Optical Antennas as Nano-probes in Photonic Crystals ... - IEEE Xplore

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Universidad Autónoma de San Luis Potosí. Sierra Leona, 550. Lomas 2ª secc. 78210. San Luis Potosí, Mexico javier.gonzalez@uaslp.mx. +Applied Optics ...
Optical Antennas as Nano-probes in Photonic Crystals and Dielectric Waveguide Structures Francisco J. González *, Javier Alda+ *

Coordinación para la innovación de la ciencia y la tecnología. Universidad Autónoma de San Luis Potosí. Sierra Leona, 550. Lomas 2ª secc. 78210. San Luis Potosí, Mexico [email protected]

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Applied Optics Complutense Group. University Complutense of Madrid School of Optics. Ave. Arcos de Jalón, 118. 28037 Madrid. Spain [email protected]

Abstract— The performance of dipole and bowtie nanoantennas coupled to a photonic crystal waveguide is analyzed by numerical simulations as a function of the antenna length. The antennas showed two resonances spectrally far apart from each other: one of them corresponds to the main antenna resonance and the other one to the allowed modes in the bandgap of the photonic crystal substrate. It is worth noting that the dipole shows a substrate resonance close to the lower edge of the bandgap and the bowtie shows a substrate resonance at the upper end of the bandgap. The results also show a nonlinear scaling between the resonant wavelength and the length of the antennas, this could be attributed to the coupling of the antenna resonance and the absorption resonance of the substrate material.

I. INTRODUCTION The possibility of confining electromagnetic radiation to subwavelength spatial domains has drawn a lot of attention to the fields of optical nano-metals and plasmonics [1]. An interesting application of plasmonics is the possibility of building antennas at optical frequencies which could benefit the areas of optical communications and near field sensing. Waveguides, specially optical fibers, can be used in sensing applications because of their ability to transmit light in a flexible and compact fashion and have potential applications in chemical, biological, and environmental detection [2]. On the other hand, photonic crystals, or photonic bandgap materials, are periodically modulated dielectric or metallic structures which give rise to bands where the propagation is prohibited for a certain frequency range [3]. Photonic crystals have been used in antenna technology to suppress surface waves, create controllable beams, and design high-gain antennas with a single feed [4]. Photonic crystal waveguides are photonic bangap materials with a linear defect which supports a linearly localized mode without relying on total internal reflection like regular waveguides [5], similar to these type of devices photonic crystal fibers have been developed and used as an alternative to conventional optical fibers.

Diverse applications can arise when combining photonic crystal waveguides and optical antennas. One of the main problems in designing optical antennas is the non-ideal behavior of metals at optical frequencies [6], and the change in radiation characteristics when the antenna is placed on a complex substrate such as a photonic crystal waveguide. In this contribution we analyze numerically the response of a dipole and bowtie nano-antenna embedded in a photonic crystal structure in order to assess their potential use as probes for near-field sensing applications. II. METHOD The performance of two nanoantennas, a dipole and a bowtie was evaluated when placed on a photonic crystal waveguide. The length of the dipole and bowtie nanoantenna varied from 0.25 µm to 1 µm, the width and length was set constant at 100 nm. The metal used for the dipole in the simulation was gold and the optical constants used took into account the dispersion of the metal at the simulated frequencies [6]. The photonic crystal structure chosen was the one analyzed by Guo et al. [7] consisting of 25 GaAs (ε=11.56) rods in air with radii of 0.20a and 0.60a, for the regular rods and defect rod respectively, where “a” is the lattice constant that in our case has been selected to be a=1.0 μm. The single GaAs rod had a 0.6 μm radius and was surrounded by air. The simulated rods were 6 μm long. Without the antenna the photonic crystal structure has a bandgap given by fmin=0.29 c/a to fmax=0.42 c/a [7] for a wave propagating within the plane of the photonic crystal in the TM mode, which in this case gives a frequency band of 87 THz (3.44 µm) to 126 THz (2.38 µm). The simulations were performed by launching a plane wave with an electric-field amplitude set to 1 V/m and calculating the induced current in the nanoantenna as a function of the plane wave’s wavelength by integrating the surface current density over the antenna cross-section at its geometrical center. Matched boundary conditions were used

in the FEM simulations and tetrahedral elements were used to discretize the computational domain.

graph it can be seen that the main resonance does not follow a linear relation as a function of antenna length.

III. RESULTS Figure 1 shows the spectral response of four different dipoles with lengths ranging from 0.25-1.0 µm the graph shows two resonances the one around 50 THz is the main dipole resonance and the smaller resonance around 87THz corresponds to the lower end of the bandgap of the photonic crystal structure.

Fig. 3: Resonant frequency for bowtie and dipole nanoantennas on a photonic crystal waveguide as a function of antenna length.

IV. CONCLUSIONS

Fig. 1: Spectral response of a dipole nanoantenna on a photonic crystal waveguide for different antenna lengths.

Figure 2 shows the spectral response of four different bowtie nanoantennas with lengths ranging from 0.25-1.0 µm similarly to Fig. 1, in this graph two resonances can be seen, one around 50 THz and a smaller resonance around 100 THz which corresponds to the upper end of the bandgap of the photonic crystal structure.

Fig. 2: Spectral response of a bowtie nanoantenna on a photonic crystal waveguide for different antenna lengths.

Figure 3 shows the main resonant frequency of dipole and bowtie nanoantennas as a function of antenna length, from the

The performance of a dipole and bowtie nanoantenna coupled to a photonic crystal waveguide was analyzed by numerical simulations as a function of antenna length. The results show that two resonances are present, a main resonance which is consistent with the main resonance of the nanoantenna and a second resonance which is consistent with the bandgap of the photonic crystal structure that acts as the substrate. It is worth noting that the dipole shows a substrate resonance close to the lower edge of the bandgap and the bowtie shows a substrate resonance at the upper end of the bandgap. The results also show that the resonance does not follow a linear relation with the antenna length, for the dipole an effective substrate index of 10.88, 6.22, 4.6 and 3.7 appears to be in effect for dipole lengths of 0.25, 0.5, 0.75 and 1.0 µm respectively, this is consistent with the nonlinear scaling between the resonant wavelength and the length of antennas observed by Šikola et al. [8] and which they attributed to the coupling of the antenna resonance and the absorption resonance of the substrate material. ACKNOWLEDGMENTS This work has been possible thanks to the support of the Ministerio de Ciencia e Innovacción through the project TEC2006-01882, and by a grant from the University Complutense of Madrid, and the support for mobility of the University Autónoma de San Luis Potosí. Francisco J. González acknowledges support from PROMEP, FOMIX-SLP and CONACyT through grants PROMEP /103.5/04/1386, FMSLP-2008-C01-87127 and CB2006-60349 respectively.

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