Near dispersion-less surface plasmon polariton resonances at a metal-dielectric interface with patterned dielectric on top
Sachin Kasture1, P. Mandal1, Amandev Singh1, Andrew Ramsay2, Arvind S. Vengurlekar1, S. Dutta Gupta3, and Achanta Venu Gopal1*
1DCMPMS, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai-400005, India 2Department of Physics and Astronomy, University of Sheffield, Sheffield S37RH 3School of Physics, University of Hyderabad, Hyderabad 500046
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 2-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 2-D pattern. The anti-crossings resulting from the in-plane coupling of different SPP modes are also shown.
I. INTRODUCTION that they can be excited as well as their position Surface modes at an interface especially surface controlled by using 2D dielectric patterns on top of plasmon polaritons (SPPs) at metal-dielectric interface dielectric-metal interface. One of the drawbacks of are well known solutions of Maxwell‟s equations subject utilizing plasmon mediated effects is that the feature is to appropriate boundary conditions. Such modes are available for specific angles (of incident light). In this typically excited using prism (in Otto, Kretschmann or paper we show that the proposed flat dispersion-less Sarid configurations) or grating coupling [1,2]. In the mode would enable broad angle coupling of light to context of grating coupling, several variations using plasmon mode. periodically patterned dielectric or metal structures have The structure of the paper is as follows: in section II been used. Extra-ordinary transmission through patterned we will describe the conditions under which dispersion- metal has led to the recent interest in plasmonics [3]. less modes may be excited. In section III we will present Lately, 1-D gratings and 2-D patterns are being utilized experimental conditions followed by results and in plasmon mediated enhancement of magneto-optical discussion in section IV and summary in section V. properties, plasmon assisted photonics and active plasmonics [4-6]. Amongst all possible variations of II. Origin of the flat mode patterned structures, dielectric patterns on metal- For a single metal-dielectric interface, with a 2D dielectric interface have received very little attention. In periodic structure on top of the interface, light is coupled this paper we present results on such a structure and point to plasmon modes matching one of the Bragg harmonics out the novel possibilities with the coupled modes of the incident light energy. In addition, the momentum leading to a 'flat' dispersion-less mode. conservation requires matching of the light momentum
Dispersion-less plasmon modes are either localized k=(k0sincos, k0cos, k0sinsin) and the wave vectors or particle plasmons and are of interest, for example, for kG,a = (kx,G,ax, ky, kz,G,az). In these expressions, G is the making use of local field enhancement related grating vector, ax is period in x- direction and az is period modification of semiconductor carrier dynamics and in z-direction, the launch field is at an angle to the optical nonlinearities. Their interaction with propagating normal to the interface and is the in-plane angle which SPPs or coupled plasmon modes and coupling induced the field subtends with the 2D pattern as shown in Fig. 1. changes in dispersion in planar and corrugated structures For such a 2-D system, the SPP dispersion relation is are reported [7-10]. In various sub-wavelength structures, given by Eq. (1) which comes from the conservation of these coupled localized and propagating plasmons are in-plane momentum mentioned above [17]. studied for basic understanding as well as for different applications [11-16]. 2 2 m2 n2 However, one of the structures that is least studied is k sin()cos() k sin()sin() k d m k (1) 0 a 0 a 0 SPP the unpatterned metal-dielectric interface with dielectric x z d m pattern on top. In addition, to our knowledge there is no report of flat dispersion-less plasmon modes at metal- where 2/ax (Gx) and 2/az (Gz) are grating vectors in dielectric interface. In this work we show that near reciprocal space in the two orthogonal directions, and m dispersion-less surface plasmon modes are possible and and n are integers. d and m are permittivities of dielectric and metal, respectively. k0 is the light controlling one or all of the following parameters, top momentum given by 2/0 where 0 is the resonant pattern, orientation of the launch field and refractive wavelength. Let, dm/(d+m) = . index of the dielectric materials. The observed results are Solutions to k0 in Eq. (1) are given by the following universal and are valid for structures with dielectric pillar for A=22sin, M=m.cos/ax and N=n.sin/az, pattern on metal-dielectric interface and corrugated metal films as well. 2 AM N AM N 4sin 2 'G 2 G 2 k x z (2) III. EXPERIMENT 0 2 sin 2 ' Two dimensional (2d) metallo-dielectric plasmonic crystals with arrays of air holes in dielectric and For each of the k0 values in Eq.