www.advmat.de www.MaterialsViews.com
Ward Brullot, Tom Swusten, and Thierry Verbiest*
Nonreciprocal asymmetric transmission, i.e., the dependence of optical transmittance on the direction of light propagation in the material, is currently under intensive research. Research efforts are boosted because the effect could be used in many applications ranging from optical isolators,[1–3] all-optical computing and processing devices,[4,5] to building blocks for integrated photonic circuits.[6] Currently, known ways to achieve nonreciprocal asymmetric transmission are amongst others magneto-optically active structures,[7] liquid crystals,[8] photonic crystals,[6] optoacoustically driven processes,[9] anisotropic and planar chiral structures,[10] nonlinear materials,[2] and composition-graded semiconductor nanowires.[4] While many of these materials show large asymmetries, they suffer from a required input polarization or mode,[6–8,10,11] a high operating threshold intensity,[2,4] large losses,[12] a too large footprint for on-chip integration,[5] a narrow spectral asymmetry bandwidth,[12,13] or use of difficult/ costly/nonintegrable fabrication methods. The search for alternative mechanisms to achieve nonreciprocal and polarizationindependent asymmetric transmission is thus very active and relevant. Brown et al. observed a large difference in the backscattering spectra of single, isolated mismatched plasmonic nanoparticle pairs (diameter per nanoparticle around 150 nm) when changing the propagation direction of the incoming light under transversal excitation in a dark-field microscope setup.[14] The observed local asymmetry was attributed to retardation effects and the relatively weak plasmon coupling under these circumstances. While the measured effect was significant, it cannot be used on the macroscale since it was measured on isolated, single nanoparticle pairs. In this work, we produced near-field coupled aggregates of small plasmonic nanoparticles on transparent glass substrates. This is in contrast to the use of large nanoparticles, like Brown et al.,[14] which give rise to strong scattering effects that hamper applicability in transmission optics. Plasmonic nanoparticle aggregates were produced in an optically isotropic and repro-
Dr. W. Brullot, T. Swusten, Prof. T. Verbiest Division of Molecular Imaging and Photonics Department of Chemistry KU Leuven, Celestijnenlaan 200D, Box 2425, 3001, Heverlee, Leuven, Belgium E-mail: [email protected]
DOI: 10.1002/adma.201405409
Adv. Mater. 2015, 27, 2485–2488
COMMUNICATION
Broadband Nonreciprocal Quadrupolarization-Induced Asymmetric Transmission (Q-AT) in Plasmonic Nanoparticle Aggregates
ducible way by a recently developed layer-by-layer method to achieve broadband nonreciprocal asymmetric transmission in a macroscopic (partially) transparent sample (see Figure 1).[15] Briefly summarized, the nanoparticle aggregates are produced by layer-by-layer deposition of first a low-density silver nanoparticle (9.6 ± 0.2 nm) layer, then a layer of functional complementary iron oxide nanoparticles (7.9 ± 2.4 nm) acting as “glue” and local refractive index enhancer and finally a highdensity gold nanoparticle (9.2 ± 1.3 nm) layer on microscope slides. Compositionally, asymmetric near-field coupled silver– gold nanoparticle aggregates are the result of this procedure. The aggregates’ principal axes are on average perpendicular to the substrates’ surface.[14–16] Both sides of the glass substrate are covered with nanoparticle aggregates. In this work, we show that self-assembled near-field coupled plasmonic-dielectric aggregates are an alternative and attractive way to achieve broadband nonreciprocal asymmetric transmission that can even be observed when using unpolarized light. Further, we phenomenologically explain the experimental observations and the origin of the effect in terms of induced electric quadrupole terms. Experimental UV–vis–NIR measurements using unpolarized light show broadband asymmetric transmission for goldmagnetite-silver aggregate samples with one side removed (see Figures 2 and 1, Supporting Information). Observed asymmetric transmission spans from the UV to the IR spectral region (400–2000 nm). Spectra were first measured in the forward, then backward and then again forward direction to ensure proper data acquisition. Compared with the two forward spectra, the backward spectrum is significantly different (see Figure 2a, Supporting Information). Expressed in dB, the largest asymmetric transmissions can be observed red-shifted from the around 530 nm and in the NIR. The peak around 530 nm corresponds to localized plasmon resonances, possibly with additional contributions from metal interband transitions and magnetite's optical transitions.[17] Near-field-coupled plasmon modes are the origin of the broad NIR peak. If the sample still has both sides of the glass substrate covered, and the total sample thus is symmetric (inversion symmetry), little or no asymmetric transmission can be observed in UV–vis–NIR measurements (see Figures 3, Supporting Information). This is a first indication for the nonreciprocal nature of the effect. If the effect would be reciprocal, like circular dichroism, then the observed asymmetry in transmission would be twice as large for a substrate covered on both sides as for a single-side covered substrate.
