1. Introduction

To couple light into a waveguide supporting nanoscale mode size and hence to squeeze light into an ultrasmall spot are critical to imaging quality, optical data storage, manipulation of nanostructures, and optical lithography in semiconductor industry. The extremely high light intensity resulted from the ultrasmall spot will greatly increase the nonlinear effect and can be used to make ultrasmall and ultrafast electric-optic or all-optic modulators. Recent progress in plasmonics provides new insight into this topic [1,2]. One approach is based on the small mode size supported by plasmon-based media and light can be squeezed into a subwavelength aperture or propagates in a subwavelength waveguide. Directly coupling light into a deep subwavelength circular or square aperture was shown with very low efficiency. Therefore, recent work is focused on transmitting light through deep subwavelength slits or coupling light into waveguides with deep subwavelength dimension only in one direction [3]. Extraordinary optical transmission was first observed through arrays of subwavelength holes. Each hole has a diameter (150 nm) slightly smaller than diffraction limit of light (λ=326 nm) [4]. The transmission through the aperture can be enhanced by fabricating periodic grooves surrounding the apertures [5]. Following the same principle, beaming light from a single subwavelength aperture was reported [6]. Two types of apertures were used in this work: a circular aperture with diameter 250 nm, which is slightly smaller than diffraction limit for visible light, and a slit aperture with deep subwavelength dimension in one direction, 40 nm, but in another dimension, 4400 nm. If another deep subwavelength confinement by metal is applied, a cutoff frequency will be imposed and the transmission is extremely small. Resonant optical antennas considerably shorter than one-half the wavelength were shown to enhance field in the antenna feed gap and lead to white-light supercontinuum generation [7]. However, the low coupling efficiency and side lobes constitute significant drawbacks for practical applications. Light propagation along a chain of gold particles with dimensions 100×100×40 nm3 deposited on an ITO substrate was observed in the visible light regime (λ=633 nm)[8]. Yin, et al. [9], demonstrated light (λ=532 nm) guiding along a silver strip with cross section 250×50 nm². Numerical simulation of a nanowire taper [10] and experimental demonstration of a planar taper [11] were recently reported, where photons are converted into surface plasmon polaritons (SPPs) and propagate along the surface of a tapered nanowire or waveguide. These research results are exciting and indeed constitute breakthroughs towards deep subwavelength photonics. However, they either provide deep subwavelength dimension only in one direction, or require very complicated coupling configurations, or are not easy to integrate into a nanophotonic chip. For the tapered nanowire presented in [10], it is very difficult to address several challenges for practical applications: (1) how to couple light onto such a tapered nanowire; (2) how to integrate it into a photonic chip; (3) how to decrease surface scattering; (4) how to avoid unacceptably large loss at the tip. Herein, we propose a straightforward yet effective approach, as shown in Fig. 1, to three-dimensionally squeeze near infrared light through a single aperture and focus it into a spot with dimensions only 20~30 nanometers. To this end, we have combined two recent findings: (1) high efficiency can be achieved for directly coupling light from a dielectric waveguide into a metal-dielectric-metal plasmonic waveguide; (2) a 3D nanoscale metal-dielectric-metal (MDM) plasmonic waveguide with large dielectric constant contrast supports a small size mode with acceptably low loss (effective index is very small). In this device, the squeezing process is accomplished in two steps: in a coupling process, the vertical dimension is shrunk; in a tapering process, the horizontal dimension is squeezed.

2. Design and Modeling

To decrease the surface scattering, an MDM plasmonic waveguide is used in our device. Efficient light coupling from dielectric waveguides into MDM plasmonic waveguides was numerically investigated in recent work [12,13]. It has been shown that the effective transmission cross section of an MDM waveguide is surprisingly much larger than the geometrical dimension of the dielectrics between the metal slabs. This helps the transmission cross section match between a dielectric waveguide and an MDM plasmonic waveguide. A detailed theoretical explanation based on impedance matching viewpoint is recently presented [13], which successfully interpret the surprisingly high coupling efficiency and sheds light on further optimization method of direct-coupling scheme. Although a detailed microscopic explanation for this has not been seen yet, the light transmission enhancement on nanoscale antennas [14] or by periodic textures may partially account for the high transmission [15]. In particular, the surface plasmon polaritons at the coupling boundary play a key role in improving the efficiency. The light wave from the dielectric waveguide excites SPPs along the dielectric-plasmonic boundaries and the SPPs will be “funneled” into the MDM plasmonic waveguide. Note that SPPs can propagate along sharp bends with low loss [16].

