Lorentz Nanoplasmonics for Nonlinear Generation - Nano Letters

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Lorentz Nanoplasmonics for Nonlinear Generation Esmaeil Rahimi, Haitian Xu, Byoung-Chul Choi, and Reuven Gordon Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b04257 • Publication Date (Web): 14 Nov 2018 Downloaded from http://pubs.acs.org on November 15, 2018

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Lorentz Nanoplasmonics for Nonlinear Generation Esmaeil Rahimi,† Haitian Xu,‡ Byoung-Chul Choi,‡ and Reuven Gordon∗,† Department of Electrical and Computer Engineering, University of Victoria, Victoria BC, Canada, and Department of Physics and Astronomy, University of Victoria, Victoria BC, Canada E-mail: [email protected] Phone: +1 250 472 5179. Fax: +1 250 721 6052

Abstract While past works have suggested that the Lorentz magnetic contribution to second harmonic generation from metal nanostructures is negligible as compared to other terms, here we demonstrate a dominant Lorentz contribution from T-shaped apertures in a gold film. The apertures are designed to have overlapping magnetic and electric near-field intensities at the plasmonic resonance. This gives 65% greater nonlinear generation from the Lorentz term than the sum of the other two terms. We demonstrate this effect experimentally by milling of nanoapertures of different size and orientation in a metal film and measuring their second harmonic generation. Good agreement is seen between the experiments and comprehensive calculations. In the development of highly efficient nonlinear metasurfaces, careful optimization of the Lorentz contribution should be considered, in addition to all other contributions. Following the approach of this work, the Lorentz contribution may also be optimized for THz generation. ∗

To whom correspondence should be addressed University of Victoria ‡ University of Victoria †

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Introduction Second harmonic generation (SHG) from metals has been studied since 1965, 1 and since 1974 for surface plasmons specifically. 2 Hydrodynamic theory has been used to describe quantitatively the nonlinear response. 3,4 Our increased ability to design metal nanostructures has lead to renewed interest in harmonic generation using metals. 5–40 Recent advances in metasurfaces have seen increased efficiency of harmonic generation from a single nanostructured surface approaching 1%. 41–44 Further improvements are envisioned by fully utilizing the nonlinear response, and this includes understanding how to design structures to maximize the various nonlinear contributions. Classical theory presents three main bulk contributions to second order optical nonlinearities in metals: Coulomb, convection and the Lorentz magnetic force. 3 The investigation of SHG in nanoscale split ring resonators showed negligible contribution from the Lorentz magnetic force. 45 This is surprising since these split ring resonators are well known for their magnetic response. 46,47 A fundamental question arises about whether the Lorentz magnetic force is always weak in metal nanostructures and therefore may be safely neglected. It is well known that metal structures typically provide weak magnetic resonances at high frequencies, as described by the Landau-Lifshitz argument, but this can be overcome under certain conditions. 48 By analogy, it is worth considering whether the Lorentz force can play a non-negligible (or even dominant) role in SHG. There is a basic reason why the Lorentz magnetic force is generally weak: it depends on the cross product of the electric and magnetic fields. Usually the magnetic and electric fields do not have their maxima in the same location in resonant structures. The simplest example is for cavities formed either by perfect electric conductor or by perfect magnetic conductor mirrors. For the perfect electric conductor cavity, the transverse magnetic field is maximum at the conductor and the transverse electric field is zero there. For a perfect magnetic conductor cavity the situation is reversed. Next we consider resonances for subwavelength structures. Metal nanoparticles, for example, are typically treated in the quasi-static regime 2


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where to first order the magnetic field is absent. 49 Apertures in metal films on the other hand are treated as magnetic dipoles 50 and magnetic fields only arise at higher order. 51 So it appears that the magnetic field and electric field will not be maximized in the same location and so the Lorentz force is usually doomed to be small. Collections of nanostructures allow for interactions that form higher order modes, however, these couple weakly to radiation as size is reduced. 52 In this work, we describe a general approach to enhance the Lorentz magnetic force for second harmonic generation in metal nanostructures. Contrary to previous works which suggested that the Lorentz contribution was negligible when compared to convective and Coulomb contributions, here we demonstrate the design approach to maximize the Lorentz contribution. We also demonstrate, in theory and experiment, that it surpasses the other contributions. We do this by creating structures that show both magnetic and electric field enhancements in the same location. As one may expect, these structures are more complicated and they have to be engineered to generate such overlapping fields. In some ways, this is analogous to superscattering of metal nanostructures above the fundamental single channel limit, where careful engineering is required to produce overlapping resonances in the same regime of the optical spectrum. 53,54 We present both theory and experiment of metal nanostructures formed by apertures in metal films that show simultaneous enhanced magnetic and electric field enhancement in the same region and therefore show a dominant Lorentz force contribution to the SHG.

