We propose a novel metal-insulator-metal (MIM) waveguide mode transition scheme by the use of the abrupt junction of MIM plasmonic waveguide. Power coupling between anti-symmetric plasmonic mode and fundamental photonic mode can be easily done by reflection at the waveguide junction with an oblique MIM mode incidence due to the field intersection between those modes. With numerical simulation we find that mode conversion efficiency can be obtained up to 60% for single junction geometry, and it can be further increased up to 82% with the suppression of non-transited mode by adapting Bragg grating structure composed of periodical arranges of MIM junctions.
© 2013 Optical Society of America
Surface plasmon polaritons (SPPs) are often referred to as quasi-particles that originate from the coupling of light and collective oscillation of free electrons existing at the surface of conductive materials [1,2]. Using SPPs has attracted a great deal of interest in optical systems due to their possibilities on field enhancement and subwavelength confinement characteristics. Especially, considerable research on metal-insulator-metal (MIM) plasmonic waveguide structure has shown that this structure provides better performance both in field enhancement and light confinement compared to other kinds on plasmonic waveguide geometries [3,4]. Moreover, detailed research on characteristics of existing mode in MIM waveguides has become a route for utilizing them not only for guiding purpose but also for various plasmonic devices such as filters [5,6], trapping-light devices [7,8], electro-optical modulator , and effective negative index materials [10–12].
Indeed, these applications on MIM plasmonic waveguide are based on the characteristics of plasmonic modes propagating along the waveguide. For example, electro-optic modulator based on MIM plasmonic waveguide, which has been referred to as “PlasMOStor” , is operated by controlling the core index of MIM waveguide in order to cutoff the propagation of anti-symmetric plasmonic mode. In the same sense, effective NIM condition in MIM plasmonic waveguide was also found by analyzing the dispersion diagram of symmetric plasmonic mode at very narrow slit condition . Thus, it is important to understand the characteristics of modes themselves and coupling characteristics of them at given geometry.
However, most of these studies are focused on the specific mode existing inside the MIM waveguide, even for the multi-mode condition. Although there are quite successful achievements for the efficient coupling of plasmonic and photonic waveguides in order to interconnect plasmonic waveguides with a low-loss photonic waveguide [13–15], only few studies have been done for the mode-to-mode transition within a single type of plasmonic waveguide when propagating plasmonic mode abruptly encounters the different type of waveguide. Mode transitions between two modes having totally different characteristics are recently studied for understanding electromagnetically induced transparency  and realizing nonreciprocity in silicon photonics [17–19]. Moreover, control of mode transition in waveguide  or nano-cavity  has become an important issue for realizing nano-scale lasing systems .
Therefore, in this paper, we will propose a simple but efficient plasmonic-photonic mode converting scheme that is based on the junction of two different types of MIM plasmonic waveguides. Two existing modes – one is TE-like photonic mode and the other is TM-like anti-symmetric plasmonic mode – can be efficiently converted to each other by oblique reflection at the junction of MIM plasmonic waveguides. In addition, we show that the periodically arranged junctions of two plasmonic waveguides can act as a Bragg reflector which can efficiently convert the incident mode without non-transited reflection when the momentum matching between two existing modes is satisfied.
2. Configuration of proposed structure and basic principle
Figure 1(a) shows the structure of the proposed MIM plasmonic waveguide junction. Here, we define the incident MIM layer for Layer A, whereas Layer B gives an abrupt junction which has the same core thickness but lower core refractive index. Before we explain the principle of proposed structure, we will discuss on the dispersion relation of MIM guided modes at each layer.
In Fig. 1(b), dispersion relations of possible modes in both layers are plotted. The width of core and permittivity of dielectrics are set to w = 80 nm, εA = 6, and εB = 4, respectively. The permittivity of silver layer is modeled by a Drude model in accordance with . There can exist three different modes in this circumstance, which are symmetric plasmonic (PLsymm, solid lines), anti-symmetric plasmonic (PLanti or PLa, dash-dotted lines), and fundamental photonic (PT, dotted lines) modes.
