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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 20 — Sep. 28, 2009
  • pp: 17471–17482
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Plasmonic multi-mode interference couplers

Yu-Ju Tsai, Aloyse Degiron, Nan M. Jokerst, and David R. Smith  »View Author Affiliations


Optics Express, Vol. 17, Issue 20, pp. 17471-17482 (2009)
http://dx.doi.org/10.1364/OE.17.017471


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Abstract

Plasmonic multi-mode interference (MMI) couplers have been investigated both numerically and experimentally at the telecommunication wavelength of 1.55 μm. In this study, the couplers are implemented using thin Au stripes that support long-range surface plasmons. We first detail the operation principle of these devices with numerical simulations and show that useful effects can be obtained despite the high material losses inherent to metallic structures. A series of MMI couplers is subsequently fabricated and experimentally characterized, showing a quantitative agreement with our numerical predictions. We conclude by discussing some of the possible applications for these structures.

© 2009 OSA

1. Introduction

Surface plasmons (SPs) are electromagnetic waves coupled to the free electron density of a metal surface [1

1. R. H. Ritchie, “Plasma Losses by Fast Electrons in Thin Films,” Phys. Rev. 106(5), 874–881 (1957). [CrossRef]

,2

2. C. J. Powell and J. B. Swan, “Origin of the Characteristic Electron Energy Losses in Magnesium,” Phys. Rev. 116(1), 81–83 (1959). [CrossRef]

]. Their mode profile is characterized by large local fields that exponentially decay away from both sides of the interface, making SPs extremely sensitive to any change in the material parameters and/or surface topology [3

3. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

]. In addition, the exponential decay is usually so strong that most SPs exhibit transverse, sub-wavelength confinement. Due to these properties, SPs have been extensively studied in recent years and are considered especially attractive for enhancing optical phenomena [4

4. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

,5

5. M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974). [CrossRef]

], detecting biochemical events [6

6. D. J. O’Shannessy, M. Brigham-Burke, and K. Peck, “Immobilization chemistries suitable for use in the BIAcore surface plasmon resonance detector,” Anal. Biochem. 205(1), 132–136 (1992). [CrossRef] [PubMed]

,7

7. R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995). [CrossRef]

] and controlling light at the nanoscale [8

8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

,9

9. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005). [CrossRef]

].

Despite their potential, most SPs are highly damped modes due to absorption in the metals, which are very lossy at visible and near-infrared wavelengths [10

10. W. L. Barnes, “Surface plasmon-polariton length scales: a route to sub-wavelength optics,” J. Opt. A, Pure Appl. Opt. 8(4), S87–S93 (2006). [CrossRef]

12

12. R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express 15(19), 12174–12182 (2007). [CrossRef] [PubMed]

]. In general, SPs exhibiting deep sub-wavelength confinement do not propagate more than a few tens of nanometers because a significant fraction of the energy travels in the metal [13

13. J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express 16(23), 19001–19017 (2008). [CrossRef]

]. Conversely, thin metal films sandwiched between two identical dielectric layers can support SPs that are poorly confined but are capable of traveling over millimeter or even centimeter distances [14

14. G. J. Kovacs, “Optical excitation of surface plasma waves in an indium film bounded by dielectric layers,” Thin Solid Films 60(1), 33–44 (1979). [CrossRef]

,15

15. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986). [CrossRef]

]. These modes, known as long-range plasmons, result from the evanescent coupling of the individual SPs that exist on both sides of the film. Long-range plasmons also exist for thin metal stripes, as first shown in [16

16. P. Berini, “Plasmon polariton modes guided by a metal film of finite width,” Opt. Lett. 24(15), 1011–1013 (1999). [CrossRef]

]. The main advantage of the stripe configuration over the film geometry is that it provides two-dimensional (transverse) confinement, thus effectively forming a low-loss plasmonic waveguide.

In general, metal stripes have a complex behavior and support a wide variety of short and long-range plasmons. However, it is possible to reduce the stripe lateral dimensions so that all the modes but one are in cutoff [17

17. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

]. This fundamental mode (known as the ssb 0 mode [17

17. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

]) is of great practical interest because it is long-ranging and can be excited by end-fire coupling a single mode fiber to the stripe input. In addition, the mode is robust to transitions, it can round moderate bends and its properties can be modeled very accurately, making it possible to design complex plasmonic circuits with overall low insertion losses. Over the years, a variety of low-loss components based on the metallic stripe geometry have thus been demonstrated, including directional couplers, Y-Junctions, Bragg gratings, Mach–Zehnder interferometers, thermo-optic attenuators and electro-optic modulators [18

18. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005). [CrossRef] [PubMed]

26

26. S. Jetté-Charbonneau and P. Berini, “External cavity laser using a long-range surface plasmon grating as a distributed Bragg reflector,” Appl. Phys. Lett. 91(18), 181114 (2007). [CrossRef]

].

