Surface plasmon polaritons have become a research area of great importance. We present theoretical investigations on the realization of components and Y-splitters for surface plasmon polaritons guided by dielectric-loaded waveguides. The effect of the limited resolution of the fabrication process on the characteristics of fabricated Y-splitters is analyzed. A more efficient and robust configuration of the Y-splitter for surface plasmon polaritons is proposed.
©2008 Optical Society of America
Plasmonic waveguides are considered as a promising alternative to optical waveguides in future highly integrated photonic devices , since the confinement of surface plasmon polaritons (SPPs) could be very high. Various configurations of SPP waveguides have been suggested and demonstrated [2,3,4]. Among them are dielectric-loaded SPP waveguides (DLSPPW) [5,6]. This type of plasmonic waveguides provides the required localization of the SPP field and is easy to fabricate. For example, waveguides could be created on a metal surface by structuring of a thin polymer layer deposited on the metal surface. Different techniques have been applied to the fabrication of such waveguides including standard UV lithography [7, 8] and direct laser writing .
In order to achieve high functionality of the SPP based photonic devices, waveguiding plasmonic components have to be developed. The ability to split signals carried out by guided plasmons is crucial for future SPP devices. One of the ways to achieve splitting of the guided plasmons is to use so-called Y-splitters. This splitter is well known from integrated optics  and can also be applied to dielectric-loaded SPP waveguides. The Y-splitter consists of an input waveguide and two branching waveguides as shown in Fig. 1. It was demonstrated previously, that compact size and minimum excess losses of the Y-splitter are achieved with a cosine arc shape of the branching waveguides . The application of Y-splitters to branch the SPPs guided by dielectric-loaded SPP waveguides has recently been analyzed theoretically . However, practical issues of the fabrication of SPP Y-splitters and optimization of their parameters were not considered so far. Practical limitations on the shape of the Y-splitter are imposed by the resolution of the existing fabrication techniques. Especially, the quality of the gap region between two branching waveguides is influenced by the resolution limitation. It is well known from integrated optics that shape distortions resulting from resolution limitations lead to increased excessive losses in the Y-splitter due to radiation scattering at the branching point. Practical implications of the structural defect resulting from limited resolution of the UV lithographic process and located at the branching point of DLSPPW Y-splitter are discussed in ref. . Experimental and theoretical results demonstrate substantial increase of the DLSPPW Y-splitter excess losses caused by this defect.
In this paper, we investigate numerically a real Y-splitter taking into account fabrication defects and present a new configuration of the splitter in order to optimize its characteristics. We start from a previously reported configuration of the DLSPPW Y-splitter  and introduce a modification of the splitter shape reflecting the limitations imposed by the resolution of fabrication technologies. Numerical simulations of the real Y-splitter show an increase in the excess losses due to scattering of the guided SPP at the branching point. Furthermore, we demonstrate that the well known solution from integrated optics of the problem of scattering of the guided radiation on the non-perfect waveguide branching is not applicable for the realization of SPP devices due to high ohmic losses experienced by SPPs. To solve this problem, a new more robust configuration of the DLSPPW Y-splitter with less excess losses is suggested. Properties of the novel configuration of the DLSPPW Y-splitter, with respect to resolution limitations imposed by the fabrication technology, are analyzed.
2. Modeling of a real DLSPPW Y-splitter
We are starting from a well known configuration of the DLSPPW Y-splitter . The ideal (without any fabrication failure) configuration of the splitter is shown in Fig. 1 where all the required splitter parameters are defined.
Following ref.  we use a 600 nm×600 nm cross-section of the polymer stripe forming the DLSPPW. The polymer stripe is located on the top of a glass substrate covered with a 50 nm gold layer. The refractive indices of the glass substrate and polymer waveguide stripe are 1.5 and 1.545, respectively. The complex refractive index of gold is n gold=0.55+i11.5 . All simulations were preformed for 1550 nm radiation wavelengths. The shape of the branching waveguides is described by the following equation:
where d Y is the distance between the exit arms of the Y splitter, which is set in our simulations to d Y=3 µm. L B=7 µm is the length of the branching sections.
The mode solver software FemSim and the 3-D FDTD Maxwell equation solver FullWave from RSoft Design Group were used for numerical modeling. First we have simulated characteristics of the SPP guided mode propagating in the DLSPPW described above. The mode profile obtained with FemSim is illustrated in Fig. 2.
Our modeling also confirms the absence of any other eigenmode of the DLSPPW apart from the fundamental guided SPP mode. The FDTD modeling of the SPP guided mode propagation in the straight section of the DLSPPW allows determination of its propagation lengths. It was found to be 41 µm, that is in a good agreement with the previously reported data [12,13]. For this and all subsequent calculations the grid in the FullWave calculations was set to 75 nm for bulk material and to 5 nm for edge regions.
