LIGHT confinement and low loss propagation are the

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1 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 6, JUNE Metal Dielectric Slot-Waveguide Structures for the Propagation of Surface Plasmon Polaritons at 1.55 m Ning-Ning Feng, Mark L. Brongersma, and Luca Dal Negro Abstract We present a deep-subwavelength-size metal slot-waveguide structure which can efficiently propagate surface plasmon polaritons (SPPs) at 1.55 m within a high-index material. Through a systematic design analysis, we investigate the intrinsic tradeoffs and suggest solutions to substantially increase the propagation length of SPPs combining high-index dielectrics and metal structures. By studying several metal/dielectric geometries, we have found that the slot-waveguide size can be significantly decreased by the use of high-index materials without compromising the overall propagation losses. Our analysis also indicates that the device size-scaling is ultimately limited by a cutoff thickness for the metal film in which the slot is defined. For film thicknesses below cutoff, radiation modes exist which leak out of the guiding region. For certain operating frequencies, the radiant energy leaks out into both free space modes as well as surface plasmons guided along the top/bottom metal surfaces of the device. We have shown that, by using a silicon filling, the cutoff thickness of a 100-nm-wide slot waveguide can be as small as 90 nm, compared with 750 nm for the unfilled reference structures. In addition, we have demonstrated that by the use of SiO 2 gap regions surrounding the Si dielectric core in a nm silver slot region (partially filled metal slot), we can considerably reduce the overall propagation losses to less than 0.14 db m, corresponding to a propagation length of approximately 50 m. Index Terms Field localization, metal slot waveguide, plasmonic mode, propagation loss, radiation mode, surface plasmon polaritons (SPPs). I. INTRODUCTION LIGHT confinement and low loss propagation are the two enabling concepts for a miniaturized, high-speed, integrated lightwave technology combining photonics and electronics devices on a chip. The conventional lightwave-guiding approach, based on total internal reflection at the core/cladding interfaces, ensures low-loss transport of transverse light modes. As a consequence of the classical diffraction limit, the minimum core size of conventional dielectric waveguides is of the order of the wavelength of light, posing a fundamental limit to the size scaling of integrated optical chips. However, several Manuscript received October 19, 2006; revised February 24, N.-N. Feng and L. Dal Negro are with the Department of Electrical and Computer Engineering, Boston University, Boston, MA USA ( fengn@bu.edu; dalnegro@bu.edu). M. L. Brongersma is with the Geballe Laboratory of Advanced Materials, Stanford University, Stanford, CA USA ( markb29@stanford.edu). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JQE schemes have been already proposed in order to transport optical information over long distances by means of deep subwavelength modes [1], [2]. Recently, dielectric slot-waveguide structures have been proposed, able to confine light fields over nanoscale (deep subwavelength) low-refractive-index dielectric regions [3] [5]. These structures are based on nanoscale (low refractive index) regions sandwiched by high-refractive-index dielectrics. It has been shown that, depending on the actual design characteristics, deep subwavelength localization and sizeable field-enhancement effects can be achieved due to the large-refractive-index discontinuity at the dielectric boundary regions [3] [5]. An alternative approach to achieve high field confinement is based on the excitation of surface plasmon polaritons (SPPs) in metal/dielectric waveguide structures. SPPs are surface localized light waves at dielectric metal interfaces which are coupled to free electron oscillations in the metal [6] [8]. However, high propagation losses are typically associated with SPPs due to the losses in the metal, and a fundamental tradeoff has to be achieved between field localization (SPP mode extension) and propagation losses. Recently, SPPs in metal slot waveguides (air gap sandwiched by metals) have been intensively studied and proposed as a solution for a well-balanced tradeoff between mode extension and propagation losses [9] [16]. However, most of the studies are focused in the visible wavelength range where deep-subwavelength SPPs can be excited at the cost of very high 3dB m propagation losses. On the other hand, in the near-infrared region, SPPs are only weakly localized although they suffer from lower propagation losses. As we will show later, around 1.55 m, a metal slot waveguide (with SiO inside the slot) can sustain bound