1. Introduction

Light-emitting diodes (LEDs), nanolasers, single-photon emitters, and fluorescent markers, to cite a few, would largely benefit from a highly efficient coupling with electromagnetic radiation. Over the last few decades, the explosive growth of nanophotonics has driven research into a variety of nanoscale light sources, such as semiconductor nanowires [1], quantum dots and nanocrystals [2,3], organic molecules [4], and color centers in solids [5]. Although these systems offer a wide range of opportunities for applications, they are intrinsically limited by an emission pattern that spans a wide solid angle. In addition, most of the light cannot be extracted due to total internal reflection, especially when the refractive index of the active medium is large. Typically, advanced nanofabrication and sophisticated external optics are required to overcome these issues. Examples include a variety of dielectric [6,7] and metallic [8–12] antenna structures, waveguides [13–15], cavities [16–18], gratings [19,20], photonic crystals [21], solid immersion lenses [22,23] and metasurface [24].

Recently, a planar structure that beams the emission of single molecules has been proposed [25]. It relies on the concept of an optical Yagi-Uda antenna [26], where reflector and director elements are here implemented using thin metal films. This geometry is considerably simpler to fabricate, it does not rely on precise positioning of the emitter in three dimensions, and it is scalable. Altogether, these features make a planar Yagi-Uda antenna highly promising for applications involving light emission. However, the existence of surface plasmon polaritons (SPPs) at the interface between the metal films and the dielectric layers seems to pose an insoluble limitation on the outcoupling efficiency.

Here, we theoretically report on a simple strategy to nearly suppress the excitation of SPP modes, which leads to outcoupling efficiencies above 90% in combination with emission patterns having a half-width at half maximum (HWHM) below 10°. Our approach is based on the inclusion of dielectric thin films with the provision that their refractive index be smaller than that of the medium hosting the source or, likewise, the absorber. Our scheme, presented in detail for light emitters in diamond and GaAs membranes, is general and it can be applied to other material systems, sources and also to absorbers, by invoking reciprocity.

2. Results and discussion

2.1 Antenna configurations

A dipole emitter positioned a distance d₁ away from a metallic layer, named reflector, induces an image dipole [27]. When the two dipoles radiate with an appropriate phase delay, they give rise to a beaming effect in one direction. This occurs provided that d₁ falls within the range λ/(6n) < d₁ < λ/(4n), where λ is the emission wavelength and n is the refractive index of the medium hosting the dipole source, named active medium. Further directionality can be obtained by positioning a thin metallic layer in the radiation direction, named director, at a distance d₂ away from the dipole. The distance d₂ is also governed by a simple relationship between d₂, λ and n [25]. The dipole source can have a horizontal or perpendicular orientation with respect to the layers. However, the latter has a stronger near field that couples a considerable amount of energy to SPP modes present at the reflector and director interfaces and it does not exhibit a single-lobe emission pattern. Therefore, in our study we will consider only a horizontal dipole.

The proposed antenna configuration is generalized in Fig. 1. Figure 1(a) is the standard case, where the active medium is placed between two planar metallic layers [25]. Intermediate dielectric layers space the active medium apart from the reflector and director in Fig. 1(b). A further dielectric layer spaces the director from the collection medium in Fig. 1(c). The coordinates of the dipole with respect to reflector and director, d₁ and d₂ respectively, together with the thicknesses and refractive indices of the additional layers, remain the essential design parameters of the antenna. In what follows, we investigate the role of these new dielectric layers in improving the outcoupling efficiency and beaming.

 

Fig. 1 Planar Yagi-Uda antennas. (a) Basic configuration (reflector, active layer and director) and adopted coordinate system. (b) Configuration to improve outcoupling efficiency and directionality (reflector, bottom intermediate layer, active layer, top intermediate layer, director). (c) Configuration to further improve outcoupling efficiency and directionality (reflector, bottom intermediate layer, active layer, top intermediate layer, director, top layer). A horizontal arrow indicates a Hertzian dipole in the active medium placed at a distance d₁ and d₂ from reflector and director, respectively. The refractive indices of the intermediate layers in Figs. 1(b) and 1(c) must be smaller than the refractive index of the active medium, but not necessarily equal to each other. The refractive index of the top layer should be smaller than the refractive index of the collection medium.