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
wileyonlinelibrary.com
2485
www.advmat.de
COMMUNICATION
www.MaterialsViews.com
Figure 1. Asymmetric transmission in plasmonic nanoparticle aggregates occurs when the transmission coefficient (or refractive index) is not equal for forward and backward propagating light beams. The asymmetry in refractive index is due to induced electric quadrupole moments.
When using elliptically polarized laser light instead of unpolarized/randomly polarized bulb light, a large asymmetry in transmission can be observed (see Figure 4, Supporting Information). This result indicates that while asymmetric transmission occurs for all light polarizations, its intensity has a dependency on the used polarization. Besides experimental data, in silico discrete dipole approximation (DDA) simulations of a gold nanoparticle aggregate that is plasmonically coupled to a silver nanoparticle in a high refractive index medium (n = 2) confirm broadband asymmetric transmission (see Figure 5, Supporting Information).[18–20] Although it is an idealized structure, the calculated asymmetry is of the same magnitude as experimentally observed, further strengthening the experimental observations. Differences between the simulated and experimental asymmetry values can be attributed to deviations from the idealized structure or the optimal configuration of the aggregate for asymmetric transmission.
Figure 3. The magnitude of asymmetric transmission of five similar samples in an assembly is approximately five times larger than for a single sample.
While we acknowledge that the observed effect is comparably small, keep in mind that the samples are on average only approximately 20 nm-thick. Further, individual nanoparticle aggregate samples can be stacked to increase the magnitude of the effect. The magnitude of the asymmetric transmission, expressed in dB asymmetry, of five similar samples placed in a consecutive assembly is approximately five times larger than for a single sample (see Figure 3 and Figure 2b, Supporting Information). This linear scalability allows optimization of the effect and is an important asset for possible applications. When the near-fields of individual small plasmonic nanoparticles (intra-aggregate) or plasmonic aggregates at close proximity (interaggregate) couple, electric quadrupole moments, which are strong electric field gradients on the nanoscale, are induced.[14,21] In the presented samples, these gradients are enhanced by the high refractive index iron oxide nanoparticles. DDA simulations of aggregates in media with different refractive indices support this claim (see Figure 6, Supporting Information). Since the quantities we are interested in are the input and output radiation fields and not the local nanoscopic fields, we use a simplified tensorial approach in which, multiple reflections in the thin nanocomposites are neglected.[22,23] For a polar medium, implying a directional plasmonic coupling, in which quadrupole moments are induced under normal incidence of light (no Ez components), we can then write that (see Supporting Information for analysis) E radiated ≈ χ effectiveE input
Figure 2. Transmission in forwards (green and black lines) and backwards (red line) direction are asymmetric over a very broad (400–2000 nm) wavelength range. Expressing the ratio of forward to backward transmission in dB (blue line) shows resonant asymmetry around the plasmon wavelength (± 500 nm) and a broad peak in the infrared region.
2486
wileyonlinelibrary.com
⎡ ⎢ ≈⎢ ⎢ ⎢ ⎣ ⎡ ⎢ ⎣
⎡ Ex ⎢ Ey ⎣
⎤ ⎥ ⎦ radiated
⎤ ⎛ ee eq qe ⎞ 0 ⎥ ⎜⎝ χ xx + χ xzx ∇ z − 6 χ xzx ⎟⎠ ik ik qe ⎞ ⎥ eq ⎛χ yyee + χ yzy ∇ z − χ yzy ⎟ ⎥ ⎜⎝ 0 6 ⎠ ⎥ ⎦ Ex ⎤ E y ⎥⎦ input
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
(1)
Adv. Mater. 2015, 27, 2485–2488
www.advmat.de www.MaterialsViews.com
samples, covered on both sides with aggregates, do not show asymmetric transmission and that an incoming light polarization dependence exists. Using a phenomenological model, we show that induced electric quadrupole moments are the root cause of the asymmetric transmission, which explains all observations and unequivocally establishes the nonreciprocity of the observed effect.