plasmonic modes only beyond a certain cutoff thickness [10] [13] (which depends on the slot width) comparable with the size of a normal dielectric (silicon) waveguide. In this paper, we present a new design for SPP waveguide structures with deep-subwavelength dimensions for propagation in the m wavelength range. Our approach is based on the dielectric partial filling of metal slot waveguides (called partially filled metal slots), as shown in Fig. 1. This design offers additional degrees of freedom for balancing the inherent tradeoffs between localization and propagation losses in metal/dielectric structures. Through a systematic design analysis, we will investigate the intrinsic tradeoffs and suggest solutions to substantially increase the propagation length of SPPs combining high-index dielectrics and metal structures. In addition, we will show deep-subwavelength localization with strong field enhancement, even within a high-refractive-index dielectric region. This effect cannot be achieved using standard /$ IEEE

2 480 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 6, JUNE 2007 Fig. 1. Schematic diagram of the dielectric filling metal slot waveguide. dielectric slot-waveguide structures (where high field-enhancement effects are restricted to low-refractive-index regions) and can have a large impact for the fabrication of novel photonic devices based on high-index dielectrics. II. PROPAGATION PROPERTIES OF DIELECTRIC-FILLED METAL SLOTS A schematic diagram for the proposed partially filled metal slot-waveguide structure is shown in Fig. 1. The structure is composed of a thin-film metal slab deposited on a substrate, with a small trench (the slot region) etched and partially filled with a high-index dielectric medium. In this paper, we assume the metal to be silver and we use a dielectric constant at the operating wavelength m (corresponding to a refractive index ) [17]. For all of the simulation results shown here, we consider a SiO substrate with a refractive index. Unless specifically pointed out, we also assume SiO for the upper cladding, which means. The metal slot has a width and a thickness. The choice of the parameters for the dielectric filling of the slot is crucial for the optimization of the waveguide propagation properties. In this section, we will first focus on the properties of the structures with a slot region completely filled by the high-index dielectric, which means and. Similar structures have been recently reported in [16]. A proposed design for novel partially filled structures will be discussed in Section III. SPPs are bound electromagnetic waves which propagate on metal surfaces and satisfy the Maxwell s equations. Therefore, a full-vectorial optical mode solver [18], [19] can be directly applied to compute the SPP modes supported by the waveguides. The use of perfectly matched layer (PML) [20], [21] boundary conditions is crucial to obtain the complex SPP modes. By using a full-vectorial mode solver approach [18], [19], we computed the propagation properties of the proposed dielectric/metal slot structures. In Fig. 2(a), we show the normalized propagation constant of the plasmonic mode versus slot thickness for structures with different filling dielectrics and slot region sizes. In this paper, is the propagation constant of the SPP mode and is the wavenumber of light in vacuum. From the imaginary part of, we can calculate the propagation losses of the guided modes as. We first notice that the results shown in Fig. 2 agree, in the limiting case of large slot thickness, with the well-known behavior of plasmonic modes confined within infinite metal slabs. In fact, we notice that the propagation constant of the plasmonics modes for large slot thicknesses [right-hand side of Fig. 2(a)] is mostly determined by the refractive index of the filling dielectrics as opposed to the thickness of the slot [22]. As can be expected, Fig. 2. Propagation properties of the dielectric filling metal slot waveguide as functions of the slot thickness t. (a) Normalized propagation constants of the plasmonic modes =n k. (b) Propagation loss (db m). (c) Propagation length L (m). we additionally notice that higher propagation constants are obtained for slot structures filled with the higher index dielectrics as a result of an enhanced dielectric contrast and field penetration into the metal region [22]. However, we found that the

