Near dispersion-less surface plasmon polariton resonances at a metal-dielectric interface with patterned dielectric on top

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1 Near dispersion-less surface plasmon polariton resonances at a metal-dielectric interface with patterned dielectric on top Sachin Kasture 1, P. Mandal 1, Amandev Singh 1, Andrew Ramsay, Arvind S. Vengurlekar 1, S. Dutta Gupta, and Achanta Venu Gopal 1* 1 DCMPMS, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai , India Department of Physics and Astronomy, University of Sheffield, Sheffield S7RH School of Physics, University of Hyderabad, Hyderabad Abstract Omni-directional light coupling to surface plasmon polariton (SPP) modes to make use of plasmon mediated near-field enhancement is challenging. We report possibility of near dispersion-less modes in structures with unpatterned metal-dielectric interfaces having -D dielectric patterns on top. We show that the position and dispersion of the excited modes can be controlled by the excitation geometry and the -D pattern. The anti-crossings resulting from the in-plane coupling of different SPP modes are also shown. I. INTRODUCTION Surface modes at an interface especially surface plasmon polaritons (SPPs) at metal-dielectric interface are well known solutions of Maxwell s equations subject to appropriate boundary conditions. Such modes are typically excited using prism (in Otto, Kretschmann or Sarid configurations) or grating coupling [1,]. In the context of grating coupling, several variations using periodically patterned dielectric or metal structures have been used. Extra-ordinary transmission through patterned metal has led to the recent interest in plasmonics []. Lately, 1-D gratings and -D patterns are being utilized in plasmon mediated enhancement of magneto-optical properties, plasmon assisted photonics and active plasmonics [4-6]. Amongst all possible variations of patterned structures, dielectric patterns on metaldielectric interface have received very little attention. In this paper we present results on such a structure and point out the novel possibilities with the coupled modes leading to a 'flat' dispersion-less mode. Dispersion-less plasmon modes are either localized or particle plasmons and are of interest, for example, for making use of local field enhancement related modification of semiconductor carrier dynamics and optical nonlinearities. Their interaction with propagating SPPs or coupled plasmon modes and coupling induced changes in dispersion in planar and corrugated structures are reported [7-10]. In various sub-wavelength structures, these coupled localized and propagating plasmons are studied for basic understanding as well as for different applications [11-16]. However, one of the structures that is least studied is the unpatterned metal-dielectric interface with dielectric pattern on top. In addition, to our knowledge there is no report of flat dispersion-less plasmon modes at metaldielectric interface. In this work we show that near dispersion-less surface plasmon modes are possible and that they can be excited as well as their position controlled by using D dielectric patterns on top of dielectric-metal interface. One of the drawbacks of utilizing plasmon mediated effects is that the feature is available for specific angles (of incident light). In this paper we show that the proposed flat dispersion-less mode would enable broad angle coupling of light to plasmon mode. The structure of the paper is as follows: in section II we will describe the conditions under which dispersionless modes may be excited. In section III we will present experimental conditions followed by results and discussion in section IV and summary in section V. II. Origin of the flat mode For a single metal-dielectric interface, with a D periodic structure on top of the interface, light is coupled to plasmon modes matching one of the Bragg harmonics of the incident light energy. In addition, the momentum conservation requires matching of the light momentum k=(k 0 sincos, k 0 cos, k 0 sinsin) and the wave vectors k G,a = (k x,g,ax, k y, k z,g,az ). In these expressions, G is the grating vector, a x is period in x- direction and a z is period in z-direction, the launch field is at an angle to the normal to the interface and is the in-plane angle which the field subtends with the D pattern as shown in Fig. 1. For such a -D system, the SPP dispersion relation is given by Eq. (1) which comes from the conservation of in-plane momentum mentioned above [17]. d m 0 kspp d m m n k sin( )cos( ) k0sin( )sin( ) k0 a x a z where /a x (G x ) and /a z (G z ) are grating vectors in reciprocal space in the two orthogonal directions, and m and n are integers. d and m are permittivities of (1)