n 2 = 1 + 4π χ effective
Experimental Section
ik qe ⎞ ⎛ n ± = 1 + 4π ⎜ χ ee ± χ eq ∇ z ∓ χ ⎟ ⎝ ⎠ 6
(2)
(3)
The refractive index is different for forward and backward propagation, which gives rise to asymmetric transmission. Further, the tensor is asymmetric over the propagation axis and the origin of the effect is electric quadrupole contributions. As such, the quadrupolarization-induced asymmetric transmission effect in a polar medium fulfils the De Hoop’s nonreciprocity criteria, explicitly demonstrating the nonreciprocal nature.[24] Analyzing the model for different input beam polarizations shows that asymmetric transmission is allowed but not equal in magnitude for all polarizations (see Supporting Information). This explains why the effect can be observed even for unpolarized light and is larger for circular than for linear polarized light. According to the model, no asymmetric transmission can be observed for centrosymmetric media since the tensor components that cause asymmetric transmission then vanish. This is in-line with the reported observations. We observed asymmetric transmission for an asymmetric single-side covered sample, but no asymmetry for a centrosymmetric sample with both sides covered. The presented model not only explains all experimental observations but also demonstrates nonreciprocity and identifies the root cause of the asymmetry, induced electric quadrupole moments. Two distinct routes to improve the magnitude of the observed quadrupolarization-induced asymmetric transmission (Q-AT) effect can be identified. As first, to optimize the effect for individual nanoparticle, aggregate samples. This can be done by inducing stronger quadrupole moments/electric field gradients over a wide spectral region. Possibilities include changing the current or adding more plasmonic metals to intensify the nearfield coupling, changing the size of the nanoparticles to induce stronger asymmetry or changing the length of the linker molecule in the layer-by-layer procedure to tune the interparticle distance. A second route to improvement is to assemble more than one Q-AT active sample in a single entity. One possibility might be to construct a stack of samples by depositing an optically transparent insulating polymer layer between consecutive nanoparticle aggregates. In conclusion, broadband nonreciprocal Q-AT was observed in layer-by-layer synthesized plasmonic-dielectric nanoparticle aggregates on glass substrates even for unpolarized light. The effect was shown to increase linearly with the number of samples in an assembly. Further, we observed that centrosymmetric
Adv. Mater. 2015, 27, 2485–2488
Produced samples consist of a first, low-density silver nanoparticle (9.6 ± 0.2 nm) layer that is self-assembled on an aminosiloxane coated glass substrates. A second layer, consisting of aminosiloxane coated iron oxide nanoparticles (7.9 ± 2.4 nm), self-assembles on top of the already present silver nanoparticles. As third and last, gold nanoparticles (9.2 ± 1.3 nm) are allowed to self-assemble. Vacancies in the first silver nanoparticle layer surrounded by amine-groups from the substrate and magnetite nanoparticles recruit gold nanoparticles, filling up this first layer. Further, gold nanoparticles occupy vacancies in the iron oxide nanoparticle layer and assemble on top of the oxide nanoparticles, thus creating aggregates with their principal axes perpendicular to the substrates’ surface (see Figure 1). Initially, both sides of the glass slide are covered with nanoparticle aggregates. For asymmetric transmission measurements, aggregates on one side of the glass substrate are removed except otherwise noted. On an average, the thickness of these structures is 20 nm but aggregate sizes up to 50 nm are possible.[15,16] Layer-by-layer methods allow for reproducible synthesis of samples and can ensure scalability of synthesis from very small to very large surfaces if desired.[15] The used functionalized iron oxide nanoparticles ensure optimal self-assembly of the gold nanoparticles and further increase the local refractive index value, which has been shown to enhance near-field coupling intensity.[21] The silver and gold aggregates, which are within near-field coupling distances and differ in size due to the layer-by-layer process, have their principal axis perpendicular to the substrate and transversal to the incoming light beam as required to observe asymmetric transmission.[14–16] UV–vis–NIR measurements were performed on a Perkin Elmer Lambda 900 spectrophotometer.
