In recent years, plasmonic nano-antennas have been used in a wide range of applications in sensing, particle detection, imaging and Surface Enhanced Raman Scattering (SERS) detection. Also, arrays of nano-antennas have been recently developed to produce more directional radiation beams or to operate over a wide range of wavelengths. In this article, it is shown that small arrays of nano-antennas can be created by recycling the power that flows through their antenna gaps.
©2013 Optical Society of America
Antennas have been widely used to transmit and receive information over a wide range of frequencies in the electromagnetic spectrum: roughly from 3 kHz to 300 GHz. These devices basically convert guided or confined electromagnetic waves into radiated waves and vice-versa. The major obstacle to develop antennas at higher frequencies was the difficulty in fabricating devices at micrometer and nanometer scales; however, in recent years, nano-antennas working at optical frequencies have been developed . These optical nano-antennas are finding a wide range of applications in bio-sensing, imaging of molecular interactions , analysis of materials by using Surface Enhanced Raman Scattering [3–6] and high efficiency photovoltaics [7,8]. All these applications come from the ability of nano-antennas to generate highly intense electric fields in small regions , which is used to enhance many photophysical phenomena .
Single element antennas such as dipole and bow-tie nano-antennas have already been demonstrated in practice . These single-element antennas generally produce a non-directional radiation pattern, but the directionality of the antennas can be further improved by adding elements to the antenna and creating antenna arrays. Multi-element antennas such as Yagi-Uda antennas have recently been studied in the literature [10, 11]. Arrays of nano-antennas can also be designed to operate over a wide range of wavelengths, with the potential of improving the collection of the broad solar spectrum . Other applications of arrays include control of plasmon lifetime  and optical beam steering . Arrays of nano-antennas could also work as distributed sensors.
Most nano-antennas are excited by external large laser sources with significantly larger spot-size diameters compared with the dimensions of the antenna – this can lead to considerable waste of power, with significant part of the power not reaching the antennas. In order to improve the use of power by nano-antennas, it has been recently proposed to integrate nano-antennas with micro-lasers such as micro-disk lasers  and triangular lasers . In particular, triangular lasers [16–18] are attractive to feed nano-antennas because they have fewer resonant modes than microdisk lasers with similar dimensions and an adequate integration with a triangular laser could reduce the undesired reflection of light by the nano-antenna .
In this paper, it is shown that a single waveguide can be used to feed small arrays of nano-antennas. In fact, the design is based upon recycling power that is transmitted through the dielectric gap of the nano-antenna: part of the transmitted power can be re-utilized to feed another antenna. There are obvious limitations to this approach since the amount of power reaching antennas farther away from the feeding waveguide becomes weaker, limiting the size of the array. However, this approach could provide an easy way to control the phase and relative magnitude of the electric field in the elements of the array and thus produce a compact design. This scheme is significantly more efficient for TM polarized antennas: recycling of power of TE polarized antennas has lower yielding.
2. Device structure and general analysis
The basic device is shown in Figs. 1(a) and 1(b). Figure 1(a) shows the lateral view of the proposed device: a silica (SiO2) layer of thickness h2> 1 µm is deposited on top of a silicon (Si) substrate. This silicon sample can then be molecularly bonded to the InP device as described, for example, by Hattori et al . The thickness of the InP top layer is h1 = 400 nm. In principle, any other epitaxially layered could be used to design the array (e.g. SOI substrate).
The gold and silica layers of the nano-antenna can be deposited by etching away regions in the InP layer (e.g. with electron beam lithography and inductively coupled plasma etching systems). After etching these regions, the metallic and silica layers could be deposited by using, for example, electron beam evaporator system followed by lift-off. The final structure could be eventually fabricated by using focused ion beam (FIB) milling. The thickness of the ith nano-antenna (i = 1,2,..) (hgap,i) can be varied from 10 nm to 100 nm. The waveguides have a width Wwav = 500 nm and are designed to operate at the free-space wavelength (λ) of 1550 nm. Linear tapers are used to couple light into and out the nano-antennas as shown in Fig. 1(b): the nano-antennas have a width Wnano = 200 nm and length Lnano = 100 nm. The gap between the end (beginning) of the nano-taper and the beginning (end) of the nano-antenna is Lgap = 50 nm. The distance Lphase1 is used to control the phase of the 2nd nano-antenna with respect to the 1st nano-antenna. The nano-taper is a linear taper with larger width of 500 nm and smaller width of 100 nm.
