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A symmetric metal slab waveguide simultaneously supports two opposite types of propagation mode similar to a metal film: short-range surface plasmon (SRSP) like mode and long-range surface plasmon (LRSP) like mode. The strong field confinement of SRSP-like mode plays a crucial role for nano-optical integrated circuits in spite of short propagation length. In order to avoid the trade-off between field confinement and propagation length, we demonstrate selective mode excitation and mutual mode conversion for nanofocusing mediated by LRSP-like mode.
© 2013 Optical Society of America
1. Introduction
A plasmonic waveguide is a metal optical waveguide utilizing surface plasmon polariton (SPP). The waveguide is a promise candidate for nano-optical waveguiding since the optical beam diameter confined in the waveguide can be reduced to nanometer order beyond the diffraction limit of light [1,2]. Many studies about plasmonic waveguides have been demonstrated as a key component of nano-optical integrated circuits (NOICs) so far [3,4].
Considering plasmonic waveguides for NOICs, a planar type of plasmonic waveguides such as a metal film (IMI; insulator-metal-insulator) or a metal gap (MIM; metal-insulator-metal) waveguide is suitable [5,6]. Especially, a symmetric (i.e. the clad layers are identical) metal film waveguide has a unique property such that it simultaneously supports two propagation modes with opposite characteristics without a cut-off: Long-Range Surface Plasmon polariton (LRSP) and Short-Range Surface Plasmon polariton (SRSP). The LRSP has been studied sine 1970’s and it enables us to achieve long-distance transmission in spite of weak field confinement [7–9].
The propagation length of the LRSP is typically 100~300μm at visible frequency, which is more than 10 times longer than that of the SPP of single metal surface [9]. In contrast, the SRSP is extremely lossy, resulting in short propagation length of typically several microns. The SRSP, however, enables us to achieve strong field confinement to achieve nanoguiding and nanofocusing of optical beams [1,2]. Such kind of trade-off relation between the field confinement and the propagation length limits the realization of NOICs. Thus, mutual mode control between LRSP and SRSP is needed. We have already proposed the selective excitation of LRSP/SRSP by two phase controlled incident beams [10,11]. If efficient mode conversion is realized between LRSP and SRSP, we achieve optimum treatment of SPP modes in NOICs: excitation and transmission through LRSP and nanofocusing and nanoguiding through SRSP on demand.
A metal slab waveguide embed in a dielectric is one of major planer plasmon waveguides [12]. The metal slab waveguide has attracted significant interest recently as a base for active plasmon components, such as a plasmon sources, modulators, amplifiers and interconnects [13]. This is because of the existence of both LRSP- and SRSP-like mode similar to a metal film waveguide (a metal slab with infinite width); it enable us to realize the plasmon transmission for long distances as well as plasmon nanoguiding with strong localization. This means that a metal slab waveguide has a characteristic to severally satisfy two important goals of plasmonics: the bridge between photonics and electronics, and concentrating and delivering light energy into nanoscale regions [14]. Furthermore, the ease of the fabrication and its integration has superiority for practical use. Therefore, the metal slab waveguides are now considered as a more important platform for active plasmonics and its potential applications [15].
The optical waveguiding characteristics of symmetric and asymmetric metal slab waveguides have been studied numerically by Berini [16–18]. Such studies, however, offered limited case of guiding structures, since they mainly analyzed slab structures with relatively wide width. Though a lot of experiments for plasmonic guiding are demonstrated in a metal slab waveguide, many of them have been performed in a simple metal slab formed on a dielectric substrate: i.e. an asymmetric metal slab [19–21]. No LRSPs are supported in these asymmetric metal slabs.