COMMUNICATION
In Equation (1), χeffective is an effective susceptibility, terms in χee are electric dipole contributions while terms in χeq or χqe are due to electric quadrupole contributions. Note that for samples that are in-plane (xy) isotropic, the xx and yy components of the effective susceptibility χeffective are equal. Denoting forward and backward propagation (+z and –z) with a + or – index, we can write the following general equations for the refractive index
Supporting Information Supporting Information is available from the Wiley Online Library or from the author.
Acknowledgements W. Brullot is grateful for a Ph.D. grant by the Agency for Innovation by Science and Technology (IWT) Flanders and a postdoctoral mandate (PDM) from the KU Leuven. T. Verbiest acknowledges financial support from the KU Leuven (GOA Research Grant) and the FWO-Vlaanderen through Research project G.0C02.13N. The authors would like to thank M. Bloemen and M. Vanbel for useful discussions on the topic and critical review of the manuscript. Received: November 26, 2014 Revised: February 12, 2015 Published online: March 9, 2015
[1] D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic´, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, H. Renner, Nat. Photonics 2013, 7, 579.
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
wileyonlinelibrary.com
2487
www.advmat.de
COMMUNICATION
www.MaterialsViews.com
2488
[2] L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, Science 2012, 335, 447. [3] J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, Nat. Commun. 2013, 4, 1599. [4] J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, A. Pan, Sci. Rep. 2012, 2, 820. [5] E. Lenferink, G. Wei, N. Stern, Opt. Express 2014, 22, 16099. [6] W. Aroua, F. AbdelMalek, S. Haxha, S. Tesfa, H. Bouchriha, IEEE J. Quantum Electron. 2014, 50, 633. [7] L. Bi, J. Hu, P. Jiang, D. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, Nat. Photonics 2011, 5, 758. [8] J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, H. Takezoe, Nat. Mater. 2005, 4, 383. [9] M. S. Kang, A. Butsch, P. S. J. Russell, Nat. Photonics 2011, 5, 549. [10] A. Schwanecke, A. Krasavin, D. Bagnall, A. Potts, A. Zayats, N. Zheludev, Phys. Rev. Lett. 2003, 91, 247404. [11] M. Mutlu, S. Cakmakyapan, A. E. Serebryannikov, E. Ozbay, Phys. Rev. B 2013, 87, 205123. [12] H. Lira, Z. Yu, S. Fan, M. Lipson, Phys. Rev. Lett. 2012, 109, 033901.
wileyonlinelibrary.com
[13] S. Manipatruni, J. Robinson, M. Lipson, Phys. Rev. Lett. 2009, 102, 213903. [14] L. V Brown, H. Sobhani, J. B. Lassiter, P. Nordlander, N. J. Halas, ACS Nano 2010, 4, 819. [15] W. Brullot, R. Strobbe, M. Bynens, M. Bloemen, P.-J. Demeyer, W. Vanderlinden, S. De Feyter, V. K. Valev, T. Verbiest, Mater. Lett. 2014, 118, 99. [16] W. Brullot, Development, Synthesis and Characterization of Multifunctional Nanomaterials, Leuven, KU Leuven, 2014. [17] A. Schlegel, S. F. Alvarado, P. Wachter, J. Phys. C: Solid State Phys. 1979, 12, 1157. [18] W. Brullot, T. Verbiest, Proc. SPIE 2014, 9163, 91633H. [19] B. T. Draine, P. J. Flatau, J. Opt. Soc. Am. A 1994, 11, 1491. [20] B. T. Draine, P. J. Flatau, J. Opt. Soc. Am. A 2008, 25, 2693. [21] P. K. Jain, M. A. El-Sayed, Chem. Phys. Lett. 2010, 487, 153. [22] M. Zdanowicz, S. Kujala, H. Husu, M. Kauranen, New J. Phys. 2011, 13, 023025. [23] B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, M. Kauranen, J. Opt. A Pure Appl. Opt. 2006, 8, S278. [24] R. J. Potton, Rep. Prog. Phys. 2004, 67, 717.
