Huge light-enhancement by coupling a bowtie nano-antenna’s plasmonic resonance to a photonic crystal mode Ali El Eter,1 Thierry Grosjean,1 Pierre Viktorovitch,2 Xavier Letartre,2 Taha Benyattou,2 and Fadi I. Baida1∗ 1 D´ epartement
d’Optique P.M. Duffieux, Institut FEMTO-ST UMR 6174 CNRS Universit´e de Franche–Comt´e, 25030 Besanc¸on Cedex, France 2 Institut de Nanotechnologie de Lyon (INL) CNRS UMR 5270, Universit´ e de Lyon INSA Lyon 16 Avenue Jean Capelle 69621 Villeurbanne, France ∗ [email protected]
Abstract: We numerically demonstrate a drastic enhancement of the light intensity in the vicinity of the gap of Bowtie Nano-antenna (BA) through its coupling with Photonic Crystal (PC) resonator. The resulting huge energy transfer toward the BA is based on the coupling between two optical resonators (BA and PC membrane) of strongly unbalanced quality factors. Thus, these two resonators are designed so that the PC is only slightly perturbed in term of resonance properties. The proposed hybrid dielectric-plasmonic structure may open new avenues in the generation of deeply subwavelength intense optical sources, with direct applications in various domains such as data storage, non-linear optics, optical trapping and manipulation, microscopy, etc. © 2014 Optical Society of America OCIS codes: (230.4555) Coupled resonators; (350.4238) Nanophotonics and photonic crystals; (250.5403) Plasmonics; (260.3910) Metal optics.
References and links 1. A. Yariv, Quantum Electronics (John Wiley and Sons, 1989). 2. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009). 3. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). 4. V. Nieuwstadt, J. A. H Sandtke, M. Harmsen, R. H. Segerink, F. B. Prangsma, J. C. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). 5. H. Rigneault, J. M Lourtioz, A. Delalande, and A. Levenson, “La Nanophotonique, Herm`es Sciences, Paris,” (2005). 6. E. Barakat, M. -P. Bernal, and F. I. Baida, “Theoretical analysis of enhanced nonlinear conversion from metallodielectric nano-structures,” Opt. Express 20, 16258–16268 (2012). 7. M. Roussey, M. -P. Bernal, N. Courjal, D. Van Labeke, F. I. Baida, and R. Salut, “Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons,” Appl. Phys. Lett. 89, 241110 (2006). 8. L. Novotny and N. Van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011). 9. N. P. De Leon, B. J. Shields, C. L. Yu, D. E. Englund, A. V. Akimov, M. D. Lukin, and H. Park, “Tailoring light-matter interaction with a nanoscale plasmon resonator,” Phys. Rev. Lett. 108, 226803 (2012). 10. S. Dodson, M. Haggui, R. Bachelot, J. plain, S. Li, and Q. Xiong, “Optimizing electromagnetic hotspots in plasmonic bowtie nanoantennae,” Phys. Chem. Lett. 4, 496–501 (2013). 11. P. Muhlschlegel, H. -J. Eisler, O. J. Martin, B. Hecht, and D. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
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Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14464
12. H. Fischer and O. J. Martin, “Engineering the optical response of plasmonic nanoantennas,” Opt. Express 16, 9144–9154 (2008). 13. F. J. Gonz´alez and J. Alda “Optical nanoantennas coupled to photonic crystal cavities and waveguides for nearfield sensing,” Selected Topics in Quantum Electronics, IEEE Journal of 16, 446–449 (2010), 14. K. Terukazu, Y. Kadoya, and H. -F. Hofmann, “Directional control of light by a nano-optical Yagi–Uda antenna,” Nat. Photon. 4, 312–315 (2010). 15. J. Qi, T. Kaiser, R. Peuker, T. Pertsch, F. Lederer, and C. Rockstuhl, “Highly resonant and directional optical nanoantennas,” J. Opt. Soc. Am. A 31, 388–393 (2014). 16. M. Chamanzar and A. Adibi, “Hybrid nanoplasmonic-photonic resonators for efficient coupling of light to single plasmonic nanoresonators,” Opt. Express 19, 22292–22304 (2011). 17. P. Schuck, D. Fromm, A. Sundaramurthy, G. Kino, and W. Moerner, “Improving the Mismatch between Light and Nanoscale Objects with Gold Bowtie Nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005). 18. A. Belarouci, T. Benyattou, X. Letartre, and P. Viktorovitch, “3D light harnessing based on coupling engineering between 1D-2D Photonic Crystal membranes and metallic nano-antenna,” Opt. Express 18, A381–A394 (2010). 19. M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nusse, T. Aichele, B. Lochel, C. Sonnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10, 891–895 (2010). 20. J. -S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010). 21. B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005). 22. L. Ferrier, P. R. Romeo, X. Letartre, E. Drouard, and P. Viktorovitch, “3D integration of photonic crystal devices: vertical coupling with a silicon waveguide,” Opt. Express 18, 16162–16174 (2010). 23. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
1.
