Efficient directional excitation of surface plasmons by a singleelement nanoantenna (Supporting Information)

Transcription

1 Efficient directional excitation of surface plasmons by a singleelement nanoantenna (Supporting Information) Wenjie Yao, #, Shang Liu, #, Huimin Liao, *, Zhi Li, *, Chengwei Sun,, Jianjun Chen,, and Qihuang Gong, School of Physics, Peking University, Beijing , China State Key Laboratory for Mesoscopic Physics, Peking University, Beijing , China * HMLiao@pku.edu.cn; z_li@pku.edu.cn Section 1. Different modes in the metallic grooves In this Section, we illustrate some basic properties of different waveguide modes in the metallic grooves, including propagation constants, field distributions, dispersion relations and cut-off wavelengths. Propagation constants and field distributions of different waveguide modes The main groove and the auxiliary groove are regarded as vertical MDM (Metal-Dielectric-Metal) waveguides in this study. Corresponding waveguide modes propagating in these metallic grooves are eigenmodes of such waveguides. Considering a MDM waveguide along the y-direction with width w (schematically shown in Figure S1a), the refractive indexes of the surrounding metal and central dielectric are n m and n d, respectively. By solving Maxwell s equations and applying the specific boundary condition, the modal field distributions can be obtained analytically. Here, we focus on TM waves (magnetic fields along the z-direction) since TE waves (electric fields along the z-direction) cannot excite SPPs. These TM solutions can be divided into two sets: one with even symmetry of H z which we call symmetric mode and the other with odd symmetry of H z which we call anti-symmetric mode, with corresponding effective refractive index n eff determined by Equations 1a and 1b, respectively, and k 0 is the free-space wave vector. n n n tanh( kw ) n n n d eff m n eff nd m eff d n n n coth( kw ) n n n d eff m n eff nd m eff d (1a) (1b) These two equations have their own sets of solutions which correspond to different waveguide modes. The number of solutions of each set is infinite regardless of the waveguide width or

2 incident wavelength if all values are considered to be complex. We sort these solutions according to the descending sequence of the real part of n eff. The reason for such an arrangement is that the real part of n eff indicates the mode s ability to propagate because the carried average power flow by a mode is proportional to the real part of n eff. Conversely, the imaginary part of n eff indicates the propagation loss of a mode and determines the propagation length. The descending sequence of the real part of n eff is equivalent to an ascending sequence of the imaginary part of n eff. Therefore, the first few modes are generally more important in this arrangement due to their stronger ability to carry power flows and less propagation losses. According to the derived effective refractive index, the propagation constant and the field distribution of a certain mode can be calculated. The propagation constant k y is equal to the product of effective refractive index and free-space wave vector, whereas the wave vector along the x-direction differs in metal and dielectric and is given by Equation 2 where n=n m or n d. k n k y eff 0 k n n k 2 2 x eff 0 (2) The field distributions of the symmetric and anti-symmetric modes are provided by Equations 3a and 3b, respectively. The superscripts d or m in k x indicates the wave vector along the x-direction is in the dielectric or in the metal. Noticing that k x is a complex value, the sine or cosine functions in the equations doesn t mean the field distribution is exactly the form of sine or cosine, but the functions indicate the symmetry of field distribution explicitly. m w ikx x d w 2 iky y w H0cos( kx ) e e ( x ) 2 2 d iky y w w H z( x, y) H0cos( kxx) e ( x ) 2 2 m w ikx x d w 2 iky y w H0cos( kx ) e e ( x ) 2 2 (3a) m w ikx x d w 2 iky y w H0sin( kx ) e e ( x ) 2 2 d iky y w w H z( x, y) H0sin( kxx) e ( x ) 2 2 m w ikx x d w 2 iky y w H0sin( kx ) e e ( x ) 2 2 As typical examples, Figures S1b, S1c and S1d show the calculated field distributions of the first three modes which are symmetric mode, anti-symmetric mode and symmetric mode, respectively. The waveguide width is set to w = 550 nm in reference to the 550-nm-wide main groove in the manuscript and the wavelength is set to λ = 800 nm. (3b)