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Mater. 2015, 27, 2485–2488
Ward Brullot, Tom Swusten, and Thierry Verbiest*
Nonreciprocal asymmetric transmission, i.e., the dependence of optical transmittance on the direction of light propagation in the material, is currently under intensive research. Research efforts are boosted because the effect could be used in many applications ranging from optical isolators,[1–3] all-optical computing and processing devices,[4,5] to building blocks for integrated photonic circuits.[6] Currently, known ways to achieve nonreciprocal asymmetric transmission are amongst others magneto-optically active structures,[7] liquid crystals,[8] photonic crystals,[6] optoacoustically driven processes,[9] anisotropic and planar chiral structures,[10] nonlinear materials,[2] and composition-graded semiconductor nanowires.[4] While many of these materials show large asymmetries, they suffer from a required input polarization or mode,[6–8,10,11] a high operating threshold intensity,[2,4] large losses,[12] a too large footprint for on-chip integration,[5] a narrow spectral asymmetry bandwidth,[12,13] or use of difficult/ costly/nonintegrable fabrication methods. The search for alternative mechanisms to achieve nonreciprocal and polarizationindependent asymmetric transmission is thus very active and relevant. Brown et al. observed a large difference in the backscattering spectra of single, isolated mismatched plasmonic nanoparticle pairs (diameter per nanoparticle around 150 nm) when changing the propagation direction of the incoming light under transversal excitation in a dark-field microscope setup.[14] The observed local asymmetry was attributed to retardation effects and the relatively weak plasmon coupling under these circumstances. While the measured effect was significant, it cannot be used on the macroscale since it was measured on isolated, single nanoparticle pairs. In this work, we produced near-field coupled aggregates of small plasmonic nanoparticles on transparent glass substrates. This is in contrast to the use of large nanoparticles, like Brown et al.,[14] which give rise to strong scattering effects that hamper applicability in transmission optics. Plasmonic nanoparticle aggregates were produced in an optically isotropic and repro-
Dr. W. Brullot, T. Swusten, Prof. T. Verbiest Division of Molecular Imaging and Photonics Department of Chemistry KU Leuven, Celestijnenlaan 200D, Box 2425, 3001, Heverlee, Leuven, Belgium E-mail: [email protected]
DOI: 10.1002/adma.201405409
Adv. Mater. 2015, 27, 2485–2488
COMMUNICATION
Broadband Nonreciprocal Quadrupolarization-Induced Asymmetric Transmission (Q-AT) in Plasmonic Nanoparticle Aggregates
ducible way by a recently developed layer-by-layer method to achieve broadband nonreciprocal asymmetric transmission in a macroscopic (partially) transparent sample (see Figure 1).[15] Briefly summarized, the nanoparticle aggregates are produced by layer-by-layer deposition of first a low-density silver nanoparticle (9.6 ± 0.2 nm) layer, then a layer of functional complementary iron oxide nanoparticles (7.9 ± 2.4 nm) acting as “glue” and local refractive index enhancer and finally a highdensity gold nanoparticle (9.2 ± 1.3 nm) layer on microscope slides. Compositionally, asymmetric near-field coupled silver– gold nanoparticle aggregates are the result of this procedure. The aggregates’ principal axes are on average perpendicular to the substrates’ surface.[14–16] Both sides of the glass substrate are covered with nanoparticle aggregates. In this work, we show that self-assembled near-field coupled plasmonic-dielectric aggregates are an alternative and attractive way to achieve broadband nonreciprocal asymmetric transmission that can even be observed when using unpolarized light. Further, we phenomenologically explain the experimental observations and the origin of the effect in terms of induced electric quadrupole terms. Experimental UV–vis–NIR measurements using unpolarized light show broadband asymmetric transmission for goldmagnetite-silver aggregate samples with one side removed (see Figures 2 and 1, Supporting Information). Observed asymmetric transmission spans from the UV to the IR spectral region (400–2000 nm). Spectra were first measured in the forward, then backward and then again forward direction to ensure proper data acquisition. Compared with the two forward spectra, the backward spectrum is significantly different (see Figure 2a, Supporting Information). Expressed in dB, the largest asymmetric transmissions can be observed red-shifted from the around 530 nm and in the NIR. The peak around 530 nm corresponds to localized plasmon resonances, possibly with additional contributions from metal interband transitions and magnetite's optical transitions.[17] Near-field-coupled plasmon modes are the origin of the broad NIR peak. If the sample still has both sides of the glass substrate covered, and the total sample thus is symmetric (inversion symmetry), little or no asymmetric transmission can be observed in UV–vis–NIR measurements (see Figures 3, Supporting Information). This is a first indication for the nonreciprocal nature of the effect. If the effect would be reciprocal, like circular dichroism, then the observed asymmetry in transmission would be twice as large for a substrate covered on both sides as for a single-side covered substrate.