Introduction
Light-matter interaction strongly depends on the light intensity and on the matter electromagnetic properties [1]. For example, the fluorescence rate is proportional to the exciting intensity [2], trapping efficiency is linked to the electromagnetic field gradient [3], and non-linear effects [4–7] are directly proportional to the light intensity. Generally, two ways are possible to increase this interaction. The first one deals with the enhancement of the incoming light power whereas the second one consists of strongly confining optical waves. Far field techniques to confine light undergo the fundamental diffraction limit [8], and one has to resort to evanescent waves as an alternative solution to generate sub-wavelength light spots. Nano-antennas (NA) and nano-apertures have proven outstanding ability to confine light down to the nanoscale. Due to their plasmon resonance properties, huge field intensities, several orders of magnitude higher than the incident one, have been achieved within these structures, allowing study of light-matter interaction at the nanoscale [9, 10]. One important achievement is that the optical resonances can be tuned with geometrical shape and dielectric constant of the nano-structures and also with the illumination properties (polarization, wavelength) [11–15]. Nevertheless, the overlap between diffraction-limited incoming waves and the deeply subwavelength resonant mode is generally weak and alternative solutions were recently proposed to improve light coupling into the plasmonic nano-structures. These solutions are based on the coupling between NA and optical dielectric resonators of higher quality factors [16–20]. In these hybrid configurations, the high-Q dielectric resonator plays the role of photon reservoir for the NA (of low Q factor)that operates like a nanometer scale loss channel for the dielectric resonator. In this paper, we study the optical coupling between a Bowtie Nano-antenna (BA) and a Photonic Crystal (PC) membrane. On the basis of 3D-FDTD homemade code, we show that dramatic light enhancement can occur in the nanometer scale gap of the BA due to an optical resonance combination. The latter is obtained thanks to the contrast between the resonators quality factors together with very different mode volumes. Numerical demonstration of optimized coupling is done after a study of the optical resonant properties of each one. After this,
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Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14465
the coupling properties are studied as a function of the distance between the two resonators. A coupling efficiency of 62 % is demonstrated meaning that the electric field enhancement is 0.62 times the product of the two enhancements obtained by each of the non-coupled resonators. 2.
Study of the PC
The PC structure is formed in a 235 nm thick InP membrane waveguide bonded on a Silica 1 μ m thick. The PC consists in a 2D array of holes drilled through the InP membrane. This PC can support a resonant slow Bloch mode, resulting in efficient lateral confinement of wave-guided photons (in-plane mode). In order to spatially confine the optical energy, the 2D PC comprises two areas: an inner square shaped core area where slow Bloch modes are efficiently confined laterally by an outer area which behaves as a cladding photonic barrier. This can be easily achieved by forming holes of different radii in the two areas, as described in [21]. In addition the structure is designed for surface addressing along the vertical direction (see reference [22] for example).
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Fig. 1. Schematic representation of the modeled PC structure illuminated at normal incidence from the Si substrate.
The operation wavelength is set close to λ = 1.3 μ m corresponding to a minima of absorption in water. The simulated structure is shown in Fig. 1 and it is supposed to be immersed in water in view of trapping applications. Numerical simulations [22] lead thus to a PC period of a = 310 nm, small radius r = 93 nm and an external PC hole radius r = 112 nm. In all simulations, the internal PC is composed of 7 × 7 periods and it is surrounded by 15 × 15 periods of the external PC. The homemade FDTD code allows for the calculation of both near-field response and the light confinement in the vicinity of the structure, simultaneously. A non-uniform meshing is performed in the FDTD algorithm in order to faithfully describe the small details and Perfectly Matched Layers (PML) absorbing boundary conditions are used all around the calculation window to cancel parasitical reflections on its non-physical boundaries. The spatial step is kept constant along the x and y-directions (δ x = δ y = 10 nm) while it varies from δ z = 10 nm around the central part of the PC to δ z = 30 nm away from this zone. The simulation window has 9.31 × 9.31 × 3.48 μ m3 volume and it is described through 931 × 931 × 148 cells along the x, y and z directions respectively. The structure is supposed to be illuminated by a Gaussian beam, centered on the PC, polarized along the x-direction and having a beam-waist of 4 μ m. The measured electric intensity 50 nm above the PC is then normalized by the same quantity calculated without the PC. We thus derive the enhancement factor χPC presented on Fig. 2(a). After 200000 timesteps in the FDTD simulations (3.33ps), a rather sharp resonance is obtained #208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14466
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Fig. 2. (a): Normalized near-field spectral response at 50 nm above the center of the PC structure. A rather sharp resonance is obtained at λPC = 1272.56 nm. (b): Diffracted zero order reflection (red solid line) and transmission (blue dashed line) spectra of the PC when it is illuminated at normal incidence by a linearly polarized Gaussian beam from the substrate side.
at λPC = 1272.56 nm together with an enhancement factor of χPC = 23. The quality factor of this resonance is QPC = 167. The far-field emission of the PC was also analyzed, using FDTD simulations. As mentioned above, when the Bloch mode is excited, the PC structure behaves as a reflector meaning that its reflectivity is larger than its transmission. These two latter spectra are presented on Fig. 2(b) where the reflectivity along the vertical direction, at the PC resonance, reaches 72 % while the transmission ratio falls down to 8 % (blue dashed line). Note here that only the diffracted zero order (along the normal axis Oz) energy is calculated. This means that, at resonance and due to the energy conservation, a part of the incident energy (almost 20 %) is diffracted along oblique direction.
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Fig. 3. Spatial distributions of the three electric field components at the PC resonance (λPC =1272.56 nm) recorded at 50 nm above the structure. White circles denote the hole positions.
Nevertheless, at resonance, the PC plays the role of light reservoir. The electromagnetic energy density inside the PC increases and the electric field is exalted with respect to free space incident beam counterpart. Consequently, the near-field above the PC also increases as confirmed by√the spectrum of Fig. 2. In fact, the electric field amplitude 50 nm above the center of the PC is 23 times larger than the incident field at the same location. However, this field
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Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14467
enhancement is localized spatially because the electric field is not homogeneous over the PC area. It is thus important to determine the spatial distribution of the electric field above the PC in order to determine the optimum position of the BA to warrant efficient coupling. Due to the polarization sensitivity of the BA (see next section), one must examine the three components – at least the two transversal components - of the electric field and not the electric field intensity. From Fig. 3, it can clearly be seen that the BA’s arms must be oriented along the x direction (polarization direction of the incident beam) which corresponds to the predominant electric field-component. Unfortunately, the two maxima of this component (Ex) are located over two PC holes compromising the deposition of the BA at this location. Nonetheless, an alternative solution is proposed in the next section. 3.
