Efficient directional beaming from small apertures using surface-plasmon diffraction gratings

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1 Efficient directional beaming from small apertures using surface-plasmon diffraction gratings Youngkyu Lee, Kazunori Hoshino, Andrea Alù, and Xiaojing Zhang Citation: Applied Physics Letters 101, (2012); doi: / View online: View Table of Contents: Published by the AIP Publishing Articles you may be interested in Schottky-type surface plasmon detector with nano-slit grating using enhanced resonant optical transmission J. Appl. Phys. 116, (2014); / Effect of plasmonic losses on light emission enhancement in quantum-wells coupled to metallic gratings J. Appl. Phys. 114, (2013); / Spontaneous emission and collection efficiency enhancement of single emitters in diamond via plasmonic cavities and gratings Appl. Phys. Lett. 103, (2013); / Excitations of surface plasmon polaritons in double layer metal grating structures Appl. Phys. Lett. 100, (2012); / Surface-plasmon-induced enhancement of magneto-optical Kerr effect in all-nickel subwavelength nanogratings Appl. Phys. Lett. 97, (2010); /

2 APPLIED PHYSICS LETTERS 101, (2012) Efficient directional beaming from small apertures using surface-plasmon diffraction gratings Youngkyu Lee, 1 Kazunori Hoshino, 2 Andrea Alù, 1 and Xiaojing Zhang 2 1 Electrical and Computer Engineering, The University of Texas at Austin, Texas 78712, USA 2 Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA (Received 23 April 2012; accepted 9 July 2012; published online 23 July 2012) We demonstrate efficient optical directional beaming using an array of sub-wavelength patterns on a metallic surface. Specifically, a sub-wavelength sized slit placed next to a periodic grating is designed and optimized to realize maximum coupling efficiency and directional radiation into a leaky-wave plasmonic mode. Collective scattering from the corrugations forming the grating is synthesized to radiate towards the desired direction, and efficient beaming is achieved through tailoring the design parameters with a simple analytical model. We also prove that directivity can be further enhanced by improving the slit-grating coupling efficiency through efficient plasmon generation, showing improved angular response in far-field radiation. VC 2012 American Institute of Physics. [ Since the discovery of extraordinary optical transmission, 1 interest in tailoring the radiation from small apertures with surface-plasmon polaritons (SPPs) has considerably grown of special interest to nanophotonic applications and compact optical devices. Within this recent progress, the possibility of beaming the radiation from a small aperture using plasmons 2 has been reported as a potential way to realize directive optical radiation from sub-wavelength-sized sources. By tailoring the collective scattering from small grooves, diffracted light can be out-coupled in the desired direction. Springing from the demonstration of this beaming effect, various efforts have been made to realize and optimize directional beaming 3 5 to pursue efficient optical energy transfer to free-space. Obviously, the realization of efficient light emission with high directionality is essential for several nanophotonic applications; however, directive optical radiation from aperture-based emitters is in general lowered because of inherent diffraction from small apertures, 6 which out-scatter light in a broad angular range. In this letter, we introduce and experimentally verify a method to realize efficient directional beaming from a slitbased light emitter coupled with surface-plasmon diffraction gratings. Our goal is to efficiently couple incident energy into surface-plasmon modes and to tailor their propagation into directional leaky mode, while suppressing unwanted slit-related diffraction. We discuss how to design a slitgrating emitter with a special emphasis on efficient light coupling between a slit and grating corrugations, through a simple analytical model derived from scattering wave equations. Efficient SPP generation is then explored both theoretically and experimentally to enhance the radiation directivity. The proposed configuration consists of a subwavelength slit