3 FENG et al.: METAL DIELECTRIC SLOT-WAVEGUIDE STRUCTURES FOR THE PROPAGATION OF SPPS AT 1.55 m 481 Fig. 3. The leaky field patterns of a metal slot waveguide with thickness below cutoff thickness. (a) Real part of E and (b) real part of E components for structure with t = 500 nm, w = 200 nm, and n = 1:46. The normalized propagation constant =0:733n k in this case. propagation constant of the guided SPP mode becomes strongly affected by the slot structure as its thickness is continuously reduced. In particular, we found that, as shown in Fig. 2, the size scaling of the devices is limited by a cutoff slot thickness which is associated with the excitation of radiation modes with (indicated by the arrows in the figure). Moreover, an increase in the refractive index of the slot-filling dielectric region results in a dramatic decrease of the cutoff thickness of the metal slot and strongly enhances the slot mode confinement. This is clearly understandable in terms of an increase in the SPP propagation constant of the slot due to the presence of the dielectric. For instance, without the filling dielectric region, which is the case when, the slot waveguide shows a cutoff thickness of about 750 nm, as opposed to a cutoff of approximately 90 nm when Si is filling the slot. Below the cutoff thickness, the bound SPP modes degenerate into radiation modes which radiate out of the slot region. We have found that, consistently with the results in [12], the effective index of radiation SPP modes becomes less than the index of the cladding region [see Fig. 2(a)]. In Fig. 3, we show the leaky field patterns of a metal slot waveguide with a thickness below cutoff. From the figures, it can be clearly observed that the radiant energy can escape from the guiding region in two different ways: 1) radiation into the cladding (for the component) and 2) excitation of SPPs guided along the surrounding metal surfaces (for the component). By filling the slot region with a dielectric material of refractive index, the waveguide cutoff is reduced to 300 nm, and it drops to about 90 nm when a high-index dielectric is considered. The high-index dielectric region increases the SPP propagation constant and leads to an improved spatial localization of the SPP modes. However, we notice that, in the case of a wider slot (200 nm) structure [see Fig. 2(a)], the propagation constant is reduced as a result of a weaker field confinement into the slot region. The significant field penetration into the substrate and cladding media reduces the effective index of the SPP mode. In Fig. 2(b) and (c), we show the propagation loss coefficient (defined by the power attenuation per unit propagation length) and the propagation length (defined by the field decay length of the SPPs modes) versus the metal slot thickness. We have found that the SPPs propagation losses increase as we increase the refractive index of the slot-filling dielectrics. This behavior is explained by the enhanced penetration depth of the fields at the metal interfaces as the index of the dielectric slot region is increased [22]. These observations show the existence of a fundamental tradeoff between SPP mode localization (improved by the high-index slot filling) and propagation length (compromised by localization and improved by employing a low-index filling). It is thus clear that deep subwavelength localization can only be obtained at the cost of considerable propagation losses. However, our calculations demonstrate that the metal slot thickness is a crucial parameter for the engineering of low-loss devices. As shown in Fig. 2(b) and (c), if we consider a metal slot with dimensions nm and nm, fully filled with silicon, we can achieve db m propagation losses corresponding to a propagation length of approximately m. These values can be improved to db m and m for a thicker slot nm filled with a lower index dielectric material. The simulation data clearly highlights the fundamental tradeoff between field localization (high dielectric filling) and low propagation losses. Notice in particular that the structures without any dielectric filling (worse SPPs localization) always show lower propagation losses and can support up to m propagation length if the slot thickness is increased up to nm The results discussed previously have indicated that propagation losses can be reduced by structures with large slot width and thicknesses, at the expenses of field localization. This behavior becomes clear by studying the electric field distribution for silicon-filled slot waveguides versus the slot thickness, as shown in Figs. 3 and 4. As is evident from Fig. 4(a) and (b), when using a -nm-thick slot waveguide, the electric field components in both the polarizations ( and field components) are tightly confined in the slot region. On the other hand, if -nm-thick slot waveguides are considered [see Fig. 4(c) and (d)], the field components tend to spread out of the slot region and to extend significantly over the substrate and metal regions, yielding high propagation losses and defining the onset of the cutoff region for finite-thickness slot structures. Further decreasing the metal thickness will make the structure eventually become radiating, which is similar to the case we have shown in Fig. 3.

