Coherent control of the optical absorption in a plasmonic lattice coupled to a luminescent layer GiuseppePirruccio,1,∗ MohammadRamezani,1 SaidRahimzadeh-KalalehRodriguez,1,† andJaimeGómezRivas1,2,‡ 1Center for Nanophotonics, FOM Institute AMOLF, c/o Philips Research Laboratories, High Tech Campus 4, 5656 AE Eindhoven, The Netherlands 2COBRA Research Institute, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands (Dated: January 19, 2016) We experimentally demonstrate the coherent control, i.e., phase-dependent enhancement and suppression, of the optical absorption in an array of metallic nanoantennas covered by a thin lu- minescent layer. The coherent control is achieved by using two collinear, counter-propagating and 6 phase-controlledincidentwaveswithwavelengthmatchingtheabsorptionspectrumofdyemolecules 1 coupled to the array. Symmetry arguments shed light on the relation between the relative phase 0 of the incident waves and the excitation efficiency of the optical resonances of the system. This 2 coherentcontrolisassociatedwithaphase-dependentdistributionoftheelectromagneticnear-fields n in the structure which enables a significant reduction of the unwanted dissipation in the metallic a structures. J 8 Methodsforcontrollingopticalabsorptionandsponta- semble of randomly dispersed dye molecules in a poly- 1 neousemissionareattheheartofdiversefieldsofphysics. mer matrix to a periodic array of metallic nanostruc- ] In general, these methods can be classified in two types. tures. Coherent control in plasmonic systems has been s c One type of control thrives on the interplay between the used in pioneering works of nanoscopy [15, 16], and to i excitation field and the energy levels of the emitter. Co- achieve femtosecond and nanoscale control over electro- t p herenceandquantuminterferencearetheessentialingre- magnetic hotspots [17–19]. Our array displays localized o dientsofspontaneousemissioncontrolmethodsemployed and collective electromagnetic modes weakly coupled to . s in atomic physics [1–5] and, recently, in solid-state sys- the molecules at the emission and absorption frequen- c temssuchasquantumdotsusingpolychromaticincident cies, respectively. Previous works have shown that the i s fields [6]. A second type of control is based on Purcell’s emission spectrum from similar systems can be designed y remark: spontaneous emission is not an inherent prop- by resonant processes at the emission frequencies [20– h p erty of the emitter, but it also depends on the environ- 23], while the intensity can be enhanced by processes [ ment [7]. Within this paradigm structures are designed at the absorption frequencies under single-wave illumi- to modify the electromagnetic field intensity at the po- nation [24]. Here, we combine these approaches by driv- 1 v sition of the emitter, thereby affecting its spontaneous ing the coupled array-emitter system with two coherent, 1 emission [8, 9]. This second approach is attractive in the collinear and counter-propagating laser waves whose rel- 1 context of non-resonant molecular fluorescence. There, ative phase is controlled. The dependence of the reso- 6 the excitation and emission frequency are different, and nances of the array on the relative phase of the driv- 4 thecoherenceoftheexcitationislostviarovibrationalre- ing fields allows us to demonstrate resonantly enhanced 0 . laxationwithintheexcitedstatemanifold. Consequently, phase-dependent absorption and emission intensity in a 1 relaxation to the ground state via spontaneous emission coupled resonator-emitter system. The phase-sensitive 0 canbemodifiedbyresonantstructuressuchasopticalan- electromagneticfieldenhancementsatthepositionofthe 6 1 tennas [10, 11], or non-resonant periodic structures such emitters and of the metallic nanostructures are analyzed : as photonic crystals [12–14]. A major difference between throughfull-wavesimulations. Ourcentralfindingisthat v the first and second type of absorption and spontaneous the ratio of the