3 Figure S1 MDM waveguide and field distributions of the first three waveguide modes. (a) Schematics of the MDM waveguide. Magnetic field distributions and profiles of the (b) 1st, (c) 2nd, and (c) 3rd modes. The incident wavelength is set to λ = 800 nm and the displayed area is of size 0.95 µm 0.95 µm. The waveguide is composed of a 550-nm-wide dielectric layer of air between metal of Au. Dispersion relations and cut offs of different waveguide modes Although the number of solutions of Equation 1 is infinite, only a few of them are important in practice. This is because only the first few modes are propagating waveguide modes while others are non-propagating modes. Generally, these non-propagating modes are less important due to their significant propagation losses. This point is more clearly shown by the dispersion relations of different modes which display the real and imaginary parts of n eff of different modes as functions of the incident wavelength. Figure S2a displays the calculated dispersion relations of the first three modes with waveguide width of w=550 nm, just corresponding to the upper main groove width in the manuscript. It is observed that, Re(n eff ) of the 1st and 2nd modes are much larger than Im(n eff ) over the whole considered wavelength range. This means these two modes are propagating modes in the study. Typical modal field distributions at λ = 800 nm shown in Figures S1b and S1c clearly demonstrate the propagating nature of these two modes along the y-direction. In contrast, Re(n eff ) of the 3rd mode is larger than Im(n eff ) only in the short-wavelength region, and Im(n eff ) begin to overwhelm in the long-wavelength region. This tells that the 3rd mode is only propagative at short wavelengths. If the incident wavelength is longer than a specific cut-off wavelength, the 3rd mode becomes non-propagative and decays rapidly due to the large Im(n eff ). For instance, the 3rd mode at λ = 800 nm shown in Figure S1d evidently presents a non-propagating nature along the y-direction. In this case, the mode decays exponentially with the increase of the propagation distance. Consequently, the SPPs excited by this mode are nearly negligible at λ = 800 nm. At the short-wavelength region, the contribution of this mode needs to be considered due to the decreased Im(n eff ). For modes with orders higher than 3, Im(n eff ) of these modes are much larger than that of the 3rd mode. So, these modes decays more rapidly than the 3rd mode and are nonpropagating modes over the whole considered wavelength range. Therefore, the SPPs contributed by these modes are negligible compared with that contributed by the first three modes and are not considered in the study.

4 Figure S2 Dispersion relations of the first few modes in the MDM waveguide. The waveguide width is fixed to (a) w=550 nm and (b) w=200 nm. The 1st, 2nd and 3rd modes are denoted by the red, green and blue lines, respectively, while Re(n eff ) and Im(n eff ) are indicated by solid and dashed lines. Figure S2b displays the calculated dispersion relations of the first two modes with waveguide width of w=200 nm which is equal to the lower auxiliary groove width in the study. Because of the reduced waveguide width, Im(n eff ) of the 2nd mode increases largely compared with that in the main groove. Now the 2nd mode is non-propagating over the whole wavelength range, so that only the 1st mode needs to be considered in the 200-nm-wide auxiliary groove. From Figures S2a and S2b, it is also observed that the 1st mode always shows an Re(n eff ) bigger than 1 and will never be cut off. Therefore, this mode is a true plasmonic mode. Other modes are in fact photonic modes. Their Re(n eff ) are smaller than 1. For a fixed waveguide width, these photonic modes will be cut off when the incident wavelength is larger than some specific cut-off wavelengths. In this study, we mainly focus on the SPP excitation property on the front metal surface. Since the plasmonic mode (1st mode) and the photonic modes (other modes) do not show essential difference in exciting the SPPs on the front metal surface, we do not emphasize their differences in the study. Cut-off wavelength of a waveguide mode In this subsection, we provide a strict definition of the cut-off wavelength of a waveguide mode. We start our analysis by introducing the idealized, lossless metal. A real metal always contains loss which is indicated by the imaginary part of its permittivity or the real part of its refractive index. If we simply neglect the real part of the refractive index, we get an idealized, lossless metal. In this case, the cut-off wavelength of a waveguide mode has a clear definition. It is the wavelength when Re(n eff ) = Im(n eff ) = 0. For instance, the purple solid and dashed lines in Figure S3 show the calculated Re(n eff ) and Im(n eff ) of the 3rd mode as functions of the incident wavelength, with the real part of the refractive index of gold being removed. At λ < 610 nm, Re(n eff ) > 0 and Im(n eff ) = 0. This means the 3rd mode has no propagation loss but only propagation phase shift. So it is a purely propagating mode. On the contrary, at λ > 610 nm, Re(n eff ) = 0 and Im(n eff ) > 0. The 3rd mode shows no propagation phase shift but only propagation loss. So it is a purely non-propagating (or evanescent) mode. Thus, the transition wavelength (about 610 nm in the current case) at which Re(n eff ) = Im(n eff ) = 0 can be defined as the cut-off wavelength of the mode. The situation becomes a little complex for a real metal. For

