a 2 in the ydirection and a repeating length of λ SPP /{1-[1-(pλ SPP /3a 2 ) 2 ] 1/2 in the x-direction, where p is the diffraction order of SPPs at the grooves.The MPM has M/2 periods along the x-direction and the launched SPPs at all periods should constructively interfere.Therefore, a 1 should be carefully chosen.Through numerical calculations, a 1 = 410 nm is found to be applicable.However, the designed MPM has a doubled period of 6a 2 in the y-direction because the designed MPM is the intersection pattern of the groove sets of PL and PAI.As a result, the multiple spots of PAI have a period of 6a 2 = 2.6 µm in the y-direction.Here, the extra phase shift and the scattering loss of SPPs crossing over a single groove are ignored.

Experiment
A scanning electron microscopy (SEM) image of the fabricated PAI (x-direction)/PL (ydirection) is shown in Fig. 4(a).The sample was fabricated using a focused ion beam milling system on a 50 nm-thick gold film that was sputtered onto a microscope slide glass substrate.A linear polarized laser beam from a wavelength-tunable CW Ti-Sapphire laser was normally incident upon the sample from the air side.The polarization of the light was tuned using a half-wave plate.The SPP intensity distribution was detected using a leakage radiation microscope (LRM) equipped with a high NA oil-immersion objective (100 × , NA = 1.4), three auxiliary lenses with a focal length of 120 mm, and a charge coupled device.A spatial filter was introduced to filter out the directly transmitted light through the gold film [23].
For a y-polarized (θ = 90°) incident beam with λ 0 = 873 nm, the LRM image of the SPP intensity distribution are shown in Fig. 4(b).The SPPs are symmetrically emanating in the vertical direction and they are focused into two focal spots at (0, ± 49µm).The transverse (x) and longitudinal (y) intensity profiles of the upper focus are shown in Fig. 4(c), which show that the transverse and longitudinal full widths at half-maxima (FWHMs) are 1.3 and 17 µm, respectively, by fitting them to a Gaussian profile.The PL may hold potentials for exotic applications in optical trapping and energy delivering because of its fairly large depth of focus (~20λ SPP ) and the high aspect ratio (~13) of the focus shape.To compare with the experimental results, numerical calculation was performed using Eqs.( 1) and ( 2) with t = 1.0.Figure 4(d) shows the simulated SPP intensity distributions corresponding to Fig. 4(b).The simulated focal positions are (0, ± 49 µm), which are the same as the experimental results.The simulated transverse and longitudinal FWHMs of the focal spot are 2.0 and 27 µm, respectively, which are slightly larger than the experimental results.The deviations from the experimental results are caused by neglecting the SPP-groove scattering in our model.However, the features in the experimental images are accurately reproduced in the calculated result, which means that the calculation method using the Huygens-Fresnel principle and SPP dipole sources can describe the behavior of MPMs very well and demonstrate the design principle.When the incident laser was switched to x-polarization (θ = 0°) at λ 0 = 830 nm, PAI is activated.The experimental and simulated intensity distributions are shown in Figs.5(a) and 5(b), respectively.In the x-direction, the plasmon Talbot carpets with multiple focal spots are unfolded with a high contrast.The dashed lines in Fig. 5(a) indicate the positions of three focus arrays at x = −32, −24, and −17 µm.The intensity profiles along these dashed lines are extracted and shown in Fig. 5(c), which reveals an averaged spot spacing and transverse FWHM of 2.6 and 1.0 µm, respectively.The profile at x = −24 µm undergoes a lateral shift by half a Talbot distance along the y-direction with respect to those at x = −32 and −17 µm.This result is a typical half-period revival phenomenon in the Talbot image.Therefore, the repeating length in the experiment is 15 µm, which is exactly the same as the simulation result.The MPM also functions as a demultiplexing element because the two functions are designed for different wavelengths.To investigate its demultiplexing properties, the experimental results corresponding to the incident light wavelength λ 0 from 800 to 880 nm with a fixed polarization θ = 45° are shown in Fig. 6.At λ 0 = 830 nm, which is the design wavelength of PAI, only the function of PAI is available.The launched SPPs propagating along the ± y-direction are fairly weak and have no focal spot at all.When the incident wavelength was tuned to 873 nm, which is the design wavelength of PL, two strong focal spots are obtained on the y axis, and the launches of SPPs along the ± x-direction are restricted.Therefore, such a device implements different functions for different incident wavelengths.In addition, the two functions can be also being designed for the same working wavelength by tuning the grid size.

