Superfocusing of electric or magnetic fields using conical metal tips : effect of mode symmetry on the plasmon excitation method

We compare singleand double-sided excitation methods of adiabatic surface plasmon polariton (SPP) wave superfocusing for scattering-type metallic near-field scanning optical microscopy (s-NSOM). Using the results of full 3D finite difference time domain analyses, the differences in field enhancement factors are explained and reveal the mode selectivity of a conical NSOM tip for adiabatic SPP superfocusing. Exploiting the mode-symmetric nature of the tip further, we also show that it is possible to selectively confine either the electric or magnetic field at the NSOM tip apex, by simply adjusting the relative phase between the SPP waves in the double-sided excitation approach. ©2011 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (180.4243) Near-field microscopy; (230.3810) Magneto-optic systems. References and links 1. B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. 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Especially, exploiting the benefits of adiabatic plasmon superfocusing [21][22][23] and with sharper tip apex, metallic NSOM tips have been the foci of most recent studies.In adiabatic focusing concepts, SPP wavepackets are launched onto a metallic NSOM taper and are focused at the nanometer-sized taper apex.As the SPP group velocity slows down toward the metal tip end, a giant accumulation of energy is achieved [21][22][23], only limited by the size of the tip apex.Series of experimental and numerical investigations have been carried out, analyzing the superfocusing effect and the properties of the localized hot spots for the metallic NSOM probes.Most of the previous work assumes experimentally challenging radially polarized illumination for the SPP excitation [15], or analyzes different geometries or materials for the NSOM tip [16][17][18][19].Meanwhile, much less attention has been paid to the method of plasmon excitation for the tip, especially related to the symmetry of the tip structures, or field patterns at the tip apex.
In this paper, we investigate the effect of mode symmetry in the SPP excitation process on the efficiency of the field enhancement in adiabatic superfocusing (Fig. 1).Interpreting the NSOM tip as a symmetric mode combiner, we then reveal and explain the differences in the field enhancement between: 1) single-sided-, 2) double-sided E-symmetric (E in-phase, H out-of-phase), and 3) double-sided H-symmetric (E out-of-phase, H in-phase) SPP excitation with linearly polarized lights.Our results show that it is possible to selectively enhance either the electric or the magnetic field at the tip apex.Switching between E-and H-field is simply achieved by controlling the relative phase between the incident waves in a double-sided excitation scheme.Excellent field enhancement up to |E apex | 2 / |E inc | 2 = 145.6 for the doublesided E-symmetric excitation, and μ|H| 2 /ε|E| 2 ~11 for the double-sided E-antisymmetric (or Hsymmetric) excitation were achieved for the NSOM tip geometry used in the study.

