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We propose a novel design for a sub-5-nm-gap plasmonic cavity to couple it efficiently with an integrated low loss silicon waveguide. We numerically obtain over 90% efficient coupling between a nano-gap plasmonic cavity with a modal volume of less than 10−7 λ3 and a conventional silicon-on-insulator (SOI) waveguide by utilizing the anti-symmetric second-order resonance mode of the cavity and engineering its geometry to reduce the modal size to less than 5 nm. The electromagnetic field efficiently coupled to the small cavity, leading to extreme enhancement of the field intensity. For a 2-nm-gap cavity, the intensity enhancement was calculated to be more than 100,000,000 compared to that of light in an SOI waveguide.
© 2016 Optical Society of America
1. Introduction
Recent advances in plasmonic cavities have allowed for the confinement of light in deep sub-wavelength space [1–6], leading to strong field enhancement. It has helped in the realization of future applications, such as super-resolution optical imaging [7,8], ultra-small high performance optical communication [9–13], single molecule spectroscopy [14–16], and effective single photon sources [17,18]. Among the many plasmonic devices, gap-plasmonic cavities with nanometer size air gaps, such as bowtie antennas [19–21] and nano-pore/hole metallic cavities [22], have received much attention because of the huge enhancement of electric fields near the nano air-gaps. Recent developments in fabrication techniques have enabled sub-5-nm gaps to be realized [5, 19, 23, 24]. However, as their size become smaller, inevitable challenges arise in their coupling with external optics because of widely divergent diffraction angles and the requirement to engineer near- and far-field patterns of the cavity mode within a small area [25,26]. Most of the single nano-gap plasmonic cavities exhibit dominant vertical radiation, making coupling with horizontal on-chip optics very inefficient. However, for practical on-chip applications of gap-plasmonic cavities, the method to couple a single gap-plasmonic cavity with a low-loss on-chip waveguide efficiently should be studied. For the past decade, several coupling methods have been proposed and demonstrated [27–30]. In 2014, M. Eggleston et al. demonstrated a large coupling efficiency of 77% between a 50-nm-gap plasmonic nanoLED and an integrated low-loss InP waveguide by engineering the waveguide width and thickness [30].
In this work, we suggest a novel design for a sub-5-nm-gap plasmonic cavity to couple it to a low-loss silicon waveguide with more than 90% efficiency. By designing the cavity as a double nano-gap (DNG) structure and utilizing the anti-symmetric second-order resonance mode, we achieve over 90% efficient coupling between the gap-plasmonic cavity with a modal volume of <10−7 λ3 and a silicon-on-insulator (SOI) waveguide. The efficient coupling within a very small cavity leads to enhancement of the field intensity by a factor of more than 108 in a 2-nm DNG cavity compared to that of light in an SOI waveguide. We believe that our proposed structure paves the way for on-chip integration of nanoscale plasmonic devices with silicon photonics for next-generation optical communication and biological applications.
2. Double-nano-gap (DNG) plasmonic cavity
In recent years, nano-gap plasmonic cavities have been considered high-profile devices for achieving large field enhancements in nano air-gaps. A gap-plasmonic cavity can be formed by simply drilling an air-hole through a metallic plate, as shown in Fig. 1. In this study, we use a rectangular air hole in order to simplify the resonant conditions, and use a low-loss silver metal plate to reduce the absorption losses by the metal. We took the optical constants of silver from Ref [31]. and fitted them with the classical Drude–Lorentz model [32,33]. The fundamental resonance mode is excited under the hole length of L = λeff / 2, as shown in Fig. 1(a), where λeff is an effective wavelength defined by λeff = λ0 / neff. λ0 and neff are the resonant wavelength and effective refractive index, respectively. In this mode, the dominant electric fields and wavevectors are y- and x-components, Ey, and kx, respectively. If the gap (g) is pinched at the center of a rectangular air-hole to a few nanometers in size (i.e. by forming a single-nano-gap (SNG) structure), the electric fields are strongly concentrated in the vicinity of the central gap by the large charge accumulation [5], as shown in Fig. 1(b). Such geometric engineering significantly reduces the modal area (Am) of the gap-plasmonic cavity in the xy-plane. When g is reduced from 150 nm to 5 nm, Am decreases from 1.95 × 10−2 λ02 to 7.54 × 10−5 λ02, respectively, where λ0 is 1550 nm. Since the fundamental cavity mode has a symmetric phase distribution in the near field regime with respect to the y-axis at x = 0, as shown in Fig. 1(b), large emissions in the vertical direction are inevitable.
