Invited Paper
Surface plasmon routing in dielectric-loaded surface plasmon polariton waveguides J. Grandidier, S. Massenot, A. Bouhelier, G. Colas des Francs, J.-C. Weeber, L. Markey and A. Dereux Institut Carnot de Bourgogne, UMR 5209 CNRS - Universit´e de Bourgogne, 9 Av. A. Savary, BP 47 870, 21078 Dijon, FRANCE ABSTRACT Waveguiding by dielectric-loaded surface plasmon-polaritons (DLSPP) structures are numerically and experimentally investigated. We used the effective index model to understand the influence of basic waveguide parameters such as width and thickness on the properties of the surface plasmon guided modes. A waveguide was fabricated and experimentally studied. The effective indices of the modes supported by the waveguide and their propagation length are evaluated by leakage radiation microscopy in both the Fourier and imaging planes. Several excitation schemes were tested including surface plasmon coupling by diascopic or episcopic illumination as well as defectmediated excitation of guided modes. We found good agreement between theoretical values predicted by the effective index model and experimental values deduced from leakage radiation images. Keywords: plasmonics, surface plasmon waveguide.
1. INTRODUCTION During the last decade, a significant research effort has been focused toward the development of surface plasmon based devices. A surface plasmon polariton (SPP) mode couples an electromagnetic wave to a collective oscillation of the free electrons of a metal1 with potential applications for integrated optics2 and biodetection3 for instances. Surface plasmon may play an important role in chip-to-chip optical interconnects for their ability to propagate in the relevant length scale and to utilize the same support of information as current Si-based microelectronic, i.e. a metal circuitry. Towards this goal, the control of surface plasmon propagation along well-defined paths is a prerequisite for transporting and guiding datacom into a plasmonic platform. Surface plasmon waveguides can take many forms. Metallic stripes for instance were successfully employed to confined surface plasmon modes in micron-wide waveguides.4 Groove-like channels were also shown to have outstanding propagation properties.5 To actively and dynamically control surface plasmon propagation a concept of hybrid surface plasmon waveguide were recently developed where the guiding properties could be modified by an active medium placed atop a stripe waveguide.6–8 These dielectric-loaded surface plasmon waveguides are benefiting from an enhancement of the field inside the structure and the access to the optical, electrical, or mechanical properties of the dielectric load. In these dielectric-loaded surface plasmon polariton waveguides (DLSPPW), the guided mode is essentially confined at the metal-dielectric interface due to the very nature of the plasmon mode. In this paper, we study DLSPPW using leakage radiation microscopy (LRM).9–11 This method of observation gives a direct access to both the mode’s effective index and propagation length.12 This allows a better understanding of the mode properties used for developing more advanced functionalities. In section 2, we numerically determine the effective index of the modes propagating inside DLSPPW by using the so-called effective index model (EIM).7 The numerical values concerning the optimal dimensions of a waveguide were then use to fabricate a waveguide structure. The fabricated waveguides were characterized by leakage radiation microscopy (LRM).9–11 In section 3, we analyze the waveguide in Fourier space to retrieve the effective indices of the propagating modes. We also compared in that section different excitation schemes we used to launch the SP modes. In section 4, we study our waveguiding structures in direct space in order to determine the propagation length of the excited modes. We finish with a spectroscopic analysis of a curved waveguide. Further author information: (Send correspondence to J. Grandidier) E-mail:
[email protected], Telephone: +33(0)3 80 39 90 66 Plasmonics: Nanoimaging, Nanofabrication, and Their Applications IV, edited by Satoshi Kawata, Vladimir M. Shalaev, Din Ping Tsai, Proc. of SPIE Vol. 7033, 70330S, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.794574
Proc. of SPIE Vol. 7033 70330S-1 2008 SPIE Digital Library -- Subscriber Archive Copy
2. EFFECTIVE INDEX MODEL In this section we will determine the two critical parameters defining a guided mode, namely its propagation constant or effective index and its propagation length defined at the 1/e attenuation of the intensity along the propagation direction. To this aim were are using the effective index model (EIM).13 The EIM has been recently extended to the numerical analysis of surface plasmon waveguides12 and is briefly presented here. A schematic of the considered structure is shown in Fig. 1(a). It consists of vertical alignment of a dielectric substrate, a thin gold film of thickness d and dielectric rectangular structure of thickness t and width w. The problematic here is too determine the effective index Nef f of the structure. In the effective index model, the three dimensional geometry of Fig. 1(a) is decomposed into three zones labeled 1, 2 and 3 in Fig. 1(a) where zone 1 and 3 consist of substrate/Au/air multilayer (Fig. 1(b)) and zone 3 consists of a substrate/Au/dielectric/air multilayer (Fig. 1(b)). ∗ The effective indices of the two multilayers Nef f and nspp can be evaluated independently by using the Reflection Pole Method (RPM).14 The DLSPPW structure is then is assimilated to a planar waveguide with core index Nef f ∗ and clad index nspp (Fig. 1(d)). Note that the field polarization should be chosen accordingly to the initial system. The propagation length of the surface plasmon mode is determined by Lspp = λ0 /4πβ
(1)
where λo is the wavelength in the vacuum and β is the imaginary part of Nef f . Note that at a wavelength λ = 800nm, Eq. 1 gives only an estimation of the propagation length. The model does not include radiation leakage and scattering effects are not considered in this method. With increasing wavelength however, leakages are minimal and the calculated propagation length becomes more accurate.