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2.2 Outcoupling efficiency and beaming

We first analyze and compare the designs of Figs. 1(a) and 1(b). To this purpose we choose a set of parameters that outline the basic concepts behind the improved antenna configuration. Our results are based on a plane-wave expansion of the emission of a Hertzian dipole in a multilayer structure [28,29].

Figure 2(a) illustrates a color center in a diamond membrane coated with two silver films acting as reflector and director; other metals like gold can be used [25]. In Fig. 2(b) the structure incorporates two intermediate layers made of glass, which have a refractive index lower than that of the active medium. The layer thicknesses are indicated in the figure caption. For an emission wavelength λ = 738 nm, the refractive indices of diamond, glass, and silver are 2.4, 1.5, and 0.033 + 5.1i [30], respectively. The antenna designs are evaluated by calculating the total power emitted by the dipole (P_tot) in the layered structure and the power transmitted to the collection medium (P_rad), both also in terms of power densities as a function of the in-plane wavevector (k_p). The outcoupling efficiency (β) is then given by P_rad/P_tot. The radiation pattern is also investigated calculating P_rad as a function of the azimuthal and polar angles, respectively ϕ and θ. All curves are normalized to the power emitted in the active layer, considered as a homogeneous infinite medium. Therefore, P_tot corresponds to the enhancement of the spontaneous emission rate, which is always of the order of one in the studied configurations. Another relevant quantity is the beaming efficiency (η), which we define as the ratio between the power collected up to a semi-angle of 20° and P_rad, corresponding to the power collected by a high-NA single-mode fiber (NA ~0.35). We also compute the antenna gain (G), defined with respect to an ideal isotropic radiator, using the formula G = β(4π/P_rad)P_max. β is the antenna efficiency (equal to the outcoupling efficiency) and P_max is the power radiated in the peak direction. For a dipole in a homogeneous medium G = 1.5 or 1.76 dB.

 

Fig. 2 Improving outcoupling efficiency and directionality. (a) Basic antenna configuration (100 nm-thick silver reflector, 100 nm-thick diamond layer, 20 nm-thick silver director). (b) Improved antenna configuration (100 nm-thick silver reflector, 30 nm-thick glass layer, 50 nm-thick diamond layer, 50 nm-thick glass layer, 20 nm-thick silver director). For both configurations the Hertzian dipole is 55 nm from the reflector, and the collection medium is air. (c) Power density for P_tot as a function of the in-plane wavevector k_p and (d) Normalized radiation pattern integrated over the azimuthal angle for the configurations depicted in Fig. 2(a) (red curve) and Fig. 2(b) (blue curve). The peaks in (c) correspond to the excitation of SPPs. (e) and (f) Normalized radiation pattern for the configurations depicted in Fig. 2(a) (red curve) and Fig. 2(b) (blue curve) with gain 6 dB and 12.7 dB, respectively. The power is normalized with respect to its maximum value.

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We consider the configuration in Fig. 2(a) as a reference, and plot in Fig. 2(c) the power density per unit (dk_p)² associated with P_tot (red curve) as a function of the normalized in-plane wavevector k_p/k₀ [28]; where k₀ is the wavevector corresponding to λ = 738 nm in the collection medium. We notice that the power density is distributed as follows: power radiated in the collection medium peaked at small in-plane wavevectors, for k_p < k₀; an SPP mode bound to the director in the collection medium peaked near k₀, for k_p > k₀; two nearly degenerate SPP modes bound to the director in the active medium and to the reflector peaked between 3k₀ and 3.5k₀, for k_p > 2.4k₀, where 2.4 is the refractive index of diamond, i.e. the active medium. These SPP modes absorb a considerable amount of energy, resulting in β < 50%.