Although most photonic functionalities are better implemented with the fundamental ssb 0 mode, there are also exceptions to this rule. In particular, integrated components based on multimode interference (MMI) effects require the participation of higher-order propagating modes in addition to the fundamental mode [27

27. L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

]. MMI structures typically consist of a length of multimode waveguide that couples one or more input ports to a number of output ports. The operation principle of such couplers relies on the self-imaging effect—when enough modes are excited along the MMI section, an interference pattern is created that periodically contains single or multi-fold reproductions of the input field [28

28. O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Am. 63(4), 416–419 (1973). [CrossRef]

,29

29. R. Ulrich, “Image formation by phase coincidences in optical waveguides,” Opt. Commun. 13(3), 259–264 (1975). [CrossRef]

]. The various images thus obtained can be used to couple the signal to the output ports with very low insertion losses. MMI couplers are routinely used components in conventional (dielectric) optical circuits; examples of application include optical routers [30

30. J. Z. Huang, R. Scarmozzino, and R. M. Osgood, “A new design approach to large input/output-number multimode interference couplers and its application to low-crosstalk WDM routers,” IEEE Photon. Technol. Lett. 10(9), 1292–1294 (1998). [CrossRef]

], wavelength-division multiplexers [31

31. M. R. Paiam and R. I. Macdonald, “Design of phased-array wavelength division multiplexers using multimode interference couplers,” Appl. Opt. 36(21), 5097–5108 (1997). [CrossRef] [PubMed]

] and sensors [32

32. A. Cleary, S. Garcia-Blanco, A. Glidle, J. S. Aitchison, P. Laybourn, and J. M. Cooper, “An integrated fluorescence array as a platform for lab-on-a-chip technology using multimode interference splitters,” IEEE Sens. J. 5(6), 1315–1320 (2005). [CrossRef]

,33

33. T. Mazingue, R. K. Kribich, P. Etienne, and Y. Moreau, “Simulations of refractive index variation in a multimode interference coupler: Application to gas sensing,” Opt. Commun. 278(2), 312–316 (2007). [CrossRef]

]. Devices based on the self-imaging effect are less used in photonic crystal based circuits [34

34. T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. 22(12), 2842–2846 (2004). [CrossRef]

,35

35. D. Modotto, M. Conforti, A. Locatelli, and C. De Angelis, “Imaging properties of multimode photonic crystal waveguides and waveguide arrays,” J. Lightwave Technol. 25(1), 402–409 (2007). [CrossRef]

] and they are even less common in plasmonics although MMI patterns have already been observed with long-range plasmon waveguides [36

36. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]

].

In this article, we perform a quantitative study on MMI couplers based on wide metal stripes supporting multiple long-range plasmons. We present a rigorous design approach based on a full-modal numerical analysis of the structures. We discuss the formation of images along the stripes and address the issue of material losses that are inherent to the use of metals in optics. Based on these simulations, we fabricate and demonstrate various MMI couplers operating at the telecom wavelength λ=1.55 μm.

2. Modeling of MMI Couplers

2.1 Design

The structures considered in this study are schematically depicted in Fig. 1
Fig. 1 (a) Cross section of a long-range plasmonic waveguide. (b) Schematic layout of 1×N MMI couplers (top view).
. The couplers consist of wide Au stripes (εm=−132+12.65i [37

37. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, 1998).

]) symmetrically embedded in a slab of benzocyclobutene (BCB) polymer (nBCB=1.535). A set of narrower single-mode plasmonic waveguides is used to access the MMI section—on the input side, the couplers are excited with a single Au stripe; on the output side, the couplers are connected to up to three parallel Au stripes. In our simulations, the width of the input and output access waveguides is set to 5 μm while the width of the MMI sections varies from 24 to 60 μm. The metal thickness of the entire structure is 25 nm. The thickness of the BCB layer is set to 6.5 μm, which is too small for allowing the full extension of the modes. In this case, long-range plasmons modes are hybrid in nature because they are vertically confined within the BCB layer by total internal reflection [12