The structure is designed to operate with TM modes, with main electric field along the vertical direction (Ey). It is true that most quantum well lasers have much larger gain for TE modes, but tensile strained quantum wells have larger gain for TM modes and could be used to provide gain to laser devices that could drive the array . Simulations are based on 3D Finite Difference Time Domain method (3D FDTD). The computation region is terminated by perfectly matching absorbing regions. The grid sizes are very non-uniform: in the plane of the nano-antenna array, Δx = Δz = 20 nm which is refined to 3 nm at the borders of the metallic regions, while Δy = 7 nm (vertical direction) with a refined grid of 3 nm at the edges of the metallic layers. The time step is chosen to be well below the stability limit to avoid numerical divergence of the FDTD method that could be generated by the highly dispersive nature of gold (Δt = 5.7x10−18 s). The material properties of gold are inherited from the material library of RSOFT Fullwave . A Gaussian source is placed in the input waveguide with spot-size diameters of 350 nm (x-z plane) and 250 nm (y direction). In principle, the arrays could contain as many nano-antennas as desired, but it can be potentially effective for up to 3 elements: while most of the results are presented for arrays of 2 nano-antennas, the results could be easily extended to arrays of 3 or more elements. The electric field enhancement factor of the pth antenna is defined as (EFFp),
Gold is modeled by Fullwave  as a lossy dispersive material with multiple resonant frequencies (similar to a lossy Sellmeier’s equation). The relative electric permittivity is calculated as,18] and ωFW = 2π/λFW with λFW being the vacuum wavelength in units of µm. The value of the coefficients are provided in the article by Mironov et al . The relative magnetic permeability is close to 1.0.
Figure 2 shows the electric field enhancement factor for a single nano-antenna as a function of the silica gap thickness (hgap) at λ = 1550 nm. The electric field enhancement factor decreases exponentially with the gap thickness: for hgap = 20 nm, EFF = 6.1 while for hgap = 60 nm, EFF = 2.5. For a stand-alone nano-antenna, about 85% of the power generated by the source is coupled into the input waveguide and 38% of the input power is transmitted through the nano-antenna if a second collecting waveguide is placed after the nano-antenna.
Starting from an initial nano-antenna with hgap,1 = 20 nm, another nano-antenna is added as shown in Fig. 1(b). The nano-taper after the 1st nano-antenna is still capable of collecting a portion of the incident power: while 85% of the power generated by the source is transmitted through the input waveguide, around 36% of the power is re-collected by this nano-taper and reaches the 2nd nano-antenna. The recycled transmitted power flowing through the 1st nano-antenna is not very weak for TM modes but is significantly weaker for TE modes antennas: less than 20% would be re-collected by using nano-tapers.
The electric field enhancement for the 2nd nano-antenna as a function of the gap width (hgap2) is shown in Fig. 3 (a). It is clear that the electric field enhancement is lower for the 2nd nano-antenna: for example, if the array is constructed by using two identical nano-antennas, the electric field enhancement (EFF) for the first antenna is 6.4, while for the second antenna EFF is 4.9. The misbalance in amplitude can be compensated by using nano-antennas of different thicknesses: for example, if hgap,1 = 30 nm and hgap,2 = 20 nm, EFF1 = 4.02 and EFF2 = 4.07, respectively for the 1st and 2nd nano-antennas. The addition of a second nano-antenna can also change the electric field enhancement in the 1st antenna since the second nano-antenna can load the 1st nano-antenna: reflected fields from the 2nd nano-antenna return to the 1st antenna. EFF1 can change from 6.1 to 7.7 for different values of hgap2.
