Open Access
Add to BibSonomy
Abstract
Over the last few years, optical nanoantennas are continuously attracting interest owing to their ability to efficiently confine, localize resonance, and significantly enhanced electromagnetic fields at a subwavelength scale. However, such strong confinement can be further enhanced by using an appropriate combination of optical nanoantennas and Slanted Bound states in the continuum cavities. Here, we propose to synergistically bridge the plasmonic nanoantennas and high optical quality-factor cavities to numerically demonstrate six orders of magnitude local intensity enhancement without critical coupling conditions. The proposed hybrid system paves a new way for applications requiring highly confined fields such as optical trapping, optical sensing, nonlinear optics, quantum optics, etc.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High optical quality-factors cavities induced strong local field enhancement are in tremendous demand in nano-optics due to the large number of applications requiring strong light-matter interaction such as biosensors, compact spectral splitting solar cells, low-threshold lasers, and single-photon sources. In the last decades, many different approaches have been proposed to combine high quality-factors and subwavelength confinement using hybrid photonic-plasmonic structure [1–9]. However, usually, large-quality factors come at the expense of compactness. All those traditional approaches have been stymied in their effort to break this compromise because they all rely on the same core principle that, to increase the radiation quality factor, no outgoing waves must be allowed. To break free of this paradigm, it is necessary to bring a new perspective. Bound states in the Continuum (BICs) are originally proposed in a very different field of wave physics, namely quantum mechanics [10–13] to achieve high-quality factors. BICs are states that are bound, i.e., have no radiation losses, even though coupling to the radiation continuum is, strictly speaking, allowed. They offer the promise of simultaneously large quality factors, compact devices [14–22], and local field enhancement, defined as the ratio of the total intensity divided by the intensity of the incident field. However, BIC is a singularity that is often sensitive to geometrical parameters. Moreover, to enhance the local field, it is required to achieve a critical coupling condition that is sensitive to the aforementioned factors [23–27]. Despite exciting findings, achieving local field enhancement without critical coupling conditions remains elusive. Here, we combined the high Q-factor of the BIC and the ability of the plasmonic NA to confine light at subwavelength scale [28–31] and demonstrate an enhancement of three orders of magnitude larger than what can be obtained within a single resonator. This versatile platform ensures the ultra-small mode volume from the NA and the high-quality factor from the BIC cavities leading to large field enhancement and avoiding a strong coupling that can break the resonances. It paves a new way for applications requiring highly confined fields such as optical sensing, nonlinear optics, quantum optics, etc.
In this paper, we propose to use a one-dimension slanted-Bound-States-in-the-continuum cavity (SBIC) and a plasmonic optical nanoantenna as building blocks (see Fig. 1). Therefore, the structure consists of two high-index slanted (angle α) ridges (Si), separated by a narrow low-index gap (water), deposited on a SiO2 substrate. The NA is composed of two gold nanoparticles with parallelepiped geometry. The incident wave is TE polarized with the electric field E along the y-direction, impinging the grating at normal incidence. This polarization state is essential to excite the NA plasmonic resonance since the electric field is directed along the NA axis. First, we start with vertical grating (α=0°) and go towards a slanted grating (α) with symmetry breaking [32–34]. Second, we discuss the plasmonic NA design. After that, the hybrid system is designed and simulated to demonstrate a strong field intensity enhancement.
Fig. 1. Schematic of a hybrid system made of slanted Bound States in the continuum Cavities (SBIC) and plasmonic nanoantenna (NA). The grating consists of two high-index ridges (Si), separated by a narrow low-index gap (water). The NA is composed of gold nanoparticles with rectangular shapes. The incident wave is TE polarized with the electric field E along the y-direction, impinging the grating at normal incidence.
2. Design of the bound state in the continuum cavities
To analyze our proposed system, we first simulated a high refractive index vertical (α=0°) grating (Si, n=3.47) sitting on a low-index gap (SiO2, n=1.46) and surrounded by water (n=1.33). The period (p) of the grating array is 500 nm, the Si slab width (w) is 225 nm, and the height is 600 nm. The structure is illuminated along angle θ varying from 0° to 55° with polarization along the axis of the dielectric grooves (y-polarization). To design our system, we performed numerical simulations using a 3D-FDTD homemade code integrating a Critical Points model to accurately consider the chromatic dispersion of the material [35].