In this study, our focus is laid on the mode transition characteristics between PLanti and PT modes. Coupling from PLanti mode and PT mode to PLsymm mode is not possible in our configuration due to the symmetry of mode . These symmetries of field components of three modes are briefly summarized in Table 1 when the incidence is obliquely given along y-z plane. Note that the PLsymm mode has opposite symmetry with respect to other modes or does not have field component. Therefore, coupling from PLsymm to PLanti or PT mode (or vice versa) cannot happen in symmetric structure such as our MIM waveguide configuration.
As can be shown in Fig. 1(b), lower core permittivity of Layer B makes cutoff frequencies of PLanti and PT modes higher. Therefore, when we appropriately design the width of waveguide and refractive indexes of cores in both layers, it is possible to set the certain frequency region to be laid between cutoff conditions of two Layers. Then, the propagating MIM modes do not transmit through the Layer B and it is totally reflected.
Moreover, as can be shown in the plots of Fig. 1(b), dispersion curves of PLanti and PT modes are converged to each other near the cutoff condition. Therefore, the cutoff frequencies of PLanti and PT modes are exactly at the same position. This condition is always satisfied for infinite parallel plate MIM waveguides , and it means that propagation of these two modes is simultaneously prohibited below the identical cutoff frequency condition.
When PLanti or PT mode is incident through the Layer A and encounters the junction, it forms evanescently decaying electromagnetic fields inside Layer B. Similar to total internal reflection (TIR) phenomenon of plane wave or single interface SPPs , these evanescently decaying fields in Layer B cannot propagate but are reflected to the Layer A as same mode as its incident case. However, during this process, some portion of field is changed from itself to the other mode since field inside Layer B cannot be distinguished for those two modes. As a result, both PLanti and PT modes are generated from the illumination of one of two modes.
The geometry of our configuration does not have any variation through y-direction, which denotes the parallel-to-junction direction. Therefore, the momentum along y-direction cannot be changed through the reflection at junction. Therefore, the relation between incident or reflected angle of each mode simply follows the Snell’s law, , where and indicate effective refractive indexes of PLanti and PT modes, respectively. Hence, they propagate through different directions. In Fig. 1(c), we illustrate full electromagnetic field distribution for the Gaussian beam incidence of PLanti mode with θinc = 20°, which is calculated by rigorous coupled wave analysis (RCWA) method . In the Gaussian beam simulations, we used lossless metal instead of real metal to clearly show the birefringence-like reflectance at the junction. However, we do not use the results from the lossless metal for calculating physical parameters. The purpose of Fig. 1(c) and Fig. 4(d) are to show the clear propagating directions of reflected modes by using the Gaussian beam incidence. Unfortunately, plasmonic mode cannot propagate tens of micrometers without significant attenuation in the designed wavelength region. They may be disappeared and only the photonic mode will be observed after long propagation. Since the purpose of these two figures is to clearly show the birefringence-like reflectance at the junction, we thought it will be better to show the lossless case for these figures. The plane of view is at x = w/2 plane, which is one of the interfaces between metal and core. It is clearly shown that incident beam splits into two beams after it is reflected at the junction of MIM waveguide.
In Section 3, we numerically analyze the mode transition efficiency from one mode to the other, varying the geometrical parameters to find the efficient conditions for mode transition.
3. Mode transition characteristics at single junction
Throughout this paper, we used RCWA method for the numerical calculation of coupling efficiency. Since the RCWA is based on the Fourier modal method, it is quite efficient for selecting specific mode to incident. Moreover, this method can clearly separate the power coupling to specific mode because it calculates field coupling coefficients of eigenmodes that existed in certain layer . In general, RCWA method expresses the electromagnetic fields in certain waveguide region with the summation of eigenmodes multiplied with coupling coefficients. If someone needs to launch PLanti mode in Layer A, coupling coefficient related to PLanti mode is given as one, whereas those of other modes are given as zero. Coupling coefficients for reflected waves are calculated by using the extended scattering matrix method , then reflectance is obtained by the power calculated from the coupling coefficients of each reflected waves: PLanti or PT mode. Detailed mathematical formulations for RCWA method is provided in , with appropriate computational codes for various cases of electromagnetic simulations.