Design of the antenna
The second element of our device is the BA that was numerically designed to exhibit a resonance wavelength close to the PC one. 3D-FDTD simulations are performed in the case of nano-antenna made in gold (dielectric optical constant taken from ref. [23] and adapted through a Drude model that is incorporated in the FDTD algorithm) deposited on the same multilayer substrate as the PC structure: 235 nm thick InP layer /1 μ m silica/silicon substrate (see Fig. 4(a)). In these simulations, similarly to the PC structure, the BA is excited with the same Gaussian beam of 4 μ m waist from the Si substrate under normal incidence. The enhancement electric field factor χBA is defined as the electric intensity detected at 10 nm above the BA gap center normalized by the incident same electric field intensity without the BA (with the sole multilayer). The variations of this enhancement factor χBA as a function of wavelength is reported in Fig. 4(b) when the incident beam is mainly polarized in x-direction (red solid curve of Fig. 4(b)) and y-direction (blue dotted-dashed line). The optimized geometrical parameters are: edge D = 210 nm, thickness h = 40 nm and gap g = 25 nm leading a strong field enhancement of χBA = 894, only in the case of x-polarization at the resonance wavelength λBA = 1315 nm. Let us emphasize that the BA resonance is broad with a quality factor estimated to QBA = 3.5. This property of low Q-factor is required to insure a weak coupling conditions with the PC Bloch mode even if their resonance wavelengths are slightly different. The electric intensity distributions for the two polarization cases are presented in Figs. 4(c-d) and show efficient confinement in the gap zone only for the x-polarization. In order to combine the electric field enhancement of the two elements (the BA and the PC), we have to deposit the BA at the right position on the PC. As mentioned before, it is not straightforward to deposit a 210 nm-length metallic BA over a cylindrical hole of 186 nm in diameter (maxima of the Ex component as seen in Fig. 3). Meanwhile, we choose to place the BA between two PC holes and precisely at the center of the structure where Ex (see also Fig. 3) is large enough. By the way, we insure depositing all the metallic parts of the BA on the dielectric, outside the holes. 4.
Study of the coupling
The whole structure is then modeled through the same 3D-FDTD code that was used to model each single resonator. As shown in Fig. 5(a), the resonance of the whole structure (PC+BA) is red-shifted by Δλ = 0.8 nm with respect to the PC one. This small increase of the resonance wavelength denotes growing of the PC mode volume in presence of the BA. At first glance, this may seem contradictory because approaching a metallic structure leads to a squeezing of the light around the PC and thus reduces the available volume for the mode. Nevertheless, at its resonance, the BA acts as a funnel for light with high electromagnetic energy confinement inside its gap meaning an increasing of the overall mode volume that compensates the reduction #208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14468
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Fig. 4. (a) Schematic view of the modeled BA deposited on the multilayer, (b) Near-field spectral responses at 10 nm above the BA center for an x-polarized beam (red solid line) and for a y-polarized one (blue dashed-dotted line). As expected, the resonance is only obtained when the electric field of the incoming light is parallel to the two metallic triangles direction. The green dashed line corresponds to the spectra of a self-suspended BA in water in the case of an x-polarized illumination. (c) and (d) : Distributions of the electric intensity (in arbitrary units) for the two polarizations also recorded at 10 nm above the BA center showing large enhancement at the gap zone only in the case of x-polarization.
due to the metal’s presence. The part of light that penetrates the BA is then emitted in the far field both through the transmission and reflection channels. But, the transmitted part propagates in free space while the reflected one is re-injected inside the PC leading to the coupling. Moreover, as seen on Fig. 5(b), the diffracted zero-order energy increases in transmission and decreases in reflection (at the PC mode resonance). At least 10 % of the incident energy is channeled through the PC toward the BA and are converted by the BA into transmitted propagating wave (transmission of 18 % with the BA instead of 8 % without). Consequently, the BA plays a key role in the coupling phenomenon in spite of its small dimension (210 nm × 210 nm) compared to the PC one (4 μ m × 4 μ m) even though this coupling remains weak. Note here that this weak coupling allows a high energy transfer to the BA from the PC without breaking the resonance of the latter. In fact, the PC behaves as a reservoir of non-radiative electromagnetic energy due to its resonance. Under these conditions, the BA plays the role of a loss channel that extracts the energy from the PC and radiates it in the far-field. As seen on Fig. 5(a), the whole electric intensity enhancement reaches χPC+BA = 8000 instead of the unreachable value χmax = χPC × χBA = 23 × 894 = 20562 corresponding to the enhancement factor #208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14469
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Fig. 5. (a) Normalized near-field spectrum of the combined structure (solid red line). The spectrum of the PC without the BA is also plotted (blue dashed line) for comparison. (b) Zero order diffracted light (transmission and reflection) of the hybrid structure (BA on top of the PC).
product of the two resonators taken separately. This allows us to define a coupling coefficient for the enhancement factor (0.39) as the ratio between χPC+BA and χmax . In order to visualize the coupling, we have calculated the electric field distribution in a plane 10 nm above the BA at the resonance (λPC+BA = 1273.33 nm). The results for the three components are presented on Fig. 6 over an area of 3.1 μ m × 3.1 μ m centered on the BA. Close-up views of the central area are also presented in order to point out the spatial confinement of light near the BA gap zone. As expected, the x-component is predominant and is 100 times larger than the y-component. Note that, as for dipolar emission, the z-component is not negligible near the BA, which behaves as an electric dipole. 5
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Fig. 6. Spatial distributions of the electric field components (amplitude fifth root) above the BA+PC structure.