Diagram of Fig. 2 shows the transmission coefficient, in which the quality factor of the several modes (A, B, C at normal incidence and BIC 1, BIC 2, and BIC 3 at oblique incidence) can be seen to tend slowly to infinity from their vanishing linewidths. Those vanishing linewidths indicate a trapped state with no leakage named the Bound States in the continuum. To substantiate the existence of BICs, we calculated the electric field intensity distributions for all the BICs and determine those for which the enhancement occurs in water. In fact, for bio-detection applications, NA must be placed in contact with water to be sensitive to variations in its optical index induced by the presence of biological molecules. As shown in Fig. 2, only BIC 1 and BIC 3, excited at oblique incidences of θ=9.2° and θ=41.5° at λ=893.05 nm and λ=1471.09 nm respectively, exhibit light confinement in the groove central zone (water). Nevertheless, for the sake of compactness and integration (at the end of an optical fiber for instance), it is more convenient to operate at normal incidence. To this end, we propose to bring these two BICs at θ=0° by tilting the Si slabs, and thus, by breaking the mirror-symmetry of the grating primitive cell [32–34].
Fig. 2. (a) Transmission spectra for the different incident angles θ. The inset diagram is a schematic of the modeled structure. The subfigures on the right give the electric intensity distributions at the vicinity of the grating near the BICs (A, B, and C) at θ=1° at λ=934.43 nm, λ=1076.21 nm, and λ=1200.88 nm, respectively. The subfigures on the left correspond to the same distribution near the BICs that occur at oblique incidence (BIC 1 at θ=9° and λ=895.05 nm, BIC 2 at θ = 15° and λ = 1124.38 nm and BIC 3 at θ = 42° and λ = 1474.09 nm).
This symmetry breaking results in two fundamental advantages. The first one consists of simplifying the experiment conditions and the second one consists of efficiently couple the fundamental mode of the NA to the grating in view of large field enhancement. Transmission spectra at normal incidence for tilt angle α varying from −60° to 60° are depicted in Fig. 3 where one can see that the BIC 1 (new BIC 1’) is now slightly shifted toward the red spectral region (λ = 905.83 nm) for α=12° while the BIC 3 (new BIC 3’) appears at λ=1175.3 nm for α=15°.
Fig. 3. (a) Transmission spectra with different slanted angles of the grating structure. The two sub-figures at the left depict the electric intensity distribution around the grating for the two resonances denoted by BIC 1’ and BIC 3’. (b) Transmittance spectra at α=12° (left) and α=15° (right) near the BIC 1’ and BIC 3’ respectively.
Unfortunately, the intensity distribution of these two modes, presented at the left of Fig. 3(a), shows that BIC 3’ does not match electric field confinement inside the groove region. Only BIC 1’ (Q ≈ 1012) remains compatible with a normal incidence [see the insert in the lower left-hand corner of Fig. 3(a)] in addition to correspond to the smaller tilt angle (α = 12°).
3. Plasmonic NA design
The NA is made in gold, and the considered permittivity of the gold is taken from [36] and adapted through a Drude Critical Points (DCP) Model integrated into the FDTD codes. Using commercial software CST and homemade FDTD codes, we performed the numerical simulations, considering the NA on top of the same substrate (SiO2) and surrounded by water. We design the resonance of the NA by controlling the geometrical parameters to match the resonance of the grating BIC 1’. The NA dimensions are width 30 nm, thickness 30 nm, total length 185 m, and gap 15 nm. Figure 4(a) presents the intensity enhancement spectrum of the NA recorded at its gap center in the output plane [see the inset in Fig. 4(a)]. The resonant wavelength is about 910 nm. We can observe that the NA has a low-quality factor Q=13. This large bandwidth ensures a weak coupling between the NA and the narrow linewidth BIC that guarantees a small shift of the BIC resonance after the coupling without substantial modifications of its properties [37].
Fig. 4. Intensity enhancement spectra and intensity enhancement distributions. Intensity enhancement spectrum of (a) the NA. (b) the slanted grating. (c) the hybrid system. Intensity enhancement distribution of (d) the NA. (e) the slanted grating. (f) the hybrid system. (g) Intensity enhancement as a function of the tilt angle.