The blue curve in Fig. 2(c) refers to the power density for the antenna configuration of Fig. 2(b). The inclusion of two intermediate layers made of glass significantly suppresses the coupling to SPP modes, as it can be inferred from the reduction of the peaks in the power density. Consequently, P_rad increases and β doubles to 82%. In practice, placing the diamond membrane between two glass layers can considerably lower the effective refractive index of the active region (the multi-layer structure between the two metal films), and the diamond-silver interfaces are replaced by glass-silver interfaces. The latter couples less to both types of SPP modes earlier discussed. Moreover, light confinement at the interface (the transverse extension of the SPP electric field component) is inversely proportional to the refractive index of the dielectric interface layer. In that sense, interfacing silver with glass rather than diamond reduces the field in the metal layers and consequently the Joule losses [31].

In addition, as better shown in Fig. 2(d), turning the design of Fig. 2(a) into that of Fig. 2(b) narrows the radiation pattern integrated over the azimuthal angle from a half-width at half maximum (HWHM) of 29° to 19° in the polar angle, corresponding to an increase of gain from 6 dB to 12.7 dB. The intermediate layers have another important effect. Figures 2(e) and 2(f) plot the radiation pattern as a function of ϕ and θ, and show that the configuration of Fig. 2(b) yields a profile that is more favorable for coupling light to an optical system with circular symmetry, such as an optical fiber. The stronger beaming effect for the antenna configuration of Fig. 2(b) can be intuitively explained by considering that the Fresnel coefficients at the interfaces between the two intermediate layers and the active medium favor the transmission of partial waves having a smaller in-plane wavevector component.

2.3 Suppressing the excitation of surface plasmon polaritons

In order to get a better understanding to these findings, we separately consider the effect of the intermediate layers on the reflector and director alone by replacing the diamond layer with a semi-infinite medium having the same refractive index. This configuration rules out the possibility that the diamond membrane may be contributing in some way to the power density with a dielectric guided mode. Here, the distances d₁ and d₂ are chosen such that the dipole is in closer proximity to the reflector and director layers, respectively, thereby making the excitation of SPP modes stronger and thus the action of the dielectric intermediate layers more evident.

Figure 3(a) depicts a dipole in diamond near a silver reflector. The corresponding power densities are shown in Fig. 3(b). The existence of a peak in correspondence with the SPP mode at the diamond/silver interface reduces the radiation efficiency to 40%. The inclusion on a 30 nm-thick glass layer [see Fig. 3(c)] completely suppresses the SPP peak and boosts the radiation efficiency to 99.9%, as demonstrated by the overlapping power densities in Fig. 3(d). Note also that the distance d₁ is the same for both configurations.

 

Fig. 3 Suppressing the coupling to SPP modes. Hertzian dipole in diamond near a silver reflector without (a) and with (c) glass intermediate layer. (b) and (d) Power densities for P_rad (blue curve) and P_tot (red curve) as a function of the in-plane wavevector k_p for the configurations in Figs. 3(a) and 3(c), respectively. Hertzian dipole in diamond near a silver director without (e) and with (g) glass intermediate layer. (f) and (h) Power densities for P_rad (blue curve) and P_tot (red curve) as a function of the in-plane wavevector k_p for the configurations in Figs. 3(e) and 3(g), respectively.

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Figure 3(e) refers to the director, which is now sandwiched between two semi-infinite media. Here the power densities plotted in Fig. 3(f) require more discussion. The one associated with P_rad represents the power radiated in the collection medium above the director [see Fig. 3(e)], for k_p < k₀. Due to the absence of the reflector, the power density associated with P_tot includes the power radiated in both upper and bottom semi-infinite media, for k_p < k₀, and only in the bottom medium, for k₀ < k_p < 2.4 k₀. This explains why β is so small. The peaks near k_p = k₀ and k_p = 3 k₀ refer to the SPP mode residing in the collection medium (air) and in the active medium (diamond), respectively. In Fig. 3(g), a 50 nm-thick glass layer separates the director from the diamond semi-infinite medium. In the corresponding power densities [see Fig. 3(h)], the SPP peak related to the SPP mode propagating at the bottom side of the director has been completely removed. However, β remains close to 1% because most of the radiation is directed into diamond downwards.