In Fig. 2(a), we plotted the ratio of reflected power coupled to each mode, varying the incident angle. The definition of reflectance is the power ratio between incident and reflected wave at the junction. Therefore, propagation loss in incident layer is not considered in the calculation of reflectance. In this case, the incident mode is set to PLanti at 532 nm wavelength and geometrical parameters are the same as we used in Fig. 1. When the incident angle is zero (θinc = 0°), it is shown that mode transition from PLanti to PT does not occur since those two modes do not have any intersecting field components. Specifically, PLanti mode has only Ex, Hy, and Ez components whereas PT mode has Hx, Ey, and Hz components for normal incidence case, so they are not intersecting each other. However, y- and z-directional field components can exist for both types of modes at the oblique incidence case, which allows coupling between two modes. As shown in Fig. 2(a), reflected power of PT mode is gradually increased to the specific value near θinc = 20° due to the increase of field intersection. Near this maximum point, it is shown that coupling to PT mode is even much higher than coupling to PLanti mode, by simply reflecting at the junction. Then, it abruptly decreases to zero due to the critical angle condition of PT mode. Since the wavenumber of PT mode (kPT) is always smaller than that of PLanti mode, it is not possible for PT mode to propagate through the Layer A when incident angle is sufficiently large to satisfy the following condition,Figs. 2(b)-(e). Even for the oblique incidence, Ex (Hx) field component only exists for PLanti (PT) mode, so we can easily separate them by observing these fields. At the condition of θinc = 20°, it is shown that the amplitude of Hx field is much higher than that of Ex field due to the high mode transition efficiency, and their reflection angles are clearly different. On the other hand, Hx field does not propagate both in Layer A and B when incident angle is higher than condition of Eq. (1), which is shown in the Fig. 2(e). For clear observation, we selectively erase the incident field component in these figures.
In Fig. 3(a), reflected power coupled to each mode is plotted for PT mode incidence. Similar characteristics are also shown except for the absence of critical angle as shown in Fig. 2(a). Due to the reciprocity, the incident angle which gives maximum mode transition efficiency for PT incidence (θPTmax = 52°) has exactly same y-directional momentum as the condition for PLanti incidence (θPLmax = 20°), which can be simply obtained from Snell’s law. We also depicted Ex and Hx field components at the incidence condition of θinc = 52° in Figs. 3(b) and 3(c), respectively. Since there is no critical angle in this case, both modes are propagating inside the Layer A at any incident angle condition. However, the aspect of mode transition is opposite compared to Figs. 2(b) and 2(c). It is shown that the amplitude of Ex component, which means PLanti mode, is much stronger than that shown in Fig. 2(b).
Throughout these investigations, we note that the incident momentum and field intersection between modes are quite important for obtaining high mode transition efficiency. However, as depicted in parameter sweeping results, the portion of reflected power without mode conversion cannot be removed perfectly for single junction. To suppress the non-transited reflection, characteristics for periodically arranged layers of Layers A and B will be discussed in Section 4.
4. Efficient mode transition via periodically arranged junctions
Figure 4(a) shows the configuration of periodically arranged layers of Layers A and B. Although the Layer B does not permit the propagation of MIM mode, fields can penetrate into the layer; so tunneling can happen when the thickness of Layer B (LB) is sufficiently short . Then some portion of tunneled fields is reflected inside the Bragg gratings of MIM layers, and finally affects the reflection efficiency of input side. In our numerical simulations, we changed parameter LA for observing the Bragg grating characteristics. In Fig. 4(b), reflection characteristics are plotted for the case of PLanti mode incidence at θinc = 10° condition. Here, we choose much smaller incident angle condition than θPLmax = 20°, which gives relatively low coupling efficiency between the modes, in order to clearly observe mode transition characteristics caused by Bragg grating structures and other reasons which will be explained later. We fixed the value of LB as 25 nm, which is appropriately short distance to give a portion of tunneling fields, and LA is changed from 0 to 500 nm. At the condition of LA = 0 nm, reflectance directly follows the value of Fig. 2(a) since the structure is not a Bragg grating but single thick layer of Layer B.