4. Hybrid system
Last, we combined the slanted grating structure and the NA. Figures 4(a), 4(b), and 4(c) show the intensity enhancement spectra of respectively: the NA alone, the grating alone, and the entire structure while Figs. 4(d), 4(e), and 4(f) show the corresponding intensity enhancement distributions respectively. Intensity enhancement is defined as the maximum intensity divided by the intensity of the incident field. It can be observed that there is a strong increase in intensity in the center between the grating slabs and the NA gap. For the case of NA alone, the enhancement is about 6000 around 910 nm. In the case of the grating only, the maximum intensity enhancement is 1400 around 910 nm. Despite the modest intensity enhancement of the SBIC, the entire structure (SBIC cavities + NA) has maximum intensity up to 1.6 × 106 around 920 nm. It is worth to mention that the intensity enhancement at the groove bottom is about half of the one at its center. Indeed, it seems that the higher intensity enhancement could be achieved by moving the NA to the center of the groove. However, in this case, it would affect the mode of the grating significantly and reduce the intensity enhancement eventually. In fact, even if the NA is placed out from this region r, the obtained enhancement of the hybrid structure is 3 orders of magnitude larger than the one of NA alone by keeping a good localization in the gap region. The coupling efficiency is then estimated to 36% (grating enhancement of 700 at the NA position and NA enhancement of 6300 → 4.41 × 106 leading to 1.6 × 106/4.41 × 106=36.28%). This coupling efficiency is consistent with the value of 38% obtained in Ref. [4] but for a smaller enhancement factor of only 8000. To further examine the robustness of our hybrid system, we calculated the local intensity enhancement at different tilt angles. Figure 4(g) presents the intensity enhancement at different tilt angles and shows that it is mostly unchanged when the tilt angle varies from 9° to 14°, demonstrating the successful realization of a hybrid system with intensity enhancement larger than 6 orders of magnitude without critical coupling condition.
5. Conclusion
We proposed and numerically demonstrated a new hybrid platform based on plasmonic optical nanoantenna and all-dielectric grating. Our proposed platform exhibits an intensity enhancement of six orders of magnitude through a hybrid system made by plasmonic nanoantennas and slanted-bound-states-in-the-continuum cavities. This versatile platform can be used for applications requiring highly confined fields such as optical sensing, nonlinear optics, surface Raman spectroscopy, quantum optics, or for multiplex detection of antigens/antibodies, or biomarkers.
Acknowledgments
The authors gratefully acknowledge the financial support of Boston University start-up funding.
Disclosures
The authors declare no conflicts of interest.
References
1. M. Barth, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett. 10(3), 891–895 (2010). [CrossRef]
2. Y. F. Xiao, “Strongly enhanced light-matter interaction in a hybrid photonic-plasmonic resonator,” Phys. Rev. A 85(3), 031805 (2012). [CrossRef]
3. R. Ameling and H. Giessen, “Microcavity plasmonics: strong coupling of photonic cavities and plasmons,” Laser Photonics Rev. 7(2), 141–169 (2013). [CrossRef]
4. A. E. Eter, T. Grosjean, P. Viktorovitch, X. Letartre, T. Benyattou, and F. I. Baida, “Huge light-enhancement by coupling a bowtie nano-antenna’s plasmonic resonance to a photonic crystal mode,” Opt. Express 22(12), 14464 (2014). [CrossRef]
5. M. Mivelle, P. Viktorovitch, F. I. Baida, A. E. Eter, Z. Xie, T. P. Vo, E. Atie, G. W. Burr, D. Nedeljkovic, J. Y. Rauch, S. Callard, and T. Grosjean, “Light funneling from a photonic crystal laser cavity to a nano-antenna: overcoming the diffraction limit in optical energy transfer down to the nanoscale,” Opt. Express 22(12), 15075 (2014). [CrossRef]
6. H. M. Doeleman, E. Verhagen, and A. F. Koenderink, “Antenna-cavity hybrids: matching polar opposites for Purcell enhancements at any linewidth,” ACS Photonics 3(10), 1943–1951 (2016). [CrossRef]
7. J. N. Liu, Q. Huang, K. K. Liu, S. Singamaneni, and T. C. Brian, “Nanoantenna−Microcavity Hybrids with Highly Cooperative Plasmonic−Photonic Coupling,” Nano Lett. 17(12), 7569–7577 (2017). [CrossRef]
8. B. Gurlek, V. Sandoghdar, and D. Martín-Cano, “Manipulation of quenching in nanoantenna-emitter systems enabled by external detuned cavities: a path to enhance strong-coupling,” ACS Photonics 5(2), 456–461 (2018). [CrossRef]
9. H. Zhang, Y. C. Liu, C. Wang, N. Zhang, and C. Lu, “Hybrid photonic-plasmonic nano-cavity with ultra-high Q/V,” Opt. Lett. 45(17), 4794 (2020). [CrossRef]