One of the most unique prospects of plasmonic waveguides is their potential to concentrate light energy and its field enhancement in nanoscale regions as small as a few nanometres. This plasmonic nanofocusing [22,23] has been achieved using tapered metallic guiding nanostructures such as tapered metal rods [24,25], sharp metal wedges [26], tapered metal gaps [27] and lateral tapered metal films on a dielectric [28,29]. Plasmon nanofocusing can typically occur in an adiabatic tapered waveguide with a SPP mode that shows increasing wavenumber to infinity as the thickness and/or width decreases. In order to achieve nanoguiding or nanofocusing, it is needed that the selective excitations of appropriate mode in a symmetric slab waveguide.
In this paper, we propose mutual mode control of SRSP- and LRSP-like modes propagating in a metal slab waveguide. Selective mode excitation by two phase controlled beams and a mode converter for LSRP/SRSP is demonstrated experimentally and theoretically.
2. Propagation mode in symmetric metal slab waveguide
2.1 Symmetric metal film
Since some propagation modes in a metal slab are similar to those of a metal film, we briefly show basic results of a metal film. The structures of a metal film and a metal slab are shown in Fig. 1. The Cartesian coordinate axes used for the analysis are also shown, and propagation takes place along the z-axis, which is upward out of the page. The metal film and slab are said to by symmetric and asymmetric when ε1 = ε3 and otherwise, respectively [9]. In this study, only the symmetric case is studied: the structure consists of a metal (silver) slab of thickness h and width w surrounded by a dielectric (SiO2).
Fig. 1 The cross sectional view of (a) a metal film (a metal slab with infinite width) and (b) a metal slab.
Effective refractive index β/k0 of a lossless silver film is shown in Fig. 2 with respect to normalized film thickness h/λ0 at the vacuum wavelength of λ0 = 635nm, where β is wavenumber of SPP mode along z-axis and k0 = 2π/λ0 is the vacuum wavenumber. A metal film waveguide supports only TM (Transverse Magnetic field) mode as a propagation mode of SPP. For relatively thick metal film (h/λ0 > 0.2), SPPs at two metal-dielectric interface propagates separately. As the thickness decreases, SPPs at the interface couple to form even and odd coupled modes: symmetric (s) and antisymmetric (a) mode [9]. In this paper, we classify propagation mode by the symmetry of Ey field component of the TM mode, i.e. the Ey is symmetric or antisymmetric along the y-axis (normal to the interface).
Fig. 2 Propagation modes in the lossless silver film waveguide (the slab with infinite width): Effective index versus the normalized film thickness. The relative permittivity of the clad and core are 2.13 (n = 1.46) and −19 at λ0 = 635nm, respectively.
The effective index of the upper branch increases to infinity while that of the lower branch asymptotically approaches the refractive index of SiO2 (n = 1.46). The coupled mode of the lower branch (s) is LRSP which has weak field confinement with long propagation length even in lossy metals. The coupled mode of the upper branch (a) is SRSP which has strong field confinement with short propagation length. Such opposite properties of the coupled modes are useful for manipulating optical beams for opposite demands from long-range propagation to strong field confinement to form extremely narrow optical beams.
2.2 Symmetric metal slab
The symmetric metal slab considered here is shown in Fig. 1(b). The propagation modes supported by the structure are obtained by Finite Element Method (FEM). Since mode characteristics of metal slabs as a function of h and w are complicated, we focus on very thin symmetric metal slab (h/λ0 << 1) here. Unlike metal films (metal slabs with infinite width), pure TM modes are not supported by metal slabs, but hybrid modes are supported: all six field components are present for all modes. Neither LRSP nor SRSP mode is supported in the slab. Hence, identifying the modes that are supported by a symmetric metal slab, the mode nomenclature as [symmetric or antisymmetric of Ey in horizontal x-axis] [symmetric or antisymmetric of Ey in vertical y-axis] (order number in y-axis) is used according to Berini [9].