12. R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express 15(19), 12174–12182 (2007). [CrossRef] [PubMed]

,20

20. A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90 ° bends,” Opt. Lett. 32(16), 2354–2356 (2007). [CrossRef] [PubMed]

,24

24. T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668–670 (2003). [CrossRef]

]. Note that for certain geometries or devices, this field confinement has great advantages—for example, hybrid modes are good at rounding bends [21

21. A. Degiron, S. Cho, C. Harrison, N. Jokerst, C. Dellagiacoma, O. Martin, and D. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77(2), 021804 (2008). [CrossRef]

] and can be easily integrated with other waveguide technologies [22

22. A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11(1), 015002 (2009). [CrossRef]

]. Here the main reason to consider hybrid modes is one of practicality: thicker BCB layers are more difficult to fabricate. Also, we have verified that this particular thickness of 6.5 μm provides a good trade-off between the confinement of the modes and their attenuation.

2.2 Modeling

We model the structures by representing the field in the access waveguides and the MMI section by a superposition of local eigenmodes. For each of these sections, the eigenvalue problem can be conveniently formulated in two-dimensions because the geometry remains invariant along the propagation direction. We use a commercial finite-element eigensolver (Comsol Multiphysics) to obtain the transverse field profiles and the complex propagation constants of the modes.

To calculate the coupling to the output ports, we propagate the eigenmodes of the MMI section up to the coupler exit and compute the overlap integrals between each of these plasmons and the ssb 0 mode of the output access stripe(s).

2.3 Simulation Results

Figure 2
Fig. 2 Predicted field patterns for three coupler widths (24 μm, 36 μm, 60 μm). The Au thickness is 25 nm and the field amplitudes are calculated in a plane slightly above the metal stripe.
shows the amplitude of the magnetic field for three plasmonic MMI couplers with different widths. The simulations are performed at λ=1.55 μm and the field amplitudes are calculated in a plane slightly above the metal stripe. In all three cases, an interference pattern is generated that results from the superposition of the bound modes propagating along the multimode waveguide. Aside from a general attenuation caused by the Au material losses, the field pattern is periodically reproduced and exhibits a series of transverse planes where constructive interferences occur. This behavior is a universal property of MMI couplers and is known as the self-imaging effect—in fact, these periodic maxima are single or multi-fold images of the input electromagnetic field.

The position of the single and multi-fold images shown in Fig. 2 can be qualitatively understood with simple analytical arguments. Following a well-known procedure for dielectric MMI couplers, an approximate expression for the image positions can be established by factorizing Eq. (1) with exp[0z] and by introducing the beat length L=π/(β01) of the two lowest-order modes ssb 0 and asb 0. After some mathematical treatment, it can be shown that N-fold images are formed at positions approximately given by [39

39. R. M. Jenkins, R. W. J. Devereux, and J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett. 17(14), 991–993 (1992). [CrossRef] [PubMed]

,40

40. M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in N×N multimode interference couplers including phase relations,” Appl. Opt. 33(18), 3905–3911 (1994). [CrossRef] [PubMed]

]:

pN(34πβ0β1),p=0,1,2...
(3)

Table 1

Table 1. Comparison between the simple analytical model [Eq. (3)] and the full eigenmode analysis (Fig. 2). β0 and β1 have been computed with our numerical eigensolver approach.

table-icon
View This Table
compares the positions of the first single images (p=N=1) predicted by Eq. (3) and those obtained with Fig. 2. The agreement between the two data sets is excellent and they both predict that the image positions are pushed farther away from the coupler entrance as the width of the Au stripe increases. According to Eq. (3), this behavior directly results from the fact that images of the input field are found at positions inversely proportional to (β01)—this quantity tends to zero because the interval between the discrete wave vectors βν in the reciprocal space is reduced when the stripe width and the mode density increases.

It should be noted that Eq. (3) neglects the effects of absorption in the metal because it assumes real values for β0 and β1. Since this simple expression captures the general behavior of the lossy structures shown in Fig. 2, material losses do not significantly affect the position of the images for the range of parameters considered here. In addition, we have verified that absorption does not dramatically alter the quality of the images because the eigenmodes contributing to the field patterns of Fig. 2 have similar attenuation rates (results not shown here). Nevertheless, losses do impose severe constraints on the design of real structures. As shown in Fig. 2, the field becomes significantly weaker as the distance increases, thus limiting in practice the total length of actual devices. This problem is especially striking for very wide waveguides because the images of the input field are pushed farther away from the coupler entrance. In addition, the eigenmodes of such wide stripes decay more rapidly because the confinement of long-range plasmons generally improves as the lateral dimensions of the metal stripe increase [17

17. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

]. In other words, losses not only limit the length but also the width of actual couplers. An important consequence is that narrow MMI couplers only support a restricted numbers of eigenmodes and Fig. 2 shows that the resulting interference pattern is not as rich and sharp as for wider stripes. Another issue with narrow MMI sections arises when the signal is coupled to multiple output ports because cross-talk can occur between the access waveguides if they are too close to each other.