Lorentz Nanoplasmonic Structure Figure 1 (a) shows a schematic of the structure under consideration: a T-shape of nonoverlapping rectangular apertures in a 100 nm thick gold film on glass. The rectangles are 240 nm by 50 nm and separated by 50 nm. This geometry is designed to give a plasmonic resonance at 850 nm. The two apertures are chosen as a rudimentary basis where one

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Figure 1: a) Schematic of T-shape structure (in gold on glass). Simulated field intensity for field, c) the z component of E, d) the y component of H and e) b) the y component of E f) The Lorentz magnetic force contribution to the nonlinear source the z component of H. × H. current proportional to E aperture will provide maximum electric field in the gold region between the apertures, and the other aperture will provide maximum magnetic field. In this way, both the magnetic and electric fields are maximized in the same location and at the same resonance frequency of the aperture. Finite-difference time-domain (FDTD) simulations were used to calculate the field distributions in the apertures. The details of the simulation are found in the Supporting Information. Figure 1 (b-e) show the electric and the magnetic field distributions in the sample. Each rectangle has maximum electric fields along the long edges and maximum magnetic fields at the sides. For 45° excitation then, it is possible to excite both apertures × H in the gold film, as shown in Figure 1 (f). and create maximum E

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Nonlinear Response Calculations Euler’s momentum equation for an electron gas along with Maxwell and continuity equations give the current density at the second harmonic frequency as (details in the Supporting Information): 55 J2 =

i ne2 E2 + JNL 2ω + iγ me

(1)

where the nonlinear current source, JNL , is given by: JNL =

1 ine3 1 E1 (∇ · E1 ) − iμH1 × E1 + ((∇ · E1 )E1 + (E1 · ∇)E1 m2e (2ω + iγ)(ω + iγ) ω (ω + iγ) (2)

and H are the electric and magnetic The subscripts refer to first and second-order fields, E fields, me is the electron effective mass, e and n are electron charge and density, γ is the electron collision rate and μ is the permeability. For JNL , the nonlinear Coulomb term 1 (∇ · E 1 ), the magnetic Lorentz force contribution is proportional to is proportional to E 1 , and the convective term is proportional to (∇ · E 1 ) + (E 1 · ∇)E 1. 1 × H E To calculate the SHG, we use nonlinear scattering theory. 55–57 In nonlinear scattering theory, which is based on Lorentz reciprocity, we first calculate the local fields of the fundamental incident wave. From this, the nonlinear current density is calculated using hydrodynamic theory. The Lorentz contribution to this nonlinear current density is proportional to the cross product of the fields, as shown in Figure 1 (f). There are also hydrodynamic components (not shown). It is this current that generates the second harmonic frequency (but also a rectification current for the case of THz generation as calculated in the Supporting Information). We then find the overlap of those currents with an incident field at the second harmonic frequency (the time-reversal of the emitted field) to calculate the generation: PSHG =

Au

2 dV J2 · E

(3)

2 are the current density and electric field respectively where PSHG is the SHG power, J2 and E 5


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at second harmonic frequency. Figure 2 (a) shows the nonlinear scattering theory calculation of the SHG for the Tshaped structure considered above. While past works on SRRs showed a Lorentz contribution of 5.5 % to the overall SHG, 45 here we have shown the design of structures that have a dominant Lorentz contribution of 65 %. Another signature of this dominant Lorentz response is found by varying the incident polarization. While the Lorentz response is maximized for 45° excitation, the convection contributions are maximized for either 0° or 90°. We investigate a range of incident angles and dimensions in Figures 2 (b) and (c). While the SHG is presented in normalized units, the calculated conversion efficiency is estimated to be 0.9% for typical values of a 10 mW average power beam from a 140 fs pulse source at 80 MHz repetition rate with a micron squared spot size. This can be limited by saturation of the nonlinear response, including higher order nonlinear processes. Nevertheless, for metasurfaces operating below a few percent conversion efficiency, the present analysis should be appropriate. We do not consider the surface response here (calculations are shown in the Supporting Information), which has been found to give a large response for flat films 58 and large nanoparticles. 59 In nanostructures below 100 nm, as considered here, the bulk response has been suggested to dominate. 60