The behavior of the different SPP modes can be interpreted in terms of their dispersion relations. For the reflector, Fig. 4(a) respectively considers the SPP modes at the interface between semi-infinite silver and diamond, and silver and glass [see the insets]. By replacing diamond with glass, the wavevector of the SPP mode is lowered to regions closer to the light-line, where the SPP is less confined at the interface and the density of states is closer to that of a plane wave. Altogether, this reduces the weight of the SPP mode relative to radiation modes, which is evident by the suppression of the SPP peak in the power density.

 

Fig. 4 Controlling the SPP dispersion at reflector and director and role of director thickness. (a) Dispersion of the SPP mode at the reflector: a glass/silver (blue curve) and at a diamond/silver (red curve) interface. (b) Dispersion of the SPP modes at the director in an air/20-nm silver/diamond layer structure: upper (blue curve) and lower (red curve) hybrid mode. (c) Dispersion of the SPP modes at the director in an air/20-nm silver/glass layer structure: upper (blue curve) and lower (red curve) hybrid mode. The dashed curves represent the light-lines (LL) at each interface. (d) Power density for P_tot as a function of the in-plane wavevector k_p for different director thicknesses for the configuration of Fig. 2(a). The imaginary part of the dielectric function of silver is much smaller than its real counterpart [30], and therefore has been neglected in the calculation of the SPP dispersion relations.

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The director exhibits a similar trend when replacing diamond [Fig. 4(b)] with glass [Fig. 4(c)]. The structure is considered to be a 20-nm silver film sandwiched between two semi-infinite media. Notice that the finite thickness of the director generates coupling between the two SPP modes (SPP hybridization), which causes a repulsion of the two SPP branches: one is pushed towards larger wavevectors (red solid curve) and one branch towards shorter wavevectors (blue solid curve), at least in the region close to λ = 738 nm. This can also be verified by comparing the dispersion relations in Fig. 4(a) with those of Figs. 4(b) and 4(c). The shift in the SPP wavevector to lower values explains the reduction observed for the SPP peak shown in Fig. 2(c). We have also investigated the configuration made of a 20-nm silver film placed between air and a glass film on semi-infinite diamond (not shown). By varying the thickness of the glass intermediated layer, the SPP modes can be tuned between the two extreme cases shown in Figs. 4(b) and 4(c).

The thickness of the director (t_D) has been selectively increased in Fig. 4(d) to investigate the role of coupled SPP modes in a thin film [31]. The antenna configuration is similar to that of Fig. 2(a), and it is also shown in the inset. The lower SPP mode remains unperturbed by a change in the director thickness. The radiated power of the system drops down when t_D increases, but it is also evident that the peak associated with the upper SPP mode is suppressed, thereby emphasizing that the excitation of this SPP mode due to the finite thickness of the director is responsible for loss in the outcoupling efficiency. Increasing the director thickness indeed eliminates the contribution of the upper SPP mode, but unfortunately at the expense of the transmitted power, hence the outcoupling efficiency.

As shown in Fig. 2(c), addition of the intermediate layers strongly affects the SPP modes lying at the interfaces with the active medium and also considerably reduces the amplitude of the SPP mode lying in the collection medium. However, the antenna can be made to radiate more power by engineering the structure in order to further suppress the latter leakage channel in the director, as discussed in the next section.

2.4 Bandwidth, efficiency and tolerance

The planar Yagi-Uda antenna has been conceived also to operate with a much larger bandwidth in comparison with that of an optical cavity [25]. The question is whether the introduction of intermediate layers somehow affects the bandwidth and, more generally, what kind of tolerance with respect to parameters like wavelength, dipole position one should expect.

