Wireless optical coupling evaluation in a dielectric resonator nanoantenna

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DOI: 10.1364/OSAC.1.000805

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©2018

by Optical Society of America. All rights reserved.

DIRETORIA DE TRATAMENTO DA INFORMAÇÃO Cidade Universitária Zeferino Vaz Barão Geraldo

CEP 13083-970 – Campinas SP Fone: (19) 3521-6493 http://www.repositorio.unicamp.br

Wireless optical coupling evaluation in a

dielectric resonator nanoantenna

G

N. M

-S

H

E. H

-F

1_{São Paulo State University (UNESP), Campus of São João da Boa Vista, São Paulo, 13876-750, Brazil} 2_{Department of Communications (DECOM), School of Electrical and Computer Engineering (FEEC),}

University of Campinas (UNICAMP), 13083-970–Campinas, São Paulo, Brazil

*gnmsilveira@gmail.com

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)] is evaluated. For the wireless link we have studied the coupling of near- and far-fields of a circular cylindrical DRNA [8] matched to a MDMD nanostrip waveguide. For the wired link we assume an MDMD nanostrip waveguide of length d connecting two points separated by a distance d. Figure 1(b) shows a schematic cross-section of a wired link based on MDMD nanostrip waveguide versus a wireless link established by DRNAs. (Although Fig. 1(b) depicts two DRNA per chip, this study is not about array of antennas.)

#340681 https://doi.org/10.1364/OSAC.1.000805

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) show the normalized power distribution of the fundamental modes at the cross-sectional view of this nanostrip waveguide assuming arbitrary: h1 = 0.145 μm, h2 = 0.020 μm, h3 = 0.010 μm, and w = 0.340 μm (see Fig. 1 for the

corresponding dimensions). The metallic regions were assumed to be composed of Ag [Fig. 2(a)] and PEC [Fig. 2(b)], and the low-index dielectric was assumed to be composed of SiO2 in both cases.

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: 1 2 Im prop o ef L k n =     (1) 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).

Fig. 3. (a) Reflection coefficient, S11, in decibel. (b) Radiation pattern at λ0 = 1.55 μm. 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.

Figure 4(a) shows the coupling efficiency, assuming different numerical apertures (NA), from a Gaussian beam spot 0.5 μm far from the DRNA. The optimal position for coupling efficiency is obtained when there is an offset of about y = - 0.25 μm between the center of the DRNA and beam spot center. The coupling efficiency is also evaluated for the same nanostrip waveguide without a DRNA as shown in Fig. 4(b). For this case, the beam spot is located 0.5 μm far from the nanostrip. By comparing the respective NAs of both these cases, it can be noticed that the advantage of using DRNA for coupling light becomes more evident in terms of efficiency.

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.

Figure 5 shows the transmission and reflection of the DRNA operating in RX mode under the incidence of a source of light with NA = 0.7 located 0.5 μm far from the top face of the DRNA. A coupling efficiency of about 51% is obtained at the central wavelength λ0 =

1.55 µm. At this wavelength, the power reflected through the top region is about 16% lower than the incident one. For this same configuration, but in a cross-polarization, the coupling efficiency is below 0.1%. This polarization sensitivity is also interesting to avoid interferences in systems based on optical wireless inter-chip communication.

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 shows a comparison between the interconnection of two points distant away connected by a MDMD nanostrip waveguide (wired link) and a wireless link by applying the DRNA [see Fig. 1 (right)]. For the wired link, the propagation is proportional to e-αd_{, it can be noticed that for distances longer than d ~42}

µm, the wireless link is more efficient. When assuming isotropic nanoantennas (just for comparison sake) only for distances longer than d ~65 µm the wireless link becomes interesting. In especial, when the antennas are highly directive and broadside, this solution becomes very interesting when compared to that one in [6], which uses a dipole that has omnidirectional radiation pattern. Furthermore, although in our design we used a DRNA with directivity of 8.48 dBi, by using DR with different shapes and/or materials as well as in arrays [13], directivities of order of tens can be obtained in order to decrease the losses of wireless optical links.

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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