Then, it is shown that reflectance coupled to both modes are significantly decreased, until the sharp peak of reflectance coupled to PLanti mode appears near the LA = 100 nm (and LA = 140 nm for PT mode). Note that the reflectance peaks for each mode are clearly separated except for first peaks at LA = 0 nm. This phenomenon can be understood by different momentum matching conditions for each mode. When PLanti mode is incident to Bragg grating structure, period of Bragg resonance condition for the same mode (PLanti) is simply determined by its own effective refractive index,
Now we will consider the case of PT mode incidence. In Fig. 4(c), we show the reflection characteristic of each mode for the case of PT mode incidence at θinc = 24.6° condition, which is calculated from the Snell’s law to have same y-directional momentum with the case of PLanti incidence shown in Fig. 4(b). As expected, the reflectance follows the value of Fig. 3(a) at θinc = 24.6° condition when LA = 0 nm. In this case, converted mode is PLanti mode, so period of Bragg resonance for PLanti mode follows Eq. (3), whereas that for PT mode is determined by its own effective refractive index,Fig. 4(d), where the condition is marked by black circle in Fig. 4(c). As expected, incident PT mode is almost converted to PLanti mode which has different reflection angle with respect to the incident one. It seems the reflected wave (PLanti) is stronger than incident one (PT), but it is natural since plasmonic mode is much more confined at the interface between metal and dielectric than the photonic mode is.
Maintaining mode conversion characteristics even for the Gaussian beam like Fig. 4(d) means broad aspect according to the variation of incident angle. To check it and find the optimized condition for mode transition, we show the two-dimensional parameter sweep result varying the θinc and LA together in Fig. 5. Firstly, it is clearly shown in Fig. 5(b) that mode transition efficiency is much higher than the case of single junction structure discussed in Section 3. The maximum conversion efficiency is obtained up to 82%, at LA = 160 nm and θinc = 20°. When the incident angle is increased, the condition for Bragg resonances expressed in Eqs. (2)-(4) is also changed. Therefore, the condition for resonance slowly moves toward the right side (longer LA). However, at the low incident angle condition near θinc = 10° for PLanti and θinc = 24.6° for PT mode incidences, they do not change so much, hence broad angular aspect can be obtained. Moreover, due to the high coupling efficiency at the single junction, resonance conditions expressed in Eqs. (2)-(4) are not well-matched anymore in high incident angle condition. Especially this phenomenon is clearly shown when two Bragg resonance conditions are intersected. The fourth resonance line circled in Fig. 5(a) and third resonance line circled in Fig. 5(b) are a good example for intersected resonance condition. It is shown that resonance line of Fig. 5(a) started to follow the bent curve which is a resonance condition for PT mode shown in Fig. 5(b) at the high incidence angle condition. We think that such change of reflectance spectrum originates from the complex multiple mode conversion inside the Bragg structure. Therefore, to obtain a broad angular spectrum and to avoid resonance condition mixing, we choose the incident angle value smaller than the value of θmax for mode converter based on Bragg gratings.
Although we only investigate the phenomenon with numerical analysis, we would like to briefly explain how the proposed device can be fabricated. For the case of single junction, thin metal film is firstly evaporated on the flat substrates. Next, using the photolithography technique, two different dielectric materials can be developed separately. Finally, top metallic layer is evaporated again to form a MIM waveguide. It will be possible to excite and detect the light signals by carving the slit coupler at the top metal layer by using the equipment such as a focused ion beam, which will make oblique patterns with respect to the junction line. On the other hand, for the case of Bragg grating structure, the period of gratings is too small to separately develop core layers by photolithography. Therefore, we think other techniques such as direct laser writing will be needed to fabricate them.