absorption by the molecules to the ab- i X emission control concerns the role of the phase of the sorption by the metallic structures exhibits a maximum r driving field. For atoms under resonant excitation, the ataparticularrelativephaseofthedrivingfields. Ourre- a phase of the driving field represents an important degree sultselucidate anewwaytomitigatelosses inplasmonic of freedom for controlling spontaneous emission [2]. In systems with respect to the usual approach employing contrast, non-resonant molecular fluorescence enhance- gain media [25–29]. ments based on designed electromagnetic environments We have investigated the optical response of a 3×3 are widely regarded as phase-insensitive. mm2 squarearrayofaluminumnanopyramidsfabricated In this manuscript we demonstrate the coherent con- onto a silica substrate using substrate conformal imprint trol,i.e.,phase-dependentenhancementandsuppression, lithography [30]. The lattice constant is 340 nm, the of the absorption and, consequently, of the non-resonant pyramids have a height of 150 nm, are 100 nm wide at photoluminescence (PL) emission intensity from an en- the base and 80 nm wide at the top. We spin-coated semble of molecules. To achieve this, we couple an en- on top of the array a 200 nm-thick layer of polystyrene 2 dopedat1%weightconcentrationwithF305Lumogen(cid:13)c Theemissionwasmeasuredat14degreesfromthenor- dye. Thelayerhasaninternalquantumefficiencyof90%. mal to the sample. At this angle the emission intensity The absorption spectrum, exhibiting a maximum at 574 is maximum due to the coupling of this emission to the nm, is shown in the Supplemental Information (SI) [31]. (-1,0) SLR of the array. The measurements of the emis- The inset of Fig. 1(a) shows scanning electron micro- sionspectraatdifferentanglesareshowninFig. S4(a)of graphs of the array prior to the deposition of the dye the SI [31]. The emitted spectrum and intensity by the layer. Figure 1(a) shows with black line the normal inci- dye layer depend on processes taking place at emission dence extinction spectrum given by 1−T , with T the andabsorptionwavelengths. Herewefocusonthelatter. 0 0 zeroth order transmittance. The grey line indicates sim- In Fig. 1(b) we plot the peak PL intensity as a function ulationsresults,verticallyshiftedforclarity,forthesame of the phase difference between the incident waves with structureobtainedwiththeFiniteDifferenceinTimeDo- connected open circles. Since molecular fluorescence is main method. We use periodic boundary conditions and an incoherent process and we are acting only at the ab- values of the Al permittivity from Ref. [32]. The refrac- sorptionwavelength,nochangeinthespectralshapewas tiveindexoftheglasssubstrateisconstantatn =1.46, observedasafunctionof∆φ. Duetotheinterferencena- s whilethecomplexrefractiveindexofthedye-dopedpoly- ture of this phenomenon we expect the PL intensity to merlayerwasobtainedfromellipsometrymeasurements. follow a cosine square function. In Fig. 1(b) the grey The two peaks observed in experiments and simulations continuous line is a guide to the eye representing a co- at wavelengths around 560 nm and 497 nm correspond sinesquarefunctionwithperiodslightlysmallerthan2π. to photonic-plasmonic resonances in the particle array. The deviation from 2π is likely due to a small misalign- The peak at λ = 560 nm is associated to localized sur- mentintheinterferometerthatmayresultinadifference face plasmon resonances (LSPRs) in individual metallic between nominal read-outs of the piezo actuator and the nanostructures and we call this wavelength λ . The real path difference introduced. The connected open tri- LSPR peak at λ = 497 nm corresponds to collective resonances angles in Fig. 1(b) correspond to the PL resulting from termedassurfacelatticeresonances(SLRs)[33]andthis theincoherentsumofthetwoincidentwavesilluminating wavelength is called λ . The origin of the SLRs is thesampleeitherfromtheair-sideorfromthesubstrate- SLR the radiative coupling