Controlling plasmonic Bloch modes on periodic nanostructures
B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, A. Lagendijk
aa r X i v : . [ phy s i c s . op ti c s ] A p r Controlling plasmonic Bloch modes on periodic nanostructures
B. Gjonaj, ∗ J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk FOM-Institute for Atomic and Molecular Physics AMOLF,Science Park 104, 1098 XG Amsterdam, The Netherlands Complex Photonic Systems, Faculty of Science and Technology,and MESA+ Institute for Nanotechnology, University of Twente,PO Box 217, 7500 AE Enschede, The Netherlands
We study and actively control the coherent properties of Surface Plasmon Polaritons (SPPs)optically exited on a nano-hole array. Amplitude and phase of the optical excitation are externallycontrolled via a digital spatial light modulator (SLM) and SPP interference fringe patterns areobserved with high contrast. Our interferometric observations revel SPPs dressed with the Blochmodes of the periodic nano-structure. The momentum associated with these Dressed Plasmons (DP)is highly dependent on the grating period and fully matches our theoretical predictions. We showthat the momentum of DP waves can in principle exceed the SPP momentum. Actively controllingDP waves via programmable phase patterns offers the potential for high field confinement applicablein sensing, Surface Enhanced Raman Scattering and plasmonic structured illumination microscopy.
Important systems such as biological cells, singlemolecules, and nanodevices, strongly interact with vis-ible light on sub-wavelength scales. Yet standard mi-croscopy and related applications in sensing and imagingare diffraction limited. Plasmonics [1] offers an alter-native route to control light with sub-wavelength pre-cision through the excitation of Surface Plasmon Polari-tons (SPPs) [2, 3]. These surface waves, bound to a metaldielectric interface, are a hybrid mode of photons andelectronic change-density oscillations. The intrinsic mo-mentum associated with these evanescent waves is higherthan that of free propagating photons. Thus, for a fixedlight frequency, SPPs have a higher effective refractiveindex and tighter confinement of electromagnetic energy[4].Innovation in nano fabrication has enabled a remark-able degree of control over SPPs using metallic nanos-tructures. Specially tailored samples allow plasmonicwaves to be coupled into the topological modes of a fab-ricated structure. The light field confinement, and there-fore the resolution, addressed through the mode volumeof these geometrically Dressed Plasmons (DP) exceedsby more than one order of magnitude that of standardSPP confinement. Successful geometries include couplednanoantennas [5–7] that fully localize modes in the gapbetween neighboring antennas, and V-grooved [8, 9] andnanowire [10, 11] waveguides that support 1D propagat-ing modes deeply confined inside the waveguide.Yet there are limitations in using dressed plasmons forsensing applications. The electromagnetic field is only lo-cally enhanced due to the fixed geometry of the structureyielding very high resolution but no field of view. Fur-thermore the specimen has to be inserted within the fewnanometers width of the waveguide or the gap betweennanoantennas, an extremely difficult task using currentmethods. However, theoretical works [12, 13] have shownthat it is possible to use periodic nanostructures [14],such as well designed gratings [15], to support extended DP waves to obtain both high resolution and large field ofview. Furthermore, actively controlling these DP waveshas the potential for plasmonic structured illuminationmicroscopy [16] and related applications in imaging andsensing.Here we show experimental observation and control ofextended dressed plasmons supported by periodic nanos-tructures. Using a Spatial Light Modulator we shape theamplitude profile of the incident laser beam over a large2D field of view. The SLM is imaged onto the surface ofthe sample thus addressing each pixel of the SLM to acorresponding area on the sample.This arrangement al-lows us to measure with high contrast fringe patterns gen-erated from two counterpropagating SPP waves. Tuningthe SLM phase pattern allows these fringes to be shiftedand/or tilted at will. The momentum associated with thestanding waves shows strong dependence on the latticeperiod of the grating and revels the Bloch-mode dressingof the surface plasmons. Combining high momentum DPwith focusing and scanning experiments [17] has the po-tential to revolutionize far field bio-sensing applications.A diagram of the setup is given in Fig. 1. The SLM isimaged on the sample via a lens (L1) and the objective,referred to hereafter together as the imaging system. TheSLM is at the focal plane of lens L (focal length 130cm). The image at infinity created by L is projectedonto the sample at the focal plane of the objective. OurSLM (Holoeye LC-R 720) is a reflective display based onTwisted Nematic Liquid Crystal on Silicon technology.The display has a total of 1280 x 768 pixels operating at60 Hz with a response time of 3 ms. Each pixel is 20 µ min size and addressed with a 8-bit voltage. The objective(Nikon LU PLAN FLUOR P 100X) is infinity correctedand metallurgic (no coverslip compensation) with a Nu-merical Aperture (NA) of 0.9 and a magnification of 100times (defined for a tube lens of 20 cm focal length). Thefocal length of L is 6.5 times larger than that of the stan-dard tube lens yielding a corresponding 650 times demag- L BSCCD L C SLMP. BSIrisSampleObjectiveB. ExHe:Ne