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
wileyonlinelibrary.com
2485
www.advmat.de
COMMUNICATION
www.MaterialsViews.com
Figure 1. Asymmetric transmission in plasmonic nanoparticle aggregates occurs when the transmission coefficient (or refractive index) is not equal for forward and backward propagating light beams. The asymmetry in refractive index is due to induced electric quadrupole moments.
When using elliptically polarized laser light instead of unpolarized/randomly polarized bulb light, a large asymmetry in transmission can be observed (see Figure 4, Supporting Information). This result indicates that while asymmetric transmission occurs for all light polarizations, its intensity has a dependency on the used polarization. Besides experimental data, in silico discrete dipole approximation (DDA) simulations of a gold nanoparticle aggregate that is plasmonically coupled to a silver nanoparticle in a high refractive index medium (n = 2) confirm broadband asymmetric transmission (see Figure 5, Supporting Information).[18–20] Although it is an idealized structure, the calculated asymmetry is of the same magnitude as experimentally observed, further strengthening the experimental observations. Differences between the simulated and experimental asymmetry values can be attributed to deviations from the idealized structure or the optimal configuration of the aggregate for asymmetric transmission.
Figure 3. The magnitude of asymmetric transmission of five similar samples in an assembly is approximately five times larger than for a single sample.
While we acknowledge that the observed effect is comparably small, keep in mind that the samples are on average only approximately 20 nm-thick. Further, individual nanoparticle aggregate samples can be stacked to increase the magnitude of the effect. The magnitude of the asymmetric transmission, expressed in dB asymmetry, of five similar samples placed in a consecutive assembly is approximately five times larger than for a single sample (see Figure 3 and Figure 2b, Supporting Information). This linear scalability allows optimization of the effect and is an important asset for possible applications. When the near-fields of individual small plasmonic nanoparticles (intra-aggregate) or plasmonic aggregates at close proximity (interaggregate) couple, electric quadrupole moments, which are strong electric field gradients on the nanoscale, are induced.[14,21] In the presented samples, these gradients are enhanced by the high refractive index iron oxide nanoparticles. DDA simulations of aggregates in media with different refractive indices support this claim (see Figure 6, Supporting Information). Since the quantities we are interested in are the input and output radiation fields and not the local nanoscopic fields, we use a simplified tensorial approach in which, multiple reflections in the thin nanocomposites are neglected.[22,23] For a polar medium, implying a directional plasmonic coupling, in which quadrupole moments are induced under normal incidence of light (no Ez components), we can then write that (see Supporting Information for analysis) E radiated ≈ χ effectiveE input
Figure 2. Transmission in forwards (green and black lines) and backwards (red line) direction are asymmetric over a very broad (400–2000 nm) wavelength range. Expressing the ratio of forward to backward transmission in dB (blue line) shows resonant asymmetry around the plasmon wavelength (± 500 nm) and a broad peak in the infrared region.
2486
wileyonlinelibrary.com
⎡ ⎢ ≈⎢ ⎢ ⎢ ⎣ ⎡ ⎢ ⎣
⎡ Ex ⎢ Ey ⎣
⎤ ⎥ ⎦ radiated
⎤ ⎛ ee eq qe ⎞ 0 ⎥ ⎜⎝ χ xx + χ xzx ∇ z − 6 χ xzx ⎟⎠ ik ik qe ⎞ ⎥ eq ⎛χ yyee + χ yzy ∇ z − χ yzy ⎟ ⎥ ⎜⎝ 0 6 ⎠ ⎥ ⎦ Ex ⎤ E y ⎥⎦ input
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
(1)
Adv. Mater. 2015, 27, 2485–2488
www.advmat.de www.MaterialsViews.com
samples, covered on both sides with aggregates, do not show asymmetric transmission and that an incoming light polarization dependence exists. Using a phenomenological model, we show that induced electric quadrupole moments are the root cause of the asymmetric transmission, which explains all observations and unequivocally establishes the nonreciprocity of the observed effect.