between LSPRs and the degener- side. ate (±1, 0), (0, ±1) Rayleigh Anomalies (RAs), i.e., the The PL is strongly modulated by the absorption ef- diffractedordersradiatinggrazingtotheplaneofthear- ficiency of the dye at different pump phases. This, in ray [34–43]. These RAs are marked with dashed line in turn,isduetotheelectricfielddistributioninthesystem, Fig. 1(a). The spatially-resolved near-field at these two which is related to the excitation efficiency of the SLR. resonances is shown in Fig. S3 in the SI [31]. Whilethesinglewavetime-integrateddissipatedpoweris For the coherent control measurements we used a phase-insensitive,thepresenceoftwowavesdramatically Mach-Zenderinterferometercomprisingtwocollinearand changes this situation. This phenomenon is explained in counter-propagating continuous waves (a control and a detail in what follows. signal) from an Ar-Kr laser emitting at the wavelength WehaveperformedFDTDsimulationstoillustratethe λ , illuminating the sample at normal incidence (see interference mechanism that determines the absorption SLR SIfortheschemeoftheset-up[31]). Weensuredthatthe in the structure and gives rise to the measured PL mod- twoincidentwaveshaveequalintensity. Thecontrolwave ulation. Two separate simulations have been done with propagating from the air-side is phase-delayed with re- a single plane wave impinging either from the air-side or spect to the signal wave propagating from the substrate- fromthesubstrate-side. Theabsorptionofthedye-doped side. The phase difference between the two waves is con- polymer layer was included via the complex refractive trolledbychangingtheopticalpathlengthofthecontrol index n = 1.59+i0.003 at λ . The complex electro- l SLR wave with a computer-controlled piezo mirror. A similar magnetic field components were calculated as a function approach was used to demonstrate time-reversed lasing of the relative phase between the two waves, ∆φ, using in thick slabs [44, 45] and coherent absorption in thin the superposition principle for the fields. In absence of layers [46–49]. However, the applicability of these tech- the nanopyramids, the two counter-propagating incident niques to the realm of coherent absorption in plasmonic waves form a quasi-standing wave for the wavelengths systems and spontaneous emission control has hitherto λ and λ , i.e., the shift in the position of its LSPR SLR remained unexplored. The extension is far from triv- node and antinode along z is negligible compared to the ial because the far-field spectrum of metallic nanostruc- height of the nanopyramid [33]. We define ∆φ = 0 when turescandifferfromtheirnear-field[50–55],andemitters this quasi-standing wave has a node approximately at a are sensitive to the latter [56, 57]. Moreover, in our ex- heightthatcorrespondstothemid-heightofthenanopy- periments the emitters and the resonators are spatially ramids. Correspondingly, for ∆φ = π the total field has separated, and the presence of strong field gradients can an antinode at this height. modifytheabsorptionintheemitterswithrespecttothe The absorptance of the system as a function of in- absorption in the metal. cident wavelength, λ, and phase difference between 3 the two incident waves, ∆φ, is given by A(λ,∆φ) = dipolarandsymmetricforλ . Therefore, theSLRis LSPR πcλ(cid:15)0 (cid:82)V (cid:15)(λ)(cid:48)(cid:48)|Etot(λ,∆φ)|2dV, with (cid:15)0 the vacuum per- efficiently excited only when the total driving field is an- mittivity, c the speed of light, (cid:15)(cid:48)(cid:48) the imaginary com- tisymmetricanditissuppressedwhenthedrivingfieldis ponent of the permittivity of the dye layer or of the symmetric. The opposite occurs for the LSPR. We con- metallic nanopyramids and V the integration volume. clude that by controlling the symmetry of the field dis- |E (λ,∆φ)|2 = |E (λ,φ )+E (λ,φ )|2 is the intensity tributionviatherelativephasesofthedrivingfields,itis tot 1 1 2 2 of the total electric field normalized by the incident field possible to control