5 instance, the blue solid and dashed lines in Figure S3 display the calculated Re(n eff ) and Im(n eff ) for real gold (with loss). Both Re(n eff ) and Im(n eff ) are positive values now. This means the waveguide mode always has propagation loss and propagation phase shift simultaneously. Therefore, it is reasonable to define the cut-off wavelength, λ c, to be the wavelength at which Re(n eff ) = Im(n eff ). At λ < λ c, Re(n eff ) > Im(n eff ), the waveguide mode mainly presents propagation phase shift and can be regarded as a propagating mode. At λ > λ c, Re(n eff ) < Im(n eff ), the mode is dominated by its propagation loss and can be regarded as a non-propagating mode. The specific value of λ c can be achieved by calculating Re(n eff ) and Im(n eff ) as functions of the incident wavelength. Here, we can also see that the above defined cut-off wavelength (609 nm) for a real metal is actually almost the same as the strictly defined cut-off wavelength (610 nm) for an idealized, lossless metal, as long as the metal loss is small. Figure S3 Cut-off wavelength of the 3rd mode. Calculated real (solid lines) and imaginary (dashed lines) parts of the effective refractive index, n eff, of the 3rd mode as functions of the incident wavelength for real gold metal (blue lines) and idealized, lossless gold metal (purple lines). The cut-off wavelength λ c is denoted by a dashed cyan vertical line. Section 2. Semi-analytical model In this Section, we provide a semi-analytical model which theoretically describes the processes of mode conversion and mode interference in the proposed asymmetric groove structure. The calculation results by this model agree with the direct simulation results. Thus, the underlying physical mechanism in the asymmetric groove is clearly shown. As typical examples, the following calculations by this model are all performed under the specific condition of λ = 800 nm, w 1 = 550 nm, and w 2 = 200 nm. Thus, according to the results in Figures S2a and S2b, only the 1st and 2nd modes need to be considered in the upper main groove while only the 1st mode needs to be considered in the lower auxiliary groove. This is the basis of the semi-analytical model. Model establishment The main idea of the model is to decompose the complex processes of SPP excitation by the asymmetric groove (see Figure S4a) into some basic processes. In the first stage, normally incident light is tightly focused onto the entrance of the upper main groove, the symmetric 1st

6 mode in the main groove is excited with a high efficiency and a portion of SPPs is also excited along the front metal surface in both the left and right directions (see Figure S4b). In the second stage, the excited 1st mode propagates downward and gets reflected at the bottom of the main groove. This reflection will results in both upward-propagating 1st and 2nd modes. Then, these two modes are reflected back and forth between the top and bottom of the main groove (see Figure S4c). The final steady state can be described by a self-consistent equation. The third basic process is that the upward-propagating 1st and 2nd modes in the main groove partly convert into SPPs at the top of the upper main groove (see Figure S4d). Figure S4 Illustration of the semi-analytical model. (a) The SPP excitation by the asymmetric groove. (b) The first basic process: normally incident light impinging on the entrance of the main groove. (c) The second basic process: reflections and cross conversions of the 1st and 2nd modes at the top and bottom sides of main groove. (d) The third basic process: the upward-propagating 1st and 2nd modes in the main groove partly convert into SPPs at the top of the main groove. According to this decomposition, we can define corresponding basic scattering coefficients and derive the self-consistent equation to compute the mode amplitudes in the upper main groove. To begin with, we introduce some notations. Superscripts in, lsp (or rsp), g 1 are engaged to represent incident light, leftward (or rightward) SPPs on the front metal surface, waveguide modes in the, 1 upper main groove (groove 1), respectively. Therefore, in Figure S4b, coefficient matrix S in g in, lsp in, rsp (2 1 matrix) and coefficient S (or S ) denote the excitation coefficients of the waveguide modes in groove 1 and the leftward (or rightward) SPPs by the directly incident light, respectively. Subscripts are engaged to indicate mode indexes of waveguide modes in the metallic groove. For instance, in Figure S4c, I i represents the complex amplitude of the upward propagating i-th mode in the main groove. However, we should be careful with I i because it is defined as the part of the complex amplitude of the downward i-th mode reflected from the upward modes but not the total downward i-th mode which also include the additional component excited by the directly incident light. The reflection and cross conversion behaviors