(2), there will be a dielectric pillars have been fabricated using holographic corresponding kSPP defined by k0. From Eq. (2), the interferometry. On fused quartz pieces, thin gold (Au) 2 basic condition for weak -dependence is || > > sin (), layer was deposited by thermal evaporation. A 500nm which could be satisfied for metal-dielectric interface due thick photoresist (SHIPLEY S1805) was spin coated and to large m. Further, one of the conditions to be satisfied subsequently 2-D lattices with arrays of holes or pillars (for A(M+N)=0 for non-zero ) is (i) = 45º and m = -n, were obtained by double exposure of the samples to (ii) = 0º, m = 0 and (iii) = 90º, n = 0. For case (i), the interference pattern of a laser beam (442 nm He-Cd line). weak -dependence is possible only in one half of the By optimizing the laser power of each of the two dispersion plane (either positive or negative ). A special interfering beams, the exposure time and the angle case of this may be found in the data of reference [18]. In between the two beams, 2-D patterns were obtained over principle, for case (ii) (and case (iii)), weak - 1cm diameter sample after developing with a standard dependence is possible for all n (and m) values. In developer. 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, 2, and 3) and thickness of 2nd layer (t) by [19], ( ) 2 2 1 3 3 1 tanh(2t) 2 2 (3) (132 213 ) 2 2 2 where j =k -k0 j, j=1,2,3. One can combine the kSPP value from Eq. (1) with Eq. (3) and solve for the SPP mode dispersion for three layer system. Eq. (3) gives the coupled SPP mode solutions where the coupling strength depends on the thickness of the gold film (t). Earlier, Figure.1 Schematic of the 2-D dielectric pattern on metal- long range surface modes supported by thin films were dielectric interface (Top). Launch orientation (angles and ) investigated in detail in such three layer structures [19]. and the lattice constant in the x (ax) and z (az) directions are Also, in 1D thin film metal gratings, independent SPP shown. Height of the air holes is d, of unpatterned dielectric is dispersion was shown for TE polarized light with = 900 h, and that of the metal is t. Below are shown the SEM images [20]. However, there is no work, to our knowledge, to of the rectangular (right „A‟) and near square (left „B‟) lattices. report the near dispersion-less modes in three-layer The two orientations with = 0º and ≠ 0º are also shown. structures with top 2D pattern. In the following we will demonstrate the near flat The grating parameters of two of the structures dispersion modes in non-square and square lattices. estimated from AFM images are given below. Structure Instead of modifying the metal-dielectric interface by A has ax= 660nm and az = 730nm, thickness of the gold patterning the metal (or dielectric and depositing metal), layer (t) is 55nm, depth of the air holes (d) is 60nm and we will have a uniform metal-dielectric interface over fill factor (dielectric to air ratio) is 0.4 in X-direction and which there is a top dielectric with airholes arranged in a 0.45 in Z-direction. Similarly, the parameters for the 2D pattern. Our results show that the excited SPP modes structure B are 780nm, 750nm, 40nm, 80nm, 0.61, and depend on the top dielectric pattern. This shows the 0.68, respectively. Each of the samples has a 400nm possibility to excite the SPP modes including the thick unpatterned dielectric (h) above the gold. dispersion-less SPP modes as per requirement by SPP dispersion in different samples was studied by 2.15, respectively. The thickness of gold and the grating angle resolved white light transmission measurements parameters are measured using profilometer and AFM. with a collimated 100W tungsten halogen lamp output The orientation of the sample is varied from = 0º and a fiber based