Figures 5(a) and 5(b) illustrate various relevant figures of merit as a function of wavelength for the configurations of Figs. 2(a) and 2(b), respectively, but with collection in a glass medium (n = 1.5) instead of air. For both of them we find similar trends with wavelength, although the design of Fig. 2(b) is clearly more performing in terms of β and η. Specifically, it is found that β is nearly constant to a value close to 90%, while η exhibits a broad peak in correspondence of beaming. The bandwidth, where beaming takes place, is quite comparable for the two situations, although in the case with intermediate layers η can be as high as nearly 70% (values up to 90% can also be obtained, not shown). P_tot is larger for the case without intermediate layers, while P_rad is almost the same.

 

Fig. 5 Outcoupling efficiency and beaming. (a) and (b) P_rad (blue solid curve), P_tot (blue dashed curve), η (red solid curve) and β (red dashed curve) as a function of wavelength for the configurations of Figs. 2(a) and 2(b), respectively. Material dispersion is taken into account.

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A further added value of the intermediate layers is that they make the antenna’s figures of merit nearly independent of the dipole’s position in the active region. In other terms, the planar Yagi-Uda antenna does not function based on cavity-like nor plasmonics effects, i.e. where the position of the dipole needs to be precisely set in order to maximize the coupling to the electric field of a certain mode. This is illustrated in Fig. 6, where the dipole position is swept along the thickness of the diamond layer. In moving from the bottom interface towards the top one, both efficiencies are nearly constant, demonstrating that the dipole can be placed with a precision of about 20-30 nm. Another important benefit of the intermediate layers is the enforcement of a minimum distance between the emitter and the metal surfaces that avoids fluorescence quenching [32].

 

Fig. 6 Tolerance with respect to dipole position. (a) and (b) P_rad (blue solid curve), P_tot (blue dashed curve), η (red solid curve) and β (red dashed curve) as a function of dipole position in the active layer for the configurations of Figs. 2(a) and 2(b), respectively.

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2.5 Refractive index of the intermediate layers

Our scheme can be readily extended to other quantum emitters and materials. As an example, we demonstrate how the outcoupling efficiency of a quantum dot (QD), emitting at λ = 950 nm in a GaAs membrane, can be significantly enhanced with the aid of our structure. At room temperature, the refractive indices of silver and GaAs at the aforementioned operational wavelength read n = 0.04 + 6.74i [30] and n = 3.539 [33,34], respectively. In the configuration depicted in Fig. 7(a), the QD is embedded in a 50 nm GaAs host membrane, sandwiched between two dielectric layers. Figure 7(b) illustrates how powers and efficiencies depend on the refractive indexes of the bottom (n_B) and top (n_T) intermediate layers. Already for layers made of SiO₂ (n = 1.451), the efficiencies β and η have reached 88% and nearly 56%, respectively, corresponding to a gain of 13.4 dB (β and η can respectively reach 90% and 60% with a configuration similar to that of Fig. 1(c), not shown).

 

Fig. 7 Refractive index of the intermediate layers and efficiencies. (a) Planar antenna configuration (100 nm-thick silver reflector, 25 nm-thick intermediate layer, 50 nm-thick GaAs layer, intermediate layer with variable thickness, 18 nm-thick silver director). The Hertzian dipole is 50 nm from the reflector and the collection medium is glass. (b) P_rad (blue solid curve), P_tot (blue dashed curve), η (red solid curve) and β (red dashed curve) as a function of the refractive index of the intermediate layers (n_B, n_T) for the configuration depicted in (a). The thickness of the upper intermediate layer (t_T) is adapted in order to maximize efficiency. The gain is 13.4 dB when the intermediate layers are made of SiO₂. (c) Evolution of the power density for P_tot, as a function of the in-plane wavevector k_p, in response to the change of the effective refractive index on the bottom side of the director. The refractive indices of the bottom and top intermediate layers are the same and simultaneously changed. Accordingly, only the thickness of the top intermediate layer is tuned to maximize β.