The ideal, defect-free, DLSPPW Y-splitter, as shown in Fig. 1, was modeled with the 3-D FDTD Maxwell equation solver. Excitation point and sensor positions are shown in Fig. 1. The point z=0, where the branching of the waveguides is started, is chosen as the Y-splitter input. The input sensor (Sensor 2) is located at this point. Sensor 1 is implemented to monitor the SPP excitation. Two output sensors are located in each output arm at the cross section z=L B. This cross section is defined as the output of the Y-splitter. Power flows through the input and output waveguides of the splitter were obtained by integration of the Poynting vector over the cross sections of the input/output waveguides at the sensor locations. The input waveguide of the splitter was exited by the electromagnetic wave with a transversal profile, matching the profile of the guided SPP mode of the DLSPPW. In order to exclude transitional effects taking place near the excitation cross section, this cross section is located at 5 µm distance from the Y-splitter input. The excess losses of the splitter were calculated as ExcessLoss=1-(I out 1+I out 2)/I in, where I in, I out 1, and I out 2 are the integral power flows at the input and both output waveguides of the DLSPPW Y-splitter, respectively. For the ideal, defect free, DLSPPW Y-splitter with the geometrical characteristics mentioned above, excess losses of about 32% were obtained by 3-D FDTD modeling. Similar excess losses of the ideal Y-splitter were reported previously .
For practical implementation of the DLSPPW Y-splitter, limitations imposed by the resolution of the fabrication techniques have to be taken into consideration. The gap size between two branching output waveguides is affected by the limited resolution in the first place. A smooth, sharp branching is impossible if the resolution of the fabrication technique is limited. Instead, the Y-splitter with the configuration shown in Fig. 3 can be fabricated. The minimum gap width between the branching waveguides is defined by the fabrication resolution. Effectively, the difference between the real DLSPPW Y-splitter and ideal one could be modeled by introducing a defect in the branching area. This defect is shown as black filling in Fig. 3. The defect structure itself is approximated by a polymer filling between the two arms of the splitter. Although the defect width is defined by the fabrication resolution only, the defect length depends on both fabrication resolution and shape of the branching waveguides. The length of the defect structure, L Defect is defined as the distance from the point where the arms of an ideal splitter start separating, to the end of the defect structure, as shown in Fig. 3.
Typical resolution limitations of the standard UV-lithographic techniques, which can be applied for the fabrication of SPP components, have been well investigated before. Systems with resolutions of 500 nm to 250 nm are commercially available . The fabrication resolution down to about 100 nm or better can be achieved using two photon polymerization, which is recently developed direct laser writing technique [15,16]. The data on the defect length for different geometrical characteristics of the Y-splitter and for different fabrication resolutions are presented in Table 1. The defect lengths were calculated for the branching waveguides described by Eq. (1) and the minimum gap sizes defined by the fabrication resolution.
The parameter of a main interest for the real DLSPPW Y-splitter is the dependence of the excess loss on the minimum gap width between the branching waveguides. This dependence was calculated from 3-D FDTD modeling of the real DLSPPW Y-splitter with 7 µm length of the branching section and 3 µm distance between the output arms (these parameters are used in all following simulations). The resulting dependence is shown in Fig. 4.
As expected, the excess losses of the real DLSPPW Y-splitter grow with the increasing minimum gap width between the branching waveguides. The limited fabrication resolution results in a significant excess loss. The excess losses of an ideal Y-splitter of 30% grow to 34% for 100 nm resolution (which corresponds to the minimum gap width) provided by the 2PP fabrication. A further increase of the excess losses to 43% and 60% is observed for the fabrication resolutions of 250 nm and 500 nm, respectively. The origin of the increased excess losses is scattering of the guided SPP on the defect in the branching area. This source of the excess losses due to the limited fabrication resolution of a real Y-splitter is well known from integrated optics. For optical splitters there exists a very simple and efficient solution which allows overcoming the resolution limitations. In the next section we will demonstrate that this known solution is not applicable for the DLSPPW Y-splitter. To resolve this issue a novel configuration of the DLSPPW Y-splitter will be proposed.
3. Low loss DLSPPW Y-splitter
Conventional optical Y-splitters have additional excess losses due to scattering of guided light in the branching area. This scattering appears due to the presence of a fabrication defect between the branching output waveguides. The issues related to the limited fabrication resolution of the optical Y-splitters were successfully overcome with a multimode interface (MMI) Y-splitter . The schematic drawing of the MMI Y-splitter is shown in Fig. 5. In this case the multimode waveguide section or MMI is introduced between the input single-mode waveguide and the branching section. The width of the MMI section is 1200 nm. The optical filed in the single-mode input waveguide has its intensity maximum on the splitter axis. In the MMI the input mode is converted into a higher order mode with zero intensity on the splitter axis and two side lobs. The MMI is designed to achieve 100% conversion of the input mode into this higher order mode on the length scale of the MMI section. The transversal profile of the guided mode at the output of the MMI section is matched with the profile of the super-mode of the Y-splitter branching section. By this way scattering losses in the imperfect branching section can be avoided.