FIG. 1. Experimental Setup. The Spatial Light Modulator(SLM) is projected onto the sample via the imaging system(lens L , objective). The sample is imaged on the CCD cam-era via the system (objective, lens L C ). The abbreviationsB. Ex, BS and P. BS stand for beam expander, beam splitterand polarizing beam splitter respectively. Inset: SEM image(5 x 5 µ m) of 450 nm nanohole array. nification of the image. The distance between L and theobjective is 1 m i.e. smaller than the focal length of L (non-telecentric imaging system). In this configurationthe average angle of illumination is position dependent,which is an important condition for the SPPs launching.The light emitted in reflection from the sample isimaged on the CCD (AVT Dolphin F145 B) using lens L C as tube lens. This light includes both the direct re-flection of the illuminating beam and the scattered lightfrom SPPs. Thus the resulting image is a combinationof both the SLM amplitude pattern and the generatedSPP pattern. To distinguish between the two we chooseillumination patterns that allow SPP observation in anon-illuminated area. The amplitude and phase of theexcitation pattern is controlled by applying the 4-pixeltechnique [18] to the SLM. Four adjacent pixels aregrouped into a superpixel by selecting a first diffractiveorder with the neighbor-pixel fields being π /4 out ofphase. In this work we use 32 x 32 superpixels. EverySLM superpixel is imaged on a sample area of 440 x 440nm containing nearly one unit cell of the grating. Sucha superpixel grouping provides continuous modulationover full amplitude ( A ∈ [0 , ∈ [0 , π ])ranges with a cross modulation of less than 1%.Our samples, nanohole arrays similar to those usedtypically for Enhanced Optical Transmission experi-ments, were fabricated using focused ion beam milling.A 200 nm gold film was deposited on top of 1 mm BK7glass substrate with a 2 nm chromium adhesion layer.Square holes were milled with sides of 177 nm. The holearray covers an area of 30 x 30 µ m . Five samples werefabricated with array periods ( a ) varying from 350 nmto 450 nm. The sample was placed with the gold sidetowards the objective to observe SPP waves from thegold-air interface. We calculate the SPP momentum for incident radiation of λ = 633 nm ( k = 2 π / λ ) usingtabulated values [19] of the dielectric constants of gold ε m and air ε d k S = k Re r ε m ε d ε m + ε d = ( m, n ) k G + k sin θ, (1)where the last equality expresses the fact that the SPPmomentum is a vectorial sum of the ( m , n ) k G gratingorders ( k G = 2 π/a ) and the in-plane component of theincident light. With our oblique illumination scheme, theaverage angle of incidence θ is not uniform but positiondependent.This illumination scheme and its role on how SPPs arelaunched is illustrated in Fig. 2. Each SLM’s superpixel isprojected onto the sample with a different average angleof incidence (Fig. 2a) and thus with a different in-planecomponent of the incident light. The momentum con-servation described in Eq. 1 will be satisfied only withinspecific angular bands which are position dependent. InFig. 2b-d we show the surface of three different samplesilluminated with a uniform amplitude profile across theSLM with horizontal polarization.For the reference bare gold film and a uniform SLMamplitude and phase profile, the reflected image is identi-cal to incident beam profile since no SPP can be launched(Fig. 2b). When the same uniform amplitude and phaseprofile is projected onto a nanohole array, dark and brightareas are clearly distinguishable as shown in Fig. 2c-d.Dark areas correspond to suppressed reflection from thesample. We interpret these dark areas as the spatial (an-gular) bands that satisfy Eq. 1 and thus where plasmons θ µ m a bcd µ m FIG. 2. (a) Sketch of the sample illumination. Each SLMpoint is imaged on the surface of the sample with a differentaverage angle of incidence θ . (b-d) Reflection from differentsamples illuminated with a uniform amplitude and phase pro-file. (b) On the bare gold sample the reflection is also uniformsince no SPPs are launched. (c) The dark areas of low reflec-tion from the 400 nm hole array indicate the angular (spatial)bands for SPP launching. (d) These bands are sample depen-dent as shown for the 425 nm hole array. Inset: SEM imageof the samples. are efficiently excited from the incident light. The loca-tion of these bands