spectrometer having 0.5nm wavelength to = 90º. In Fig. 2, SPP dispersion at two orientations, resolution in the 400-1000nm wavelength range. Angle = 0º (a) and ~ 90º (b) are shown for structure A of air resolution of the setup is 0.0375º angle in the -35º to 35º holes in dielectric. Three types of modes are clearly angle range. A Glann-Thompson polarizer (extinction observed: pure diffraction orders at the top (air - 5 ratio 10 :1) is used in the incident path to linearly dielectric grating) and bottom (dielectric grating- polarize the light on to the sample. The spectra are dielectric) interfaces are shown by dashed lines (labeled normalized with those through a quartz reference sample. (m,n)G) and the SPP modes (labeled (m,n)P) described by For propagation direction along y, the relevant field Eq. (3) are shown by the dotted lines. The dispersion-less components are Ex, Hy and Ez for TM polarized light. mode (0,2)P at about 650nm is seen in this sample and is Fig. 1 shows the schematic of the sample with different of type (ii) discussed. For = 0º the sample is oriented layers (top) and 2-D pattern along with the SEM images such that the 660nm period is along z-axis and thus the (bottom). 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 730nm. One can control the SPP dispersion by controlling the orientation (). For ~ 90º, the mode is comparatively more dispersive as seen in Fig. 2(b).
Figure.2 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 3. For a mode (m,n), subscript P denotes a plasmon Figure.3 Anti-crossings of coupled plasmon modes due to in- mode and subscript G denotes grating order. (m,n)A and (m,n)S plane interaction are possible. Such anti-crossings are shown are anti-symmetric and symmetric plasmon modes arising due for = 60° and TM polarized incident light. Lines shown are to coupling between SPPs at the top and bottom interfaces of different possible plasmon modes based on Eq (3) and the metal. Transmission spectra at few angles are shown on the rectangles highlight the regions where these modes are anti- right. Lines are to guide the eye about the shift in the crossing. transmission dip with angle. Due to the coupled modes (in the direction normal to IV. RESULTS AND DISCUSSION the interface) at the dielectric - metal and metal-quartz SPP dispersion (wavelength vs angle of incidence) is interfaces, we expect the modes to split into symmetric plotted in Fig. 2 for rectangular lattice (structure A) taken and anti-symmetric modes. Some of the observed between -25º and 25º incident angles at 0.3º steps. coupled modes are labeled in the figure like (2,1) and Spectra are presented in a contour plot with colour A (2,1)S, where subscript A stands for Antisymmetric and coding showing transmission dips to be dark. Thus, the S for Symmetric for given (m,n) mode. In addition to the darker curves in the contour plot represent dips in the coupled plasmon modes in the normal to interface transmission spectrum which correspond either to the direction, the structure and the excitation geometry diffraction orders or SPP modes. results in additional in-plane coupling which is The measured SPP dispersion curves are fitted to Eq manifested as anti-crossing between different modes. (3) with the solutions for in-plane momentum taken from These are seen in Fig. 3 and are marked by rectangles. the left hand side of Eq. (1) and the fits are presented as The deviation of the fits from the measured data could be lines in Figs. 2-4. The real part of the dielectric constant due to the constant dielectric constant value for dielectric of gold is used for the fits where the values are taken used. By properly incorporating the dispersion of the from Johnson-Christie [21]. The best fits are for dielectric, one may get better fits. In addition, the fits do dielectric constant of the resist and quartz to be 2.7 and not include in-plane coupling of SPP modes which matter samples. Though data not presented, similar results were for ≠ 0º case where the coupled SPPs are expected. also observed in dielectric pillar patterns on metal- dielectric 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 Figure. 4 Measured SPP dispersion and the fits (dotted lines) help control the position of the dispersion-less mode. This for a square lattice for TM polarized incident light. 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.
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