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Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14470
As it is well-known, the coupling between two resonators greatly depends on the distance between them. Consequently, as studied in [18] for the case of a 2D structure, we performed extensive numerical simulations to study the coupling rate versus the distance between the BA and the PC. When we change the distance, we expect to reach a coupling regime that leads to an optimal enhancement of the electric intensity at the BA gap [18]. Figure 7 gives the enhancement factor and the position of the resonance wavelength function of the distance d between the BA and the PC. A non uniform behavior is obtained with a maximum at d = 10 nm for both the enhancement factor and the resonance wavelength shift. Because of the large value of the spatial discretization along the z direction (here δ z = 10 nm), this result allows us to state that an optimal coupling between BA and PC is obtained for d ∈]0, 20[ nm. Nevertheless, and in order to eliminate numerical artifacts that can be induced by the spatial discretization (inaccuracy in the description of the contact between the BA and the PC due to the fact that the EM field components in the FDTD algorithm are spatially interleaved), we have performed numerical simulations to check the optical response of a BA when it is very close to an homogeneous substrate, at distances ranging from (0 to 20 nm). The results show that both enhancement and resonance wavelength evolve monotonically between 0 and 20 nm confirming the fact that the maximum coupling observed in Fig. 7(a) is not due to the BA-substrate contact but to the coupling with the PC. Unfortunately, FDTD simulations, including the entire PC and BA structure described by a spatial meshing of 1 nm cannot be supported by our computational workstations due to an inaccessible memory capacity (more than 42 TB of RAM). We can conclude that it is possible to optimize the coupling and get enhancement factor greater or equal to χtot = 11000 (value corresponding to d=10 nm on Fig. 7(a)) but certainly never reach the ideal value of χmax = 20562 as it was demonstrated in [18], simply due to metal dissipation. In fact, this optimal coupling occurs simultaneously with a significant modification of the wavelength (λres (d = 10 nm) = 1273.58 nm > λPC = 1272.56 nm) but also with a decreasing of the quality factor of the resonance. Consequently, the photons lifetime inside the structure decreases corresponding to smaller stored energy in the PC. The latter behaves less like an energy reservoir for the BA. Let us note that the results of Fig. 7 are obtained for a point-detector that follows the BA when it moves away from the PC meaning that the asymptote values, for both the enhancement factor and the wavelength, correspond to those of a self-suspended BA in water (see spectrum in dashed green line in Fig. 4(b)). Spatial distributions of the fifth root of the electric intensity in the xOz vertical plane cutting the BA along its symmetry axis is presented on Figs. 7(c-e) for different values of d in comparison with the case of the PC without the BA (Fig. 7(b)). The case where the BA is directly deposited on the crystal is shown in Fig. 7(c). The spatial distribution of the PC mode intensity is greatly modified by the presence of the BA. One can see that the electric intensity is mostly affected in the zone near the BA. The latter extracts the light from the PC and dissipates it in radiative and non-radiative channels. The transmitted light is then highly directed along the normal direction (main central lobe) with two smaller obliquely diffracted lobes. This result is consistent with the one of Fig. 5(b) (blue line) relative to the transmission increasing. Note also that the light distribution in the reflected medium (SiO2 ) is also modified with regard to the case of the single PC leading to weaker fringes visibility. For d = 10 nm (Fig. 7(d)), the light distribution inside the PC seems to almost recover the case of the unperturbed mode (without the BA) meaning that the coupling between the BA and the PC is more efficient without significant modification of the two resonances. If d = 70 nm (see Fig. 7(e)) the PC mode is almost totally recovered and the BA influence can be neglected. Note that the electric field enhancement (χtot ) calculated for d = 100 nm is smaller than 2755 which corresponds to the value of a self-suspended BA in water (see dashed green line of Fig. 4(b)) due to long-range interaction
#208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14471
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between the BA and the InP substrate (far-field interference phenomenon). 5.
Summary
We theoretically study and demonstrate a hybrid nano-device that combines photonic crystals and nano-antennas to provide a huge electromagnetic field enhancement when the whole structure is addressed by a freely propagating weakly focused Gaussian beam. The coupling between these two resonators leads to an optimized light enhancement in the gap area of the bowtie nano-antenna. This is obtained thanks to the discrepancy between their resonance properties. An optimal coupling can be reached by adjusting the distance between the PC and the BA. The giant and confined evanescent electromagnetic field in this structure is high enough to open the way to a wide range of applications with fibred systems where light cannot be tightly focused onto the nano-antenna. These applications cover optical trapping of nanometer-size objects, fluorescence, lithography and data storage, as well as the enhancement of non-linear phenomena at the nanoscale. Acknowledgments The authors would like to thank Philippe Boyer for helpful discussions and for computational technical support. This work is funded by “Agence Nationale de la Recherche” under contract number ANR10-NANO-002. It is also supported by the “Pˆole de comp´etitivit´e Microtechnique”, the Labex ACTION, the computing center: “M´esocentre de calcul de Franche-Comt´e” and the regional program “BQR PRES Bourgogne Franche-Comt´e”.