MPM with non-orthogonal outputs
Thus far, we demonstrated an MPM with mutually perpendicular outputs.Essentially, directions of the outputs can be tuned using non-orthogonal grids.To this end, a rhombic grid is employed to implement an MPM with two monofocal PLs operating along the directions of + y axis and [ + 1, + 1].The design wavelengths are 809 and 873 nm (λ SPP = 793 and 858 nm), respectively.The primitive lattice vector basis a 1 is along + x axis and a 2 along [-1, + 1] with a 1 = 607 nm and a 2 = 561 nm as shown in Fig. 7(a).The groove set {(m, n)} 1 of the PL along the y-direction is determined by applying Eq. ( 3) with f n = 52 µm, which corresponds to a focus at (0, 52µm).With a designed focus at R = (37 µm, 37 µm), the groove set {(m, n)} 2 of the second PL could be generated using Eq. ( 4), where l = 0, 1, 2,…, and ε = 0 or 1 for m that is odd or even, respectively, r m,n ± 0.5a 2 a 2 are the positions of the midpoints of the upper and lower sides of the groove (m, n), and d m is the distance between the focus and the mth column, which is located on the line y = -x + ma 1 .and (38 µm, 38 µm), respectively.For the incident wavelength of λ 0 = 840 nm, which is between the two design wavelengths, no focal spot can be found, as shown in Fig. 7(e).In this work, rectangular and rhombic grids were used and the current designs essentially show different functionalities for two directions.In principle, it is possible to expand our designs to three or even more directions by using a triangular, hexagonal or octagonal grids.The challenge is that, in such cases, the resultant groove set {(m, n)} is derived by intersection of more than two groove sets {(m, n)} 1 ∩{(m, n)} 2 ∩{(m, n)} 3 ….Therefore, a small number grooves are retained in {(m, n)}, which inevitably degrades the performance.One possible solution is to expand the device footprint (larger M and N), so that more grooves would be included.As a result, a tradeoff has to be made between the functionality and the compactness of the device.Recently, polarization-dependent SPP unidirectional excitation using circular polarization are realized where the direction of SPP excitation can be well controlled by changing the helicity of the incident light [24,25].To response to circular polarization, more complicated building-blocks for the MPMs are desired and the design method should be improved correspondingly.

Conclusions
In conclusion, we proposed and demonstrated a multifunctional and multi-output metaelement for controlling SPPs by using well-designed nonperiodic subwavelength groove arrays.We integrated a PL and a PAI in an MPM with perpendicular output directions.We also show that the directions of the outputs are tunable by simply altering the grid geometry.
The agreement between the experimental and simulation results shows the feasibility of the proposed phase-sieve method.The method offers a new way of achieving a high density of functionality and effectively scales down the size of integrated optical circuits.

Fig. 1 .
Fig. 1.Schematic of an MPM.(a) The MPM consists of many grooves of uniform size fabricated on a gold film.A laser beam is incident upon the MPM and launches SPPs that propagate at the gold/air interface.(b) Rectangular grid of the MPM.The coordinate origin is at the center of the MPM.r and r s are the vectors of the field and source points, respectively.The red double-headed arrow represents the polarization direction of the incident beam, φ s is the azimuthal angle between the polarization direction and the vector r-r s .

Fig. 2 .
Fig. 2. Simulated focal length f' is plotted with respect to the design parameter f, which is varied from 15.0 to 60.0 µm with an increment of 5.0 µm.f' is determined from numerical calculation using Eqs.(1) and (2) with t = 1.0.

Fig. 3 .
Fig. 3. (a) Pattern of the groove set of the designed bifocal PL.The even and odd rows are drawn in red and black, respectively, for clarity.(b) Pattern of the groove set of the designed PAI.The inset is the magnified image of a part of the pattern containing four unit cells, in which one unit cell is indicated in red to guide the eyes.

Fig. 4 .
Fig. 4. Performance of PL (y-direction) operating at λ 0 = 873 nm and polarization angle θ = 90°.(a) SEM image of the fabricated MPM with a footprint of 25 µm × 26 µm.(b) LRM image of PL.(c) Intensity profiles in the longitudinal and transverse directions through the upper focus in (b).(d) Simulated SPP intensity distribution.The white box marks the MPM boundary.

Fig. 7 .
Fig. 7. Performance of the MPM comprising two monofocal PLs operating along the directions of + y axis and [ + 1, + 1] for polarization angle θ = 77.5°.(a) Schematic of the rhombic grid.The coordinate origin is at the center of the MPM.(b) SEM image of the fabricated MPM with a footprint of 24 µm × 37 µm.(c)-(e) are the LRM images of the MPM at λ 0 = 809, 873, and 840 nm, respectively.The insets show the simulated SPP intensity distributions in the focal area.