n 2 = 1 + 4π χ effective
Experimental Section
ik qe ⎞ ⎛ n ± = 1 + 4π ⎜ χ ee ± χ eq ∇ z ∓ χ ⎟ ⎝ ⎠ 6
(2)
(3)
The refractive index is different for forward and backward propagation, which gives rise to asymmetric transmission. Further, the tensor is asymmetric over the propagation axis and the origin of the effect is electric quadrupole contributions. As such, the quadrupolarization-induced asymmetric transmission effect in a polar medium fulfils the De Hoop’s nonreciprocity criteria, explicitly demonstrating the nonreciprocal nature.[24] Analyzing the model for different input beam polarizations shows that asymmetric transmission is allowed but not equal in magnitude for all polarizations (see Supporting Information). This explains why the effect can be observed even for unpolarized light and is larger for circular than for linear polarized light. According to the model, no asymmetric transmission can be observed for centrosymmetric media since the tensor components that cause asymmetric transmission then vanish. This is in-line with the reported observations. We observed asymmetric transmission for an asymmetric single-side covered sample, but no asymmetry for a centrosymmetric sample with both sides covered. The presented model not only explains all experimental observations but also demonstrates nonreciprocity and identifies the root cause of the asymmetry, induced electric quadrupole moments. Two distinct routes to improve the magnitude of the observed quadrupolarization-induced asymmetric transmission (Q-AT) effect can be identified. As first, to optimize the effect for individual nanoparticle, aggregate samples. This can be done by inducing stronger quadrupole moments/electric field gradients over a wide spectral region. Possibilities include changing the current or adding more plasmonic metals to intensify the nearfield coupling, changing the size of the nanoparticles to induce stronger asymmetry or changing the length of the linker molecule in the layer-by-layer procedure to tune the interparticle distance. A second route to improvement is to assemble more than one Q-AT active sample in a single entity. One possibility might be to construct a stack of samples by depositing an optically transparent insulating polymer layer between consecutive nanoparticle aggregates. In conclusion, broadband nonreciprocal Q-AT was observed in layer-by-layer synthesized plasmonic-dielectric nanoparticle aggregates on glass substrates even for unpolarized light. The effect was shown to increase linearly with the number of samples in an assembly. Further, we observed that centrosymmetric
Adv. Mater. 2015, 27, 2485–2488
Produced samples consist of a first, low-density silver nanoparticle (9.6 ± 0.2 nm) layer that is self-assembled on an aminosiloxane coated glass substrates. A second layer, consisting of aminosiloxane coated iron oxide nanoparticles (7.9 ± 2.4 nm), self-assembles on top of the already present silver nanoparticles. As third and last, gold nanoparticles (9.2 ± 1.3 nm) are allowed to self-assemble. Vacancies in the first silver nanoparticle layer surrounded by amine-groups from the substrate and magnetite nanoparticles recruit gold nanoparticles, filling up this first layer. Further, gold nanoparticles occupy vacancies in the iron oxide nanoparticle layer and assemble on top of the oxide nanoparticles, thus creating aggregates with their principal axes perpendicular to the substrates’ surface (see Figure 1). Initially, both sides of the glass slide are covered with nanoparticle aggregates. For asymmetric transmission measurements, aggregates on one side of the glass substrate are removed except otherwise noted. On an average, the thickness of these structures is 20 nm but aggregate sizes up to 50 nm are possible.[15,16] Layer-by-layer methods allow for reproducible synthesis of samples and can ensure scalability of synthesis from very small to very large surfaces if desired.[15] The used functionalized iron oxide nanoparticles ensure optimal self-assembly of the gold nanoparticles and further increase the local refractive index value, which has been shown to enhance near-field coupling intensity.[21] The silver and gold aggregates, which are within near-field coupling distances and differ in size due to the layer-by-layer process, have their principal axis perpendicular to the substrate and transversal to the incoming light beam as required to observe asymmetric transmission.[14–16] UV–vis–NIR measurements were performed on a Perkin Elmer Lambda 900 spectrophotometer.