#208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14472
d’Optique P.M. Duffieux, Institut FEMTO-ST UMR 6174 CNRS Universit´e de Franche–Comt´e, 25030 Besanc¸on Cedex, France 2 Institut de Nanotechnologie de Lyon (INL) CNRS UMR 5270, Universit´ e de Lyon INSA Lyon 16 Avenue Jean Capelle 69621 Villeurbanne, France ∗ [email protected]
Abstract: We numerically demonstrate a drastic enhancement of the light intensity in the vicinity of the gap of Bowtie Nano-antenna (BA) through its coupling with Photonic Crystal (PC) resonator. The resulting huge energy transfer toward the BA is based on the coupling between two optical resonators (BA and PC membrane) of strongly unbalanced quality factors. Thus, these two resonators are designed so that the PC is only slightly perturbed in term of resonance properties. The proposed hybrid dielectric-plasmonic structure may open new avenues in the generation of deeply subwavelength intense optical sources, with direct applications in various domains such as data storage, non-linear optics, optical trapping and manipulation, microscopy, etc. © 2014 Optical Society of America OCIS codes: (230.4555) Coupled resonators; (350.4238) Nanophotonics and photonic crystals; (250.5403) Plasmonics; (260.3910) Metal optics.
References and links 1. A. Yariv, Quantum Electronics (John Wiley and Sons, 1989). 2. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photon. 3, 654–657 (2009). 3. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). 4. V. Nieuwstadt, J. A. H Sandtke, M. Harmsen, R. H. Segerink, F. B. Prangsma, J. C. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97, 146102 (2006). 5. H. Rigneault, J. M Lourtioz, A. Delalande, and A. Levenson, “La Nanophotonique, Herm`es Sciences, Paris,” (2005). 6. E. Barakat, M. -P. Bernal, and F. I. Baida, “Theoretical analysis of enhanced nonlinear conversion from metallodielectric nano-structures,” Opt. Express 20, 16258–16268 (2012). 7. M. Roussey, M. -P. Bernal, N. Courjal, D. Van Labeke, F. I. Baida, and R. Salut, “Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons,” Appl. Phys. Lett. 89, 241110 (2006). 8. L. Novotny and N. Van Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011). 9. N. P. De Leon, B. J. Shields, C. L. Yu, D. E. Englund, A. V. Akimov, M. D. Lukin, and H. Park, “Tailoring light-matter interaction with a nanoscale plasmon resonator,” Phys. Rev. Lett. 108, 226803 (2012). 10. S. Dodson, M. Haggui, R. Bachelot, J. plain, S. Li, and Q. Xiong, “Optimizing electromagnetic hotspots in plasmonic bowtie nanoantennae,” Phys. Chem. Lett. 4, 496–501 (2013). 11. P. Muhlschlegel, H. -J. Eisler, O. J. Martin, B. Hecht, and D. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
#208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14464
12. H. Fischer and O. J. Martin, “Engineering the optical response of plasmonic nanoantennas,” Opt. Express 16, 9144–9154 (2008). 13. F. J. Gonz´alez and J. Alda “Optical nanoantennas coupled to photonic crystal cavities and waveguides for nearfield sensing,” Selected Topics in Quantum Electronics, IEEE Journal of 16, 446–449 (2010), 14. K. Terukazu, Y. Kadoya, and H. -F. Hofmann, “Directional control of light by a nano-optical Yagi–Uda antenna,” Nat. Photon. 4, 312–315 (2010). 15. J. Qi, T. Kaiser, R. Peuker, T. Pertsch, F. Lederer, and C. Rockstuhl, “Highly resonant and directional optical nanoantennas,” J. Opt. Soc. Am. A 31, 388–393 (2014). 16. M. Chamanzar and A. Adibi, “Hybrid nanoplasmonic-photonic resonators for efficient coupling of light to single plasmonic nanoresonators,” Opt. Express 19, 22292–22304 (2011). 17. P. Schuck, D. Fromm, A. Sundaramurthy, G. Kino, and W. Moerner, “Improving the Mismatch between Light and Nanoscale Objects with Gold Bowtie Nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005). 18. A. Belarouci, T. Benyattou, X. Letartre, and P. Viktorovitch, “3D light harnessing based on coupling engineering between 1D-2D Photonic Crystal membranes and metallic nano-antenna,” Opt. Express 18, A381–A394 (2010). 19. M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nusse, T. Aichele, B. Lochel, C. Sonnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10, 891–895 (2010). 20. J. -S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010). 21. B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005). 22. L. Ferrier, P. R. Romeo, X. Letartre, E. Drouard, and P. Viktorovitch, “3D integration of photonic crystal devices: vertical coupling with a silicon waveguide,” Opt. Express 18, 16162–16174 (2010). 23. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6, 4370–4379 (1972).
1.