 

Fig. 1. Illustration of the coupler and nanotaper.

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The theory of operation and efficiency optimization of the coupler are not the center of our attention in this work. Instead, we use the reported finding to realize light-squeezing in one direction. Two-dimensional finite-difference frequency-domain simulations were performed in [12] for light direct coupling from a dielectric waveguide into an MDM plasmonic waveguide with high efficiency. The 2D simulations promise to be valid for plasmonic waveguides with large dimensions in the third direction. To verify this, we performed a 3D finite-difference time-domain (FDTD) simulation of light (λ=1550 nm) coupling from a dielectric waveguide (Si, ε_r=12.25) with width W=320 nm and height H _D=300 nm into a plasmonic waveguide with dielectrics (SiO₂, ε_r=2.25) thickness t=20 nm sandwiched between two silver slabs. The dielectric and MDM plasmonic waveguides are aligned at the center. The overall dimensions of the MDM waveguide, D=400 nm and H _p=400 nm, are designed to be larger than the dielectric waveguide to eliminate the transmission through edges. In the simulation, the E ^z ₁₁ mode (the main component of electric field is along the z-axis; the main component of magnetic field is along the y-axis) of the dielectric waveguide is chosen to effectively excite surface plasmon polaritons. This is essentially the configuration of light coupling from a dielectric waveguide into a nanoscale slit if the length of the plasmonic waveguide is very small. A plasmon dispersion model is applied in the simulation with dielectric constant of silver based on [17], ε_r=-129-3.2j, and set in a commercialized software package [18]. In particular, we use a nonuniform orthogonal grid with mesh size 1 nm in the plasmonic waveguide to satisfy accuracy in allowed computation capability. The coupling efficiency is found to be 81% excluding the propagation loss in the plasmonic waveguide. It has been shown that the coupling efficiency can be improved to over 90% if suitable multisection tapers are designed [12,13]. On the other hand, the coupling efficiency will be very poor if the dimension in the horizontal direction is deep subwavelength simultaneously because this will decrease the effective transmission cross section of the MDM plasmonic waveguide.

 

Fig. 2. Simulation of light coupling from a dielectric waveguide into the MDM plasmonic taper: (a) the Sx distribution in the horizontal plane; (b) the Sx in the vertical plane.

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Once light is coupled into the nanoscale MDM plasmonic waveguide, very good confinement can be achieved in the vertical direction. The size of the mode in the vertical direction, determined by the geometric thickness of the dielectrics and the evanescent tails (<1 nm in this case) in the surrounding metal slabs, is calculated to be 21 nm.

 

Fig. 3. The x-component of power flow (Px) along the x-axis.

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To also achieve nanosqueezing in the horizontal direction, we introduce an integrated taper in the horizontal direction into our structure, as shown in Fig. 1. Various plasmonic taper designs have been studied theoretically or experimentally for multiple applications. The first group of tapers adiabatically decrease the distance between metal cladding. Pile, et al. [19] and Ginzburg, et al. numerically investigated, and Chen, et al. [20] experimentally demonstrated light coupling from a dielectric waveguide into plasmonic tapers. However, their tapers provide deep subwavelength confinement only in one direction. In addition, their structures are formed by tapering the gap between the metal slabs. In contrast, our sandwiched taper is surrounded by air and nanoscale guided modes can be supported between the metal layers (i.e. smaller spot size can be obtained). Our approach is also different from the work presented in [11], where light is originally with a large evanescent tail into substrate and finally gets “stuck” on metal surface like that in a conical waveguide described in [10]. As shown in Fig. 1, the input port width of our taper is D=400 nm, the width of the taper tip is d=20 nm, and the taper length is L=550 nm. Between the silicon waveguide and the plasmonic taper there is a section of uniform transient plasmonic waveguide (δ=50 nm). By combing the input silicon waveguide, we repeat the FDTD simulation of the 3D structure at 1550 nm. In this case, the 20nm-by-20nm nanotip is inserted into a PML to avoid back-reflection from the air. We approximate here a situation that no output waveguide is attached so as to focus on the photonic-plasmonic conversion of the taper and temporarily neglect the transition loss from taper-tip to additional devices. Our simulation shows that this is a reasonable approximation which does not hide any features of our coupler. Figures 2(a) and 2(b) show S _x, power flow distribution along the propagation direction, in the horizontal (z=0) and vertical (y=0) planes, respectively. The MDM plasmonic taper gathers a large amount of power from the dielectric waveguide and the power density becomes progressively stronger when light propagates toward the taper tip. As shown in Fig. 3, by integrating S _x in the dielectric waveguide and the plasmonic waveguide taper and considering the back-reflection (negative value, 18%) from their interface, the overall efficiency (including propagation loss) is 62%. About 20% of power accounts for the transverse scattering at the interface and propagation loss in the MDM plasmonic taper.