Settings for the analysis
Due to the large computational space required to run full 3D FDTD calculations for adiabatic superfocusing (physical domain of 12 x 14 x 18 µm 3 meshed into 752 x 1,078 x 756 computational grids), spatially varying grid sizes are used with a minimum grid size of 0.625 nm.The structure of the metal tip used in the simulations is shown in Fig. 1.A conical gold tip with an opening angle of 30° was considered, to get the maximum field enhancement at the apex [17].The radius of curvature at the apex was set to 40 nm.The dielectric function of gold around the wavelength of interest (780 nm) in the study was accounted for by using the Drude model (ε = ε inf -ω p 2 /ω(ω + iγ), ω p = 13.666x10 15 rad/s, γ = 40.715x10 12rad/s, and ε inf = 1.0) [19].Seven rectangular grooves with a period of 706 nm and depth of 100 nm were engraved on the shaft of the cone in an axisymmetric manner, to match the phase of the incident light to that of SPP on the metal surface [24].The axial distance between the apex and the first groove was set to 4 µm in order to isolate the SPP focused field at the tip apex from the direct contribution of the incident free-space wave.SPP excitation was achieved using a pulse with a Gaussian spectral profile, centered at a wavelength of 780 nm.To note, the spectral width of the pulse, 206 nm (full-width-at-half-maximum, FWHM), was twice as broad as the SPP-coupling wavelength window of grooves (SPP excitation dropping about 10%, at 780 +/ 20 nm).Incident normal to the shaft of the probe, the pulse is focused to a Gaussian spot on the shaft, with a spatial FWHM of 3.12 µm.
As shown in Fig. 1, three different SPP excitation schemes were considered: single-sided, double-sided E-symmetric and double-sided E-antisymmetric.For single-sided excitation, the cone shaft was illuminated from the bottom of the shaft with linearly p-polarized light.For double-sided E-symmetric and E-antisymmetric excitation, the structure is illuminated from the top and bottom of the shaft with two pulses of the same power as that of single-sided excitation.For each excitation scheme, the time-averaged value of the superfocused field intensity |E apex | 2 or |H apex | 2 at the apex was measured at a plane located 10 nm away from the apex, and was normalized to the intensity |E inc | 2 of the incident light.2e and Fig. 2f, the conical tip allows (or suppresses) the superfocusing of SPP for the E-symmetric (or E-antisymmetric) excitations, functioning as a symmetric, mode selective combiner.When both fields are in phase (E-symmetric, E total (E bottom , E top ) = E(1, 1), see Fig. 1b) constructive interference results in enhancement of the Efield at the tip apex.In contrast, with the relative phase π between two fields (Eantisymmetric, E(1,-1), Fig. 1c) the E-field at the apex is suppressed.Now, for the case of single-sided excitation, decomposing its field into the sum of even-and odd-mode excitation (E(1, 0) = E(1/2, 1/2) + E(1/2, 1/2)), we obtain the field intensity of 1/2 ( = (1/2) 2 + (1/2) 2 ) at the tip apex from the odd-mode rejecting, symmetrical tip geometry.Comparing to the case of double-sided E-symmetric excitation (E(1, 1)) for which we retain the full field intensity of 2 ( = 1 2 + 1 2 ) at the even-mode tip apex, we obtain a factor-of-4 difference in the field intensity |E apex | 2 between two cases -in agreement with the FDTD obtained value of 3.96.Considering the increasing attention for optical magnetism and H-field focusing [25][26][27], it is also worth to investigate the behavior of H-field intensity |H| 2 at the tip apex.For this, we focus our attention to the symmetries of the H-field.Given the k vectors of the incident wave pointing toward the tip axis (Fig. 1), the symmetry of the incident H-field has the opposite parity compared to that of E-field, resulting in complementary behavior in their modecombining effects.In line with the mode symmetry interpretation, now for H-field, field enhancement factors |H apex | 2 / |H inc | 2 of 0.794 and 3.263 were found for single-sided and double-sided E-antisymmetric (or H-symmetric) excitations, respectively.This is in sharp contrast to the total suppression of the H-field (|H apex | 2 / |H inc | 2 = 0.004) for the E-symmetric (or H-antisymmetric) SPP excitation case (Fig. 3).Even though a strong net enhancement for H-field at the tip apex is not possible due to the azimuthal H φ nature of the SPP mode [15], the simultaneous suppression of E-field resulting from the aforementioned parity reversal in the E-and H-field symmetries is noteworthy.Compared to the NSOM tip design dedicated for H-field superfocusing (H Z , μ|H| 2 /ε|E| 2 ~6) [26], our double-sided, H-symmetric SPP excitation method thus provides comparable H-field isolation (H X , μ|H| 2 /ε|E| 2 ~11) without the need of changing the NSOM tip geometry.As is evident from Fig. 3, the H-field at the tip apex in the double-sided H-symmetric excitation scheme is only weakly spatially localized.Stronger H-field localization may be achieved by using more sophisticated taper geometries, for example using structures which allow circulation of current near the tip apex.It seems worthwhile to compare these results concerning the excitation mode symmetry to the alternative, most commonly used method for NSOM tip excitation, utilizing a direct illumination of the tip apex [2,19].As shown in Fig. 4, the selective enhancement of E-or Hfield with E-symmetric / E-antisymmetric excitations are evident for both illumination methods.For direct illumination, |E apex | 2 / |E inc | 2 of 4.36 and 17.27 were observed (at 780 nm) for the single-sided (not shown) and double-sided E-symmetric (Fig. 4a) excitations, respectively.Their difference by a factor of 3.96 can again be explained in terms of the mode symmetry.Compared to a nonlocal illumination on the tip shaft groove, much smaller field enhancement was found for direct illumination, due to the smaller flux-acceptance area near the tip apex.The calculated superfocusing efficiency for direct illumination was 0.35~0.61% of the incident light, compared to the efficiency of 2.5~4.8% for nonlocal illumination, depending on the excitation method (single-, double-sided) under the given NSOM geometry.To note, for the H-symmetric excitation, with the rather substantial far-field background noise from the incident wave it was hard to estimate the net effect of the SPP superfocusing.Finally, understanding that E-symmetric or H-symmetric double sided SPP excitation can be achieved by providing proper phase differences between the two incident waves, we report the behavior of the field enhancement of E and H, as a function of the relative phase differences δ = ( top   bottom ). Figure 5a shows the field enhancement as a function of phase difference δ.Complementary behavior for the field enhancement of E and H was observedas expected from the mode symmetry arguments, by simply controlling the relative phase between the excitation waves (for example, by interferometrically adjusting the relative timing of the two incident pulses).In the case of H-field focusing (δ = π), H-field intensities that exceed those of the E-field can only be achieved in a narrow range around δ = π.We estimate that the precision / tolerance in phase control (in pulse timing or groove fabrication) that is needed to achieve reasonable isolation (μ|H| 2 /ε|E| 2 ~5) from E-field contaminations, is on the order of +/ π /40 (+/ 10 nm for 780nm), which can readily be achieved with current experimental techniques.