The results for the lossy silver slab with h = 30 nm at λ0 = 635 nm are shown in Fig. 3. Note that the symmetry of the Ey field component along the x-axis is fixed to the symmetric mode in this study, since antisymmetric modes in x-axis are nearly impossible to excite in practical cases. Furthermore, although the first mode for ss0 and the first and second modes for sa (sa0 and sa1) are presented here, the existence of higher-order modes that have a number of field extrema along the x-axis has been observed for the present structure. Leaky modes are known to exist in metal slab structures, and although they have not been searched for in the present study, their existence is anticipated.
Fig. 3 Propagation modes in the lossy silver slab waveguide with h = 30nm for λ0 = 635nm: (a) Real and (b) imaginary part of the effective index versus normalized slab width. ss0(blue solid line), as0 (light blue solid line), sa0(red solid line), aa0 (green solid line), sa1 (orange dashed line), aa1(green dashed line). s (LRSP) and a (SRSP) for infinite width waveguide are also plotted for comparison as dash-dotted lines.
For relatively wide metal slabs (w/λ0 > 1), as the width increases, ss0 and sa1 modes asymptotically approach the value of the effective index of LRSP (s) and SRSP (a) mode supported by a metal film with h = 30 nm (the values are presented as dash-dotted lines in Fig. 3). Their field distribution for w = 5μm are shown in Fig. 4(a) and 4(b). These modes correspond to vertically coupled SPP mode bound in x-z interfaces. On the other hand, as the width increases, the effective indices of sa0 and aa0 modes asymptotically approach β/k0~2.4. This is the similar value of a SPP mode supported by an isolated corner (the side edge) in a semi-infinite metal film. Thus, these modes correspond to horizontally coupled SPP mode bound in y-z interfaces and edges [18].
Fig. 4 The distributions of electric field of propagation modes shown in Fig. 3: Ey of (a) ss0 (LRSP-like mode) at w = 5μm, (b) sa1 at w = 5μm, (c) ss0 at w = 200nm, (d) sa0 (SRSP-like mode) at w = 200nm, and (e) Ex, (f) Ey, (g) Ez of sa0 at w = 30nm. Note that each scale bar is normalized by the field maximum. The maxima are not equal each other.
Metal slabs with small width (w/λ0 < 1), however, strong mode coupling between left and right edges occurs: it leads to unique propagation modes including super long-range guiding as well as nanolocalized guiding. Note that a metal slab is sometimes called a metal stripe in such region. As the width of the slab decreases, ss0 and sa0 modes begin to change in character while sa1 mode has a cutoff level at w/λ0~0.5.
As shown in Fig. 3(b), ss0 mode for w/λ0 < 0.5 presents the extremely lower loss factor than that of a metal film (s) and have the expanded fields into a dielectric layer as clearly shown in Fig. 4(c). Thus, ss0 mode is LRSP-like mode and is so to speak “super-LRSP mode”. In contrast, although sa0 mode show relatively strong dissipation and significantly smaller propagation length rather than the ss0 mode, the effective index increases to infinity for w/λ0 < 0.1; it presents strong subwavelength localization in two dimensions (the x-y plane) as shown in Fig. 4(d). Thus, sa0 mode is SRSP-like mode. From the field distribution shown in Fig. 4 (e), (f) and (g), the property of the sa0 mode is very similar to that of a metal rod [1]. Also, this mode can be understood as the reverse case for a metal slot with small gap: the SPP mode coupled wedge plasmons along the four edges. Note that these two modes supported by the metal slabs with small width do not have a cutoff width; thus their specific characteristics can further be highlighted by decreasing the slab width. Although it is reported that nonlocal effect diminishes the field enhancement at the apex in a smooth metal surface, it also increases the robustness in a real rough metal surface, resulting in improving the performance of nanofocusing [30].
The ss0 (LRSP-like) mode can be used for optical signal transmission with long distances, and it has the superiority to standard LRSPs in a metal film or a wider metal slab waveguide for long-range guiding. The sa0 (SRSP-like) mode has the potential for strong subwavelength localization and can be considered as one of the candidates for plasmon nanoguiding. The existence of the LRSP-like and the SRSP-like modes as well as their interesting characteristics makes a metal nano-slab waveguide attractive for applications requiring extremely long-range guiding or nanoguiding.