strongly depends on the array mo-mentum. Even a 25 nm variation of the array periodfrom a = 425 nm (Fig. 2c) to a = 400 nm (Fig. 2d)yields a spatial band shift of nearly 2 µ m.SPPs waves launched in the momentum matchedbands propagate towards each other and interfere(Fig. 2). Yet this interference pattern is observed on ahigh background due to the direct reflection of the inci-dent light. To remove the background and enhance thecontrast of the SPP interference pattern we spatially de-sign the incident amplitude profile with “on” areas ofamplitude A = 1 and an “off” background of A = 0.Each “on” area is composed of 10 x 8 superpixels andis located in the vicinity of the two symmetric angularbands. The SPP interference patterns are then observedin the central non-illuminated area which is our SPP fieldof view.Results from this designed amplitude profile are shownin Fig. 3. When the two counterpropagating SPP waveslaunched in the “on” areas interfere, a standing wave pat-tern of intensity is created. For SPPs propagating on anideally smooth and non-corrugated sample we expect theperiod of the fringe pattern to be half the SPP wavelength f [ µ m −1 ] N o r m a l i z e d I n t e n s i t y [ a . u ] grating 375 nmgrating 400 nmgrating 425 nmgrating 450 nm ac bd µ m e FIG. 3. SPP fringe formation via counter propagating waves.The image geometry and the incident amplitude profile areshown in the inset. The polarization of the incident light ishorizontal. (a-d) we observe different fringe patterns for arrayperiods of 375 nm (a), 400 nm (b), 425 nm (c) and 450 nm(d). In (e) are shown the line Fourier transforms of thesefringe patterns. G [ µ m −1 ] F r i n g e M o m e n t u m k f [ µ m − ] S k f = 2| k S + k G |k f = 2| k S − k G | Experiment
FIG. 4. SSP fringe momentum versus the grating momentum.The experimental data shows SPPs convoluted with the m = − ( λ S = 2 π/k S = 590 nm ). Instead, the measured fringeperiod is found to be sample dependent (Fig. 3a-d). Wemeasured fringe periods P of 1 ± . µ m, 0 . ± . µ m,0 . ± . µ m, 0 . ± . µ m and 0 . ± . µ m forgrating pitches of 450 nm, 425 nm, 400 nm, 375 nm and350 nm respectively. The different filling fractions of oursamples, that perturb the SPP wavelength within fewpercent, can not explain the large deviations we observe.We attribute the fringe patterns to a mixing of theoriginal SPP wave with the hole array [20]. We can an-alyze the results using a one dimensional model becausefor all our samples we observe only horizontal propaga-tion. Theoretically there are two ways to mix SPPs withthe hole array: intensity mixing (expected for incoher-ent forms of scattering such as fluorescence) and fieldconvolution (expected for coherent scattering processes).We will discuss both ways even though the experimen-tal observations confirm only the field convolution. Wefirst consider intensity convolution: a SPP standing in-tensity pattern with momentum 2 k S is formed, but sincewe observe the pattern through the scattering of a pe-riodic structure with momentum k G , the fringe momen-tum appears to be 2 k S ± k G . This intensity convolutiondoes not match the experimental observations. The sit-uation is completely different for the field convolution:the hybridization of the bare SPPs with the Bloch modesof the array results in dressed plasmonic (DP) waves ofmomentum k S + m · k G ( m integer). These DP wavesthen result in standing intensity patterns of momentum2( k S + m · k G ).A comparison between experiment and the amplitudeconvolution approach for these DP waves is shown inFig. 4. The modulus of the fringe momentum ( k f ) isplotted against the module of the grating momentum( k G ). The two lines are the theoretical predictions forSPPs convolved with the first positive ( m = 1) and thefirst negative ( m = −
1) grating orders. The experimen-tal data perfectly follow only the m = − P f ( k ) = B ( k ) X m ∈ Z η m · δ ( k − | k S + mk G | ) , (2)where every delta represents the standing pattern fromone of the m orders of the array, η m represents the cou-pling efficiency of SPPs into this m − th order and B ( k ) isthe momentum bandwidth of our detection optics. Ourbandwidth is shown as the light blue quadrate in Fig. 4and we approximate it with a step function limited bythe optical diffraction limit and the SPP field of view(the distance between the two “on” areas). Upon insert-ing this bandwidth in Eq. 2 only SPP hybridization withthe m = − ab Phase −π S u p e r p i x e l s Phase −π S u p e r p i x e l s Phase −π S u p e r p i x e l s Phase −π S u p e r p i x e l s FIG. 5. Scanning the fringes by phase tuning. (a) Thephase of the left “on” area is kept constant while the phaseof the right “on” area has a step jump between the lowerand upper part as shown in the wings of the figure. Theresulting fringe pattern in the upper part is shifted comparedto the lower one. (b) The fringes are rotated due to a linearlyincrementing phase on the right “on” area.