Experimental Results We fabricated the nanoapertures considered above using focused ion beam milling of 100 nm thick gold-on-glass with a 5 nm Ti adhesion layer. Figure 3 (a) shows schematic of the structures that were fabricated. They were fabricated with varying dimension and orientation to probe the resonance and different polarizations of excitation. Figure 3 (b) shows a scanning electron microscope image of the fabricated structure. We then measured the nonlinear response in transmission using a Zeiss LSM880 laser microscope with a 140 fs excitation at 850 nm. The confocal setup excites a single T-shape aperture at a time to avoid interference

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Figure 2: a) Lorentz magnetic force dominates SHG at the resonance of T-shaped aperture (same dimensions as described previously). b) Color map of calculated SHG intensity for different aperture length dimensions and incident polarizations, for Lorentz and other terms in Eq. 1, and c) is the same as b) but considering only the Lorentz contribution to the SHG. 7 ACS Paragon Plus Environment

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from neighbouring apertures to first order. Details of the fabrication and experimental setup are found in the Supporting Information. The experimental results are presented in Figure 3 (c) and (d). The incident polarization is horizontal, so rotating the structure is equivalent to rotating the incident polarization. Figure3 (c) shows the total SHG in transmission. For Figure 3 (d), we have added a polarizer after the sample and before the detector to isolate the 45° SHG corresponding to the Lorentz magnetic contribution. (The Supporting Information shows for result of different analyzer polarizations; 45° shown here is the maximum). By putting a power meter right before the detector, we measured the output SHG power. For 20 mW average incident power, the output power is 146 μW, which gives a detected conversion efficiency of 0.73%. We have also analyzed the surface response and found that it is maximized for 0° angle (see Supporting Information for details). Therefore, the off-axis polarization maximum seen in the experiments and found in the theory do not coincide with a surface response. It is interesting to note, however, that past works have looked at the indistinguishableness of bulk and surface responses in media with inversion symmetry, 61 as well as suggested that in nanostructures with multiple beams distinguish-ability may be found once again. 58 This points to an interesting area for further investigation where the distinguish-ability of different components in nanostructures made from materials with inversion symmetry. We note that for a centrosymmetric material, the tangential contributions to the nonlinear surface response vanish, and therefore only the normal surface contribution is retained. 58,62–64 Since we have shown that the normal surface contribution does not contribute a 45° response (by symmetry and calculations), this cannot explain the observations (see Supporting Information Figure 3). The tangential components of the effective nonlinear surface response result from the bulk only, and these are represented by the hydrodynamic model presented here.

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Figure 3: a) T-shaped apertures of different size and orientation. b) Fabrication of these apertures in a gold film. c) SHG measured in transmission shows highest response for 45° aperture, showing that the Lorentz force is dominant. d) A 45° analyzer further confirms the dominant role of the Lorentz force in SHG.