 

Fig. 4. The spot size at different locations along the x-axis.

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3. Results and Analysis

Figures 4(a)–4(c) show S _x in the dielectric waveguide, in the transient plasmonic waveguide, and at output ports, respectively. As can be seen, the light power from the silicon waveguide is focused into a nanospot in both horizontal and vertical directions after the two-step squeezing process. In the coupling process, the vertical dimension is shrunk; in the tapering process, the horizontal dimension is squeezed. The dimensions of the spot at the output port are measured by full width at half maximum to be 21 nm in the vertical direction and 24 nm in the horizontal direction, which are close to the mode dimensions of a 20nm-by-20nm silver- SiO₂-silver plasmonic waveguide.

 

Fig. 5. (a). The distribution of electric field amplitude |E(r)| at the plane z=0. (b) The electric field amplitude |E(r)| at the central axis (y=0; z=0) along the propagation direction.

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With propagating light confined to such small dimensions, remarkable field enhancement is also observed. To illustrate the enhancement, Fig. 5(a) shows the electric field amplitude |E(r)| distribution at the plane z=0 and Fig. 5(b) plots the electric field amplitude along the propagation direction at the central symmetry axis (y=0; z=0). In both case, the maximum amplitude at the plane z=0 is normalized to 1. As can be seen, an electric field enhancement of 31 times, or 961 times of light intensity (by |E(r)|²) can be obtained at the very end of the output port. At the dielectric-metal boundaries, the enhancement is even stronger (over 3 orders of magnitude of intensity). The variation of the amplitude along x-axis is due to the Fabry-Perot effect.

In our case, the taper functions as a mode converter from a mode with large dimension (~200 nm) into a mode with small dimension (24 nm) in the horizontal direction. The MDM plasmonic waveguide, even with dimensions 20nm-by-20nm, supports a fundamental bound mode with size is almost linear to the physical dimension of the dielectric core, exhibiting no cutoff in deep subwavelength regime [21,22]. Due to large magnitude difference between the dielectric constant of the dielectrics (ε_r=2.25) and that of silver (ε_r=-129-3.2j) at λ=1550 nm, the effective index of the plasmonic waveguide is very small [22]. As a result, the propagation loss in the taper can be controlled in an acceptable range as shown in Fig. 6(a). Note the propagation distance in the MDM plasmonic waveguide, even with dimensions 20nm-by- 20nm (with propagation loss 0.45 dB/µm), can run up to several micrometers, matching the predictions given in [22]. Although shorter tapers may help decrease the total propagation loss, we find shorter tapers will result in larger back reflection. Figure 6(b) shows the relation between the taper length and the efficiency. In addition to the obvious Fabry-Perot effect, there is a tradeoff between taper length and propagation loss.

 

Fig. 6. (a). The effective index and loss for the 20 nm thick MDM plasmonic waveguide with different widths. (b) The overall efficiency for tapers with different lengths.

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4. Conclusions

We have proposed a novel plasmonic device that can effectively convert photonic mode into plasmonic mode. Two-directionally modal size reduction from 232 nm by 156 nm to 24 nm by 21 nm is achieved with high efficiency. A key feature of our device is that it is a planar structure and can be fabricated with standard semiconductor techniques. The patterns of the dielectric waveguide and plasmonic taper can be defined by electron-beam lithography and dry etch. The three-layer MDM plasmonic taper can be formed following a layer-by-layer deposition. A bilayer photoresist process needs to be applied to easily lift off the deposited materials on photoresist. We will report the experimental results in future work. We are investigating whether similar approach can be applied to visible light regime. The design can be our first step to finally achieve a light spot of 10 nm by 10 nm. In the future, a nano-optic beam may take over partial work currently done by expensive electron-beam lithography and focused ion beam milling. This technique may also find a large variety of applications in ultrafast modulation, optical data storage, and nano-particle manipulation.