Fig. 1 (a) Ey distribution of a fundamental resonance mode in a rectangular air-gap plasmonic cavity, (b) Ey and |E|2 distributions in a single-nano-gap (SNG) plasmonic cavity with a minimum gap-size (g) of 5 nm, (c) Ey distribution of a second-order resonance mode in an air-gap plasmonic cavity, (d) Ey and |E|2 distributions in a double-nano-gap (DNG) plasmonic cavity with g of 5 nm.
We can also excite a higher-order resonance mode by elongating L. Under the hole length of L = λeff, the anti-symmetric second-order resonance mode is excited in the gap-plasmonic cavity, as shown in Fig. 1(c). In contrast to the symmetric fundamental mode, this mode has anti-symmetric phase distribution with respect to the y-axis at x = 0, which strongly suppresses radiation in the vertical direction by cancelling opposing electric fields along this direction. In a similar way to reduce the modal size in the fundamental mode [Fig. 1(b)], the modal area of the second-order resonance mode can be modified by engineering the geometry. By pinching two gaps at the positions of maximum electric field (x = ± L / 4) (i.e. by fabricating a double-nano-gap (DNG) plasmonic cavity), the modal area is significantly reduced by concentration of the electric fields into two nano gaps, as shown in Fig. 1(d). When g is reduced from 150 nm to 5 nm, Am of a DNG cavity decreases from 4.01 × 10−2 λ02 to 1.59 × 10−4 λ02, respectively. It should be noted that the DNG plasmonic cavity sustains the anti-symmetric phase distribution similarly to the original cavity in Fig. 1(c). Therefore, the DNG plasmonic cavity with an extremely small modal volume is able to suppress radiation in the vertical direction.
From the basic study illustrated in Fig. 1, we performed a three-dimensional (3D) finite-difference time-domain (FDTD) simulation to investigate the realistic performance of the DNG plasmonic cavity. Figure 2(a) shows the DNG plasmonic cavity with a 30-nm-thick silver plate on a SiO2 (n = 1.45) substrate. L, w, and, g were 500 nm, 150 nm, and 5 nm, respectively and λ0 was 1550 nm. As expected in Fig. 1(d), the simulation result shows that the electric fields in the DNG cavity are strongly localized near the double nano-gaps along the xy-plane. Vertically, the maximum fields are located at the interface between the SiO2 substrate and DNG cavity. The calculated modal volume and quality factor as a function of g are shown in Fig. 2(b). The modal volume rapidly decreases as g decreases. For the cavity with g < 20 nm, the rate of decrease of the modal volume is larger than with g of > 20 nm because of the rapid increase of the effective refractive index in the regime of large wavevectors [4]. However, the quality factor shows the opposite trend with modal volume, as shown in Fig. 2(b). This is because the radiation is more highly suppressed by reducing g. If the electric fields are strongly localized at the double nano-gaps, those fields act as point-like sources with opposite phases, leading to perfect cancellation of the vertical radiation. For a 2-nm-DNG cavity, the modal volume and quality factor are calculated to be 5.24 × 10−8 λ03 and 66, respectively. The ratio of absorption loss to the total losses from the cavity is calculated to be 13%, indicating that the absorption and radiation quality factors (Qabs and Qrad) are 507 and 76, respectively.