Introduction
Light-matter interaction strongly depends on the light intensity and on the matter electromagnetic properties [1]. For example, the fluorescence rate is proportional to the exciting intensity [2], trapping efficiency is linked to the electromagnetic field gradient [3], and non-linear effects [4–7] are directly proportional to the light intensity. Generally, two ways are possible to increase this interaction. The first one deals with the enhancement of the incoming light power whereas the second one consists of strongly confining optical waves. Far field techniques to confine light undergo the fundamental diffraction limit [8], and one has to resort to evanescent waves as an alternative solution to generate sub-wavelength light spots. Nano-antennas (NA) and nano-apertures have proven outstanding ability to confine light down to the nanoscale. Due to their plasmon resonance properties, huge field intensities, several orders of magnitude higher than the incident one, have been achieved within these structures, allowing study of light-matter interaction at the nanoscale [9, 10]. One important achievement is that the optical resonances can be tuned with geometrical shape and dielectric constant of the nano-structures and also with the illumination properties (polarization, wavelength) [11–15]. Nevertheless, the overlap between diffraction-limited incoming waves and the deeply subwavelength resonant mode is generally weak and alternative solutions were recently proposed to improve light coupling into the plasmonic nano-structures. These solutions are based on the coupling between NA and optical dielectric resonators of higher quality factors [16–20]. In these hybrid configurations, the high-Q dielectric resonator plays the role of photon reservoir for the NA (of low Q factor)that operates like a nanometer scale loss channel for the dielectric resonator. In this paper, we study the optical coupling between a Bowtie Nano-antenna (BA) and a Photonic Crystal (PC) membrane. On the basis of 3D-FDTD homemade code, we show that dramatic light enhancement can occur in the nanometer scale gap of the BA due to an optical resonance combination. The latter is obtained thanks to the contrast between the resonators quality factors together with very different mode volumes. Numerical demonstration of optimized coupling is done after a study of the optical resonant properties of each one. After this,
#208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14465
the coupling properties are studied as a function of the distance between the two resonators. A coupling efficiency of 62 % is demonstrated meaning that the electric field enhancement is 0.62 times the product of the two enhancements obtained by each of the non-coupled resonators. 2.
Study of the PC
The PC structure is formed in a 235 nm thick InP membrane waveguide bonded on a Silica 1 μ m thick. The PC consists in a 2D array of holes drilled through the InP membrane. This PC can support a resonant slow Bloch mode, resulting in efficient lateral confinement of wave-guided photons (in-plane mode). In order to spatially confine the optical energy, the 2D PC comprises two areas: an inner square shaped core area where slow Bloch modes are efficiently confined laterally by an outer area which behaves as a cladding photonic barrier. This can be easily achieved by forming holes of different radii in the two areas, as described in [21]. In addition the structure is designed for surface addressing along the vertical direction (see reference [22] for example).
PC
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Fig. 1. Schematic representation of the modeled PC structure illuminated at normal incidence from the Si substrate.
The operation wavelength is set close to λ = 1.3 μ m corresponding to a minima of absorption in water. The simulated structure is shown in Fig. 1 and it is supposed to be immersed in water in view of trapping applications. Numerical simulations [22] lead thus to a PC period of a = 310 nm, small radius r = 93 nm and an external PC hole radius r = 112 nm. In all simulations, the internal PC is composed of 7 × 7 periods and it is surrounded by 15 × 15 periods of the external PC. The homemade FDTD code allows for the calculation of both near-field response and the light confinement in the vicinity of the structure, simultaneously. A non-uniform meshing is performed in the FDTD algorithm in order to faithfully describe the small details and Perfectly Matched Layers (PML) absorbing boundary conditions are used all around the calculation window to cancel parasitical reflections on its non-physical boundaries. The spatial step is kept constant along the x and y-directions (δ x = δ y = 10 nm) while it varies from δ z = 10 nm around the central part of the PC to δ z = 30 nm away from this zone. The simulation window has 9.31 × 9.31 × 3.48 μ m3 volume and it is described through 931 × 931 × 148 cells along the x, y and z directions respectively. The structure is supposed to be illuminated by a Gaussian beam, centered on the PC, polarized along the x-direction and having a beam-waist of 4 μ m. The measured electric intensity 50 nm above the PC is then normalized by the same quantity calculated without the PC. We thus derive the enhancement factor χPC presented on Fig. 2(a). After 200000 timesteps in the FDTD simulations (3.33ps), a rather sharp resonance is obtained #208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14466
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Fig. 2. (a): Normalized near-field spectral response at 50 nm above the center of the PC structure. A rather sharp resonance is obtained at λPC = 1272.56 nm. (b): Diffracted zero order reflection (red solid line) and transmission (blue dashed line) spectra of the PC when it is illuminated at normal incidence by a linearly polarized Gaussian beam from the substrate side.
at λPC = 1272.56 nm together with an enhancement factor of χPC = 23. The quality factor of this resonance is QPC = 167. The far-field emission of the PC was also analyzed, using FDTD simulations. As mentioned above, when the Bloch mode is excited, the PC structure behaves as a reflector meaning that its reflectivity is larger than its transmission. These two latter spectra are presented on Fig. 2(b) where the reflectivity along the vertical direction, at the PC resonance, reaches 72 % while the transmission ratio falls down to 8 % (blue dashed line). Note here that only the diffracted zero order (along the normal axis Oz) energy is calculated. This means that, at resonance and due to the energy conservation, a part of the incident energy (almost 20 %) is diffracted along oblique direction.
930 nm
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Fig. 3. Spatial distributions of the three electric field components at the PC resonance (λPC =1272.56 nm) recorded at 50 nm above the structure. White circles denote the hole positions.
Nevertheless, at resonance, the PC plays the role of light reservoir. The electromagnetic energy density inside the PC increases and the electric field is exalted with respect to free space incident beam counterpart. Consequently, the near-field above the PC also increases as confirmed by√the spectrum of Fig. 2. In fact, the electric field amplitude 50 nm above the center of the PC is 23 times larger than the incident field at the same location. However, this field
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Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14467
enhancement is localized spatially because the electric field is not homogeneous over the PC area. It is thus important to determine the spatial distribution of the electric field above the PC in order to determine the optimum position of the BA to warrant efficient coupling. Due to the polarization sensitivity of the BA (see next section), one must examine the three components – at least the two transversal components - of the electric field and not the electric field intensity. From Fig. 3, it can clearly be seen that the BA’s arms must be oriented along the x direction (polarization direction of the incident beam) which corresponds to the predominant electric field-component. Unfortunately, the two maxima of this component (Ex) are located over two PC holes compromising the deposition of the BA at this location. Nonetheless, an alternative solution is proposed in the next section. 3.