Note that a simple way to reduce the losses by absorption consists in decreasing the thickness of the metal stripes [17

17. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

]. However, it is well-known that depositing less than ~20 nm of Au with current metal deposition techniques results in uncontrolled surface roughness that generates unwanted radiative losses [41

41. P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98(4), 043109 (2005). [CrossRef]

]. In this case, it is not possible to use the bulk permittivity of Au in the simulations, which in turn limits our understanding of the structures because fitting parameters must be included in the model. In order to avoid this problem, we do not optimize the metal thickness of our simulated and fabricated structures. As explained in section 2.1, all the structures considered here are 25 nm thick.

3. Fabrication

The fabrication process is summarized as follows. We first apply a layer of BCB (thickness 3.25 μm) to a SiO2-on-Si wafer by spin-coating. The BCB is then partially cross-linked by curing the sample at 210°C for 40 minutes in a vacuum oven. The MMI couplers are produced by a combination of UV lithography (using a layer of AZ 5124-E photoresist, a negative tone photomask and a Suss MicroTec MJB3 mask aligner) and Au deposition (with a CHA Industries Solution electron beam evaporator). After lift-off, the resulting structures are coated with a 3.25 μm thick BCB layer and cured at 210°C for 55 minutes. Finally, the sample is cleaved at both ends so that the input and output access stripes have clean and sharp end facets.

4. Experimental Characterization

To characterize the couplers, we perform transmission measurements with the experimental setup shown in Fig. 4(a)
Fig. 4 . (a) Experimental characterization setup. (b) Infrared images obtained at the output ports of a 1×3 splitter.
. The structures are excited with infrared laser light (λ=1.55 μm) using a single mode fiber in an end-fire coupling configuration. The fiber is maintained in the same position throughout the measurements; it is mounted so that the field has the same (TM-) polarization as the long-range ssb 0 mode of the input access stripe. Before each measurement, we also carefully align the structures with the optical fiber by maximizing the output signal at the other end of the sample. With this procedure, we ensure that the input power carried by the input metal stripe is the same for all MMI couplers. Since all input access stripes of a given sample have the same length, it also implies that all MMI sections are excited with the same initial conditions.

To measure the transmission, we record the light emitted at the output ports by imaging the end-facet of our sample with a pixelized InGaAs detector array coupled to an optical microscope. Figure 4(b) shows a typical image obtained for a 1×3 coupler: three spots are clearly visible, corresponding to the light emitted at the end of the output metal waveguides. The intensity carried by each stripe is then calculated by integrating the signal over the corresponding spot. It should be noted that in our design, the output access waveguides of adjacent structures have different lengths, as shown in Fig. 3. To compare the transmission of the various couplers, we normalize all measurements by the attenuation rate of the output access waveguides. This attenuation rate is experimentally obtained by measuring the output power from a number of stripes with incrementally smaller lengths (“cut-back technique”).

Another difficulty with our experimental procedure is that it is difficult to obtain the coupling efficiencies between the optical fiber and the input access stripes. For this reason, we cannot measure the absolute value of the transmission but only relative ratios. To compare our measurements with the absolute values given by the simulations, we normalize all the experimental data against an arbitrary constant. This normalization constant is chosen so that one of the experimental data points matches the corresponding simulation results. All other measurements are normalized using that same constant and therefore this procedure does not change the experimental relative ratios between the different data points.

5. Results and Discussions

5.1 Self-imaging and 1x1 couplers

We start this section by investigating the formation of single images in the fabricated plasmonic MMI structures. To this end, we measure the transmission of symmetric 1×1 couplers with coupling lengths ranging from 400 µm to 1 mm (Fig. 5(a)
Fig. 5 (a) Schematic diagram of the structures under investigation. Optical and AFM measurements indicate that the width of the input and output waveguides is 4.3 μm, the width of the MMI section is 24.6 μm and the Au thickness is 29.4 nm. (b) Measured and calculated transmission as a function of the coupling length.
). The experimental results are summarized in Fig. 5(b). Each data point represents the average transmission of two independently measured couplers and the results are plotted as a function of the coupling length. The error bars account for the occasional defects in real structures as well as the uncertainties in the measurements.