2 dielectric and metal, respectively. k 0 is the light momentum given by / 0 where 0 is the resonant wavelength. Let, d m /( d + m ) =. Solutions to k 0 in Eq. (1) are given by the following for A=sin, M=m.cos/a x and N=n.sin/a z, k AM N AM N 4sin ' G x G z sin ' 0 For each of the k 0 values in Eq.(), there will be a corresponding k SPP defined by k 0. From Eq. (), the basic condition for weak -dependence is > > sin (), which could be satisfied for metal-dielectric interface due to large m. Further, one of the conditions to be satisfied (for A(M+N)=0 for non-zero ) is (i) = 45º and m = -n, (ii) = 0º, m = 0 and (iii) = 90º, n = 0. For case (i), the weak -dependence is possible only in one half of the dispersion plane (either positive or negative ). A special case of this may be found in the data of reference [18]. In principle, for case (ii) (and case (iii)), weak - dependence is possible for all n (and m) values. In addition for square lattice, due to the symmetry, one would expect case (ii) and case (iii) to be degenerate. For non-square lattices this degeneracy is lifted and different near dispersion-less modes can be excited based on the excitation orientation. Bottom part of Fig. 1 shows the two orientations showing = 0º (field component along the x-axis) and 0º (field component not matching either of the axes). For three layer structure with a thin metal layer sandwiched between two infinite layers, the general dispersion relation for surface modes is given in terms of the dielectric constants ( 1,, and ) and thickness of nd layer (t) by [19], ( 1 1) tanh( t ) () ( ) 1 where j =k -k 0 j, j=1,,. One can combine the k SPP value from Eq. (1) with Eq. () and solve for the SPP mode dispersion for three layer system. Eq. () gives the coupled SPP mode solutions where the coupling strength depends on the thickness of the gold film (t). Earlier, long range surface modes supported by thin films were investigated in detail in such three layer structures [19]. Also, in 1D thin film metal gratings, independent SPP dispersion was shown for TE polarized light with = 90 0 [0]. However, there is no work, to our knowledge, to report the near dispersion-less modes in three-layer structures with top D pattern. In the following we will demonstrate the near flat dispersion modes in non-square and square lattices. Instead of modifying the metal-dielectric interface by patterning the metal (or dielectric and depositing metal), we will have a uniform metal-dielectric interface over which there is a top dielectric with airholes arranged in a D pattern. Our results show that the excited SPP modes depend on the top dielectric pattern. This shows the possibility to excite the SPP modes including the dispersion-less SPP modes as per requirement by 1 () controlling one or all of the following parameters, top pattern, orientation of the launch field and refractive index of the dielectric materials. The observed results are universal and are valid for structures with dielectric pillar pattern on metal-dielectric interface and corrugated metal films as well. III. EXPERIMENT Two dimensional (d) metallo-dielectric plasmonic crystals with arrays of air holes in dielectric and dielectric pillars have been fabricated using holographic interferometry. On fused quartz pieces, thin gold (Au) layer was deposited by thermal evaporation. A 500nm thick photoresist (SHIPLEY S1805) was spin coated and subsequently -D lattices with arrays of holes or pillars were obtained by double exposure of the samples to interference pattern of a laser beam (44 nm He-Cd line). By optimizing the laser power of each of the two interfering beams, the exposure time and the angle between the two beams, -D patterns were obtained over 1cm diameter sample after developing with a standard developer. Figure.1 Schematic of the -D dielectric pattern on metaldielectric interface (Top). Launch orientation (angles and ) and the lattice constant in the x (a x ) and z (a z ) directions are shown. Height of the air holes is d, of unpatterned dielectric is h, and that of the metal is t. Below are shown the SEM images of the rectangular (right A ) and near square (left B ) lattices. The two orientations with = 0º and 0º are also shown. The grating parameters of two of the structures estimated from AFM images are given below. Structure A has a x = 660nm and a z = 70nm, thickness of the gold layer (t) is 55nm, depth of the air holes (d) is 60nm and fill factor (dielectric to air ratio) is 0.4 in X-direction and 0.45 in Z-direction. Similarly, the parameters for the structure B are 780nm, 750nm, 40nm, 80nm, 0.61, and 0.68, respectively. Each of the samples has a 400nm thick unpatterned dielectric (h) above the gold.

