Coupling Effect between Silicon Nitride Optical Waveguide
and Gold Nanoparticle Chain in the Visible Spectrum
1, 2
Yida Wen
1
2, 3
2, 3
, Philippe Gogol , Jean-René Coudevylle , Abdelhanin Aassime
1
1
2, 3
David Barat , Laetitia Pradere and Beatrice Dagens
2, 3
,
PSA Peugeot Citroën, Direction Scientifique, Centre technique de Vélizy, route de Gisy 78140 Vélizy-Villacoublay, France
2
Institut d’Électronique Fondamentale, Univ Paris-Sud, 91405 Orsay, France
3
Centre National de la Recherche Scientifique, UMR 8622, 91405 Orsay, France
[email protected]
Abstract: We theoretically demonstrate that a TE dielectric waveguide mode can be partially
coupled into a metal nanoparticle chain’s transverse plasmon mode in the visible spectrum range
with a compromise between resonance wavelength and coupling efficiency.
OCIS codes: (250.3140) Integrated optoelectronic circuits; (240.6680) Surface plasmons
1. Introduction
Dipolar interactions between closely spaced metal nanoparticles (MNPs) can realize energy transfer by means of a
MNP chain formed plasmonic waveguide below the diffraction limit [1,2]. The hybrid localized surface plasmon
(LSP) mode between MNP chain and dielectric photonic waveguide has been intensively investigated in theory and
experimentally. For the purpose of fabricating the LSP based nanometer scale devices in photonic integrated circuit,
Février et al demonstrated a giant coupling effect between ridge-like silicon optical waveguide (RWG) and gold
nanoparticle chain [3]. The numerical simulation study and experimental microscopy observation in near-field show
that optical energy carried by a TE mode can be totally transferred into a transverse plasmon mode supported by the
MNP chain over the telecommunication band. Arango et al studied the plasmonic antennas at a resonance
wavelength of 800 nm composed by a silicon nitride waveguide and a classic 5-element Yagi-Uda type gold
nanoparticle chain [4]. Chamanzar et al experimentally demonstrated efficient extinction spectroscopy of single
plasmonic gold nanorods to individual plasmonic nanoparticles for an integrated LSP resonance sensing and
spectroscopy application at a visible wavelength [5]. In our work, we are inspired by the interest of the giant
coupling effect between the optical TE mode carried by a silicon nitride waveguide and the plasmonic mode
occurred in a short gold nanoparticles chain, and we demonstrate that based on our FDTD simulation results, there is
a compromise between the blue shift of the resonance wavelength and the extinction efficiency indicated by the
silicon nitride RWG fundamental TE mode transmission within the MNP chain at visible wavelength.
2. Modeling and fabrication of the dielectric waveguide structure
The schematic view of a MNP chain on top of a Si3N4 RWG is shown in Fig. 1 (left). As silicon nitride has a high
refraction index (i.e., n = 2 at 633 nm) and very low propagation losses in the visible wavelength range, our RWG is
made by Si3N4 that supports a quasi-transverse electric (TE) mode of the source semiconductor laser at 633 nm. For
the purpose of the monomode excitation from photonic mode to LSP mode, we keep only the TE fundamental mode
(TE00) in Si3N4 RWG by limiting its cross-section below the multimode criteria.
Fig. 1. (left) Schematic view of a MNP chain on top of the Si3N4 ridge waveguide. The surface plasmonic mode of the MNP chain will be
excited by the TE fundamental mode travelling along the RWG at 633 nm. (right) Scanning electron micrograph of cross-section of Si3N4 ridge
waveguide on top of a SiO2 substrate.
The first step is to determine the width and the thickness of waveguide. Using the classical effective index
method (EIM) introduced by Yariv [6], we can quickly and approximately estimate the relation between the crosssection of Si3N4 RWG and the optical effective index of the global waveguide structure. Several effective index
calculation results are shown in Fig. 2. We suppose that the Si3N4 RWG with MNP chain should be covered by SiO2
in order to keep a homogeneous index environment for the fundamental TE mode guided in the Si3N4 RWG. In our
2D effective index calculation modeling, the refraction index of all space surrounding the Si3N4 RWG is set to 1.45
at 633 nm. In this case, the TE00 mode will have a round-like electric field distribution.
Fig. 2. 2D effective index calculation in function of the cross-section of the Si3N4 ridge waveguide surrounded by SiO2. The effective index
method (EIM) simulation results are presented by “--” and the results in “**” are calculated by a FDTD simulation software.
According to the evaluated effective index, we choose a cross-section of 300 nm (width) × 250 nm (height) so as
to satisfy the requirement for fundamental guided TE mode. The Si3N4 RWG was fabricated by using electron beam
lithography followed by a reactive ion etching process. Both Si3N4 and SiO2 layers are deposited by PECVD [7]. A
scanning electron micrograph of Si3N4 RWG made in our cleanroom is shown in Fig. 1 (right).