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The powers instead decrease to values comparable to emission in GaAs treaded as a homogeneous infinite medium. The thickness of the GaAs membrane has been made large enough to give space for positioning the QD a sufficient distance away from the membrane’s interfaces, to preserve the QD from quenching and dephasing due to surface states. Although the refractive index of GaAs is much larger than that of diamond, the intermediate layers manage to considerably reduce the effective index of the active region, thereby completely suppressing the SPP modes, as observed for the black curve in Fig. 7(c). A HWHM angle of 13° is foreseen for that case.

2.6 Adding a thin film between director and collection medium

The role of the geometrical parameters in the director region is more complex. Increasing the director thickness compresses the beam waist and, at the same time, reduces β owing to the increased opaqueness of the director. On the other hand, reducing the thickness gives the director more transparency and more light can be coupled out from the structure. Unavoidably, this also decreases the control of the director and the radiation pattern develops a broader beam waist. Moreover, we have shown that the peak associated with the SPP mode in the collection medium is very sensitive to the width t_D of the director [see Fig. 4(d)]. A straightforward way to suppress the coupling to this mode has been to increase t_D, which has proven to be an inefficient option as it unavoidably compromises the outcoupling efficiency. In other words, since β depends both on the transmittance of the director and on the coupling to the SPP mode in the collection medium, a trade-off seems necessary in order to maximize β.

With a low-refractive index dielectric layer, such as low-index SiO₂ (n = 1.05) [35] or silica aerogel (n = 1.02) [36] or air (n = 1), placed between the director and a collection medium made of glass (n = 1.5) for example, the aforementioned competing effects can be settled and the figures of merit can be boosted to values never attainable before. Furthermore, this layer, if chosen to be silica aerogel, preserves the silver layer from oxidation, which can severely deteriorate the antenna’s performance by changing the director thickness and introducing a high-refractive index epi-oxide layer.

In practice, the coupling to the SPP mode in the collection medium can be modified in a straightforward manner by varying the refractive index on the upper side of the director. As it can be inferred from Fig. 4(c), for a collection medium made of glass the addition of a thin air layer after the director transforms the SPP mode into a radiative one. Its dispersion relation lies between the light lines in air and glass. If the air layer is thin in comparison to the lateral extension of the SPP mode, the dispersion curve is near to the glass light line. Consequently, the SPP peak in the power density is smeared out by the large radiation losses. As the thickness of the air layer gets larger, the mode gradually shifts towards the light line in air and the SPP peak re-emerges in the power density causing a narrow secondary lobe in the radiation pattern.

In Fig. 8 we address the role of the top layer, first shown in Fig. 1(c), through two selective configurations, where in the first one we boost the outcoupling efficiency to 92%, and in the second to 94%; the HWHM angle can be tightened down to 12° and 6°, respectively. Further enhancements are foreseen with judicious choice of material and thickness. A comparison is drawn in Figs. 8(a) and 8(b) based on the figures of merit for the configuration of Fig. 2(b), for which the collection medium is glass (n = 1.5) or silicon nitride (n = 2), respectively, and the layer that separates it from the director is air. The thickness of this layer is scanned from 0 to 400 nm, which affects more the efficiencies than the powers. Notice that β tends to decrease when η increases and vice versa. Moreover, the combination of a collection medium with a large refractive index with a low-index thin layer can make the emission pattern very narrow, as shown in Fig. 8(b). There is an optimal thickness, which weakly depends on the antenna parameters and on the wavelength.