Since the waveguides are not very lossy, the phase between nano-antennas can be adjusted by choosing an adequate value of Lphase1. As an example, when Lphase1 = 1.32 µm, the two nano-antennas are in-phase. In another application, Lphase1 could be adjusted to produce high electric fields in different regions of the sample: this could be used, for example, to assess the properties of different parts of the sample. Figure 3(b) (left inset) shows the magnetic field distribution when Lphase1 = 1.32 µm: although the magnitude of the electric field is weaker in the second waveguide, it is not much weaker. In the right corner inset in Fig. 3(b), a lateral view of the electric field profile (Ex) shows that the electric field is high in the gap and edges of the nano-antennas –although most of the transmitted power seems to flow through the gap of the first antenna, some power may be coupled through the edges of the 1st antenna.
The array could be extended to include a third element. However, the transmitted power going to the third antenna is reduced to less than 20%: when all antennas have the same thickness of 20 nm, only 18% of the incident power would reach the 3rd nano-antenna, producing electric field enhancements of 5.5, 3.8 and 3.3, for antennas 1, 2 and 3, respectively. In order to produce similar amplitude in the nano-antennas, one option would be to choose hgap1 = 70 nm, hgap2 = 45 nm and hgap3 = 30 nm, resulting in electric field enhancements of 2.2, 2.4 and 2.7, respectively.
At first glance, the electric field enhancement factor (EFF) does not look very high. However, some considerations need to being taken into account. Firstly, it should be mentioned that we are comparing the electric field at the dielectric gap of the nano-antenna with the electric field in the waveguide which is already high (order of magnitude of kV/m) – significantly higher than the electric field that would be generated by a large laser source, for example. Secondly, if the electric field is enhanced too much at the dielectric gap of the nano-antenna, metal ablation can occur as described by Mironov et al . Given these two initial considerations, EFF could be increased by reducing the thickness of the dielectric gap as shown, for example in Fig. 2 – however a dielectric gap of less than 20 nm can lead to difficulties in fabrication of the device and produce surface irregularities.
3. Nano-antenna array
3.1 Basic characteristics of the antenna designs
Besides a potential application in distributed sensing, a more practical application of the proposed device is the production of nano-antenna arrays. We placed electric field monitors at a distance of 6 µm away from the antenna and calculated the far-field radiation pattern of arrays with 2 nano-antennas (Lphase1 = 1.32 µm with two antennas in-phase) for two cases: (a) when the two nano-antennas have equal gap thicknesses hgap1 = hgap2 = 20 nm and (b) when the two nano-antennas have equal amplitude, i.e., hgap1 = 30 nm and hgap2 = 20 nm. It would be possible to extend the array to include three elements but unfortunately simulations of the radiation pattern of an array of 3 nano-antennas would require more than 10 Gbyte of memory which is beyond our available computer capacity. The far-field electric field pattern is calculated at a distance of 6 µm away from the 2nd nano-antenna and normalized with respect to the maximum electric field. The triangles in the figures are used to cover the region that includes the feeding waveguide whose radiation field affects the reading of the field monitors.
Figures 4(a) and 4(b) show the radiation patterns at three wavelengths: 1500 nm (red), 1550 nm (dotted plot) and 1600 nm (blue). Figures 4(a) and 4(b) show the radiation pattern for cases (a) and (b), respectively When the nano-antennas have nearly equal amplitudes, the antenna array is slightly more directional: the half-power beamwidth is 66 degrees for case (a) against 52 degrees in case (b) at λ = 1550 nm. Also, there is a significant variation in electric field magnitude in the wavelength range between 1500 nm and 1600 nm – more than 6.6 dB change in amplitude. At 60 degrees, the amplitude change is about 10 dB in case (b). The position of the maximum of the lateral lobe changes from 50° (1500 nm) to 60° (1600 nm).