3. Selective mode excitation
3.1 Selective mode excitation by two incident beams
In order to control propagation modes in a metal slab waveguide, we perform numerical simulation of selective mode excitation by finite-difference time domain (FDTD) method. The waveguide consists of a lateral tapered lossless silver slab of 30 nm thickness with taper angle 17.8◦, surrounded by SiO2, and the fields of guiding SPPs are calculated. Firstly, a conventional end-fire method using single beam irradiated from the single side of the slab is used to excite SPP. The simulations show many modes are excited by the single beam and complicated interference patterns are observed (not shown). Instead, by using two incident beams with phase difference between the beams, the symmetry of excited modes can be controlled selectively by the symmetry of incident electric field [10,11].
Figure 5 shows the simulated results of the ss0 (LRSP-like) and the sa0 (SRSP-like) modes propagating in a lateral tapered waveguide. The each SPP mode is excited selectively by using two indent beams (λ0 = 635 nm) illuminated at a metal edge. For the case of ss0 mode, the optical energy can reach the tip without a cutoff, but the beam at the tip shows a finite width and the remarkable field enhancement cannot be observed. On the other hand, sa0 mode propagates along the slab edge and is focused at the tip with high energy; this phenomenon can be considered as plasmon nanofocusing in a metal nano-slab waveguide. Strong field confinement in the tip is observed as shown in the field profile of Fig. 5. This result can be understood by the extremely large effective index of sa0 mode in a small slab width [Fig. 3(a)], and also presents one of the unique functions of a metal slab waveguide.
Fig. 5 Simulated results of electric field intensity (|E|2 on the Ag surface) in a tapered lossless silver slab waveguide with h = 30nm: (a) selective excitation of ss0 mode in both sides with phase difference of 0 and (b) selective excitation of sa0 mode in both sides with phase difference of π. Note that each scale bar is normalized by the field maximum. The maxima are not equal each other.
3.2 Sample and measurement
In order to observe the LRSP- and SRSP-like mode, we fabricate a tapered metal slab waveguide and perform a measurement by using two incident laser beams. The details of the fabrication process and the measurement are reported in the previous paper [11]. The geometry of the sample and the measurement scheme are shown in Fig. 6(a). The metal slab (a 30nm thick silver film) is fabricated on a glass substrate covered in SiO2 (2μm). The thickness of SiO2 is sufficiently lager than half of the beam width of the LRSP. An index-matched polymer is coated with the thickness of 100μm (GA700H, n = 1.46). An optical microscope image of the plasmonic waveguide is shown in Fig. 6(b). The width of the waveguide is 5 μm, and the triangularly shaped tapered structure starts at a distance of 5μm from the edge. The taper structure has a base width of 5μm and a length of 16μm (taper angle 17.8◦). The LRSP- or SRSP-like mode is selectively excited by two incident laser beams (λ0 = 635nm) with the phase difference of Δϕ (0~π).
Fig. 6 (a) The schematic concept of selective excitation method by two incident beams and (b) the optical microscope image of the sample. The two beams are focused onto the edge of the metal slab from the upper and lower sides with the phase difference of Δϕ.
3.3 Experimental results
The measured optical images for the Δϕ = 0 and Δϕ = π are shown in Fig. 7. A clear difference is noticeable between Δϕ = 0 and Δϕ = π in the experiments. For the Δϕ = 0, the strong scattering from the tip can be observed [Fig. 7(a)]. In contrast, for the Δϕ = π, the scattering from the tip is very weak [Fig. 7(b)].
Fig. 7 Observed images of the selective excitation method. The experimentally observed scattering from the tip (shown by the dashed circle) for the case of (a) Δϕ = 0 and (b) Δϕ = π. Arrows indicate polarization direction of the incident beams.