3 SPP dispersion in different samples was studied by angle resolved white light transmission measurements with a collimated 100W tungsten halogen lamp output and a fiber based spectrometer having 0.5nm wavelength resolution in the nm wavelength range. Angle resolution of the setup is 0.075º angle in the -5º to 5º angle range. A Glann-Thompson polarizer (extinction ratio 10 5 :1) is used in the incident path to linearly polarize the light on to the sample. The spectra are normalized with those through a quartz reference sample. For propagation direction along y, the relevant field components are E x, H y and E z for TM polarized light. Fig. 1 shows the schematic of the sample with different layers (top) and -D pattern along with the SEM images (bottom)..15, respectively. The thickness of gold and the grating parameters are measured using profilometer and AFM. The orientation of the sample is varied from = 0º to = 90º. In Fig., SPP dispersion at two orientations, = 0º (a) and ~ 90º (b) are shown for structure A of air holes in dielectric. Three types of modes are clearly observed: pure diffraction orders at the top (air - dielectric grating) and bottom (dielectric gratingdielectric) interfaces are shown by dashed lines (labeled (m,n) G ) and the SPP modes (labeled (m,n) P ) described by Eq. () are shown by the dotted lines. The dispersion-less mode (0,) P at about 650nm is seen in this sample and is of type (ii) discussed. For = 0º the sample is oriented such that the 660nm period is along z-axis and thus the flat mode near this wavelength is seen. For = 90º, the flat mode should correspond to the resonant period along x-axis, that is, at about 70nm. One can control the SPP dispersion by controlling the orientation (). For ~ 90º, the mode is comparatively more dispersive as seen in Fig. (b). Figure. Measured SPP dispersion is shown for rectangular lattice of air holes in dielectric on top of a metal-dielectric interface with = 0º (a) and ~ 90º (b). Lines are fits based on Equation. For a mode (m,n), subscript P denotes a plasmon mode and subscript G denotes grating order. (m,n) A and (m,n) S are anti-symmetric and symmetric plasmon modes arising due to coupling between SPPs at the top and bottom interfaces of the metal. Transmission spectra at few angles are shown on the right. Lines are to guide the eye about the shift in the transmission dip with angle. IV. RESULTS AND DISCUSSION SPP dispersion (wavelength vs angle of incidence) is plotted in Fig. for rectangular lattice (structure A) taken between -5º and 5º incident angles at 0.º steps. Spectra are presented in a contour plot with colour coding showing transmission dips to be dark. Thus, the darker curves in the contour plot represent dips in the transmission spectrum which correspond either to the diffraction orders or SPP modes. The measured SPP dispersion curves are fitted to Eq () with the solutions for in-plane momentum taken from the left hand side of Eq. (1) and the fits are presented as lines in Figs. -4. The real part of the dielectric constant of gold is used for the fits where the values are taken from Johnson-Christie [1]. The best fits are for dielectric constant of the resist and quartz to be.7 and Figure. Anti-crossings of coupled plasmon modes due to inplane interaction are possible. Such anti-crossings are shown for = 60 and TM polarized incident light. Lines shown are different possible plasmon modes based on Eq () and rectangles highlight the regions where these modes are anticrossing. Due to the coupled modes (in the direction normal to the interface) at the dielectric - metal and metal-quartz interfaces, we expect the modes to split into symmetric and anti-symmetric modes. Some of the observed coupled modes are labeled in the figure like (,1) A and (,1) S, where subscript A stands for Antisymmetric and S for Symmetric for given (m,n) mode. In addition to the coupled plasmon modes in the normal to interface direction, the structure and the excitation geometry results in additional in-plane coupling which is manifested as anti-crossing between different modes. These are seen in Fig. and are marked by rectangles. The deviation of the fits from the measured data could be due to the constant dielectric constant value for dielectric used. By properly incorporating the dispersion of the dielectric, one may get better fits. In addition, the fits do