with an array of periodic bumps on its left side, realized over a thick silver film (see Fig. 1). The slit is used to couple transverse magnetic (TM) light incident from a transparent substrate on the back of the screen (with illumination angle /) into SPPs launched at the metal/dielectric boundary. In this configuration, overall directional emission may be achieved with proper tailoring of the corrugation periodicity by perturbing the original SPP into a directional leaky mode. The scattered wave from each individual corrugation is produced by the electromagnetic interaction of the SPPs supported by the metal interface and the obstacle, related through Helmholtz equation. 7 The scattered wave E S i from each corrugation K i can be written as a relation between the perturbed E P i and unperturbed fields E U i on the surface E S i ðx; zþ ¼EP i ðx; zþ EU i ðx; zþ ¼ A i ððk o 2 ½e P ðx 0 ; z 0 Þ e U ðz 0 ÞŠ Gðx x 0 ; z; z 0 ÞE P i ðx0 ; z 0 ÞdK 0 i; (1) where G is the Green s dyadic, and perturbed or unperturbed dielectric constants on the volume of the corrugation K i are e P, e U. In the far-field and considering a perturbation method valid for small corrugations, Eq. (1) can be simplified within an expðjxtþ time convention E S i ðð k o 2 ½e P ðx 0 ; z 0 Þ e U ðz 0 ÞŠE U i ðx0 ; z 0 ÞdK 0 i expð jk o q þ jw 0 jk SP d SE i Þ; (2) where q ¼ðx 2 þ z 2 Þ 1=2 ; k SP ¼ 2p½e M e D =ðe M þ e D ÞŠ 1=2 =k; and w 0 is the phase of scattering at the left slit edge K 0.Oneinteresting finding in Eq. (2) is that the far-field scattering from the rising edge of the corrugation is out of phase with the one of the falling edge, if their distance from the SPP coupler is identical. It follows that a phase matching condition to form a collimated directional beam can be obtained as k SP d SE ( i ¼ dse d SE i k o sinh þ m i 2p; i k o sinh þ m i 2p p; i ¼ odd number i ¼ even number ; where m i is the diffraction order at the ith edge. From Eq. (3), we can deduce key design parameters such as d1 SE (3) /2012/101(4)/041102/4/$ , VC 2012 American Institute of Physics

3 Lee et al. Appl. Phys. Lett. 101, (2012) FIG. 1. Sub-wavelength slit with a single-sided array of periodic corrugations. The geometrical parameters are the grating pitch period p, thickness of metallic ðe M Þ film t F, grating thickness t G, grating width w G, slit width w S, and the distance di SE between K 0 and K i : h and / are the radiation and illumination angles, respectively. and the optimal ratio w G =p to radiate in the desired direction, parameters that were otherwise obtained only with iterative numerical simulations. 4,8 This method can provide an initial approach for the optimal design parameters of the setup, which may be then optimized using full-wave numerical simulations. In order to apply these concepts in a practical scenario, a campaign of simulations and experimental investigations has been carried out. For numerical simulations, time-domain finite integration technique (FIT) of commercially available software, CST MICROWAVE STUDIO TM, was employed to characterize the proposed configuration by varying several design parameters, starting from the design provided by Eq. (3). After proper optimization, we have realized few optimal designs and experimentally measured the far-field radiation pattern in a setup consistent with the schematic model in Fig. 2. For sample preparation, 250 nm thick Ag (e M ¼ 19 þ j0:53 at 630 nm, reported in Ref. 9) film was evaporated on a BK7 (e S ¼ 2:292 at 630 nm) microscope slide and 60 nm thick Ag corrugations were patterned on the film by electron beam lithography, film deposition, and lift-off techniques. Finally, a sub-wavelength slit perforated in the Ag film was defined by focused ion beam (FIB) milling process. The fabricated slit-grating structure has a pitch period p ¼ 414 nm and a ratio w G =p ¼ 0:5 to realize maximum directional radiation at h ¼ 25 for the operating wavelength k ¼ 630 nm (FWHM of 10 nm for the supported leakymode). For the verification of Eq. (3), interference patterns were measured in far-field and compared with simulations. For a given fixed grating configuration (fixed pitch period p ¼ 414 nm and duty ratio w G =p ¼ 0:5) but with different coupling distance