Design of the antenna
The second element of our device is the BA that was numerically designed to exhibit a resonance wavelength close to the PC one. 3D-FDTD simulations are performed in the case of nano-antenna made in gold (dielectric optical constant taken from ref. [23] and adapted through a Drude model that is incorporated in the FDTD algorithm) deposited on the same multilayer substrate as the PC structure: 235 nm thick InP layer /1 μ m silica/silicon substrate (see Fig. 4(a)). In these simulations, similarly to the PC structure, the BA is excited with the same Gaussian beam of 4 μ m waist from the Si substrate under normal incidence. The enhancement electric field factor χBA is defined as the electric intensity detected at 10 nm above the BA gap center normalized by the incident same electric field intensity without the BA (with the sole multilayer). The variations of this enhancement factor χBA as a function of wavelength is reported in Fig. 4(b) when the incident beam is mainly polarized in x-direction (red solid curve of Fig. 4(b)) and y-direction (blue dotted-dashed line). The optimized geometrical parameters are: edge D = 210 nm, thickness h = 40 nm and gap g = 25 nm leading a strong field enhancement of χBA = 894, only in the case of x-polarization at the resonance wavelength λBA = 1315 nm. Let us emphasize that the BA resonance is broad with a quality factor estimated to QBA = 3.5. This property of low Q-factor is required to insure a weak coupling conditions with the PC Bloch mode even if their resonance wavelengths are slightly different. The electric intensity distributions for the two polarization cases are presented in Figs. 4(c-d) and show efficient confinement in the gap zone only for the x-polarization. In order to combine the electric field enhancement of the two elements (the BA and the PC), we have to deposit the BA at the right position on the PC. As mentioned before, it is not straightforward to deposit a 210 nm-length metallic BA over a cylindrical hole of 186 nm in diameter (maxima of the Ex component as seen in Fig. 3). Meanwhile, we choose to place the BA between two PC holes and precisely at the center of the structure where Ex (see also Fig. 3) is large enough. By the way, we insure depositing all the metallic parts of the BA on the dielectric, outside the holes. 4.
Study of the coupling
The whole structure is then modeled through the same 3D-FDTD code that was used to model each single resonator. As shown in Fig. 5(a), the resonance of the whole structure (PC+BA) is red-shifted by Δλ = 0.8 nm with respect to the PC one. This small increase of the resonance wavelength denotes growing of the PC mode volume in presence of the BA. At first glance, this may seem contradictory because approaching a metallic structure leads to a squeezing of the light around the PC and thus reduces the available volume for the mode. Nevertheless, at its resonance, the BA acts as a funnel for light with high electromagnetic energy confinement inside its gap meaning an increasing of the overall mode volume that compensates the reduction #208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14468
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Fig. 4. (a) Schematic view of the modeled BA deposited on the multilayer, (b) Near-field spectral responses at 10 nm above the BA center for an x-polarized beam (red solid line) and for a y-polarized one (blue dashed-dotted line). As expected, the resonance is only obtained when the electric field of the incoming light is parallel to the two metallic triangles direction. The green dashed line corresponds to the spectra of a self-suspended BA in water in the case of an x-polarized illumination. (c) and (d) : Distributions of the electric intensity (in arbitrary units) for the two polarizations also recorded at 10 nm above the BA center showing large enhancement at the gap zone only in the case of x-polarization.
due to the metal’s presence. The part of light that penetrates the BA is then emitted in the far field both through the transmission and reflection channels. But, the transmitted part propagates in free space while the reflected one is re-injected inside the PC leading to the coupling. Moreover, as seen on Fig. 5(b), the diffracted zero-order energy increases in transmission and decreases in reflection (at the PC mode resonance). At least 10 % of the incident energy is channeled through the PC toward the BA and are converted by the BA into transmitted propagating wave (transmission of 18 % with the BA instead of 8 % without). Consequently, the BA plays a key role in the coupling phenomenon in spite of its small dimension (210 nm × 210 nm) compared to the PC one (4 μ m × 4 μ m) even though this coupling remains weak. Note here that this weak coupling allows a high energy transfer to the BA from the PC without breaking the resonance of the latter. In fact, the PC behaves as a reservoir of non-radiative electromagnetic energy due to its resonance. Under these conditions, the BA plays the role of a loss channel that extracts the energy from the PC and radiates it in the far-field. As seen on Fig. 5(a), the whole electric intensity enhancement reaches χPC+BA = 8000 instead of the unreachable value χmax = χPC × χBA = 23 × 894 = 20562 corresponding to the enhancement factor #208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14469
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Fig. 5. (a) Normalized near-field spectrum of the combined structure (solid red line). The spectrum of the PC without the BA is also plotted (blue dashed line) for comparison. (b) Zero order diffracted light (transmission and reflection) of the hybrid structure (BA on top of the PC).
product of the two resonators taken separately. This allows us to define a coupling coefficient for the enhancement factor (0.39) as the ratio between χPC+BA and χmax . In order to visualize the coupling, we have calculated the electric field distribution in a plane 10 nm above the BA at the resonance (λPC+BA = 1273.33 nm). The results for the three components are presented on Fig. 6 over an area of 3.1 μ m × 3.1 μ m centered on the BA. Close-up views of the central area are also presented in order to point out the spatial confinement of light near the BA gap zone. As expected, the x-component is predominant and is 100 times larger than the y-component. Note that, as for dipolar emission, the z-component is not negligible near the BA, which behaves as an electric dipole. 5
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Fig. 6. Spatial distributions of the electric field components (amplitude fifth root) above the BA+PC structure.