4 482 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 6, JUNE 2007 Fig. 4. Field distributions of the plasmonic modes for two different slot thicknesses. (a) E and (b) E components for t =400 nm. (c) E and (d) E components for t = 100 nm. An important aspect of metal/dielectric slot waveguides is related to their behavior with respect to the fluctuations of the cladding refractive index. The conventional metal slot structures characteristics are very sensitive to the upper cladding material s properties. A very tall and narrow slot region needs to be fabricated in order to support SPP modes at larger index difference between the upper cladding and the substrate layers [10]. The sensitivity of this type of SPP waveguides to the upper cladding index variations depends directly on the degree of light localization in the slot region. From the previous propagation analysis on a dielectric-filled slot, it is clear that the enhanced SPP localization will result in a very robust characteristic with respect to the surrounding material index change. The simulation results presented here strongly support this intuitive argument. In Fig. 5, we show the effect of the upper cladding layer index change on the propagation constant of different slot structures. The structures we studied are characterized by the following parameters: a common metal slot of width nm and with nm, with nm, and with nm. The third structure is a conventional metal slot waveguide with an aspect ratio of 4. All of the structures can support SPP modes when a matched upper cladding is applied, i.e.,. The simulations are carried out by changing the upper cladding index from 1.0 to 1.8. As shown in Fig. 5(a) and (b), the propagation constants and losses of the structures with dielectric-filled slots are insensitive to the index change. On the contrary, as we predicted, the conventional metal slot waveguide shows a very sensitive dependence on the index change. The SPP mode of a conventional slot waveguide approaches its cutoff quickly as the upper cladding index decreases. No bound SPP modes are supported by air-clad metal slot structures with the considered dimensions (the slot thickness has to be further increased when no dielectric is filling the slot). III. LOSS REDUCTION IN PARTIALLY FILLED METAL SLOTS In the previous sections, we have shown that the dielectric filling of a metal slot waveguide dramatically improves the field localization of guided SPP waves. However, we also found that the increased field localization in dielectric-filled metal slots is necessarily accompanied by an increase in the propagation losses. We face here an inherent tradeoff related to the use of metal/dielectric structures. A simple estimation based on the theory for single metal/dielectric interface presented in [22] shows that the propagation length of a SPP mode at a metal/sio interface is about three times longer than for a metal/si interface. It is interesting to note that the same propagation length ratio holds also for the dielectric/metal slot structures, as shown in Fig. 2. It is now clear that we need to investigate a strategy which improves field localization while keeping the propagation loss low. To this end, we propose a design based on partial dielec-

5 FENG et al.: METAL DIELECTRIC SLOT-WAVEGUIDE STRUCTURES FOR THE PROPAGATION OF SPPS AT 1.55 m 483 Fig. 5. Propagation properties of the dielectric filling metal slot waveguide as functions of the upper cladding material index n. (a) Normalized propagation constants of the plasmonic modes =n k. (b) Propagation loss (db=m) and the propagation length L (m). tric filling of metal slot waveguides (partially filled metal slots). Intuitively, the partial dielectric filling concept ensures both the advantages of enhanced localization and low propagation losses, as it represents a natural combination of the two previously presented approaches. In order to understand the performances of partially filled slot waveguides, we have first studied a structure with vertical partial dielectric filling (VPDF), i.e., and. The propagation constant and propagation length versus the dielectric thickness of VDPF structures are shown in Fig. 6(a), for two slot thicknesses. We have found that the propagation length increases by almost 150% when the dielectric thickness is decreased with respect to the slot thickness. We have calculated a mode cutoff for nm, corresponding to the maximum propagation length in the structure. In Fig. 6(b) and (c), we show the field distributions for VDPF waveguides with nm, which is less demanding from a fabrication standpoint. We see that both the and fields are strongly confined within the dielectric region in the slot. The proposed structure successfully demonstrates a very good tradeoff between field localization and propagation losses. Fig. 6. (a) Propagation properties of the vertically partial dielectric filling metal slot waveguide as functions of the thickness of the dielectric t. (b) E and (c) E field distributions for a structure with t =100nm. We have explored further design possibilities through the introduction of a horizontal partial dielectric filling (HPDF) structure where and. In Fig. 7(a), we show the propagation constant and propagation length versus the dielectric width for HPDF. An almost 200% propagation length increase has been achieved by HPDF structures for an optimized width of the filling dielectric region. In particular, in a 400-nm-thick metal slot, an HPDF structure with nm dielectric width can achieve a propagation loss level of less than 0.14 db m, corresponding to a propagation length of around 50 m. Moreover, since the optimum dielectric width is much larger than the cutoff width of the dielectric region, this optimized structure is expected to be more robust to fabrication fluctuations with respect to VPDF structures. In Fig. 7(b) and (c), we show the field distributions for the HPDF structure with