Figure 5(b) shows that the absolute value of the transmission coefficient only reaches ~30% at the optimum coupling length. In other words, the total insertion loss of the device is −5.2 dB—a value that would have been very disappointing for dielectric and photonic crystal based MMI couplers. However, these results can be considered as promising for a metallic structure, especially considering that the input and output waveguides are separated by 800 μm of metal and that the couplers are not fully optimized. As explained in section 2, it should be possible to reach much higher transmission coefficients by a careful design of the metal thickness.

The self-imaging effect in plasmonic 1×1 MMI couplers is potentially attractive for sensing applications. As already shown with dielectric configurations, the interference pattern and the coupling to the output waveguide are sensitive to small variations in the local environment [33

33. T. Mazingue, R. K. Kribich, P. Etienne, and Y. Moreau, “Simulations of refractive index variation in a multimode interference coupler: Application to gas sensing,” Opt. Commun. 278(2), 312–316 (2007). [CrossRef]

]. By monitoring the output intensity, it thus becomes possible to detect changes that occur in the vicinity of the MMI section. Evidently, the configuration studied here cannot be used for that purpose because the fields are confined in the BCB layer. To act as an integrated sensor, the MMI coupler must be directly exposed to the substance of interest and yet be in an (almost) symmetric configuration so as to support long-range plasmon modes. This condition can be satisfied by fabricating the structures on ultrathin membranes [42

42. P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7(5), 1376–1380 (2007). [CrossRef] [PubMed]

] or on a substrate that is index-matched with the medium to sense [43

43. J. Dostálek, A. Kasry, and W. Knoll, “Long range surface plasmons for observation of biomolecular binding events at metallic surfaces,” Plasmonics 2(3), 97–106 (2007). [CrossRef]

,44

44. R. Daviau, E. Lisicka-Skrzek, R. N. Tait, and P. Berini, “Broadside excitation of surface plasmon waveguides on Cytop,” Appl. Phys. Lett. 94(9), 091114 (2009). [CrossRef]

].

5.2 Multi-fold self-images

To characterize the structures, we first measure the intensity transmitted to the center output access waveguide, as shown in Fig. 6(b) where the experimental results are plotted as a function of the coupling length. Also shown are the numerical simulations which are in quantitative agreement with the measurements. According to these results, the intensity transmitted to the central output waveguide is maximized for an optimum coupling length CLopt=1.4 mm. To characterize the coupling to the side waveguides, we calculate the ratio of the intensity carried by the central stripe and the averaged intensity carried by the two other ports. The experimental and numerical results are shown in Fig. 7
Fig. 7 Ratio of the energy coupled to the center access waveguide and the energy coupled to the side access waveguides [i.e. Icenter/avg(Ileft, Iright)]. The structures studied here are the 1×3 MMI couplers already considered in Fig. 6.
. They both show that the splitting ratio approaches 1 at the optimum coupling length CLopt, implying that the signal is equally split among the three waveguides.

Interestingly, the experimental splitting ratio rapidly changes for coupling lengths smaller or larger than CLopt. In contrast, the simulations suggest that the signal remains equally distributed among the output ports for a range of coupling lengths spanning from 1.2 mm to 1.6 mm. To understand this discrepancy, it should be noted that measuring the intensity carried by the side waveguides is very difficult. Figure 8
Fig. 8 Light emitted at the output of the 1×3 splitters studied in Fig. 7 and 8. The coupling length of the structures are (a) 1150 μm, (b) 1250 μm, (c) 1292 μm, (d) 1400 μm and (e) 1600 μm, respectively. The intensity of each picture has been arbitrarily and independently adjusted so that the spots remain visible when the coupling length is not optimum.
illustrates the problem by showing the images of the light emitted at the end facet of the couplers. For couplers with MMI sections different than CLopt, (Figs. 8(a), 8(b), 8(c) and 8(e)), the side spots are ill-defined, inducing high experimental errors. The poor quality of the images can be explained by the presence of an important background noise and suggests that a significant portion of the signal carried by the MMI section is converted into radiation modes rather than being coupled to the output stripes. The only exception occurs for the structure that maximizes the transmission in Fig. 6(b). In this case, the background radiation noise is negligible and the intensity is equally distributed among the three waveguides (Fig. 8(d)).