7 of the 1st and 2nd modes at the top and bottom of the upper main groove are respectively, 1 described by reflection matrix R tg and R (2 2 matrix). Taking R as an example, the matrix element R ij (i,j=1,2) denotes the conversion coefficient from the downward j-th mode to the upward i-th mode and R ij 2 represents the power flow of the upward i-th mode when the incident power flow of the downward j-th mode is normalized to be unity at the bottom of the main groove. Details on the evaluation of R are provided in the next subsection. The propagations of g the 1st and 2nd modes in the main groove can be described by a propagation matrix P 1 which is g1 given by Equation 4, with k being the propagation constant of the i-th mode in the upper main groove. iy g ik 1 1y h 1 g e 0 1 P (4) g ik 1 2y h 1 0 e Now we are able to obtain the self-consistent equation which describes the steady states of different waveguide modes in the upper main groove. The mode reflection behaviors at the bottom and top of the main groove can be represented by two coupled-mode equations of Equations 5a and 5b, respectively. g1 in, g1 I RP ( I S ) (5a) t, g 1 g1 I R P I (5b) Solving these two equations, we can obtain the expression of the upward modes in the main groove which is given by Equation 6. g1 t, g1 g1-1 g1 in, g1 I (1- R P R P ) R P S (6) In a final step, we consider the SPP excitation processes in Figure S4d. The SPP excitation 1 coefficients by the upward 1st and 2nd mode are represented by coefficient matrix S g, lsp (1 2 1 matrix) for the left direction and S g, rsp (1 2 matrix) for the right. Then, the total SPPs excited by the asymmetric groove in Figure S4a are given by the summation of SPPs excited by directly incident light in Figure S4b and SPPs excited by the upward 1st and 2nd mode in Figure S4d. L R The final formulas are given in Equation 7, with or denoting the complex amplitude of the total leftward or rightward SPPs on the front metal surface (schematically shown in Figure S4a). L in, lsp g1, lsp g1 g1 t, g1 g1-1 g1 in, g1 S S P (1- R P R P ) R P S (7a) R in, rsp g1, rsp g1 g1 t, g1 g1-1 g1 in, g1 S S P (1- RP R P ) RP S (7b) g1 The dependence on groove depth h 1 is directly indicated by propagation matrix P. This means we can calculate SPP amplitudes as functions of h 1 by Equation 7 through simulating only a few basic scattering processes but without the need to simulate at each h 1. Besides, since the 1st and g1 2nd modes in the main groove have different propagation constants, P will inevitably result in a beating-like behavior in excited SPP amplitudes with respect to h 1, due to the interference between the two modes.

8 Evaluation of the reflection matrix R The reflection matrix R depends on the auxiliary groove depth h 2. This dependence can also be described by a semi-analytical formula. Similar to the previous analysis, the mode reflection and cross conversion at the bottom of the main groove (see Figure S5a) are also decomposed into three basic processes. In the first step (see Figure S5b), a downward 1st or 2nd mode with normalized power flow of unity propagates to the bottom of the main groove. This mode gets partly reflected into upward 1st and 2nd mode in the main groove and partly transmits into downward 1st mode in the auxiliary groove (groove 2) which is considered to be infinitely deep. bg, 1 Such a process can be described by a reflection matrix R (2 2 matrix, differing from R in that it describes the reflection behavior with regard to an infinitely deep auxiliary groove) and a 1, 2 transmission matrix T g g (1 2 matrix). The second process includes the propagation of the transmitted 1st mode in the auxiliary groove and the subsequent reflection of this mode at the 2 g2 groove bottom (see Figure S5c) which are represented by a propagator P e 1y 2 and a, 2 reflection coefficient R bg, respectively. Here, both mode propagation and mode reflection are described by a simple coefficient instead of the 2 2 matrix in the main groove, because only the g2 1st mode needs to be considered in the narrow auxiliary groove (with k being the propagation constant of this mode). In the third step, the upward 1st mode in groove 2 gets partly reflected at the top of groove 2 and partly transmits into upward 1st and 2nd mode in the upper main groove (see Figure S5d). The corresponding reflection coefficient is denoted by tg, 2 R, and the g2, g1 corresponding transmission matrix is denoted by T (2 1 matrix). 1y ik g h Figure S5 Illustration of the basic scattering processes to calculate R. The 1st and 2nd modes are indicated by red and green arrows respectively. (a) Mode reflections at the bottom of the main groove (groove 1) with a finitely deep auxiliary groove. (b) The first basic process: mode reflections and transmissions at the bottom of groove 1 with an infinitely deep auxiliary groove. (c) The second basic process: propagation and reflection of the 1st mode in the auxiliary groove (groove 2). (d) The third basic process: 1st mode reflection and transmission at the top of groove 2 with an infinitely high upper main groove.