d1 SE; the expected radiation pattern is subject to a constructive or destructive interference following a periodic behavior with periodicity p, as a function of the coupling with the grating eigenmodes. To experimentally observe this effect, we realized a 200 nm width slit supporting only the fundamental waveguide mode, placed at controlled coupling distance from the grating structure (see insets in Fig. 3(b)). Fig. 3(a) shows the simulated intensity of directional radiation at h ¼ 25 varying d1 SE ; and Fig. 3(b) presents the measured far-field radiation patterns for different d1 SE: For the given grating geometry, as estimated by Eq. (3), the intensity of directional beaming at a specific angle of interest is primarily governed by d1 SE ; showing a periodic behavior with periodicity p, due to constructive or destructive interference at about h ¼ 25 : With such simple analytical tool, optical leaky radiation from a slit-grating structure as in Fig. 1 may be modeled as the constructive interference of plasmonic grating diffraction and conventional slit diffraction, which would emit over a broad angular spectrum. In this respect, the key challenge to efficient directional beaming becomes the suppression of the slit diffraction and the maximum coupling of transmitted light through slit into a directive leaky mode supported by the plasmonic grating. Such challenges may be achieved through the combinational use of our slit-grating design approach and FIG. 2. Schematics of the optical setup, allowing for controlling both illumination and measurement angle. APD: avalanche photodiode; BS: beam splitter; CCD: charge-coupled device; Obj. Lens: objective lens; LPZ: linear polarizer; BPF: band-pass filter; LED: light emitting diode. FIG. 3. Radiation interference of slit-grating structure: (a) simulated radiation intensity at h ¼ 25 as a function of d1 SE and (b) measured far-field radiation pattern for various values of d1 SE : Each inset in (b) shows a scanning electron micrograph (SEM) image of structure corresponding to each d1 SE value (scale bar: 1 lm).

4 Lee et al. Appl. Phys. Lett. 101, (2012) slit-based efficient SPP generation. 10,11 Without changing the setup configuration, SPPs can be efficiently launched in a unidirectional manner by controlling the angle of tilted backside illumination and by employing the engineered width of the slit supporting its multimodal operation. Through slit-based efficient SPP generation, we achieve optimal conversion of the optical energy coupled through the slit into plasmonic modes and enhanced directional radiation. In addition, this approach allows suppressing conventional slit diffraction, increasing the overall directivity. Since the slit width and illumination angle are optimized to excite the plasmon mode at the slit exit aperture, we do not necessarily couple so easily with other radiation modes, producing an additional effective way of suppressing the conventional slit diffraction and direct the coupled energy primarily towards the grating leaky mode. Following this initial design, we explore the possibility of realizing more efficient SPP generation to achieve enhanced directional beaming. A geometry with d1 SE ¼ 0nm and w S ¼ 300 nm was simulated and realized (see insets in Fig. 5), with the idea of exciting higher-order guided modes inside the slit under oblique illumination. 10 The slit width of 300 nm was chosen to realize non-fundamental but monomodal propagation with tilted illumination through the slab waveguide (i.e., perforated slit) j½w S ð b 2 þ k 0 2 Þ 1=2 mpš ¼2 tanh 1h jðb 2 e M k 0 2 Þ 1=2. e M ð b 2 þ k 0 2 Þ 1=2i ; (4) where m is the order of modal slit propagation. The larger width supports two distinct modes that, with proper interference, can couple the energy in specific SPP directions for specific illumination angles. To evaluate the effectiveness of efficient SPP generation to produce directional beaming, numerical simulations have been carried out for the present geometry, analyzing the modal density profile with Fourier modal spectral analysis. 