the efficiency of the excitation of the and|E (λ,φ )|2 aretheintensitiesofthetwoincident two resonances. The growing interest towards coherent 1,2 1,2 waves. TheinsetinFig.2(a)showstheabsorptanceinte- controlofresonancesinnanoparticlesisdemonstratedby gratedoverthevolumeofthenanopyramids(greycurve) arecentwork[58]. Consequently,theabsorptanceshown andofthedyelayer(blackcurve)undersingleplanewave in Fig. 2 depends pronouncedly on the symmetry match illumination impinging from the air-side. This phase- between driving field and optical resonances. The origin independent absorptance, calculated with E (λ,φ )=0, of this effect is on the height of the nanopyramids and 2 2 is resonantly enhanced in the metal and in the dye layer the retardation of the scattered field with respect to the atthewavelengthscorrespondingtotheSLRandLSPR. incident field (see SI [31]). The field extends throughout In Figs. 2(a) and (b) the absorptance in the dye layer theunitcellwhenbothresonancesareefficientlyexcited, andinthenanopyramidsisrepresentedfor∆φ=0andπ, but it is more confined to the nanopyramid at the LSPR respectively. For∆φ=0weobservethattheabsorptance wavelength. Forbothresonances,theregionsofhighand attheSLRwavelength,i.e.,at497nm,isenhancedboth lowelectricfieldintensityinterchangewhenpassingfrom in the metal and in the dye while the absorptance at the ∆φ = 0 to ∆φ=π. LSPR wavelength, i.e., at 560, nm is reduced. The op- The change in the spatial distribution of the near field posite behavior is observed for ∆φ = π, where the SLR intensity in Fig. 3 implies a change in the relative ab- absorption is fully suppressed, while that of the LSPR sorption between nanopyramids and dye layer. To as- is significantly enhanced. These results are in agreement sess this phase-dependent change we calculate the ab- withthephase-modulatedemissionpreviouslypresented, sorptance in the volume occupied by the emitters, i.e. wheretheemissioncorrelateswiththemodulatedabsorp- the dye layer, A , and the absorptance in the metallic dye tioninthedyelayeratthewavelengthofthepumplaser, nanopyramids, A . In Fig. 4(a) we plot A (open metal dye i.e., λ = 497 nm. squares and continuous black curve) and A (open metal Next we elucidate the coherent control over the exci- triangles and continuous grey curve) as a function of ∆φ tation efficiency of the two resonances by analyzing the fortheSLRwavelength. Thedashedblackandgreylines near-fields. In Figs. 3(a-d) we plot in color the electric correspond to the absorption in the dye layer and in the field enhancement at the plane defined by the incident metallic array, respectively, for single wave illumination. polarization and wave vector. The arrows represent the Figure 4(a) shows that A and A are both a co- dye metal real part of the x−z electric field components. The in- sine square function of ∆φ. The theoretical modulation cident wavelength is λSLR in Figs. 3(a,b), and λLSPR of the absorption qualitatively agrees with the experi- in Figs. 3(c,d). Figures 3(a,c) correspond to ∆φ = 0, mental modulation of the emission in Fig. 1(b), but the while Figs. 3(b,d) correspond to ∆φ=π (the color scale latter is roughly three times lower. This is likely due to changes from figure to figure). The fields in Figs. 3(a,d), the fact that the experimental pump wavelength coin- calculated for ∆φ = 0 and ∆φ = π, respectively, qual- cides with the maximum in extinction at the SLR, but itatively resemble those for the single wave illumination the maximum in absorption is slightly shifted by 2 nm (see Fig. S2 in SI [31]). withrespecttotheextinction. Asmallsurfaceroughness By comparing Figs. 3(a,b) with Figs. 3(c,d) we notice of the dye layer (≈±20 nm) could also modify the light thatthereisanoppositeresponseofthesystemto∆φat in-coupling and out-coupling [59]. λ and λ . To explain this different response we SLR LSPR In Fig. 4(b) we plot the absorption ratio Adye = comparethesymmetryofthefielddistributionwhenthe Atot tworesonancesareexcitedwiththesymmetryofthedriv- Adye