9 In analogy to the derivation of SPP amplitude formula of Equation 7, we first construct a selfconsistent equation and then compute the amplitude of the upward mode in the auxiliary groove, finally, R can be expressed in Equation 8. b, g1 g2 b, g2 g2 t, g2 g2 1 b, g2 g2 g2, g1 g1, g2 R R P (1 R P R P ) R P T T (8) 2 The dependence of R on the auxiliary groove depth h 2 is provided by the propagator P g. This means we can calculate R as a function of h 2 by Equation 8 through simulating only three basic scattering processes (Figures S5b-d) but without the need to simulate at each h 2. Figure S6 displays the calculated amplitudes of the four matrix elements of R as functions of h 2. The lines are model predictions calculated by the semi-analytical formula of Equation 8. The circles are direct simulation results evaluated at each h 2 by using the mode orthogonality in waveguide theories. It can be seen that, the model predictions agree with simulation results. Small discrepancies can be attributed to numerical errors. The dependence of R on h 2 shows a simple g2 g2 Fabry-Perot resonance like behavior. This can be easily inferred from P, because P includes only one propagation constant. The measured period in Figure S6 is about 354 nm, which is roughly equal to half of the wavelength of the 1st waveguide mode in the auxiliary groove (800 nm/2/1.132=353 nm, with being the real part of effective refractive index of the 1st mode in the 200-nm-wide auxiliary groove). In addition, we notice that R 12 and R 21 nearly overlap with each other (a perfect overlap is observed for the model calculation results). This is not just a coincidence but results from the reciprocity. In this study, the waveguide modes are properly g2, g1 g1, g2 T normalized with E( z) H( z)d z. As a matter of fact, we should have R 12 = R 21, T ( T ) and so on. These relations highly diminish the number of unknown scattering coefficients. The small discrepancies between the simulated R 12 and R 21 in Figure 2 and Figure S6 are caused by numerical errors in the simulations. Figure S6 Reflection coefficients of R. Calculated amplitudes of the four elements of reflection matrix R as functions of the depth h 2 of the auxiliary groove (incident wavelength λ=800 nm, groove widths w 1 =550 nm and w 2 =200 nm). The lines denote model predictions by the semi-analytical formula of Equation 8 and the circles indicate direct simulation results. Model validations

10 According to Equations 7 and 8, the SPPs excited by the asymmetric groove as functions of h 1 and h 2 can be theoretically predicted by the proposed semi-analytical model. The results are exhibited in Figures S7a and S7b, with incident wavelength of λ=800 nm and groove widths of w 1 =550 nm and w 2 =200 nm. Various scattering coefficients in Equations 7 and 8 are obtained by simulating the corresponding basic scattering processes presented in Figures S4b, S4d, S5b, S5c, and S5d. For comparison, Figures S7c and S7d show the direct simulation results. It is observed that the model predictions agree well with direct simulation results, which firmly validates the proposed semi-analytical model. From the semi-analytical model, the underlying physical mechanism in the asymmetric groove structure is clearly presented, which is based on the efficient mode conversion induced by the lower auxiliary groove and the subsequent mode interference in the upper main groove. Figure S7 Leftward and rightward SPP intensities as functions of h 1 and h 2. (a) and (b) show calculation results by the semi-analytical model, while (c) and (d) show direct simulation results. The widths of the main groove and auxiliary groove are fixed to w 1 =550 nm and w 2 =200 nm, the incident wavelength is set to λ=800 nm. The four figures share the same colormap. Section 3. Comparison between the asymmetric slit and asymmetric groove structures The asymmetric slit (that is, the structure is penetrating through the metal film) structures have already been proposed to realize unidirectional SPP excitations in some literatures. These structures look quite similar to the proposed asymmetric groove except that the groove structure is not penetrating through the metal film. However, this small difference makes the underlying physics and the control mechanisms completely different. The asymmetric slit is based on the