6 484 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 6, JUNE 2007 Fig. 8. Propagation properties of the partial dielectric filling metal slot waveguide as functions of the thickness of the dielectric t with horizontal dimension w = 160 nm. tical and horizontal directions (VHPDF). We have shown the propagation results in Fig. 8. In the simulations, we have fixed the dielectric width to be the previously calculated optimal value nm, and we have decreased the filling dielectric thickness. As shown in Fig. 8, VHPDF structures do not show a significant increase in the SPP s propagation length with respect to HPDF structures. IV. CONCLUSION Fig. 7. (a) Propagation properties of the HPDF metal slot waveguide as functions of the width of the dielectric w. (b) E and (c) E field distributions for a structure with w =160nm. nm, nm, and nm. The fields, especially the component, show a very tight localization at the two narrow slots in between the metal and the filling dielectric. This enhanced field localization on deepsub-wavelength regions is reminiscent of the behavior of purely dielectric slot waveguides [3] [5] and can have interesting applications for the fabrication of novel photonic devices. In order to complete our systematic study, we also investigated a structure with partial dielectric filling along both ver- Through a systematic design analysis, we have investigated the intrinsic tradeoffs and suggested solutions to substantially increase the propagation length of SPPs combining high-index dielectrics and metal slot structures. We have studied the case of dielectric filled metal slot waveguides showing enhanced localization for the propagation of SPP modes in the mwave- length range. We have demonstrated that the scaling of the device thickness is limited by a cutoff regime where modes can escape from the guided region both as radiation modes outside the slot and as bound surface plasmons guided along the metal interfaces. We showed that, using silicon as the slot filling material, the cutoff thickness of the slot waveguide can be reduced by seven times with respect to the reference metal structure without slot dielectric filling. In addition, in order to improve the field localization while keeping the propagation loss low, we have introduced the concept of partial dielectric filling of metal slot waveguides (partially filled metal slots). Two partially filled metal slot configurations were discussed: horizontal partial dielectric filling (HPDF) and vertical partial dielectric filling (VPDF) waveguide structures. We have shown that optimized HPDF structures can propagate m SPPs modes confined within 160-nm dielectric regions with overall propagation losses as low as 0.14 db m (corresponding to propagation length of approximately 50 m) and are very robust to the refractive index fluctuations of the upper cladding. We believe that the proposed design geometries for partially filled metal slots can have a large impact for the fabrication of novel silicon-based nanophotonic devices [23].

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Brongersma, Plasmonics: The next chip-scale technology, Materials Today, vol. 9, pp , Ning-Ning Feng received the B.S. and M.S. degrees in electrical engineering from the Nanjing University of Science and Technology, Nanjing, China, in 1996 and 1999, respectively, and the Ph.D. degree in electrical and computer engineering from McMaster University, Hamilton, ON, Canada, in From 1999 to 2001, he was a Research Engineer with Apollo Photonics, Inc., Burlington, ON, Canada. He joined the Department of Electrical and Computer Engineering, Boston University, Boston, MA, as a Postdoctoral Research Associate in September He also holds a Postdoctoral Associate position with the Microphotonics Center, Massachusetts Institute of Technology (MIT), Cambridge, MA. He is mainly working in the area of photonics with emphasis on computer-aided modeling, simulation, and design of integrated photonic devices, circuits, and photonic bandgap structures. Dr. Feng was the recipient of the Governor General s Academic Gold Medal (2005), Ontario Graduate Scholarship (OGS) awards ( ), and the Natural Sciences and Engineering Research Council of Canada (NSERC) Postdoctoral Fellowship (2005). Mark L. Brongersma received the Ph.D. degree in materials science from the Foundation for Fundamental Research on Matter Institute for Atomic and Molecular Physics (FOM), Amsterdam, The Netherlands, in During , he was a Postdoctoral Research Fellow with the California Institute of Technology, Pasadena. He is currently an Assistant Professor with the Department of Materials Science and Engineering, Stanford University, Stanford, CA. His current research interests include the development and physical analysis of new materials and structures that find use in nanoscale electronic and photonic devices, Si nanocrystals and wires, optical micro-resonators, and metallic nanostructures that mold the flow of light below the diffraction limit. Luca Dal Negro received the Laurea in physics (summa cum laude) and the Ph.D. degree in semiconductor physics from the University of Trento, Trento, Italy, in 1999 and 2003, respectively. After completing his doctoral work, in 2003 he joined the Massachusetts Institute of Technology, Cambridge, as a Postdoctoral Associate. Since January 2006, he has been an Assistant Professor with the Department of Electrical and Computer Engineering, Boston University, Boston, MA. He manages and conducts research projects on silicon-based photonic materials and devices and semiconductor laser spectroscopy. His main focus is currently on quantum-dots spectroscopy, complex photonic crystals structures, and nanophotonics. He has authored and coauthored more than 50 technical articles.