Conclusion
In summary, we have compared different excitation strategies and specifically their mode symmetries for adiabatic surface plasmon superfocusing of E-and H-field on metallic NSOM tapers.We found that the NSOM tip essentially acts as an efficient spatial mode filter and that this mode selectivity provides additional functionality when using an interferometrically stabilized double-sided nonlocal SPP excitation scheme.For both the nonlocal gratingcoupled SPP excitation method and direct tip apex illumination method, it was possible to enhance or suppress the E-field at the tip apex, by adjusting the relative phase of two SPP excitation waves.Exploiting the mode symmetry further, in relation to the parity reversal between E-and H-field, concentration of H-field and at the same time strong suppression of E-field was achieved for the H-symmetric (or E-antisymmetric) SPP excitation scheme.
Compared to E-field superfocusing methods using single-sided or radial-symmetric excitation [12,15], the proposed double-sided excitation method provides strong field enhancements, and at the same time enables selective addressing of E-or H-field without the need of change for the tip geometry.We believe that our findings will be useful for the high resolution NSOM mapping of optical E-and H-fields around nano-objects.

Fig. 1 .
Fig. 1.SPP excitation methods for adiabatic superfocusing at the metal NSOM tip apex compared in the present study.(a) single-sided, (b) double-sided E-symmetric (E field inphase, H field out-of-phase), and (c) double-sided E-antisymmetric (E field out-of phase, H field in-phase) excitation.

Figure
Figure 2a-c show the FDTD calculated E-field enhancement factors for different nonlocal SPP excitation schemes.Large enhancement factors |E apex | 2 / |E inc | 2 for E-field, of 36.8 and 145.6 were observed at the design wavelength of 780 nm, for the single-sided (Fig.2a) and double-sided E-symmetric (Fig.2b) excitation configurations respectively.For the doublesided E-antisymmetric excitation method (Fig.2c), superfocusing of SPP was suppressed by destructive interference, resulting in |E z, apex | 2 / |E inc | 2 of 0.016 (|E y, apex | 2 / |E inc | 2 = 0.281).Interesting to note is the factor of ~3.96 ( = 145.6/36.8)differences in the field enhancement at the tip apex between single sided vs. double sided E-symmetric excitation methods, while the total incident power differs by a factor of ~2 only.Interpreting the conical metal tip as a local SPP mode combiner and filter, these differences in the E-field enhancement are readily

Fig. 2 .
Fig. 2. (a~c) Normalized electric field intensity (|E| 2 /|Einc| 2 ) distribution at λ = 780 nm, in the plane 10nm away from the tip apex.The overlaid graph shows the spatial distribution of the normalized intensity along the centerline of the figure.(d~f) Normalized SPP field (EZ/|Einc|) evolution near the NSOM tip end; for (a) and (d) single-sided, (b) and (e) double-sided Esymmetric, and (c) and (f) double-sided E-antisymmetric SPP excitation methods.

Fig. 3 .
Fig. 3. (a~c) Normalized magnetic field intensity (|H| 2 /|Hinc| 2 ) distribution at λ = 780 nm, in the plane, 10 nm away from the tip apex.The overlaid graph shows the spatial distribution of the normalized intensity along the centerline of the figure.(d~f) Normalized SPP field (HX/|Hinc|) evolution near the NSOM tip end; for (a) and (d) single-sided, (b) and (e) double-sided Hantisymmetric, and (c) and (f) double-sided H-symmetric SPP excitation methods.The white arrows show the direction of the magnetic field.

Fig. 4 .
Fig. 4. Normalized field intensity distribution for E-(upper row) and H-(lower row) field: I. Case of direct illumination method with (column 1: a,e) double-sided E-symmetric SPP excitation and (column 2: b,f) E-antisymmetric SPP excitation.II.Case of nonlocal illumination method with (column 3: c,g) double-sided E-symmetric SPP excitation and (column 4: d,h) double-sided E-antisymmetric SPP excitation.λ = 780 nm.Insets show the zoomed-in field image near the tip apex.Media 1, Media 2, Media 3, and Media 4 are provided for c, g, d, h, respectively.