11 interference of horizontal SPP mode in the upper slit. This mechanism is relatively simple and enables unidirectional SPP excitation to only one direction. In contrast, the proposed asymmetric groove is based on the interference of different vertical waveguide modes in the upper groove. This structure provides a new degree of freedom to manipulate the scattered field through the efficient mode conversion controlled by the lower auxiliary groove. Because of the new degree of freedom, this structure is able to provide unidirectional SPP excitation to both two directions simply by changing the groove depths. A detailed comparison between the asymmetric slit and groove structures is provided as follows. The previously reported asymmetric slit (schematically shown in Figure S8a) is illuminated by external light from the substrate side (i.e., transmission type). The fundamental vertical waveguide mode in the lower narrow slit is excited at first. Then, this mode excites horizontal SPP modes (SPPs on horizontal air/metal interface) propagating to the left direction in the upper broad slit and to the right on the front metal surface. The leftward SPPs in the upper broad slit are reflected back and forth between the two metal walls of the slit which form a horizontal SPP Fabry Perot (FP) cavity, and partly scattered into SPPs on the front metal surface. Under proper conditions, the scattered SPPs to the right direction from the FP cavity may just cancel the directly excited SPPs to the right by the lower narrow slit. Thus, unidirectional SPP launching to the opposite direction (the left) is obtained. In contrast, the proposed asymmetric groove is illuminated by external light from the front side (i.e., reflection type). The symmetric 1st mode in the upper main groove is excited at first. Then the anti-symmetric 2nd mode in the main groove can be excited through mode conversion, with the aid of the lower auxiliary groove (schematically shown in Figure S8b). Here, the modes in the grooves refer to waveguide modes propagating in the vertical direction (the metallic grooves are regarded as metal-dielectric-metal (MDM) waveguides). Because the SPPs on the front metal surface excited by the anti-symmetric 2nd mode are in anti-phase for the left and right directions, this SPP component may just cancel the SPP components excited by the symmetric 1st mode and directly incident light (these SPP components are in phase for the left and right directions) in one direction while interfere constructively in the opposite direction. Therefore, a highly efficient directional excitation of SPPs can be obtained. The above mechanism of mode conversion and mode interference can be theoretically described by the semi-analytical model provided in Section 2. The calculation results by this model quantitatively agree with the direct simulation results. This strongly validates the above mechanism of mode conversion and mode interference. Figure S8 Different physical mechanism in the asymmetric slit and groove structures. Schematic diagrams of the SPP excitation processes in the asymmetric (a) slit and (b) groove structures. The figure (a) is extracted from Figure 1 in Nano Letters 11, 2933 (2011).

12 From the above analysis, we can see that the control mechanism in the asymmetric slit is relatively simple. In this structure, the SPP excitations on the front metal surface are mainly determined by the horizontal SPP FP cavity. The excited SPP intensities show periodical response with respect to the cavity length or equivalently the upper slit width (see Figure S9a). The measured period is just equal to half of the SPP wavelength on the air/metal interface, which clearly verifies this mechanism. The lower narrow slit behaves as a simple excitation source here. A variation in the lower slit depth only changes the total SPP intensity but do not affects the ratio between the leftward and rightward SPPs. Therefore, only unidirectional SPP launching to the left can be obtained (the SPPs to this direction never get to extinction, see Figure S9a). By contrast, the control mechanism in the asymmetric groove is completely different, which is based on the efficient conversion and interference between different vertical MDM waveguide modes in the upper main groove. Figure S9b displays the calculated real parts of complex amplitudes of excited SPPs by the asymmetric groove as a function of the upper groove depth h 1. The periodical response shows a beating behavior. The beating period is measured to be roughly 3490 nm, approximately equal to 800/( )=3480 nm, with and being the real part of effective refractive index of the 1st and 2nd modes in the 550-nm-wide main groove, respectively. This phenomenon clearly verifies the interference between the two vertical MDM waveguide modes in the main groove. The lower auxiliary groove here plays a key role which controls the mode conversion efficiency and then affects the ratio between the leftward and rightward SPPs. This new mechanism of mode conversion together with mode interference enables unidirectional SPP excitation to both the left and right directions to be obtained simply by adjusting the groove depths. The simulated extinction ratio diagram is provided as Figure S10. This diagram clearly shows that, with proper groove depths h 1 and h 2, the extinction ratio can reach extremely high value of 10 4 for both the left and right directions (an extinction ratio of 10 4 to the right direction is equivalent to an extinction ratio of 10 4 to the left, see the deep blue regions in Figure S10). Typical scattered field distributions are displayed in Figures S11a and S11b, with nearly perfect unidirectional launching of SPPs to the right and left directions clearly observed. Figure S9 (a) SPP generation efficiencies to the left η L and to the right η R by an asymmetric slit for different cavity lengths L FP and depths d. This figure is extracted from Figure 2 in Applied Physics Letters 97, (2010). (b) Real parts of the complex amplitudes of excited SPPs by the asymmetric groove as a function of the upper groove depth h 1.