as function of ∆φ. The dashed line refers Ametal+Adye ingfieldinabsenceofthearray. Tofacilitatethiscompar- to the single wave illumination. The maximum absorp- ison,therealpartofthex-componentofthisdrivingfield tion ratio that can be theoretically achieved in the in- is plotted next to each color plot in Fig. 3 with a contin- vestigatedsamplereachesavalueashighas90%,signifi- uous black curve. For both wavelengths the driving field cantlyimprovingthe68%ofasinglewave. Theimproved is antisymmetric for ∆φ = 0 and symmetric for ∆φ=π, FoM is the consequence of the reduced pump enhance- bothwithrespecttothexy planecrossingthenanopyra- ment by the nanostructures, which also leads to a net midapproximatelyatitsmid-height. 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[58] Tanya Das, Prasad P. Iyer, Jon A. Schuller, arXiv:1509.01281. [59] G. Pirruccio, and J. Gomez Rivas, Opt. Express 23, 18166-18180 (2015). [60] K. Guo, G. Lozano, M. A. Verschuuren, and J. Gomez 6 ction 10..28 (a) )s/stn180000000 (b) (-1,0) ptance00..46 (a) Absorptance000...246 ptance00..46 (b) Extin 0.4 c( LP 6000 bsor0.2 0450Wavel5e5n0gth (nm)650 bsor0.2 A A 0 4000 0 0 450 550 650 750 0 1 2 3 450 550 650 450 550 650 Wavelength (nm) ( ) Wavelength (nm) Wavelength (nm) FIG. 1. (a) Measured (black) and simulated (grey) normal FIG.2. Calculatedabsorptanceinthedyelayer(blackcurve) incidenceextinctionofthearrayofaluminumnanopyramids. and in the metal nanopyramids (grey curve) as a function of For clarity, the simulation is vertically displaced by 0.5. The the incident wavelength for a phase difference between the dashed line corresponds to the degenerate (±1, 0), (0, ±1) two driving fields of (a) ∆φ = 0, (b) π. Inset: calculated RAs. Inset: SEM image of the array. The scales of the inset absorptance for single wave illumination. are 2µm (large image) and 300 nm (zoom). (b) Connected open circles: measured modulation of the maximum of the PL as a function of the phase difference between the two in- cident waves. Connected open triangles: PL of the dye layer resulting from the incoherent sum of the two incident waves. Grey continuous line: guide to the eye representing a cosine square function. 7 = 0, = 497 nm = , = 497 nm SLR SLR 50 10 200 200 (a) 200 200 (b) z (nm) 10 00 1 0 00 2|E| z (nm) 1 0 00 1 000 2|E| 0 0 -2 0 2 -170 0 170 -2 0 2 -170 0 170 Re(Ex) x (nm) Re(Ex) x (nm) = 0, = 560 nm = , = 560 nm LSPR 40 LSPR 40 200 200 (c) 200 200 (d) z (nm) 1 0 00 1 0 00 2|E| z (nm) 1 0 00 1 0 00 2|E| 0 0 -2 0 2 -170 0 170 -2 0 2 -170 0 170 Re(Ex) x (nm) Re(Ex) x (nm) FIG. 3. Color plots: spatial distribution of the normalized intensity of the total electric when the system is illuminated atnormalincidencewithtwocoherent,collinearandcounter- propagating waves. The field is plotted in the plane y = 0 crossing the nanopyramid along its center. Arrows: real part of the y-z component of the total electric field. (a,b) arecalculatedforλ while(c,d)arecalculatedforλ . SLR LSPR (a,c) are obtained for ∆φ = 0, while (b,d) are obtained for ∆φ=π. Next to each plot we show the calculated real part of the amplitude of the total incident electric field in the dye layerwithoutthearray. Thehorizontalredlinesindicatethe thicknessofthedyelayer,andthegreendashedlinerepresents theheightpositionofthetopofthenanopyramid. Thedashed blue line indicates Re(E )=0. x 1 0.2 n (a) (b) o pti 0.4 nt absor 0.2 AdyeAtot 0.8 0.1 P /Poutin e er h Co 0 0.6 0 0 1 2 0 1 2 ( ) ( ) FIG. 4. (a) Modulation of the absorptance in the dye layer (open squares and black curve) and in the metallic array (opentrianglesandgreycurve)forλ asafunctionof∆φ. SLR Dashed lines: incoherent absorption in the dye layer (black line) and in the metallic array (grey line) (b) Open circles and black curve: ratio of the absorption in the luminescent layer by the total absorption, as a function of ∆φ. Dashed horizontal line: condition of single wave illumination. Open diamonds and grey curve: P /P as a function of ∆φ. out in