Fig. 2 (a) |E|2 distributions along the xy- and xz-planes in a DNG plasmonic cavity with a 30-nm-thick silver plate on a SiO2 substrate. Here, g is 5 nm. (b) Calculated modal volumes and quality factors as a function of g
Different symmetries of near field distributions occur in different far-field radiation patterns. To compare the far-field patterns between an SNG and DNG plasmonic cavity, we calculated radiation pattern for both, as shown in Fig. 3. Figure 3(b) shows that most of the radiation from an SNG cavity propagates along the vertical direction due to the symmetry of a phase distribution in the near-field regime. It is also evident that 60% of the radiation propagates towards the SiO2 substrate, while 40% of the radiation propagates towards the air. This is because the refractive index of the SiO2 substrate (nsio2 = 1.45) is larger than that of air (nair = 1.0) [5]. Figure 3(c) shows the far-field pattern of the radiation propagating towards the substrate in an SNG cavity in polar (θ) and azimuthal (φ) coordinates. It is clear that most of the radiation from an SNG cavity is vertically propagated within a polar angle (θ) of ± 30°.
Fig. 3 (a, d) Perspective schematic views, (b, e) |E|2 profiles along the xz-plane in logarithm scale, and (c, f) far-field intensity patterns of radiation propagating towards the substrate for the SNG and DNG plasmonic cavity, respectively
Contrary to the radiation pattern of an SNG cavity, the DNG plasmonic cavity shows strong suppression of vertical radiation along the z-axis, as shown in Fig. 3(e). This is because of the anti-symmetric phase distribution in the near-field regime, as described in Fig. 1(d). Figure 3(f) shows the far-field pattern of a DNG cavity in which radiation is propagating towards the substrate. In this case, the maximum far-field intensity is located at θ = ± 35°, with no emission at θ = 0°.
3. Over 90% efficient coupling with a silicon waveguide
The inefficient coupling of a gap-plasmonic cavity with an integrated on-chip waveguide can be overcome by utilizing the DNG plasmonic cavity with the strong suppression of vertical radiation. Figure 4(a) depicts the proposed coupled structure of a sub-5-nm DNG cavity and a silicon waveguide on a SiO2 substrate. The outmost metal length and width of the DNG cavity were 500 nm and 100 nm, respectively. The thickness of the silicon waveguide was 150 nm, which is thin enough for single-mode operation. Firstly, the coupling efficiency as a function of the width of the silicon waveguide (wguide) was studied, where g was fixed at 5 nm. Here, the dipole point source was excited at the center of the minimum air-gap. For all wguide studied from 500 nm to 700 nm, large coupling efficiencies were observed, as shown in Fig. 4(b). For the case of wguide > 550 nm, the coupling efficiency exceeded 90%. This result clearly indicates that the DNG cavity couples well with the on-chip integrated waveguide. In order to compare with the case of an SNG cavity, we over-plot the calculations of coupling efficiency with those of an SNG cavity in Fig. 4(b). Here, the outermost metal length and width of the SNG cavity were equal to those of a DNG cavity. From this figure, the SNG cavity shows weak coupling with a silicon waveguide with efficiency of less than 50%. Such inefficient coupling results from the large vertical radiation in the SNG cavity because of the symmetric phase distributions of near fields in the cavity mode. Figure 4(c) shows |E|2 profiles along the xz- and xy-planes in logarithmic scale, when wguide and g are 600 nm and 5 nm, respectively. This figure clearly shows that most of the radiation from the DNG cavity couples to an integrated on-chip SOI waveguide. We also examined coupling efficiency as a function of g in Fig. 4(d). In the range of g from 2 nm to 60 nm, large coupling with efficiency of more than 90% was seen. The coupled structure with g = 2 nm had a coupling efficiency of 90.2% with a cavity quality factor of 38 and a modal volume of 2.3 × 10−8 λ03.