At a distance Lphase1 = 1.32 µm, the arrays are designed to produce reinforced electric fields in the forward direction. Different arrays with different phases between adjacent antennas could be adjusted by controlling Lphase1. Also, phased arrays could be created by using this scheme, similarly to that described by Rose and co-authors .
3.2 Methodology for designing an array23].
A general guideline for the design of a linear antenna array of equal elements would be:
- 1. Determine the electric field pattern of a single-element. It is assumed that all elements are equal although they can be positioned and fed differently.
- 2. Choose the type of array that will be designed (e.g. end-fire or broadside) and verify if the design is possible with the chosen single element. If the design is possible, then determine the Array Factor. Note that, some special functions such as Binomial and Dolph-Tschebyscheff functions can provide the desired characteristics of the array. In general, the array factor can be expressed as,
where Ap is the relative amplitude of the electric field of the pth element (p = 1,2,3,..N) with respect to a reference (e.g. if the reference is the 1st element than A1 = 1). The phase of the pth element θp will be discussed in item 4. We assume that the wave has a temporal dependence expressed by exp(i 2 π cvac t/λ) where cvac is the speed of light in vacuum.
- 3. Determine the relative magnitude of the elements toi produce the desired pattern. The relative amplitude between different elements determines Ap as mentioned previously. The array described in this article can provide a wide range of relative magnitude between different elements. However, the power decreases after passing through each element. The power could be increased by adding quantum heterostructures (e.g. quantum wells) to the waveguides that feed different elements and compensate the power loss by injecting current into the active waveguides similarly to what happens in multi-stage laser devices .
- 4. Consider the linear antenna array shown in Fig. 5. Imagine that the antenna array is placed in a medium of refractive index nback (e.g. air) and we wish to calculate the electric field at a distance r (with respect to the first element and in the far-field) and angular coordinate ϕ with respect to the antenna axis (in this case z-axis). The phase θp for the pth element will be given by ,
where Lq is the distance between adjacent elements (Lq = Lphaseq + 2Ltap + 2Lgap) as shown in Figs. 5 and 1. The phase βp is the phase of the electric field of the pth element with respect to the first element, which can be estimated as,
where neff is the effective index of the waveguide, taper and air gap.
- 5. The formulas above assume that there is no significant back reflection from one antenna element to the previous one. This may not always be the case and to have a more accurate value of the phase βp, it is better to place electric field monitors in the gap of each antenna.
- 6. Finally, impedance of different elements can be calculated and the whole structure optimized to reduce reflection. The impedance of different elements (waveguide, antenna) can be calculated as [18,26]
More details on this calculation can be found in the article by Hattori et al , although in that paper the impedance was calculated for TE modes –calculations of impedance for TM modes would be very similar to those described in that article.
This general methodology provides a general guideline for the design of a linear array and provides a better physical insight in the results of numerical calculations. In addition to that, the phase and magnitudes can be dynamically controlled by injecting electric current through the semiconductor materials.
In this article, arrays of plasmonic nano-antennas are designed by recycling the power that flows through the dielectric gaps in TM polarized nano-antennas. Although the re-collected power is lower than the incident power in the first nano-antenna, it can still be used to drive other antennas. This scheme could be used to create arrays of few antennas. This array may find applications in sensing, imaging and detection of nano-particles.
A methodology sub-section provides a general guideline of how to design a linear nano-antenna array: they provide a set of principles for initial design of the array which can be further improved by numerical simulation.
By adding complexity to the system (e.g. adding quantum wells and metallic electrodes), the phase and magnitude of the antennas could be controlled dynamically: an injection of current through the feeding waveguides could change the phase and magnitude in the nano-antennas.
The authors gratefully acknowledge the financial support of the Australian Research Council (ARC). Ziyuan Li wishes to acknowledge the financial support of the Research Publication Fellowship from UNSW@Canberra.
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