COMMUNICATION
In Equation (1), χeffective is an effective susceptibility, terms in χee are electric dipole contributions while terms in χeq or χqe are due to electric quadrupole contributions. Note that for samples that are in-plane (xy) isotropic, the xx and yy components of the effective susceptibility χeffective are equal. Denoting forward and backward propagation (+z and –z) with a + or – index, we can write the following general equations for the refractive index
Supporting Information Supporting Information is available from the Wiley Online Library or from the author.
Acknowledgements W. Brullot is grateful for a Ph.D. grant by the Agency for Innovation by Science and Technology (IWT) Flanders and a postdoctoral mandate (PDM) from the KU Leuven. T. Verbiest acknowledges financial support from the KU Leuven (GOA Research Grant) and the FWO-Vlaanderen through Research project G.0C02.13N. The authors would like to thank M. Bloemen and M. Vanbel for useful discussions on the topic and critical review of the manuscript. Received: November 26, 2014 Revised: February 12, 2015 Published online: March 9, 2015
[1] D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic´, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, H. Renner, Nat. Photonics 2013, 7, 579.
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
wileyonlinelibrary.com
2487
www.advmat.de
COMMUNICATION
www.MaterialsViews.com
2488
[2] L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, Science 2012, 335, 447. [3] J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, H. Giessen, Nat. Commun. 2013, 4, 1599. [4] J. Xu, X. Zhuang, P. Guo, W. Huang, W. Hu, Q. Zhang, Q. Wan, X. Zhu, Z. Yang, L. Tong, X. Duan, A. Pan, Sci. Rep. 2012, 2, 820. [5] E. Lenferink, G. Wei, N. Stern, Opt. Express 2014, 22, 16099. [6] W. Aroua, F. AbdelMalek, S. Haxha, S. Tesfa, H. Bouchriha, IEEE J. Quantum Electron. 2014, 50, 633. [7] L. Bi, J. Hu, P. Jiang, D. Kim, G. F. Dionne, L. C. Kimerling, C. A. Ross, Nat. Photonics 2011, 5, 758. [8] J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, H. Takezoe, Nat. Mater. 2005, 4, 383. [9] M. S. Kang, A. Butsch, P. S. J. Russell, Nat. Photonics 2011, 5, 549. [10] A. Schwanecke, A. Krasavin, D. Bagnall, A. Potts, A. Zayats, N. Zheludev, Phys. Rev. Lett. 2003, 91, 247404. [11] M. Mutlu, S. Cakmakyapan, A. E. Serebryannikov, E. Ozbay, Phys. Rev. B 2013, 87, 205123. [12] H. Lira, Z. Yu, S. Fan, M. Lipson, Phys. Rev. Lett. 2012, 109, 033901.
wileyonlinelibrary.com
[13] S. Manipatruni, J. Robinson, M. Lipson, Phys. Rev. Lett. 2009, 102, 213903. [14] L. V Brown, H. Sobhani, J. B. Lassiter, P. Nordlander, N. J. Halas, ACS Nano 2010, 4, 819. [15] W. Brullot, R. Strobbe, M. Bynens, M. Bloemen, P.-J. Demeyer, W. Vanderlinden, S. De Feyter, V. K. Valev, T. Verbiest, Mater. Lett. 2014, 118, 99. [16] W. Brullot, Development, Synthesis and Characterization of Multifunctional Nanomaterials, Leuven, KU Leuven, 2014. [17] A. Schlegel, S. F. Alvarado, P. Wachter, J. Phys. C: Solid State Phys. 1979, 12, 1157. [18] W. Brullot, T. Verbiest, Proc. SPIE 2014, 9163, 91633H. [19] B. T. Draine, P. J. Flatau, J. Opt. Soc. Am. A 1994, 11, 1491. [20] B. T. Draine, P. J. Flatau, J. Opt. Soc. Am. A 2008, 25, 2693. [21] P. K. Jain, M. A. El-Sayed, Chem. Phys. Lett. 2010, 487, 153. [22] M. Zdanowicz, S. Kujala, H. Husu, M. Kauranen, New J. Phys. 2011, 13, 023025. [23] B. K. Canfield, S. Kujala, K. Jefimovs, Y. Svirko, J. Turunen, M. Kauranen, J. Opt. A Pure Appl. Opt. 2006, 8, S278. [24] R. J. Potton, Rep. Prog. Phys. 2004, 67, 717.
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Mater. 2015, 27, 2485–2488