Clearly, the combined results of Figs. 6, 7 and 8 indicate that there is only one coupling length that maximizes and balances the transmission while minimizing the radiation losses—the coupling length that creates three-fold images of the input field at the entrance of the output access waveguides. It should be noted that these experiments do not merely allow us to locate the experimental position of self-images along the propagation direction. In fact, they also provide useful insight about the transverse distribution of the field. As explained earlier in section 3, the lateral spacing of the output waveguides has been numerically calculated so as to coincide with the position of the three-fold images. The fact that we are able to suppress the experimental radiation losses at CLopt (cf Fig. 8(d)) confirms the validity of these numerical predictions. Here, the output waveguides and the corresponding self-images are separated by 21 μm (from center to center).

To conclude this section, we note that the transmitted coefficients measured here do not exceed ~8% due to the losses by absorption (cf Fig. 6). These values correspond to the energy carried by each stripe so the total transmitted intensity is 3 times larger. In addition, we have numerically verified that the total insertion loss of fully optimized 1×3 couplers could be reduced to −2 dB or less (see for example the center plot of Fig. 2 where the field amplitude of the three-fold images reaches 48.5%). For this reason, plasmonic MMI couplers offer similar performances than other metallic power splitters, such as Y and W junctions, that do not require long interaction lengths but suffer from radiation losses.

6. Conclusion

We have presented a quantitative study on plasmonic MMI couplers. As in the case of their dielectric counterparts, the self-imaging effect that occurs in these structures can be used for routing, splitting or sensing purposes. Although losses by absorption impose severe constraints on the geometrical and material parameters, our results suggest that good performances are possible when the number of input and/or output ports is not too high.

Acknowledgements

Support for this work was provided by a Multidisciplinary University Research Initiative (MURI) from the Air Force Office of Scientific Research (Contract Number FA9550-04-1-0434).

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H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

4.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

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M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974). [CrossRef]

6.

D. J. O’Shannessy, M. Brigham-Burke, and K. Peck, “Immobilization chemistries suitable for use in the BIAcore surface plasmon resonance detector,” Anal. Biochem. 205(1), 132–136 (1992). [CrossRef] [PubMed]

7.

R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995). [CrossRef]

8.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

9.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005). [CrossRef]

10.

W. L. Barnes, “Surface plasmon-polariton length scales: a route to sub-wavelength optics,” J. Opt. A, Pure Appl. Opt. 8(4), S87–S93 (2006). [CrossRef]

11.

P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14(26), 13030–13042 (2006). [CrossRef] [PubMed]

12.

R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express 15(19), 12174–12182 (2007). [CrossRef] [PubMed]

13.

J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express 16(23), 19001–19017 (2008). [CrossRef]

14.

G. J. Kovacs, “Optical excitation of surface plasma waves in an indium film bounded by dielectric layers,” Thin Solid Films 60(1), 33–44 (1979). [CrossRef]

15.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986). [CrossRef]

16.

P. Berini, “Plasmon polariton modes guided by a metal film of finite width,” Opt. Lett. 24(15), 1011–1013 (1999). [CrossRef]

17.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]

18.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005). [CrossRef] [PubMed]

19.

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive Integrated Optics Elements Based on Long-Range Surface Plasmon Polaritons,” J. Lightwave Technol. 24(1), 477–494 (2006). [CrossRef]

20.

A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90 ° bends,” Opt. Lett. 32(16), 2354–2356 (2007). [CrossRef] [PubMed]

21.

A. Degiron, S. Cho, C. Harrison, N. Jokerst, C. Dellagiacoma, O. Martin, and D. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77(2), 021804 (2008). [CrossRef]

22.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11(1), 015002 (2009). [CrossRef]

23.

P. Berini, R. Charbonneau, S. Jette-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007). [CrossRef]

24.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668–670 (2003). [CrossRef]

25.

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833–5835 (2004). [CrossRef]

26.

S. Jetté-Charbonneau and P. Berini, “External cavity laser using a long-range surface plasmon grating as a distributed Bragg reflector,” Appl. Phys. Lett. 91(18), 181114 (2007). [CrossRef]

27.

L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

28.

O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Am. 63(4), 416–419 (1973). [CrossRef]

29.

R. Ulrich, “Image formation by phase coincidences in optical waveguides,” Opt. Commun. 13(3), 259–264 (1975). [CrossRef]

30.