Unfortunately, direct application of the MMI Y-splitter concept to plasmonics is impossible, since the typical length of the MMI section is several hundreds of micrometers . So, the propagation loss (due to ohmic losses) in the DLSPPW MMI section will be unacceptably high. Also, a relatively long length of the MMI section is in contradiction with the idea of a high integration level of plasmonic components. In order to confirm this conclusion, 3-D FDTD modeling of the propagation of the guided SPP in the DLSPPW MMI section of the Y-coupler, shown in Fig. 5, was performed. The input single-mode DLSPPW was excited by an electromagnetic wave with a transversal profile matching the profile of the SPP mode guided by this DLSPPW. The propagation losses for the SPP in the MMI section (between sensors 1 and 2) are shown in Fig. 6 depending on the MMI section length. In the same figure, the SPP profile at the MMI entrance and the SPP profiles at the MMI end cross section are presented for a 20 µm long MMI section. Although propagation losses in the MMI section are approaching 50% for the section length of 20 µm, the required mode conversion is not achieved.
The 3-D FDTD simulations of the DLSPPW Y-splitter presented in Fig. 7 were carried out for different lengths of the cut section in the left arm. The geometrical characteristics of the DLSPPW and bending sections are the same as in previous simulations. The input of the Y-splitter is the position where the branching is started (z=0). The sensor 2 is located in this position in order to measure the integral input power flow. The integral power flows of the Y-splitter are measured by the sensors 3 and 4 at the end of the branching sections (z=L B). The results of these simulations are shown in Fig. 8, where the excess loss and the splitting ratio (transmission into the left arm divided by the transmission into the right arm) of the Y-splitter are plotted. The splitting ratio of 1 is achieved with the length of the cut section of 520 nm, marked with a blue vertical line in the graphs. The excess losses of an ideal, defect-free, Y-splitter with a cut section are less than 30% for a splitting ratio equal to 1, which is a decrease of about 2% compared to the standard ideal Y-splitter. The splitting ratio can be tuned in a broad range without any significant increase of the excess losses by adjusting the length of the cut section.
Below modeling of the real DLSPPW Y-splitter with asymmetric excitation and cut section in the left arm is performed. The defect resulting from the limited resolution of the fabrication process is shown in black in Fig. 9. The numerical model used in these calculations is analogous to that applied before in simulations of the real optical Y-splitter.
The length of the cut section in the left arm is set to 520 nm, which corresponds to the splitting ratio equal to one for an ideal splitter. Simulation results of the excess losses for different values of the minimum gap width (due to the presence of defect) between the branching waveguides are shown in Fig. 10.
The excess losses of this Y-splitter remain less than 30% for fabrication processes with a resolution of 300 nm (corresponds to the minimum gap width) or better. For 500 nm fabrication resolution, the excess losses still remain about 32%, while for 100 nm fabrication resolution they are about 29.4%. Thus, this novel DLSPPW Y-splitter has a very good failure tolerance with respect to defects arising due to the limited fabrication resolution.
The dependence of the splitting ratio on the minimum gap width between the branching waveguides is shown in Fig. 11. For a minimum gap width below 400 nm the splitting ratio is nearly equal to one, while for a larger gap width the splitting ratio becomes more and more shifted to the left arm. From this it follows that a fabrication process with a resolution of 400 nm or better is necessary to achieve a splitting ratio nearly equal to one. Moreover, also for a minimum gap width larger than 400 nm a splitting ratio of one can be achieved by varying the length of the cut section.
The wavelengths dependencies of the excess loss and splitting ratio calculated for the ideal Y-splitter (Fig. 7) and the real Y-splitter with fabrication defect in the branching point (Fig. 9) are shown in Fig. 12. The calculations are performed for the splitters with the length of the cut section optimized for central wavelengths 1.55 mm as shown by blue line in Fig. 8. The real Y-splitter with 100 nm minimum gap width between the branching waveguides is modeled.
In this paper, we have simulated an ideal DLSPPW Y-splitter and extended these simulations to a real Y-splitter, taking into account practical limitations imposed by the resolution of the existing fabrication techniques. It has been demonstrated that the solution of the problem of guided radiation scattering at a non-perfect waveguide branching, well-known from integrated optics, is not applicable for the SPP devices due to the high Ohmic losses typical for SPPs. Finally, a new low loss DLSPPW Y-splitter design is suggested and investigated, which is more robust with respect to the resolution limitations of the available fabrication techniques and can facilitate a practical realization of Y-splitters for guided SPPs. Also Mach-Zehnder interferometers with the suggested Y-splitter design will demonstrate less excess losses and higher efficiency.
The authors would like to acknowledge financial support from the European Commission Project “Polymer-based Nanoplasmonic Components and Devices “(PLASMOCOM, contract no 034754, http://www.plasmocom.org).
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