13 Figure S10 Simulated SPP extinction ratio (defined as the rightward SPP intensity over the leftward one) of the asymmetric groove. The widths of the upper main groove and auxiliary groove are fixed to w 1 =550 nm and w 2 =200 nm, the incident wavelength is set to λ=800 nm. The extinction ratio can reach extremely high value of 10 4 for both the left (see the deep red regions) and right directions (an extinction ratio of 10 4 to the right direction is equivalent to an extinction ratio of 10 4 to the left, see the deep blue regions). Figure S11 Simulated magnitude of scattered magnetic field under a specific geometry. (a) At h 1 = 79 nm and h 2 = 52 nm (corresponding to the deep red region at the lower left corner in Figure S10), SPPs are unidirectional launched to the right. (b) At h 1 = 220 nm and h 2 = 260 nm (corresponding to the deep blue region at the lower left corner in Figure S10), SPPs are unidirectional launched to the left. The widths of the upper main groove and auxiliary groove are fixed to w 1 =550 nm and w 2 =200 nm, the incident wavelength is set to λ=800 nm. Moreover, the SPP excitation efficiency by the asymmetric slit is quite limited due to the low transmission efficiency of the narrow slit. Simulations show that, the asymmetric slits in Reference 18 present unidirectional SPP excitation efficiencies of about 4% for a tightly focused Gaussian incidence with a waist size of w 0 =480 nm. This efficiency is less than 1/5 of that of the proposed asymmetric groove under the same excitation condition. In conclusion, although the proposed asymmetric groove structure looks quite similar to the previously reported asymmetric slits, the underlying physical mechanism is completely different. The novel mechanism of mode conversion by the auxiliary groove offers a new degree of freedom to control the optical field. This mode conversion together with the subsequent interferences between different modes provides an efficient mean to manipulate the scattered

14 optical field at subwavelength scales. Owing to this mechanism, unidirectional SPP excitation to either the left or right direction can be obtained simply by adjusting the groove depths. Moreover, both broadband directional excitation of SPPs and inversion of SPP launching direction at different wavelengths are successfully demonstrated (see Figures 5c and 5d in the manuscript), which are unable to be obtained simultaneously in any previously reported structures. Although the current work is performed with the specific configuration of metallic groove antenna, the strategy is applicable to other antenna structures as well. Therefore, the proposed strategy based on efficient mode conversion provides new opportunities for the design of nanoscale optical devices, and may have general implications in nano-optics, especially in the research area of directional nanoantennas. Section 4. Vector diagrams and the two-mode model In this section, we provide a detailed illustration to the vector diagrams and the two-mode model, including the meaning and the calculation process. Vector diagrams As schematically demonstrated in Figure S12, the total SPPs excited by the asymmetric groove can be decomposed into different contributions which are SPPs excited by the directly incident beam at the entrance of the main groove and SPPs excited by different upward propagating waveguide modes in the main groove. Since these different SPP components have different amplitudes and phases, they are intuitively represented by different vectors in the vector diagrams of Figures 3d and 4c in the manuscript. The lengths of vectors correspond to the amplitudes of different SPP contributions, while the directions of vectors indicate the phases of SPPs. Thus, the superposition of different SPP components is directly given by the vector summation of corresponding vectors. Since the important factor is actually the phase difference between different SPP contributions but not the absolute phase, the choice of axes in the vector diagram is arbitrary. This choice does not affect the result of vector summations. The calculation of different SPP contributions follows two steps. First, the total electromagnetic field scattered by the asymmetric groove (schematically shown on the left side of the = in Figure S12) is calculated by FEM simulation. Then, the complex amplitudes of the total leftward and rightward SPPs on the front metal surface as well as the upward 1st, 2nd (and even 3rd) modes in the upper main groove can be evaluated by using the orthogonality between different waveguide modes. In the second step, the basic SPP excitation processes on the right side of the = in Figure S12 (i. e., SPPs excited at the groove entrance by direct incidence, 1st, 2nd (and even 3rd) modes) are simulated by FEM one by one. Thus, the basic SPP excitation coefficients by the directly incident light, the 1st, 2nd (and even 3rd) modes can be evaluated through these simulations. Finally, the different SPP contributions to total SPPs are given by the products of the complex amplitudes of different optical modes and the corresponding SPP excitation coefficients of each mode.