We can scan the fringe pattern across the sample byvarying the phase delay between the two “on” areas andthus introducing an optical retardation that will trans-late the DP fringes. We experimentally prove this phasescanning principle for the m = − π phase delay. In alternative, by applying alinear phase difference between the two “on” areas, the standing pattern will result in tilted plasmonic fringes(angular scan) as shown in Fig. 5b.The predicted presence of the m = 1 DP mode, whichrepresents a sub 100 nm period intensity beating on topof the observed fringe pattern, combined with the ourability to scan the pattern across the sample, suggest in-teresting prospects for subwavelength imaging. Due tothe diffraction limit we can not resolve this fast beat-ing in the current setup. However it should be possible,using near field imaging, to calibrate this sub 100 nm in-tensity pattern for different fringe patterns (line and an-gular scans). Once calibrated, the sample surface couldbe used to image sub 100 nm objects with only far fieldprobing and image correlations.We have shown here the observation of Bloch-modedressed surface plasmon polaritons (DP) propagating onnanohole arrays of different subwavelength periodicities.We recorded the standing intensity pattern of two coun-terpropagating DP waves. The dependence of the mea-sured fringe period on the period of the nano structureis perfectly described by a simple model of plasmonicBloch mode interference. By actively imposing well pro-grammed phase relations to these plasmonic Bloch modeswe achieved full control of their interference fringe pat-terns. Bloch dressed SPPs are 2D propagating waves thatcan achieve high momentum and thus actively control-ling their interference patterns has potential for super-resolution biosensing and imaging applications. ACKNOWLEDGMENTS
We thank Hans Zeijlermaker and Dimitry Lamers forsample fabrication. This work is part of the research pro-gram of the “Stichting voor Fundamenteel Onderzoek derMaterie”, which is Financially supported by the “Neder-landse Organisatie voor Wetenschappelijk Onderzoek”. ∗ [email protected]; Current address:Technion Is-rael Institute of Technology[1] W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature , 824 (2003).[2] E. Ozbay, Science , 189 (2006).[3] A. Polman, Science , 868 (2008).[4] J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S.White, and M. L. Brongersma, Nat. Mater. , 193(2010).[5] P. J. Schuck, D. P. Fromm, A. Sundara-murthy, G. S. Kino, and W. E. Moerner,Phys. Rev. Lett. , 017402 (2005).[6] P. M¨uhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht,and D. W. Pohl, Science , 1607 (2005).[7] L. Novotny and N. van Hulst, Nat. Photon. , 83 (2011). [8] T. Sndergaard, S. I. Bozhevolnyi, J. Beermann, S. M.Novikov, E. Devaux, and T. W. Ebbesen, Nano Lett. , 291 (2010).[9] M. I. Stockman, Phys. Rev. Lett. , 137404 (2004).[10] J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider,M. Salerno, A. Leitner, and F. R. Aussenegg,EPL (Europhys. Lett.) , 663 (2002).[11] E. Verhagen, M. Spasenovi´c, A. Polman, and L. K.Kuipers, Phys. Rev. Lett. , 203904 (2009).[12] A. Sentenac and P. C. Chaumet, Phys. Rev. Lett. ,013901 (2008).[13] G. Bartal, G. Lerosey, and X. Zhang, Phys. Rev. B ,201103 (2009).[14] T. S. Kao, S. D. Jenkins, J. Ruostekoski, and N. I. Zhe-ludev, Phys. Rev. Lett. , 085501 (2011). [15] S. G. Rodrigo, O. Mahboub, A. Degiron, C. Genet, F. J.Garc´ıa-Vidal, L. Mart´ın-Moreno, and T. W. Ebbesen,Opt. Express , 23691 (2010).[16] F. Wei and Z. Liu, Nano Lett. , 2531 (2010).[17] B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk,L. Kuipers., and A. Lagendijk, Nat. Photon. , 360(2011).[18] E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, Appl.Opt. , 2076 (2008).[19] P. B. Johnson and R. W. Christy, Phys. Rev. B , 4370(1972).[20] D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon,Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park,and C. Lienau, Phys. Rev. Lett.91