10. J. V. Neumann and E. Wigner, “On some peculiar discrete eigenvalues,” Phys. Z. 30, 467 (1929).
11. D. R. Herrick, “Construction of bound states in the continuum for epitaxial heterostructure superlattices,” Physica B+C 85(1), 44–50 (1976). [CrossRef]
12. F. H. Stillinger, “Potentials supporting positive-energy eigenstates and their application to semiconductor heterostructures,” Physica B+C 85(2), 270–276 (1976). [CrossRef]
13. H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A 32(6), 3231–3242 (1985). [CrossRef]
14. C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1(9), 16048 (2016). [CrossRef]
15. C. M. Linton and P. McIver, “Embedded trapped modes in water waves and acoustics,” Wave Motion 45(1-2), 16–29 (2007). [CrossRef]
16. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007). [CrossRef]
17. C. Hsu, B. Zhen, and J. Lee, “Observation of trapped light within the radiation continuum,” Nature 499(7457), 188–191 (2013). [CrossRef]
18. A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, “Lasing action from photonic bound states in continuum,” Nature 541(7636), 196–199 (2017). [CrossRef]
19. K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018). [CrossRef]
20. I. A. Shaimaa, M. S. Vladimir, B. Alexandra, and V. K. Alexander, “Formation of Bound States in the Continuum in Hybrid Plasmonic-Photonic Systems,” Phys. Rev. Lett. 121(25), 253901 (2018). [CrossRef]
21. A. Ndao, L. Hsu, W. Cai, J. Ha, J. Park, R. Contractor, Y. Lo, and B. Kanté, “Differentiating and quantifying exosome secretion from asingle cell using quasi-bound states in the continuum,” Nanophotonics 9(5), 1081–1086 (2020). [CrossRef]
22. X. Yin, J. Jin, and M. Soljačić, “Observation of topologically enabled unidirectional guided resonances,” Nature 580(7804), 467–471 (2020). [CrossRef]
23. J. W. Yoon, S. H. Song, and R. Magnusson, “Critical field enhancement of asymptotic optical bound states in the Continuum,” Sci. Rep. 5(1), 18301 (2015). [CrossRef]
24. K. Koshelev, Y. Tang, K. Li, D. Y. Choi, G. Li, and Y. Kivshar, “Nonlinear metasurfaces governed by bound states in the continuum,” ACS Photonics 6(7), 1639–1644 (2019). [CrossRef]
25. Y. Liang, K. Koshelev, F. Zhang, H. Lin, S. Lin, J. Wu, B. Jia, and Y. Kivshar, “Bound states in the continuum in anisotropic plasmonic metasurfaces,” Nano Lett. 20(9), 6351–6356 (2020). [CrossRef]
26. S. Romano, M. Mangini, E. Penzo, S. Cabrini, A. C. D. Luca, I. Rendina, V. Mocella, and G. Zito, “Ultrasensitive Surface Refractive Index Imaging Based on Quasi-Bound States in the Continuum,” ACS Nano 14(11), 15417–15427 (2020). [CrossRef]
27. S. Romano, G. Zito, S. Managò, G. Calafiore, E. Penzo, S. Cabrini, A. C. D. Luca, and V. Mocella, “Surface-Enhanced Raman and Fluorescence Spectroscopy with an All-Dielectric Metasurface,” J. Phys. Chem. C 122(34), 19738–19745 (2018). [CrossRef]
28. R. W. P. King and C. W. Harrison, Antennas and Waves: A Modern Approach (MIT Press, Cambridge, Massachusetts, 1969).
29. D. M. Pozar and D. H. Schaubert, Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays. (IEEE Press, 1995).
30. C. A. Balanis, Antenna Theory (Wiley, New York, 1996).
31. K. L. Wong, Planar antennas for wireless communications (Wiley-Interscience, 2003).
32. A. Ndao, A. Belkhir, R. Salut, and F. I. Baida, “Slanted annular aperture arrays as enhanced-transmission metamaterials: Excitation of the plasmonic transverse electromagnetic guided mode,” Appl. Phys. Lett. 103(21), 211901 (2013). [CrossRef]
33. T. Alaridhee, A. Ndao, M. P. Bernal, E. Popov, A. L. Fehrembach, and F. I. Baida, “Transmission properties of slanted annular aperture arrays. Giant energy deviation over sub-wavelength distance,” Opt. Express 23(9), 11687 (2015). [CrossRef]
34. J. Park, A. Ndao, W. Cai, L. Hsu, A. Kodigala, T. Lepetit, Y. Lo, and B. Kanté, “Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing,” Nat. Phys. 16(4), 462–468 (2020). [CrossRef]
35. M. Hamidi, F. I. Baida, A. Belkhir, and O. Lamrous, “Implementation of the critical points model in a SFM-FDTD code working in oblique incidence,” J. Phys. D: Appl. Phys. 44(24), 245101 (2011). [CrossRef]
36. E. D. Palik, Handbook of Optical Constants, (Academic Press Inc., San Diego, 1985).
37. 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(S3), A381–A394 (2010). [CrossRef]