3. Coupling effect between RWG and MNP chain
Through the evanescent field of the fundamental TE guided mode of Si3N4 RWG, a transverse localized plasmonic
mode comes out when appropriate size and spacing of gold nanoparticles are chosen. For the first step, we set MNP
spacing d small enough to be out of Bragg diffraction [8,9]. The photonic-plasmonic coupling efficiency can be
indicated by measuring the transmission spectra of the Si3N4 RWG decorated with gold nanoparticles. Our structure
consists of a 5 gold NP chain with a spacing of 130 nm on top of a 300 nm × 250 nm Si3N4 RWG. To determine the
size of nanoparticles, we used 3D finite-difference time-domain (FDTD) simulations. The simulation parameters
incorporate experimental data of the fabricated structure, such as the refractive indexes of Si3N4 and SiO2
determined by ellipsometry. All FDTD simulations for different MNP chain in this work were using a 3D mesh with
dimensions smaller than 2 nm in the MNP zone. Our targeted MNP chain resonance occurs in the transmission
window of the Si3N4 RWG (wavelength = 633 nm in vacuum) with an excitation by the TE00 waveguide mode and a
dipolar coupling between neighboring particles. The FDTD simulation results of transmission spectra of hybrid
RWG/MNP chain systems are shown in Fig. 3. We defined the nanorod shape in Fig. 1 (left) by the radius of the
axis in parallel with propagation direction ax, the radius of the axis perpendicular to propagation direction a y and its
thickness t.
As seen in Fig. 3, we noticed that the RWG guided TE mode transmission minimum corresponds to a LSP
resonance wavelength of the coupled MNP chain. This resonance wavelength will shift to the blue side when ax and
t increase, as well as ay decreases. From a point of view of ellipsoid factor, Au nanoparticles with a given spacing of
130 nm should have a longer axis in parallel with the optical propagation direction of RWG mode and a shorter axis
perpendicular to propagation direction. On the other hand, once the resonance wavelength shifts to the blue, the
spectral RWG TE mode transmission will remarkably increase and the spectrum will be broadened. That means the
photonic-plasmonic coupling effect occurs with a compromise between resonance wavelength and coupling
efficiency within the visible spectrum range. A total energy transfer from the RWG guided mode to the MNP chain
LSP mode is not possible at any visible wavelength. This must be related to plasmonic resonance wavelength of
gold embedded in SiO2, combined with near-field and far-field coupling between the chain nanoparticles, and to the
increasing confinement of the TE00 mode in the Si3N4 RWG with decreasing wavelength. Using this characteristic, a
part of the initial guided optical signal can be reserved and propagate further in the dielectric RWG through the
MNP chain region, whereas the other part excite the MNP chain with a targeted wavelength of 633 nm. The best
compromise is then a transmission of 0.8, obtained with (t = 27 nm, a x= 55 nm and ay= 20 nm) or with (t = 37 nm,
ax= 55 nm and 20 nm ≤ ay ≤ 30 nm). The second case will allow more tolerance to the fabrication. We have also
studied on the case with the silver nanoparticles chain and the case with a 200 nm × 200 nm Si 3N4 RWG. Some
primary FDTD simulation results show that the coupled plasmonic resonance wavelength of the Ag nanoparticles
chain will shift to the blue in comparison with the Au nanoparticles chain.
Fig. 3. FDTD calculation results of RWG fundamental TE mode transmission spectra. The simulated photonic-plasmonic structure consists
of a gold nanoparticles chain with 130 nm spacing on top of a 250 nm × 300 nm Si3N4 RWG embedded in SiO2.
4. Conclusion
Here we demonstrate a photonic-plasmonic coupling effect in the visible spectrum range by modeling a 5 gold
nanoparticles chain on top of a Si3N4 ridge-like waveguide. Unlike the case at infrared range, the energy transfer
from the dielectric TE mode to coupled surface plasmonic transverse mode can hardly achieve more than 70% at a
visible LSP resonance wavelength. The blue-shift of the resonance wavelength is limited by the plasmonic response
of gold and by the chain nanoparticle near-field and far-field coupling. The best compromise of resonance
wavelength and coupling efficiency at 633 nm gives a transmission of 0.8, which is useful for our application. The
fabrication and characterization of the mentioned hybrid photonic-plasmonic waveguide structure with gold or silver
NP chain and Si3N4 RWG will be done in future.
This work was partly supported by the PSA Peugeot Citroën - Université Paris-Sud Optoelectronics and
photonics research chair and by the French RENATECH network. Yida Wen grant has been funded by PSA Peugeot
Citroën and the French Association Nationale de la Recherche et de la Technologie under contract CIFRE2011/1610.
5. References
[1] M. Quinten et al., “Electromagnetic energy transport via linear chains of silver nanoparticles,” Optics Letters 23, 1331-1333 (1998).
[2] M. Brongersma et al., “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Physical
Review B 62, 16356-16359 (2000).
[3] M. Février et al., “Giant coupling effect between metal nanoparticle chain and optical waveguide,” Nano Letters 12, 1032-1037 (2012).
[4] B. Arango et al., “Plasmonic Antennas Hybridized with Dielectric Waveguides,” ACS Nano 6, 10156-10167 (2012).
[5] M Chamanzar, et al., “Hybrid integrated plasmonic-photonic waveguides for on-chip localized surface plasmon resonance (LSPR) sensing
and spectroscopy,” Optics Express 21, 32086-32098 (2013).
[6] A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Sixth edition, Oxford University Press, Inc., 2006), Ch. 3.
[7] N. Daldosso et al., “Fabrication and optical characterization of thin two-dimensional Si3N4 waveguides,” Materials Science in Semiconductor
Processing 7, 453-458 (2004).
[8] M. Février et al., “Localized surface plasmon waveguide integrated on dielectric waveguide,” in the 15th European Conference on Integrated
Optics, (Cambridge, 2010), WeP. 29.
[9] M. Février et al., “Metallic nanoparticle chains on dielectric waveguides: coupled and uncoupled situations compared,” Optics Express 21,
24504-24513 (2013).