12 Fig. 4 shows the calculated magnetic energy modal density jh y ðk x ; zþj 2 ¼j Ð H y ðx; zþe jk xx dxj 2 profile above the structure for different angles of illumination, chosen following 10,11 to couple the energy in different directions of SPP propagation: SPP generation towards the side without grating (Fig. 4(a)), towards both sides (Fig. 4(b)), and towards the side with corrugations (Fig. 4(c)) were obtained for different optimal values of /: Each inset shows the total angular power spectrum within the region of simulation. For the case in which SPPs are efficiently generated on the grating side, more optical energy is concentrated around k DIR ; corresponding to radiation at h ¼ 25 ; in comparison to Figs. 4(a) and 4(b), the case in Fig. 4(c) shows increased energy coupling efficiency into leaky radiation within radiation angles between 20 and 30 by 160% and 65%, respectively. Evidence of enhanced directional beaming can be further obtained by observing the full-width-at-half-maximum (FWHM) angle of radiation. Since more energy is confined in the spectral range of directional radiation k DIR ; one can expect sharper angular response in the far-field radiation pattern. Experimental measurements of such enhanced directional radiation are shown in Fig. 5(c) (corresponding to the simulation in Fig. 4(c)), to be compared with Figs. 5(a) and 5(b) (corresponding to simulations in Figs. 4(a) and 4(b), respectively). In Fig. 5(c), as expected, the measured directional beaming is enhanced via efficient SPP generation on the grating side, so that the obtained FWHM is drastically reduced in comparison to the case in which SPPs are launched on both sides. In contrast, no significant directional beaming is obtained if the SPPs are generated on the side without grating (see Fig. 5(a)), as expected. In conclusion, we have discussed analytical models, numerical simulations, and experimental results to control the plasmonic diffraction from a sub-wavelength slit coupled to an array of periodic corrugations. Key design parameters for the realization of efficient directional beaming have been highlighted and optimized. Further enhancement of directionality was also achieved through efficient SPP generation and coupling to the grating, by selecting the slit design and the illumination angle. Our far-field measurements agree well with the presented analytical and numerical results. FIG. 4. Calculated magnetic energy modal density jh y ðk x ; zþj 2 above the slitgrating structure and total power spectrum (each inset) for enhanced SPP generation toward the (a) non-grating side ð/ ¼ 32:6 Þ; (b) both side ð/ ¼ 0 Þ; and (c) grating side ð/ ¼ 32:6 Þ; The optimal impinging angle / for efficient SPP generation has been calculated as shown in Refs. 10 and 11. FIG. 5. Measured radiation patterns of the proposed structure with d1 SE ¼ 0 nm and w S ¼ 300 nm for the case of SPP generation toward (a) nongrating side, (b) both sides, and (c) grating side. Note that measured results, (a), (b), and (c), correspond to the simulations in Figs. 4(a) 4(c), respectively. Each inset shows a SEM image of structure with a direction indicator of launched SPPs (scale bar: 1 lm).

5 Lee et al. Appl. Phys. Lett. 101, (2012) This research was performed in the Department of Biomedical Engineering, Microelectronics Research Center (MRC), and Center for Nano and Molecular Science (CNM) at the University of Texas at Austin. We gratefully acknowledge the financial support from NSF CAREER Award Grants (No , PI: Alù, No , PI: Zhang) and the DARPA Young Faculty Award (N , PI: Zhang). 1 T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, (1998). 2 H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, (2002). 3 S. Kim, H. Kim, Y. Lim, and B. Lee, Appl. Phys. Lett. 90, (2007). 4 H. Kim, J. Park, and B. Lee, Opt. Lett. 34, 2569 (2009). 5 F. Hao, R. Wang, and J. Wang, J. Opt. 13, (2011). 6 S. Kim, Y. Lim, H. Kim, J. Park, and B. Lee, Appl. Phys. Lett. 92, (2008). 7 F. Princemin, A. A. Maradudin, A. D. Boardman, and J.-J. Greffet, Phys. Rev. B 50, (1994). 8 P. Chen, Q. Gan, F. J. Bartoli, and L. Zhu, IEEE Photon. J. 2, 8 (2010). 9 E. D. Palik and G. Ghosh, Handbook of optical constants of solids (Academic, Orlando, FL, 1985). 10 H. Kim and B. Lee, Plasmonics 4, 153 (2009). 11 Y. Lee, A. Alù, and X. J. Zhang, Opt. Express 19, (2011). 12 V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).