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Discussion Comparing Figures 2 (b) and (c) with Figures 3 (c) and (d), we see good overall correspondence between the theory and experiment. The experiment gave the maximum SHG for 240 nm length and 30° polarization, close to the theoretical maximum of 220 nm and 45° polarization. Discrepancies between these results can be attributed to fabrication tolerances (around 10 nm tolerance on the focused ion beam milling, with tapering), as well as alignment of the sample within the microscope (typically a few degrees). The present work serves as a proof-of-principle that it is possible to design structures to maximize the Lorentz contribution to the overall SHG. The Lorentz magnetic contribution was only the result of a very small region of the total structure (in a 50 nm gold bridge between the two rectangles). Therefore, it is envisioned that greater Lorentz enhancement may be achievable by designing structures with a greater overlapping region, or multiple overlapping regions. In terms of overall conversion efficiency, it is interesting to note that our structure uses a connected metal film that quickly removes heat from the hot-spot regions. It has been discussed previously that melting provides a fundamental limit to nonlinear conversion. 55,65 Therefore, the structure presented here is expected to withstand significantly larger incident powers than isolated nanoparticles. Since the conversion efficiency scales linearly with the incident field, this means that higher conversion efficiencies exceeding a few percent may be possible with the current approach. We also do not have particularly sharp features in our design, which are more prone to melting and smoothing (reflow) upon strong excitation. Another interesting feature of this study is the application to THz current generation. The Lorentz magnetic response gives the opportunity for both second harmonic (sum frequency) and DC (difference frequency) currents. Therefore, a modified version of the present structure may be used to drive a current density and generate THz current that can then be coupled to radiation by feeding an antenna. Other works have noted the potential of THz generation including the Lorentz response; 66,67 however, here we demonstrate a structure 10


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that can maximize both the magnetic and electric field in the same location, thereby maximizing the Lorentz magnetic contribution to the driving current. It is also interesting to note that the direction of the THz current can be switched by varying the incident polarization (see Supporting Information for details).

Conclusions In this work, we have shown that it is possible to design structures with dominant Lorentz contribution to SHG. The design principle is to maximize the electric and magnetic field components at the same location spatially. Hydrodynamic theory showed good agreement with our experimental measurements, confirming the role of the Lorentz magnetic response in SHG. This work is of interest for designing structures with maximized conversion efficiency including the Lorentz, Coulomb and convective contributions. Since these components are coherent, future work should take care to ensure that they interfere constructively for optimal conversion efficiency. Ideally, but maximizing all contributions, conversion efficiencies of nonlinear plasmonic metasurfaces will be able to exceed 10% in the near future. In this work we have mainly shown an approach to maximize the Lorentz contribution; future designs should aim to maximize all of the contributions. This work is also of interest for THz generation purely based on the metal response.

Supporting Information Available Contains the details of hydrodynamic model and nonlinear scattering theory, the details of simulation (with linear transmission, polarization dependence of transmission and the polarization dependence of the surface contribution to SHG), the experimental setup, the nanofabrication method, and additional second harmonic measurements with detailed descriptions. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Author Information Corresponding Author Reuven Gordon [email protected]

ORCID Reuven Gordon: 0000-0002-1485-6067

Author Contributions ER performed simulations and experiments and prepared the manuscript. HX performed preliminary simulations and experiments on the same topic under the supervision of Drs. Choi and Gordon. Dr. Gordon conceived of the concept and helped prepare the manuscript.

Notes The authors declare that there are no competing financial interests.

Acknowledgement This research was supported by the NSERC CREATE Materials for Enhanced Energy Technologies (MEET) program and an NSERC Discovery Grant. ER thanks Adarsh Lalitha Ravindranath, Elaine Humphrey, Milton Wang and Jonathan Rudge for technical assistance.

References (1) Brown, F.; Parks, R. E.; Sleeper, A. M. Physical Review Letters 1965, 14, 1029. (2) Simon, H.; Mitchell, D.; Watson, J. Physical Review Letters 1974, 33, 1531.

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(3) Sipe, J.; So, V.; Fukui, M.; Stegeman, G. Physical Review B 1980, 21, 4389. (4) Bloembergen, N.; Chang, R. K.; Jha, S.; Lee, C. Physical Review 1968, 174, 813. (5) Boyd, G. T.; Rasing, T.; Leite, J. R. R.; Shen, Y. R. Physical Review B 1984, 30, 519–526. (6) Liebsch, A. Physical Review Letters 1988, 61, 1233. (7) Kauranen, M.; Verbiest, T.; Maki, J. J.; Persoons, A. The Journal of Chemical Physics 1994, 101, 8193–8199. (8) Tuovinen, H.; Kauranen, M.; Jefimovs, K.; Vahimaa, P.; Vallius, T.; Turunen, J.; Tkachenko, N. V.; Lemmetyinen, H. Journal of Nonlinear Optical Physics & Materials 2002, 11, 421–432. (9) Hentschel, M.; Utikal, T.; Giessen, H.; Lippitz, M. Nano Letters 2012, 12, 3778–3782. (10) Nahata, A.; Linke, R. A.; Ishi, T.; Ohashi, K. Optical Letters 2003, 28, 423–425. (11) Airola, M.; Liu, Y.; Blair, S. Journal of Optics A: Pure and Applied Optics 2005, 7, S118. (12) Lippitz, M.; van Dijk, M. A.; Orrit, M. Nano Letters 2005, 5, 799–802. (13) Shan, J.; Dadap, J. I.; Stiopkin, I.; Reider, G. A.; Heinz, T. F. Physical Review A 2006, 73, 023819. (14) Lesuffleur, A.; Kumar, L. K. S.; Gordon, R. Applied Physics Letters 2006, 88, 261104. (15) Kujala, S.; Canfield, B. K.; Kauranen, M.; Svirko, Y.; Turunen, J. Physical Review Letters 2007, 98, 167403. (16) Canfield, B. K.; Husu, H.; Laukkanen, J.; Bai, B.; Kuittinen, M.; Turunen, J.; Kauranen, M. Nano Letters 2007, 7, 1251–1255. 13