15 Figure S12 Different origins of total SPPs on the front metal surface excited by the asymmetric groove structure. These origins include SPPs excited at the entrance of the upper main groove by directly incident beam and upward propagating 1st, 2nd (and even 3rd, not shown here) modes in the main groove. Although Figure S12 does not shown the SPP component excited by the 3rd mode in the main groove, this component can be calculated in a similar manner. The vector diagrams actually display SPP components excited by different modes. Although the 3rd mode itself is nonpropagating, the SPP excited by this mode is also the eigenmode on the front metal surface. So there is no essential difference between the SPPs excited by the 3rd mode and other modes, except for the specific amplitudes and phases. That is why the SPP component excited by the non-propagating 3rd mode can be displayed in the vector diagram (see blue vectors in Figure 4c in the manuscript) as well as that excited by the propagating 1st and 2nd modes. The only thing needed special attention is that, the calculation space cannot be large when evaluating the SPP excitation coefficient by the 3rd mode in the second step, because this non-propagating mode decays rapidly with the increase of propagation distance. The two-mode model The calculation of the two-mode model is similar to the calculation of the vector diagram. Here, two-mode refers to the 1st and 2nd modes in the upper main groove, and two-mode model calculates the summation of SPP components contributed by the directly incident beam, 1st and 2nd modes in the main groove (i.e., SPP components on the right side of the = in Figure S12). In contrast, the direct simulation results give the total SPPs on the front metal surface excited by the asymmetric groove, which naturally include SPP components contributed by all waveguide modes (1st, 2nd, 3rd and so on) in the main groove. Therefore, the discrepancy between the calculation results of the two-mode model and the direct simulation can intuitively reflect the SPP contributions from all non-propagating modes (3rd, 4th and so on). Because higher-order non-propagating modes (for instance, 4th mode or even higher-order mode) which are far below cut off decay rapidly with the propagation distance, the SPPs excited by these modes are generally quite weak and are negligible. Thus, the discrepancy can mainly be attributed to the SPPs excited by the lowest-order non-propagating mode which is just below cut off. This mode is the 3rd mode in the current case. Now we explain the different roles of the 3rd mode in the vector diagrams of Figures 3d and 4c in the manuscript. The main difference is that Figure 3d corresponds to an incident wavelength of λ= 800 nm while Figure 4c corresponds to λ= 626 nm. The 3rd mode in the main groove has a cut-off wavelength of λ c = 609 nm. Thus, this mode is a non-propagating mode (i.e., evanescent mode) at both λ= 626 nm and λ= 800 nm. The difference is that the Im(n eff ) of the 3rd mode (see the blue dashed line in Figure S2a) at λ= 800 nm is much larger than that at λ= 626 nm. So the

16 3rd mode decays much more rapidly at λ= 800 nm than at λ= 626 nm. Consequently, the SPPs excited by this mode is negligible at λ= 800 nm compared with that at λ= 626 nm. This point is clearly verified by Figure 4 in the manuscript. In Figure 4a, the calculation results of the twomode model (dashed lines) which does not include the SPPs contributed by the 3rd mode consists with the direct simulation result (solid lines) at λ= 800 nm. This means the SPPs excited by the 3rd mode is negligible at this long wavelength. That is why the SPP contribution by the 3rd mode is not shown in Figure 3d. In contrast, the calculation results of the model evidently deviate from the direct simulation results at λ= 626 nm, which means the SPPs excited by the non-propagating 3rd mode must be taken into account at this short wavelength. This is why the SPP component excited by the 3rd mode is directly indicated by blue vectors in Figure 4c. By taking into account this SPP contribution, the modified mode results match the direct simulation results again.