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Abstract
A theoretical study regarding wired and wireless link performance by using a dielectric resonator nanoantenna (DRNA) integrated to a metal-dielectric-metal-dielectric (MDMD) nanostrip waveguide is evaluated. Near- and far-field coupling characteristics in receiving (RX) and transmitting (TX) modes of this DRNA are investigated at optical frequencies (C-band). This nanoantenna and its coupling characteristics reveal a promising approach for coupling light to plasmonic nanostrip waveguides and implementing inter-chip communication in nanophotonics using the same or distinct platforms.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The approach of using metallic elements or layers in order to implement optical components with high modal optical confinement exploring the electric field enhancement or light propagation has encouraged the development of several applications based on the plasmonic technology [1–5]. Although plasmonic circuits are commonly ultra-compact when compared with dielectric ones, they suffer of metal absorption losses, which limit the implementation of circuits for long propagation distances. Inspired in the radio frequency (RF) domain, Alù and Engheta [6] suggested the implementation of a wireless link, mediated by dipole nanoantennas, to relief the high losses in plasmonic circuits for long distances in waveguides operating at f0 = 415 THz.
In this manuscript, a theoretical study about “long distance” links for circuits based on MDMD nanostrip waveguides [7,8] operating at central wavelength of λ0 = 1.55 µm and integrated to a DRNA [8–10] [schematic is shown in Fig. 1(a)
Fig. 1 (a) 3-D schematic of a DRNA integrated to a nanostrip waveguide. (b) Schematic cross-sections of a wireless link (intermediated by two DRNAs) compared to a wired one (top center). Both links assume the same distance, d.
2. Materials, methods, and some characteristics of MDMD and DRNA
2.1 MDMD nanostrip waveguide: modal analysis
Modal analyses of such nanostrip waveguide operating at λ0 = 1.55 μm was carried out by using finite element method. A comparison of the cases when the metal is composed of Ag [11], and when it is made of perfect electric conductor (PEC) is performed in order to evaluate the similarities and differences between the plasmonic versus the lossless/dispersionless cases. Figures 2(a) and 2(b)
Fig. 2 Longitudinal components of the power flow (temporal average) at λ0 = 1.55 μm. (a) Fundamental mode when metal is assumed to be silver. (b) Fundamental mode when metal is assumed to be a PEC. Contour map varying from light to dark colors represents the power magnitude ranging from high to low power. Effective index versus nanostrip widths, w, versus dielectric substrate heights, h1, for the cases when metal is composed of Ag (c) and PEC (d).
Although the nanostrip waveguides and the microstrip ones are geometrically similar (regardless of different scales and materials), their effective refractive indexes vary in a very different manner. Figures 2(c) and 2(d) show the variation of the real component of the effective refractive index versus nanostrip width, w, and dielectric substrate height, h1, in two distinct cases: when metal is composed by Ag and PEC, respectively. It can be noticed that the difference between the effective refractive index values for those cases is large. Furthermore, the shape of the effective refractive index function is very dissimilar between these cases. The approach assuming a PEC is commonly used during the design of equivalent waveguides operating at microwaves; where the skin depth is low and metal has not such expressive dispersion as metal has at the optical domain.
The propagation distance of plasmonic waveguides, Lprop, is commonly defined as the distance that the field amplitude decays in 1/e; which can be given by:
where Im[nef] is the imaginary component of the effective refractive index. Thus, by assuming that approximation for the dimensions taken into account and considering metal composed of Ag, we estimated Lprop ~31.63 μm for the fundamental mode at λ0 = 1.55 μm.2.2 Return loss and radiation pattern
For the calculation of the return loss and radiation pattern, we assumed that the propagating fundamental mode of the nanostrip waveguide excites the DRNA fundamental mode. In other words, the antenna is operating in TX mode. The wavelength dependence of the reflection coefficient, |Γ|, of the nanostrip waveguide coupled to the DRNA is shown in Fig. 3(a)
, where a broadband characteristic can be noticed. The radiation pattern has broadside characteristics as shown in Fig. 3(b).3. Results and discussions
3.1 Near-field coupling
A circular cylindrical DRNA composed by a-Si with r = 0.245 μm and h = 0.315 μm is positioned in such a way that its fundamental mode is matched to the fundamental mode of the MDMD nanostrip waveguide. The resonator geometry is firstly designed to operate at the central wavelength of λ0 = 1.55 μm. Then the mode matching is numerically evaluated by varying the DR position along the nanostrip waveguide terminal. When the reflection coefficient of the nanostrip waveguide reaches a minimal value, the DR assumes an optimal position. At this point, the nanostrip fundamental mode couples to the DR one. This approach of mode coupling was reported previously in [8]. Numerical simulations were carried out by using the finite-difference time-domain method.
Fig. 4 Coupling efficiency in near-field assuming different numerical apertures (ranging from 0.1 to 0.9 with a step of 0.1) from the incident field. (a) Nanostrip matched to the DRNA. The inset shows a sketch with an offset between the beam and the nanoantenna centers, as well as the offset between the antenna radius and the waveguide terminal. (b) Nanostrip without DRNA.
Fig. 5 Comparison of the coupling efficiency, in RX mode and in near field, for linear- (in red) and cross-polarization (in blue). The reflected power through the top region (in orange) is shown for the case of linear polarization.
3.2 Wireless (far-field coupling) versus wired links
The power received by one antenna from another one, under idealized conditions, a distance away is given by the Friis transmission equation [12]:
where ηt and ηr are the efficiency of the optical radiation from the transmitting and receiving antennas, respectively. Dt and Dr are the directivities of the transmitting and receiving antennas. Гt and Гr are the reflection coefficient of the link between DRNA and the plasmonic waveguide for the transmitting and receiving antennas, respectively. at.ar* are related to the polarization matching, which can be deteriorated due to the misalignment between the two antennas. λ0 is the wavelength of operation and d is the separation distance between the antennas. Pr is the received power at the receiving antenna and Pt is the feeding power in the transmitting antenna.Like in RF, the Eq. (2) can be used to estimate the optical link between nanoantennas, as shown in [6] by assuming metallic ones (dipoles). Figure 6
Fig. 6 Comparison between wired (in green) and wireless link between MDMD nanostrip waveguide. For the wireless case are assumed directivities of 1 dBi (in violet) and 8.48 dBi (in blue), the last one represents the directivity of our design of DRNA.
Finally, this broadside radiation characteristics and the polarization sensitivity are attractive to optical wireless inter-chip communication between same or distinct platforms, for example, circuits based on silicon photonics (by using grating couplers) and plasmonics (by using the approach presented here).
4. Conclusion
We investigated free-space optical coupling (near and far fields) to a MDMD nanostrip waveguide assuming RX and TX modes at central wavelength λ0 = 1.55 µm. Numerical calculations show that the coupling efficiency in this scenario may be increased by 3x when a DRNA is integrated to such a waveguide. Additionally, the coupling in broadside and presenting high polarization sensitivity may be promising to implement new hybrid platforms by means of the wireless links enhanced by means of such DRNAs.
Funding
São Paulo Research Foundation (FAPESP) (10/18857-7, 18/13321-3) and the INCT FOTONICOM/CNPq/FAPESP.
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