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Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14470
As it is well-known, the coupling between two resonators greatly depends on the distance between them. Consequently, as studied in [18] for the case of a 2D structure, we performed extensive numerical simulations to study the coupling rate versus the distance between the BA and the PC. When we change the distance, we expect to reach a coupling regime that leads to an optimal enhancement of the electric intensity at the BA gap [18]. Figure 7 gives the enhancement factor and the position of the resonance wavelength function of the distance d between the BA and the PC. A non uniform behavior is obtained with a maximum at d = 10 nm for both the enhancement factor and the resonance wavelength shift. Because of the large value of the spatial discretization along the z direction (here δ z = 10 nm), this result allows us to state that an optimal coupling between BA and PC is obtained for d ∈]0, 20[ nm. Nevertheless, and in order to eliminate numerical artifacts that can be induced by the spatial discretization (inaccuracy in the description of the contact between the BA and the PC due to the fact that the EM field components in the FDTD algorithm are spatially interleaved), we have performed numerical simulations to check the optical response of a BA when it is very close to an homogeneous substrate, at distances ranging from (0 to 20 nm). The results show that both enhancement and resonance wavelength evolve monotonically between 0 and 20 nm confirming the fact that the maximum coupling observed in Fig. 7(a) is not due to the BA-substrate contact but to the coupling with the PC. Unfortunately, FDTD simulations, including the entire PC and BA structure described by a spatial meshing of 1 nm cannot be supported by our computational workstations due to an inaccessible memory capacity (more than 42 TB of RAM). We can conclude that it is possible to optimize the coupling and get enhancement factor greater or equal to χtot = 11000 (value corresponding to d=10 nm on Fig. 7(a)) but certainly never reach the ideal value of χmax = 20562 as it was demonstrated in [18], simply due to metal dissipation. In fact, this optimal coupling occurs simultaneously with a significant modification of the wavelength (λres (d = 10 nm) = 1273.58 nm > λPC = 1272.56 nm) but also with a decreasing of the quality factor of the resonance. Consequently, the photons lifetime inside the structure decreases corresponding to smaller stored energy in the PC. The latter behaves less like an energy reservoir for the BA. Let us note that the results of Fig. 7 are obtained for a point-detector that follows the BA when it moves away from the PC meaning that the asymptote values, for both the enhancement factor and the wavelength, correspond to those of a self-suspended BA in water (see spectrum in dashed green line in Fig. 4(b)). Spatial distributions of the fifth root of the electric intensity in the xOz vertical plane cutting the BA along its symmetry axis is presented on Figs. 7(c-e) for different values of d in comparison with the case of the PC without the BA (Fig. 7(b)). The case where the BA is directly deposited on the crystal is shown in Fig. 7(c). The spatial distribution of the PC mode intensity is greatly modified by the presence of the BA. One can see that the electric intensity is mostly affected in the zone near the BA. The latter extracts the light from the PC and dissipates it in radiative and non-radiative channels. The transmitted light is then highly directed along the normal direction (main central lobe) with two smaller obliquely diffracted lobes. This result is consistent with the one of Fig. 5(b) (blue line) relative to the transmission increasing. Note also that the light distribution in the reflected medium (SiO2 ) is also modified with regard to the case of the single PC leading to weaker fringes visibility. For d = 10 nm (Fig. 7(d)), the light distribution inside the PC seems to almost recover the case of the unperturbed mode (without the BA) meaning that the coupling between the BA and the PC is more efficient without significant modification of the two resonances. If d = 70 nm (see Fig. 7(e)) the PC mode is almost totally recovered and the BA influence can be neglected. Note that the electric field enhancement (χtot ) calculated for d = 100 nm is smaller than 2755 which corresponds to the value of a self-suspended BA in water (see dashed green line of Fig. 4(b)) due to long-range interaction
#208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14471
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between the BA and the InP substrate (far-field interference phenomenon). 5.
Summary
We theoretically study and demonstrate a hybrid nano-device that combines photonic crystals and nano-antennas to provide a huge electromagnetic field enhancement when the whole structure is addressed by a freely propagating weakly focused Gaussian beam. The coupling between these two resonators leads to an optimized light enhancement in the gap area of the bowtie nano-antenna. This is obtained thanks to the discrepancy between their resonance properties. An optimal coupling can be reached by adjusting the distance between the PC and the BA. The giant and confined evanescent electromagnetic field in this structure is high enough to open the way to a wide range of applications with fibred systems where light cannot be tightly focused onto the nano-antenna. These applications cover optical trapping of nanometer-size objects, fluorescence, lithography and data storage, as well as the enhancement of non-linear phenomena at the nanoscale. Acknowledgments The authors would like to thank Philippe Boyer for helpful discussions and for computational technical support. This work is funded by “Agence Nationale de la Recherche” under contract number ANR10-NANO-002. It is also supported by the “Pˆole de comp´etitivit´e Microtechnique”, the Labex ACTION, the computing center: “M´esocentre de calcul de Franche-Comt´e” and the regional program “BQR PRES Bourgogne Franche-Comt´e”.
#208289 - $15.00 USD (C) 2014 OSA
Received 14 Mar 2014; revised 23 May 2014; accepted 28 May 2014; published 5 Jun 2014 16 June 2014 | Vol. 22, No. 12 | DOI:10.1364/OE.22.014464 | OPTICS EXPRESS 14472