(a)
z Yy
Neff
W x
(b)
Tt Dd
E
nspp
E 1
(c)
2
3
(d)
W
E
Neff*
t d
nspp
E
Neff*
Figure 1. Representation of the effective index model. The waveguide structure in (a) is decomposed into two geometries (b) and (c) characterized by nspp and Nef f ∗, respectively. These two indices are recombined in (d) to determine the effective index Nef f of the waveguide.
At a wavelength λ = 800nm, the calculated values of the effective indices of the existing modes are represented on Fig. 2 for a load thickness of 300nm as a function of the width’s ridge. The material used for the load is an electron-beam resist (PMMA) that can be easily doped. We represent on this graphic the two first TM modes T M00 and T M01 and the first TE mode T E00 . The cutoff width is determined for T M01 by Wcutof f = π/(k0 ×
(Nef f ∗)2 − (n2spp )) and appears for w > 350nm. In the limit of vanishing width, the effective index
of the waveguide asymptotically reaches the index of the mode at a Au/air interface. The plasmon mode is at 1.02 for a TM polarization.
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Mode effective index
1,40 1,35 1,30 1,25 1,20 1,15 1,10 1,05 1,00 0
100
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300
400
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Ridge width (nm)
Figure 2. Effective indices of the three first appearing modes when increasing the ridge width obtained by the EIM. Calculations are made for a wavelength λ = 800nm and a PMMA layer thickness of t = 300nm. The orientation of the electric field is indicated at each step.
3. EXPERIMENTAL SETUP - IMAGING IN FOURIER PLANE The dielectric-loaded surface plasmon waveguides were fabricated using the parameters evaluated with effective index method. A 50 nm-thick gold layer was thermally evaporated on a glass substrate of refractive index n1 = 1.5. A 330nm thick PMMA layer was then spin-coated on the gold film. By standard e-beam lithography and lift-off procedure, the exposed PMMA was removed to obtain a ridge width of W =240 nm. For this width, we expect single-mode operation if the mode is properly polarized (Fig. 2). Figure 3(a) and (b) show typical scanning electron micrographs of two fabricated waveguides. They consist of a large window of exposed Au surface on which a dielectric structure is fabricated. The bright areas are the gold layer whereas the darker areas corresponds to region covered by the PMMA. The waveguide can take any forms: straight in Fig. 3(a)) or curved in Fig. 3(b).
(b)
(a) Au surface
PMMA layer
Au surface
DLSPPW
DLSPPW I bI Thy
1L1
11R K\ X1 ••1C1)
I
MU flt••!!•!!
Figure 3. Electron micrographs of dielectric-loaded surface plasmon polariton waveguides. (a) Straight waveguide. (b) Curved waveguide.
We have developed two different excitation/detection schemes for exciting and characterizing the surface plasmon modes inside the fabricated structures. The numerical values for the effective indices indicate that a direct excitation of the mode with propagating photons incident on the air side is not possible. In order to excite the modes inside the waveguide we are either using a local defect to phase-match incoming photons with the
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propagation constant15 or we use photons incident from the substrate side16 by use of high-numerical aperture (N.A.) objectives (N.A> Nef f ). In both cases, the detection of the surface plasmon guiding properties are determined by leakage radiation microscopy. The two experimental configurations are schematically represented in Fig. 4. Single mode fiber
(b)
(a) Sample plane
Collimation lens Polarizer
Collection objective (N.A.= 1.49)
Waveplate (l/4 or l/2)
Focusing objective (N.A.= 0.52)
Sample plane LASER
Collection objective (N.A.= 1.49)
Fourier plane
Fourier plane
CCD
CCD
Tube lens
Tube lens
Image plane
Image plane
CCD
CCD
Figure 4. Leakage radiation microscopy setup. (a) Episcopic configuration: the modes are excited through a 1.49 N.A. objective and collected with the same 1.49 N.A. objective. (b) Diascopic configuration: a 0.52 N.A. objective focuses the incident light onto a defect of the structure. The modes are excited through scattering and momentum transfer. In both cases, leakage radiation of the guided modes are collected with a 1.49 N.A. objective and recorded either in the image plane or in the Fourier plane.