We propose a plasmonic-photonic mode conversion method in MIM waveguide structure which can change the power coupled to anti-symmetric plasmonic mode to the fundamental photonic mode of MIM waveguide structure. We find that an oblique incidence of PLanti or PT mode can be coupled to the other one by simple reflection at the junction of MIM geometry. The principle of mode conversion is laid on the momentum degeneration caused by a mode cutoff at the reflection layer. With RCWA simulations we find that mode conversion efficiency can be increased up to 60% for a single junction at the optimized incident angle condition. Moreover, by applying Bragg grating structure formed by periodic arrangement of junctions, much higher mode conversion efficiency up to 82% can be obtained according to our RCWA simulation, and non-transited reflection is significantly suppressed. Compared to previous works that demonstrate the mode-to-mode transition between two different waveguides [13–15], our scheme has advantages since it converts the lossy plasmonic mode into the low-loss photonic mode within a single metallic waveguide. Our scheme is one of the most compact plasmonic mode converters that have ever been reported, which needs only few micrometers size even for the Bragg grating case. Moreover, as we discussed in Section 2, the cutoff conditions of modes in MIM waveguides are quite sensitive to the refractive index of core material. Therefore, we also anticipate that our results can be applied to a compact plasmonic sensor; the refractive index change of filled material in MIM plasmonic waveguide can be detected by measuring the reflectance.
This work was supported by the National Research Foundation of Korea funded by Korean government (MSIP) through the Creative Research Initiatives Program (Active Plasmonics Application Systems).
References and links
1. H. Raether, Surface Plasmons (Springer-Verlag, 1988).
3. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72(7), 075405 (2005). [CrossRef]
4. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chipscale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]
5. J. Park, H. Kim, I.-M. Lee, S. Kim, J. Jung, and B. Lee, “Resonant tunneling of surface plasmon polariton in the plasmonic nano-cavity,” Opt. Express 16(21), 16903–16915 (2008). [CrossRef] [PubMed]
12. Y. Lim, S.-Y. Lee, K.-Y. Kim, J. Park, and B. Lee, “Negative refraction of Airy plasmons in a metal-insulator-metal waveguide,” IEEE Photon. Technol. Lett. 23(17), 1258–1260 (2011). [CrossRef]
13. C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10(8), 2922–2926 (2010). [CrossRef] [PubMed]
14. R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010). [CrossRef] [PubMed]
15. S.-Y. Lee, J. Park, M. Kang, and B. Lee, “Highly efficient plasmonic interconnector based on the asymmetric junction between metal-dielectric-metal and dielectric slab waveguides,” Opt. Express 19(10), 9562–9574 (2011). [CrossRef] [PubMed]
17. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009). [CrossRef]
21. R. Ameling and H. Giessen, “Cavity plasmonics: large normal mode splitting of electric and magnetic particle plasmons induced by a photonic microcavity,” Nano Lett. 10(11), 4394–4398 (2010). [CrossRef] [PubMed]
23. M. A. Ordal, R. J. Bell, R. W. Alexander, Jr, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24(24), 4493–4499 (1985). [CrossRef] [PubMed]
24. T. Chung, S.-Y. Lee, H. Yun, S.-W. Cho, Y. Lim, I.-M. Lee, and B. Lee, “Plasmonics in nanoslit for manipulation of light,” IEEE Access 1, 371–383 (2013). [CrossRef]
25. J. Chen, G. A. Smolyakov, S. R. J. Brueck, and K. J. Malloy, “Surface plasmon modes of finite, planar, metal-insulator-metal plasmonic waveguides,” Opt. Express 16(19), 14902–14909 (2008). [CrossRef] [PubMed]
26. S.-Y. Lee, J. Park, I. Woo, N. Park, and B. Lee, “Surface plasmon beam splitting by the photon tunneling through the plasmonic nanogap,” Appl. Phys. Lett. 97(13), 133113 (2010). [CrossRef]
27. H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A 24(8), 2313–2327 (2007). [CrossRef] [PubMed]
28. H. Kim, J. Park, and B. Lee, Fourier Modal Method and Its Applications in Computational Nanophotonics (CRC Press, 2012).