4 not include in-plane coupling of SPP modes which matter for 0º case where the coupled SPPs are expected. Figure. 4 Measured SPP dispersion and the fits (dotted lines) for a square lattice for TM polarized incident light. samples. Though data not presented, similar results were also observed in dielectric pillar patterns on metaldielectric interface samples with square and non-square lattices. Quartz side excitation also showed SPP mode excitation similar to the patterned side excitation shown above. This shows that the discussed dispersion-less SPP modes are only dependent on the top pattern and the materials chosen. V. CONCLUSIONS The signature of a sub-wavelength two-dimensional dielectric grating layer on coupled surface plasmon polariton modes in a layered configuration is studied. The grating layer comprises of square and rectangular arrays of sub-wavelength air holes in the dielectric. Near dispersion-less SPP modes and in-plane coupling between SPP modes resulting in anti-crossings are shown. Controlling the top pattern and launch conditions would help control the position of the dispersion-less mode. This could have wide practical applications in omni-directional light coupling to plasmon modes to make use of plasmon mediated near-field enhancement. ACKNOWLEDGEMENTS Partial financial support for this work is provided by DST-UKIERI. Figure.5 Measured SPP dispersion in corrugated metal sample in the form of gold deposited on patterned dielectric for 0º case for TM polarized launch. Fig. 4 shows contour plot of the measured SPP dispersion for square lattice of airholes in dielectric (Structure B) with the incident light polarization set to TM polarized light for = 0º. Similar measurements done for TE polarized light showed only the grating orders and those with cross polarized light excitation, the SPP excitation is weak and the corresponding dips in the transmission spectra are not resolvable (data not presented). The TM polarized light excitation ( = 0º) shows multiple SPP modes including the near dispersionless mode corresponding to (0,) P at about 805nm. We also measured the SPP dispersion for corrugated metal sample where gold layer is deposited on top of the dielectric pattern. For the TM incident polarization and the orientation of the sample such that 0º and 90º, light excitation of SPPs and the coupled SPP modes in SPP dispersion plot are observed as shown in Fig. 5. The coupled SPP modes observed indicate that the observed in-plane coupling is similar in both dielectric patterns on metal-dielectric interface and patterned metal REFERRENCES 1. A. S. Vengurlekar Extraordinary optical transmission through metal films with subwavelength holes and slits, Current Science 98, 100 (010).. D. Sarid, Long range surfaceplasma waves on very thin metal films, Phys. Rev. Lett. 47, 197 (1981).. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolf, Extraordinary optical transmission through sub-wavelength hole arrays, Nature 91, 667 (1998). 4. V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, Achanta Venu Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Enhanced magneto-optical effects in magnetoplasmonic crystals, Nature Nanotech. 6, 70 (011). 5. B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and Ad Lagendijk, Active spatial control of plasmonic fields, Nature Photonics 5, 60 (011). 6. K. F. MacDonald, Z. L. Samson, M. I. Stockman, N. I. Zheludev, Ultrafast active plasmonics, Nature Photonics, 55 (009). 7. D. Sarid, R. T. Deck, and J. J. Fasano, Enhanced nonlinearity of the propagation constant of a longrange surface-plasma wave, J. opt. Soc. Am. 7, 145 (198). 8. S. Dutta Gupta, G. V. Varada, and G. S. Agarwal, Surface plasmons in two-sided corrugated thin films, Phys. Rev. B 6, 61 (1987). 9. Holland and Hall, Surface-plasmon dispersion relation: Shifts induced by the interaction with

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