Figure 4(a) shows an episcopic configuration when the surface plasmon mode is excited and detected with the same objective. The lens used has a maximum N.A.=1.49 well above the expected values of Nef f for the size parameters w and t considered here. A laser beam is expended to slightly overfill the back-aperture of the excitation/collection objective. A polarizer and a λ/2 waveplate (not shown ) are placed between the laser and the objective to insure a TM polarization of the incident light. This creates a set of wavevectors capable of exciting modes until a maximum effective index limiting by the objective’s N.A. Leakage radiations emitted by the surface plasmon in the substrate are then collected through the same objective and are directed to a beam splitter. Part of the beam is focused in the image plane of the microscope and provides a mapping of the surface plasmon intensity distribution inside the waveguide. A second part of the beam is passing a lens doublet that Fourier-transforms the signal. A camera placed at the conjugated plane renders the angular distribution of emitted light mapping thus the wavevector distribution kx and ky . Figure 4(b) shows an alternative excitation scheme. This diascopic illumination uses a focusing objective placed above the structure. The aperture of the objective is 0.52 and direct excitation of surface plasmon is not possible. However, when focused on a defect or the ridge of the waveguide, scattering can provide the necessary spread of wavevectors to excite the modes of the DLSPPW. The detection of the propagating surface plasmon is similar to the one described above. Figure. 5(a) shows the image obtained at the Fourier plane for an episcopic excitation scheme (Fig.4(a)) for an excitation wavelength at 800nm. The excitation/collection objective was focused directly on a DLSPPW similar to the one displayed in Fig.3(a). The image, in kj /ko (j = x or y) coordinates, features a bright circle with a radius corresponding to the full numerical aperture of the 1.49 N.A. objective. This indicates that the complete opening of the objective is illuminated. An vertically aligned fringe-like pattern is visible
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DLSPP Guided mode
1.5
DLSPP Guided mode
SP
1.0
SP
Ky/k0
0.5
EI=1.02 NA=0.52
0
SP
-0.5 -1.0 -1.5
(a) -1.5
(b) -1.0
-0.5
0
kx/k0
0.5
1.0
1.5
Figure 5. Fourier plane images of the detected leakage radiation. (a) Episcopic excitation and (b) diascopic excitation. The horizontal line gives a measurement of the guided mode propagation constant. See text for details. λ = 800nm, polarization TM.
and originates from interference in the detection path and local inhomogeneities of the expanded laser beam. More importantly, two sets of darker features are observed in this Fourier plane image. A first set appears as narrow diametrically-opposed dark half-moons indicated by the label “SP” in the image. These details are the signature of incident wavevectors coupled to surface plasmon modes existing at the Au/air interface. They appear darker than surrounding region because of the destructive interference between incoming photons and leakage radiations.17 The two vertical moons are aligned with the polarization direction. From the image, the value obtained for the effective index of the Au/air interface is nSP P = 1.02 which is in agreement with the value calculated by EIM in the case of vanishing w (see Fig. 2). The second set of feature appears as two-diametrically opposed dark horizontal lines situated at ky /ko =1.26 as indicated by the white arrows. These two bands originate from light coupling to DLSPPW modes which propagates towards increasing y-direction (ky /k0 > 0) or decreasing y-direction (ky /k0 < 0) inside the guide. The calculated effective index value for a waveguide of t ∼ 300nm and w = 240nm is approximately 1.27 in good agreement with the experimental value. Figure 5(b) shows a Fourier plane image for a diascopic illumination (Fig.4(b)). Here, the illumination objective was focused on a defect to excite the different surface plasmon existing in the structure. A bright central disk is readily observed in the image and corresponds to illumination numerical aperture (N.A=0.52). The signatures of the surface plasmon mode at the Au/air interface and the guided mode inside the dielectric structure are observed at the same effective indices as for an episcopic illumination (Fig.5(a)). Due to scattering depolarization occuring at the defect, the SP mode existing at the Au/air interface is excited for directions that can be different from the inciming polarization. The defect used to launch the SP mode inside the DLSPPW was located close to the waveguide extremity so that propagation was favored in only one direction. This explains why the signature of the waveguided mode in the Fourier image is not symmetric with the center and only the upper branch is visible. The main difference with an episcopic excitation lays in the contrast in the image. The surface plasmons were identified by dark details in the Fourier image of Fig.5(a). A diascopic illumination provides a positive contrast for the surface plasmon: the leakage radiation emitted by the surface plasmon during propagation are no longer interfering with incoming photons since they are situated at different locations in the Fourier plane. We found that Fourier plane observation of the surface plasmon excited by a diascopic illumination typically benefits from an increased contrast compared to surface plasmon excited with an episcopic scheme and are therefore easier to observe. It can be important for multimmode waveguides for instance, where modes with weak coupling efficiencies are difficult to resolve. The drawback of this method however, is that it relies on an incidental defect placed along the waveguide to launch the mode and is therefore not always applicable.