The dependence of the output signals on the phase difference can be explained through a variation in the excitation efficiency of SPP modes. In the case of Δϕ = 0, the excitation efficiency of ss0 (LRSP-like) mode is significantly higher than that of sa0 (SRSP-like) mode, because of the field symmetry formed by the two incident beams. Because the length between the edge and the tip (21 μm) is significantly longer than the propagation length of the sa0 mode (propagation length~1μm), only ss0 mode (propagation length~42μm) can reach the tip and be observed. This is confirmed by numerical simulations. Therefore, only the selectively excited ss0 mode reaches the tip [Fig. 5(a)], without loss, and is observed as a strong output signal as shown in Fig. 7(a).
On the other hand, for the Δϕ = π, only sa0 mode show high excitation efficiency by forming an antisymmetric field and they cannot reach the tip and never contribute to the scattering at the tip due to the dissipation. Thus, in such actual lossy case, it is difficult to directly observe nanofocusing of the sa0 mode as shown in the lossless simulation of Fig. 5(b).
4. Mutual mode conversion
For nanofocusing and nanoguiding of optical beams, SRSP-like modes must be used. As described in section 3, extremely short propagation length of the SRSP-like mode limits to manipulate it experimentally. Thus, we propose mutual mode converter between LRSP and SRSP. Figure 8 shows the structure and simulated results of a mode converter formed on a lossy silver film waveguide. This mode converter consists of a metal film and higher refractive index region (length l, height d and refractive index n) on it acting as a plasmonic phase shifter. The length of the phase shifter is determined as l = 640nm at λ0 = 635nm from the equation of (β3 - β1)l = π, where β3 and β1 are wavenumber along z-axis of SPP mode in the upper and lower clad of the higher refractive index region, respectively. Inside the phase shifter, the phase of input SPP wave in the upper clad can be shifted to π with respect to that of the lower clad, resulting in reverse of symmetry of output SPP wave. Such reverse process of symmetry means mode conversion between symmetric and antisymmetric mode supported in the metal film.
Fig. 8 Simulated results of mutual mode conversion between LRSP and SRSP in a lossy silver film of h = 30nm. The length and the height of dielectric region is l = 640nm and d = 300nm, respectively: (a) Cross section of electric field distribution of the modal conversion from LRSP to SRSP and (b) from SRSP to LRSP. The wave propagates from left to right.
As shown in Fig. 8(a), the symmetry of electric field Ey clearly shows the mode conversion from symmetric mode (LRSP) to antisymmetric mode (SRSP) by the phase shift of π. The mode conversion from SRSP to LRSP also can be done as shown in Fig. 8(b), where antisymmetric mode (SRSP) converts to symmetric mode (LRSP). Note that scattering caused by the phase shifter slightly disturbs the electric fields of converted modes. Graded index or tapered structure of the phase shifter expects to reduce the disturbance. Further theoretical investigations are needed to optimize the structure as well as experimental demonstrations in future.
5. Conclusion
We have proposed theoretically selective mode excitation and mutual mode conversion of SRSP-like and LRSP-like mode supported in a symmetric metal slab. We have demonstrated experimentally that the excitation of these modes can be controlled by the symmetry of two incident beams. We have shown numerically that the mode conversion between SRSP and LRSP can be achieved by a phase shifter. We expect that our studies will highlight NOICs based on plasmonic waveguide mediated by LRSP.
Acknowledgments
This work was supported by a Grant-in-Aid for Scientific Research B (25286007) from the Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT). A part of this work was supported by the Nanotechnology Platform Project (Nanotechnology Open Facilities in Osaka University) of MEXT (Nos. F-12-OS-0003, S-12-OS-0012). The work of the second author was supported by a Grant-in-Aid for the Japan Society for the Promotion of Science (JSPS) Fellows.
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