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(17) Chen, K.; Durak, C.; Heflin, J.; Robinson, H. D. Nano Letters 2007, 7, 254–258. (18) Lesuffleur, A.; Kumar, L.; Gordon, R. Physical Review B 2007, 75, 045423. (19) Xu, T.; Jiao, X.; Zhang, G.; Blair, S. Optics Express 2007, 15, 13894–13906. (20) Feth, N.; Linden, S.; Klein, M. W.; Decker, M.; Niesler, F. B. P.; Zeng, Y.; Hoyer, W.; Liu, J.; Koch, S. W.; Moloney, J. V.; Wegener, M. Optical Letters 2008, 33, 1975–1977. (21) Eftekhari, F.; Gordon, R. IEEE Journal of Selected Topics in Quantum Electronics 2008, 14, 1552–1558. (22) Xu, T.; Jiao, X.; Blair, S. Optics Express 2009, 17, 23582–23588. (23) Butet, J.; Duboisset, J.; Bachelier, G.; Russier-Antoine, I.; Benichou, E.; Jonin, C.; Brevet, P.-F. Nano Letters 2010, 10, 1717–1721. (24) Halas, N. J. Nano Letters 2010, 10, 3816–3822. (25) Zhang, Y.; Grady, N. K.; Ayala-Orozco, C.; Halas, N. J. Nano Letters 2011, 11, 5519– 5523. (26) Capretti, A.; Walsh, G. F.; Minissale, S.; Trevino, J.; Forestiere, C.; Miano, G.; Dal Negro, L. Optics Express 2012, 20, 15797–15806. (27) Linden, S.; Niesler, F. B. P.; Förstner, J.; Grynko, Y.; Meier, T.; Wegener, M. Physical Review Letters 2012, 109, 015502. (28) Kauranen, M.; Zayats, A. V. Nature Photonics 2012, 6, 737. (29) Czaplicki, R.; Husu, H.; Siikanen, R.; Mäkitalo, J.; Kauranen, M.; Laukkanen, J.; Lehtolahti, J.; Kuittinen, M. Physical Review Letters 2013, 110, 093902. (30) Thyagarajan, K.; Butet, J.; Martin, O. J. Nano Letters 2013, 13, 1847–1851. (31) Walsh, G. F.; Dal Negro, L. Nano Letters 2013, 13, 3111–3117. 14