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4. EXPERIMENTAL SETUP - IMAGING IN DIRECT PLANE The SPP guided mode have been considered in terms of effective index by using the EIM and by images obtained in the Fourier plane. In this section, we are detecting leakage radiation in the image plane in order to spatially map in direct space the intensity distribution of the surface plasmon inside the waveguide. The underlying idea is to confirm the single-mode operation of the waveguide and to estimate the propagation length of the mode. In this section we will essentially excite the surface plasmon mode using a diascopic illumination and benefit from defect-mediated surface plasmon excitation. An episcopic configuration is not adapted in this case because of the complex surface plasmon interference phenomenon induced by the diffraction-limited focal region of the high N. A. lens.18 Figure 6(a) shows an optical image of the considered waveguide (left-hand side) with the excitation defect and the corresponding direct-plane leakage radiation map (right-hand side). In the leakage radiation image, the overexposed area at the bottom part of the figure is the focalization of the incident light by 0.52 N.A. objective. The surface plasmon guided mode is observed as a streak of light propagating toward the top of the image. The intensity of the surface plasmon decays during the propagation. Figure 6(b) is a cross sectional view of the surface plasmon intensity taken along the waveguide. A single-exponential fit accounts for the intensity decay. The 1/e attenuation gives an estimation of the propagation length LSP P ∼ 7µm .
(b)
(c)
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Experiment Exponential fit
40
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Intensity (A.U.)
6
L
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25 20 15
P2 5µm
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Figure 6. (a)Optical micrograph of a typical PMMA waveguide fabricated on a gold substrate. The DLSPPW modes are excited by focusing a TM polarized beam on a defect. Observation of the propagation of the SP mode along the waveguide. (b) Intensity decay along the guide with a single-exponential fit (red curve). (c) Optical micrograph of a curved waveguide with a bend of 1µm deviation. (d) Analysis of the bend losses as a function of the excitation wavelength.
We now study the influence of a curved structure on the SPP propagation and analyze bend losses. The curvature of the bend follows an equation of the form: f (x) = (D/2)(1 − cos(πx/L)). The distance l along the L 1 + [f (x)]2 . The left-hand side of Fig. 6(c) shows a bright-field optical image curve is estimated from l = 0 of the curved waveguide. We defined 4 points of reference along the waveguide with P1 and P2 placed in the straight part of the guide and P3 , P 4 placed before and after the bend. The distance separating P1 to P2 is equal to the distance between P3 to P4 . Note the defect used for excitation placed slightly below P1 . The waveguide bend introduces here a 1µm deviation. The leakage radiation direct-plane image is shown in the right hand side of Fig. 6(c). The guided SPP mode is propagating from bottom to top. The losses of the bend can described by the following loss function:19 α[dB] = −10 log
P4 P1 P3 P2
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(2)
Figure 6(d) represents the loss α(ω) for an excitation wavelength between 750nm and 820nm. The losses are typically very small and a 1µm deviation introduces losses that are confined within the experimental errors of the intensity measurement.