J. Z. Huang, R. Scarmozzino, and R. M. Osgood, “A new design approach to large input/output-number multimode interference couplers and its application to low-crosstalk WDM routers,” IEEE Photon. Technol. Lett. 10(9), 1292–1294 (1998). [CrossRef]

31.

M. R. Paiam and R. I. Macdonald, “Design of phased-array wavelength division multiplexers using multimode interference couplers,” Appl. Opt. 36(21), 5097–5108 (1997). [CrossRef] [PubMed]

32.

A. Cleary, S. Garcia-Blanco, A. Glidle, J. S. Aitchison, P. Laybourn, and J. M. Cooper, “An integrated fluorescence array as a platform for lab-on-a-chip technology using multimode interference splitters,” IEEE Sens. J. 5(6), 1315–1320 (2005). [CrossRef]

33.

T. Mazingue, R. K. Kribich, P. Etienne, and Y. Moreau, “Simulations of refractive index variation in a multimode interference coupler: Application to gas sensing,” Opt. Commun. 278(2), 312–316 (2007). [CrossRef]

34.

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. 22(12), 2842–2846 (2004). [CrossRef]

35.

D. Modotto, M. Conforti, A. Locatelli, and C. De Angelis, “Imaging properties of multimode photonic crystal waveguides and waveguide arrays,” J. Lightwave Technol. 25(1), 402–409 (2007). [CrossRef]

36.

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]

37.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, 1998).

38.

A. W. Snyder, and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, London, 1983).

39.

R. M. Jenkins, R. W. J. Devereux, and J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett. 17(14), 991–993 (1992). [CrossRef] [PubMed]

40.

M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in N×N multimode interference couplers including phase relations,” Appl. Opt. 33(18), 3905–3911 (1994). [CrossRef] [PubMed]

41.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98(4), 043109 (2005). [CrossRef]

42.

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7(5), 1376–1380 (2007). [CrossRef] [PubMed]

43.

J. Dostálek, A. Kasry, and W. Knoll, “Long range surface plasmons for observation of biomolecular binding events at metallic surfaces,” Plasmonics 2(3), 97–106 (2007). [CrossRef]

44.

R. Daviau, E. Lisicka-Skrzek, R. N. Tait, and P. Berini, “Broadside excitation of surface plasmon waveguides on Cytop,” Appl. Phys. Lett. 94(9), 091114 (2009). [CrossRef]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(240.6680) Optics at surfaces : Surface plasmons
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: July 10, 2009
Revised Manuscript: August 21, 2009
Manuscript Accepted: August 24, 2009
Published: September 15, 2009

Citation
Yu-Ju Tsai, Aloyse Degiron, Nan M. Jokerst, and David R. Smith, "Plasmonic multi-mode interference couplers," Opt. Express 17, 17471-17482 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-17471