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(32) Czaplicki, R.; Makitalo, J.; Siikanen, R.; Husu, H.; Lehtolahti, J.; Kuittinen, M.; Kauranen, M. Nano Letters 2014, 15, 530–534. (33) Capretti, A.; Pecora, E. F.; Forestiere, C.; Dal Negro, L.; Miano, G. Physical Review B 2014, 89, 125414. (34) Hajisalem, G.; Hore, D. K.; Gordon, R. Optical Materials Express 2015, 5, 2217–2224. (35) Cirac`ı, C.; Scalora, M.; Smith, D. R. Physical Review B 2015, 91, 205403. (36) Metzger, B.; Gui, L.; Fuchs, J.; Floess, D.; Hentschel, M.; Giessen, H. Nano letters 2015, 15, 3917–3922. (37) Hille, A.; Moeferdt, M.; Wolff, C.; Matyssek, C.; Rodrguez-Oliveros, R.; Prohm, C.; Niegemann, J.; Grafstrm, S.; Eng, L. M.; Busch, K. The Journal of Physical Chemistry C 2016, 120, 1163–1169. (38) Butet, J.; Martin, O. J. JOSA B 2016, 33, A8–A15. (39) Metzger, B.; Hentschel, M.; Giessen, H. Nano letters 2017, 17, 1931–1937. (40) Levi, S.; Samueli, R.; Choudhary, M.; Niv, A. Optical Letters 2018, 43, 3662–3665. (41) Nezami, M. S.; Yoo, D.; Hajisalem, G.; Oh, S.-H.; Gordon, R. ACS Photonics 2016, 3, 1461–1467. (42) Lee, J.; Nookala, N.; Gomez-Diaz, J. S.; Tymchenko, M.; Demmerle, F.; Boehm, G.; Amann, M.-C.; Al` u, A.; Belkin, M. A. Advanced Optical Materials 2016, 4, 664–670. (43) Klein, M. W.; Wegener, M.; Feth, N.; Linden, S. Optics Express 2007, 15, 5238–5247. (44) Butet, J.; Brevet, P.-F.; Martin, O. J. ACS Nano 2015, 9, 10545–10562. (45) Cirac`ı, C.; Poutrina, E.; Scalora, M.; Smith, D. R. Physical Review B 2012, 85, 201403.

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(46) Linden, S.; Enkrich, C.; Wegener, M.; Zhou, J.; Koschny, T.; Soukoulis, C. M. Science 2004, 306, 1351–1353. (47) Klein, M. W.; Enkrich, C.; Wegener, M.; Linden, S. Science 2006, 313, 502–504. (48) Merlin, R. Proceedings of the National Academy of Sciences 2009, 106, 1693–1698. (49) Mie, G. Annalen Der Physik 330, 377–445. (50) Bethe, H. A. Physical Review 1944, 66, 163–182. (51) Bouwkamp, C. J. Philips Research Reports 1950, 5, 321–332. (52) Lassiter, J. B.; Sobhani, H.; Fan, J. A.; Kundu, J.; Capasso, F.; Nordlander, P.; Halas, N. J. Nano Letters 2010, 10, 3184–3189. (53) Ruan, Z.; Fan, S. Physical Review Letters 2010, 105, 013901. (54) Chen, S.; Jin, S.; Gordon, R. Optics Express 2014, 22, 13418–13426. (55) Rahimi, E.; Gordon, R. Advanced Optical Materials 2018, 1800274. (56) Zeng, Y.; Hoyer, W.; Liu, J.; Koch, S. W.; Moloney, J. V. Physical Review B 2009, 79, 235109. (57) OBrien, K.; Suchowski, H.; Rho, J.; Salandrino, A.; Kante, B.; Yin, X.; Zhang, X. Nature Materials 2015, 14, 379. (58) Wang, F. X.; Rodr´ıguez, F. J.; Albers, W. M.; Ahorinta, R.; Sipe, J.; Kauranen, M. Physical Review B 2009, 80, 233402. (59) Bachelier, G.; Butet, J.; Russier-Antoine, I.; Jonin, C.; Benichou, E.; Brevet, P.-F. Physical Review B 2010, 82, 235403. (60) Benedetti, A.; Centini, M.; Bertolotti, M.; Sibilia, C. Optics Express 2011, 19, 26752– 26767. 16


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(61) Sipe, J.; Mizrahi, V.; Stegeman, G. I. Physical Review B 1987, 35, 9091. (62) Maytorena, J.; Mochán, W. L.; Mendoza, B. S. Physical Review B 1995, 51, 2556. (63) Mendoza, B. S.; Mochán, W. L. Physical Review B 1996, 53, 4999. (64) Schaich, W. Physical Review B 2000, 61, 10478. (65) Nezami, M. S.; Gordon, R. Optics Express 2015, 23, 32006–32014. (66) Durach, M.; Rusina, A.; Stockman, M. I. Physical Review Letters 2009, 103, 186801. (67) Vengurlekar, A. S.; Ishihara, T. Applied Physics Letters 2005, 87, 091118.

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