5. CONCLUSION We investigated the properties of the surface plasmon propagation in dielectric-loaded surface plasmon polariton waveguides. The effective index method was applied to estimate the effective indices of the plasmon mode for different size parameters of the waveguide. The development of leakage radiation microscopy in Fourier and direct plane imaging permitted to retrieve experimentally the value for the effective index and the propagation distance of the plasmon mode. We found a good agreement between numerical estimations and experimental data. We compared and tested different excitation mechanisms and found that a surface plasmon excitation mediated by the presence of a defect under a diascopic illumination leads to an increased contrast in the images than other approaches. Finally we characterized a cosine S-bend waveguide in the near infra-red domain and found that losses are negligible. We expect that pushing the concept towards telecom wavelength where ohmic losses are limited, DLSPPW opens up interesting perspectives for integrated plasmonic-based devices.
ACKNOWLEDGMENTS The Authors gratefully acknowledge the European Commission for their financial support through the PLASMOCOM project (EC FP6 IST 034754 STREP).
REFERENCES [1] Barnes, W. L., Dereux, A., and Ebbesen, T. W., “Surface plasmon subwavelength optics,” Nature 424, 824 (2003). [2] Ebbesen, T., Genet, C., and Bozhevolnyi, S. I., “Surface-plasmon circuitry,” Physics Today May, 44 (2008). [3] Lakowicz, J. R., Malicka, J., Gryczyski, I., Gryczynski, Z., and Geddes, C. D., “Radiative decay engineering: The role of photonic mode density in biotechnology,” J. Phys. D: Appl. Phys. 36, R240 (2003). [4] Weeber, J., Bourillot, E., Dereux, A., Chen, Y., Goudonnet, J.-P., and Girard, C., “Observation of light confinement effects with a near–field optical microscope,” Phys. Rev. Lett. 77, 5332–5335 (1996). [5] Bozhevolnyi, S. I., Volkov, V. S., Devaux, E., and Ebbesen, T. W., “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95, 046802 (2005). [6] Steinberger, B., Hohenau, A., Ditlbacher, H., Stepanov, A. L., Drezet, A., Aussenegg, F. R., Leitner, A., and Krenn, J. R., “Dielectric stripes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88, 94104 (2006). [7] Holmgaard, T. and Bozhevolnyi, S. I., “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75, 245405 (2007). [8] Krasavin, A. V. and Zayats, A. V., “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90, 211101 (2007). [9] Hecht, B., Bielefeldt, H., Novotny, L., Inouye, Y., and Pohl, D. W., “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889 (1996). [10] Bouhelier, A., Huser, T., Tamaru, H., Gu¨ untherodt, H.-J., Pohl, D. W., Baida, F. I., and Labeke, D. V., “Plasmon optics of structured silver films,” Phys. Rev. B 63, 155404 (2001). [11] A.Hohenau, J.R.Krenn, A.L.Stepanov, A.Drezet, H.Ditlbacher, B.Steinberger, A.Leitner, and F.R.Aussenegg, “Dielectric optical elements for surface plasmons,” Opt.Lett. 30, 893 (2005). [12] Massenot, S., Grandidier, J., Bouhelier, A., Colas des Francs, G., Markey, L., Weeber, J.-C., Dereux, A., Renger, J., Gonzlez, M. U., and Quidant, R., “Polymer-metal waveguides characterization by fourier plane leakage radiation microscopy,” Appl. Phys. Lett. 91, 243102 (2007). [13] Marcuse, D., [Theory of dielectric optical waveguides], Academic Pr (1991). [14] Amenogiannis, E., Glytsis, E. N., and Gaylord, T. K., “Efficient solution of eigenvalue equations of optical waveguide structures,” J. Light. Technol. 7, 929 (1999).
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[15] Ditlbacher, H., Krenn, J. R., Schider, G., Leitner, A., and Aussenegg, F. R., “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. 81, 1762 (2002). [16] Bouhelier, A. and Wiederrecht, G. P., “Surface plasmon rainbow jet,” Opt. Lett. 30, 884 (2005). [17] Raether, H., [Excitation of Plasmons and Interband Transitions by Electrons], vol. 88 of Springer Tracts in Modern Physics, Springer-Verlag, Berlin (1980). [18] Bouhelier, A., Ignatovich, F., Bruyant, A., Huang, C., Colas des Francs, G., Weeber, J.-C., Dereux, A., Wiederrecht, G. P., and Novotny, L., “Surface plasmon interference excited by tightly focused laser beams,” Opt. Lett. 32, 2535 (2007). [19] Weeber, J.-C., Gonz´ alez, M. U., Baudrion, A.-L., and Dereux, A., “Surface plasmon routing along right angle bent metal strips,” Appl. Phys. Lett. 87, 221101 (2005).
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