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References

  1. R. H. Ritchie, “Plasma Losses by Fast Electrons in Thin Films,” Phys. Rev. 106(5), 874–881 (1957). [CrossRef]
  2. C. J. Powell and J. B. Swan, “Origin of the Characteristic Electron Energy Losses in Magnesium,” Phys. Rev. 116(1), 81–83 (1959). [CrossRef]
  3. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  4. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
  5. M. Fleischmann, P. J. Hendra, and A. J. McQuillan, “Raman spectra of pyridine adsorbed at a silver electrode,” Chem. Phys. Lett. 26(2), 163–166 (1974). [CrossRef]
  6. D. J. O’Shannessy, M. Brigham-Burke, and K. Peck, “Immobilization chemistries suitable for use in the BIAcore surface plasmon resonance detector,” Anal. Biochem. 205(1), 132–136 (1992). [CrossRef] [PubMed]
  7. R. D. Harris and J. S. Wilkinson, “Waveguide surface plasmon resonance sensors,” Sens. Actuators B Chem. 29(1-3), 261–267 (1995). [CrossRef]
  8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  9. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005). [CrossRef]
  10. W. L. Barnes, “Surface plasmon-polariton length scales: a route to sub-wavelength optics,” J. Opt. A, Pure Appl. Opt. 8(4), S87–S93 (2006). [CrossRef]
  11. P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14(26), 13030–13042 (2006). [CrossRef] [PubMed]
  12. R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express 15(19), 12174–12182 (2007). [CrossRef] [PubMed]
  13. J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, “Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries,” Opt. Express 16(23), 19001–19017 (2008). [CrossRef]
  14. G. J. Kovacs, “Optical excitation of surface plasma waves in an indium film bounded by dielectric layers,” Thin Solid Films 60(1), 33–44 (1979). [CrossRef]
  15. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B 33(8), 5186–5201 (1986). [CrossRef]
  16. P. Berini, “Plasmon polariton modes guided by a metal film of finite width,” Opt. Lett. 24(15), 1011–1013 (1999). [CrossRef]
  17. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000). [CrossRef]
  18. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005). [CrossRef] [PubMed]
  19. R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive Integrated Optics Elements Based on Long-Range Surface Plasmon Polaritons,” J. Lightwave Technol. 24(1), 477–494 (2006). [CrossRef]
  20. A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90 ° bends,” Opt. Lett. 32(16), 2354–2356 (2007). [CrossRef] [PubMed]
  21. A. Degiron, S. Cho, C. Harrison, N. Jokerst, C. Dellagiacoma, O. Martin, and D. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77(2), 021804 (2008). [CrossRef]
  22. A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11(1), 015002 (2009). [CrossRef]
  23. P. Berini, R. Charbonneau, S. Jette-Charbonneau, N. Lahoud, and G. Mattiussi, “Long-range surface plasmon-polariton waveguides and devices in lithium niobate,” J. Appl. Phys. 101(11), 113114 (2007). [CrossRef]
  24. T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82(5), 668–670 (2003). [CrossRef]
  25. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85(24), 5833–5835 (2004). [CrossRef]
  26. S. Jetté-Charbonneau and P. Berini, “External cavity laser using a long-range surface plasmon grating as a distributed Bragg reflector,” Appl. Phys. Lett. 91(18), 181114 (2007). [CrossRef]
  27. L. B. Soldano and E. C. M. Pennings, “Optical Multi-Mode Interference Devices Based on Self-Imaging: Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]
  28. O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Am. 63(4), 416–419 (1973). [CrossRef]
  29. R. Ulrich, “Image formation by phase coincidences in optical waveguides,” Opt. Commun. 13(3), 259–264 (1975). [CrossRef]
  30. J. Z. Huang, R. Scarmozzino, and R. M. Osgood, “A new design approach to large input/output-number multimode interference couplers and its application to low-crosstalk WDM routers,” IEEE Photon. Technol. Lett. 10(9), 1292–1294 (1998). [CrossRef]
  31. M. R. Paiam and R. I. Macdonald, “Design of phased-array wavelength division multiplexers using multimode interference couplers,” Appl. Opt. 36(21), 5097–5108 (1997). [CrossRef] [PubMed]
  32. A. Cleary, S. Garcia-Blanco, A. Glidle, J. S. Aitchison, P. Laybourn, and J. M. Cooper, “An integrated fluorescence array as a platform for lab-on-a-chip technology using multimode interference splitters,” IEEE Sens. J. 5(6), 1315–1320 (2005). [CrossRef]
  33. T. Mazingue, R. K. Kribich, P. Etienne, and Y. Moreau, “Simulations of refractive index variation in a multimode interference coupler: Application to gas sensing,” Opt. Commun. 278(2), 312–316 (2007). [CrossRef]
  34. T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, and M. Mansuripur, “Multimode interference-based photonic crystal waveguide power splitter,” J. Lightwave Technol. 22(12), 2842–2846 (2004). [CrossRef]
  35. D. Modotto, M. Conforti, A. Locatelli, and C. De Angelis, “Imaging properties of multimode photonic crystal waveguides and waveguide arrays,” J. Lightwave Technol. 25(1), 402–409 (2007). [CrossRef]
  36. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated Optical Components Utilizing Long-Range Surface Plasmon Polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]
  37. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, 1998).
  38. A. W. Snyder and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, London, 1983).
  39. R. M. Jenkins, R. W. J. Devereux, and J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett. 17(14), 991–993 (1992). [CrossRef] [PubMed]
  40. M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in N×N multimode interference couplers including phase relations,” Appl. Opt. 33(18), 3905–3911 (1994). [CrossRef] [PubMed]
  41. P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98(4), 043109 (2005). [CrossRef]
  42. P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7(5), 1376–1380 (2007). [CrossRef] [PubMed]
  43. J. Dostálek, A. Kasry, and W. Knoll, “Long range surface plasmons for observation of biomolecular binding events at metallic surfaces,” Plasmonics 2(3), 97–106 (2007). [CrossRef]
  44. R. Daviau, E. Lisicka-Skrzek, R. N. Tait, and P. Berini, “Broadside excitation of surface plasmon waveguides on Cytop,” Appl. Phys. Lett. 94(9), 091114 (2009). [CrossRef]

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