Fig. 4 (a) Proposed coupled structure of a sub-5-nm DNG cavity and a silicon-on-insulator (SOI) waveguide, (b) Coupling efficiencies of the DNG and SNG cavity as a function of the width of the silicon waveguide (wguide) when g = 5 nm, (c) |E|2 profiles of the coupled structure with the DNG cavity along the xz- and xy-planes in logarithmic scale, when wguide and g are 600 nm and 5 nm, respectively, (d) Coupling efficiency as a function of g for the DNG cavity
4. Extreme field enhancement in a nano-gap plasmonic cavity
Efficient coupling to an extremely small cavity boosts energy density and leads to a large field enhancement. We investigate the field enhancement in our coupled structure with a sub-5-nm DNG plasmonic cavity. The fundamental transverse electric-field (TE) mode in an SOI waveguide is launched from the left side of a waveguide and its enhancement arises at nano gaps in the cavity. The |E|2 enhancement factor is defined by |Ecavity|2 / |Ein|2, where |Ecavity| and |Ein| are the maximum field amplitudes in a cavity and in a waveguide without a cavity, respectively. Figures 5(a) and 5(b) show the calculated spectra of |E|2 enhancement and transmittances with different lengths (L) of air holes, where g and wguide were fixed at 5 nm and 600 nm, respectively. As shown in these figures, the cavity resonance has a strong dependency on L. For a cavity with L = 240 nm, the resonant wavelength, |E|2 enhancement factor, and the transmission dip were calculated to be 1530 nm, 1.6 × 107, and −17.5 dB, respectively. The scattering loss was estimated at 2.4%. Interestingly, the large extinction ratio of more than 17 dB is observed in the transmission spectra of Fig. 5(b). It results from the large coupling between the DNG cavity and SOI waveguide. Figure 5(c) shows |E|2 profiles along the xz-planes in logarithm scale for cases of on- and off-resonance. Under the on-resonance condition, the large coupling to the DNG cavity from the waveguide is seen, while under the off-resonance condition, most of the light passed through the waveguide without strong coupling to the cavity. In Fig. 5(a), some additional plasmonic modes are observed at wavelengths shorter than 1400 nm. These are generated from the finite metal sizes of 500 nm x 100 nm in the coupled structure of Fig. 4(a). Figure 5(d) shows the |E|2 enhancement factor as a function of g. It should be noted that the field intensity has a strong dependency on g and is extremely enhanced when g < 10 nm. For a DNG cavity with g = 2 nm, the enhancement factor of the field intensity is calculated to be 11,000,000 compared to that of light in an SOI waveguide.
Fig. 5 Calculated spectra of (a) |E|2 enhancement factors and (b) transmittances with different lengths (L) of air holes of the DNG cavity, where g and wguide were fixed at 5 nm and 600 nm, respectively, (c) |E|2 profiles along the xz-plane in logarithm scale for cases of on- and off-resonance, (d) |E|2 enhancement factors as a function of g
5. Misalignment tolerance
Finally, we examined the misalignment tolerance of our coupled structure on coupling. We tested two cases: 1) shifting the cavity along the y-axis from the center of a silicon waveguide at a distance of y-shift and 2) rotating the cavity on the z-axis along the xy-plane with an angle of θ. As shown in Fig. 6, the coupling degraded for both cases because of field overlap mismatch between the cavity and waveguide modes. However, our coupled structure shows relatively strong tolerance for misalignment on coupling. The large coupling was sustained with efficiency of more than 80% with a y-shift of < 130 nm and θ of < 20°. Such a strong tolerance for misalignment results from the large modal overlap between the silicon waveguide and point-like DNG cavity mode.
Fig. 6 Coupling efficiencies in two cases; (a) shifting the cavity along the y-axis from the center of a silicon waveguide at a distance of y-shift and (b) rotating the cavity on the z-axis along the xy-plane with an angle of θ.
6. Summary
In summary, we have suggested a new design for a nano-gap plasmonic cavity for its efficient coupling to a low-loss silicon waveguide. Over 90% efficient coupling to an SOI waveguide was achieved by designing the cavity as a double nano-gap (DNG) structure and utilizing the anti-symmetric second-order resonance mode. The efficient coupling caused enhancement of the field intensity in a 2-nm DNG cavity by a factor of more than 108 compared to that of light in an SOI waveguide. We believe that our study paves the way for on-chip integration of nanoscale plasmonic devices into silicon photonics for next generation optical communication and biological applications.
Funding
National Research Foundation of Korea (NRF) grant (MSIP) (NRF-2014R1A1A1008604, NRF-2016M3C1A3904133); The KIST Institutional Program (2E26680-16-P024); The KU-KIST Graduate School of Converging Science and Technology Program.
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