 

Fig. 8 Narrowing the emission pattern and collection medium. (a) and (b) Antenna configuration (100 nm-thick silver reflector, 30 nm-thick glass layer, 50 nm-thick diamond layer, 50 nm-thick glass layer, 20 nm-thick silver director, air layer of variable thickness) with glass and silicon nitride as collection medium, respectively. The Hertzian dipole is 55 nm from the reflector. (c) and (d) P_rad (blue solid curve), P_tot (blue dashed curve), η (red solid curve) and β (red dashed curve) as a function of thickness of the air top layer for the configurations depicted in Figs. 8(a) and 8(b), respectively. (e) and (f) Normalized radiation pattern, integrated over the azimuthal angle, as a function of thickness of the air top layer for the configurations depicted in Figs. 8(a) and 8(b). For t_TL = 50 nm the gain is 16.1 dB and 18.4 dB, respectively.

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The impact of the top layer, specifically on the upper SPP mode, can be observed in Figs. 8(c) and 8(d), where the power densities are plotted for different values of the top layer thickness (t_TL). The top layer thickness, in conjunction with the refractive index of the collection medium, can be exploited to tune the effective index on the topside of the director. In this way, one can have control on the remaining SPP contribution observed earlier, Fig. 2(c) (red curve), in a more practical way without having to change the fixed design parameters of the antenna (refractive index and thickness of the intermediate layers); as explained in Fig. 7(c) for GaAs. It has been observed that the SPP diminishes and shifts towards smaller wavevectors, and the mode eventually becomes radiative (k_p < k₀). For example, a 50 nm top layer effectively suppresses the SPP mode, as shown by the green curves in Figs. 8(c) and 8(d). Increasing the thickness beyond 190 nm gives the SPP modes a radiative nature; identified by the weak side-lobes in Figs. 8(e) and 8(f) that result from the merging of the SPP mode with the central radiated lobe, where the radiation pattern integrated over the azimuthal angle is plotted as a function of the polar angle. Despite these additional lobes, the central lobe becomes narrower and, consequently, η increases. For t_TL = 50 nm the gain is 16.1 dB and 18.4 dB, respectively. Simultaneous variation of the effective refractive index on both sides of the director will not be covered in the paper; however, this approach allows for efficiencies superior to that obtained with the former approaches, for example, η reaches 90%.

The increased directionality, observed along the thickness range t_TL = 100 nm to 300 nm, can be attributed to the fact that the low index top layer together with the relatively higher index collection medium function as a planar lens. Light transmitted from the director and traversing a low index medium (top layer) is refracted according to Snell’s law when entering the collection medium. Therefore, the divergence of the emitted light can be made minimal with a large refractive index contrast between the two media and with an appropriate thickness for the top layer. In this context, the interface between the two layers has only one normal to it. On the contrary, a solid immersion lens (SIL) has the opposite refractive index contrast and its curved interface has an infinite number of normals. Our conceived planar lens, in its simplest form, can be a tunable-thickness air gap. The practicality of this configuration allows for recalling the efficiencies plotted in Figs. 8(a) and 8(b) readily without having to reconfigure the main structure of the antenna. Tight HWHM angles down to 1.9° are foreseen when coupling to high refractive index materials, like silicon.

3. Conclusions

We have shown that a planar Yagi-Uda antenna can lead to very high efficiency in terms of outcoupling and beaming or, equivalently, gain, even for active media with a large refractive index. In practice, a major issue in such antennas was the excitation of SPP modes that exist at the interface between a metal and a dielectric. Here we have introduced fairly simple design strategies that effectively eliminate the contribution of SPP modes to the emitted power, hence maximizing the outcoupling efficiency to values larger than 90%. This can be obtained by inserting low-refractive index layers between the active medium and the metal layers (reflector and director). These modify the dispersion relation of the SPP modes towards the light-line, hence making their relative weight in the power densities closer to a radiative mode. In addition, by adding another low-refractive index layer between the director and the collection medium and by increasing the refractive index of the latter, even narrower radiation patterns can be attained, with gains larger than 18 dB. These designs are robust against variations of the dipole position, layer thicknesses and wavelength, hence providing a simple and intuitive way to interface sources and detectors with free space, optical fibers, and other waveguiding structures. We thus envision that planar Yagi-Uda antennas will become of practical use in optics and photonics.