An active metal strip hybrid plasmonic waveguide (MSHPW) using gain materials as loss compensation is proposed with an extremely simple fabrication procedure. Gain materials are introduced either in the low-index layer or in the high-index layer of MSHPW. The effects of waveguide dimensions and material gain coefficients on loss compensation are analyzed at the communication wavelength. For one configuration presented here, a critical material gain as low as 3.8cm−1 is sufficient for fully compensation of the loss when using a high-index gain material. The active MSHPW with low critical material gain opens up opportunities for practical plasmonic devices in active applications such as amplifiers, sources, and modulators.
© 2012 OSA
Plasmonics is drawing increased attention due to its outstanding capability of confining and controlling light beyond the diffraction limit , thereby potentially enabling devices integration in nanoscale [2–4]. As the building block of integrated circuits, various plasmonic waveguides have been proposed . However, a typical challenge for plasmonic waveguides is the trade-off between propagation loss and field confinement. In other words, they can perform either low propagation loss with diffused field (e.g., long-range surface plasmon polaritons (LRSPP) ), or compact mode size at the expense of large losses (e.g., metal-insulator-metal waveguides (MIM) [7, 8]). Recently, a new type of plasmonic waveguide called “hybrid plasmonic waveguide (HPW)” was proposed to attempt both low propagation loss and strong field confinement [9–14].
Many passive devices based on HPW have been demonstrated either theoretically or experimentally, such as splitters  and ring resonators . By contrast, active plasmonic devices are of critical significance for future integrated plasmonic device technology, and it is beneficial to make active devices based on HPW whose intrinsic modal loss is low. However, there are only some limited researches focusing on active applications of HPW [17–19]. Furthermore, structures of previously proposed HPW with gain materials are complicated (e.g., semicylinders or ribs with low experimental tolerance are included), thus the feasibility in practice is seriously constrained. Meanwhile, some gain materials are very difficult to be etched, as a result, choices of gain materials for those structures with the etching process are heavily restricted. Consequently, a practical configuration suitable for active plasmonic devices is urgently needed.
In this paper we propose and analyze an active metal strip hybrid plasmonic waveguide (MSHPW) with gain materials in different regions. Compared to the previous work, MSHPW is particularly suitable to introduce gain materials for active applications due to its extremely simple fabrication procedure and low intrinsic modal loss. Effects of waveguide parameters and material gain coefficients on propagation properties are analyzed in detail. Our simulation indicates that the critical material gain to fully compensate the loss in MSHPW is so small that it can be easily obtained by current gain materials.
2. Waveguide structure
The waveguide geometry is shown in Fig. 1 . It is composed of a metal layer,a narrow low-index dielectric gap, a high-index dielectric layer, a buffer layer and substrate. In traditional HPW, the metal layer and the low index layer can be patterned to strips, and the high-index layer is usually patterned to a cylindrical  or rectangular  core to provide lateral confinement. By contrast, in MSHPW, only the metal layer is patterned to strip, while the other layers are slabs (infinite in direction). Therefore, the fabrication procedure for MSHPW is extremely simple.
On account of the significant status of Si photonics as one of the most promising candidates for optoelectronic integration , we choose materials in silicon series to introduce the fabrication procedure. Thus the structure could be fabricated on an SOI wafer and fabrication processes are compatible with CMOS technology. The corresponding substrate, buffer layer and high-index layer are Si, SiO2 and Si, respectively. Processes we need to do are forming a low-index dielectric gap on the SOI wafer and patterning a metal strip on the low-index dielectric gap. First, the low-index material could be SiO2 obtained by thermal oxidation of Si or deposition. The next step is to form a strip pattern by photolithography or e-beam lithography. Then deposit a metal layer on the top and obtain a metal strip in lift-off process. One sees that there is no etching process and only once lithography, which may avoid extra losses from fabrication (e.g., etched surface roughness and alignment error) and make the structure quite practical. The waveguide could be characterized by various methods. For example, dielectric waveguides with tapers could be fabricated at the two ends of the waveguide for coupling light in and out, and then the whole system is able to be tested on a common waveguide test platform . Near filed imaging using near-field scanning optical microscope (NSOM) is also feasible . In addition, scattered light from the waveguide can be detected by etching slits or grating at the metal layer, which has been proofed effectively .
Though a typical material system is taken for analysis, a wide range of materials, especially gain materials, can be utilized in this waveguide. For example, the low-index gain materials could be PMMA with PbS quantum dots , Er silicate  etc., while the high-index gain materials could be InGaAsP , Er-doped silicon , etc. MSHPW is practically suitable for active devices due to its unique properties. Firstly, there is no strict temperature limitation which is a typical obstacle for active plasmonic devices. Specifically, frequently-used metals for plasmonics such as Au and Ag cannot endure high temperature, while some gain materials such as nanocrystal silicon  and Er silicate  need high temperature (e.g., around 1000°C) annealing process to obtain a good active performance. Therefore, in some cases (e.g., MIM waveguides), researchers need to take very complicated fabrication process  to avoid the temperature’s incompatibility. By contrast, in MSHPW the metal layer is deposited at last and not affected by processes for other layers. Secondly, unlike some hybrid plasmonic waveguides which need to etch the low-index and high-index dielectric layers, MSHPW makes it possible to utilize those gain materials difficult to etch, such as the erbium silicate. In summary, MSHPW is compatible to a wide range of gain materials as well as chemical and physical processes, and this good compatibility makes it a promising candidate for practical active devices.
3. Simulation and analysis of the waveguide
As shown in Fig. 1, we suppose the propagation direction is along the axis. There are two waveguide parameters that must be taken into account for optimization of the waveguide: the height of the low-index dielectric gap and the width of the metal strip . Apart from the metal layer, other layers are supposed to be infinite in direction. For all cases below, heights of the metal strip and the high-index dielectric layer are fixed to be 100nm and 300nm, respectively. We set materials for the metal strip, the low-index gap, the high-index layer and the buffer layer as Ag, SiO2, Si, and SiO2, respectively. The telecommunication wavelength = 1550nm is chosen as the work wavelength and corresponding refractive indices for materials are , = 1.445 and = 3.455.
We simulated the structure by the finite element method (FEM). The key parameter that characterizes the mode is the effective modal index defined as , where and are the propagation constant of the hybrid mode and the free space wave number, respectively. is a complex number written as . Here is positive for lossy materials and becomes negative when sufficient gain is induced in the structure. The modal propagation loss (or gain ) is
3.1 Field profile
Figure 2 illustrates the perpendicular electric field (Ey) distribution of the fundamental quasi-TM mode along axis through the center of metal strip as the dashed line in the inset shows, while the inset shows the Ey field profile of the whole cross section. Geometrical dimensions are = 300nm, = 30nm as an example. One sees that there is a strong field enhancement in the gap layer, which is due to the combination of surface plasmon at the Ag-SiO2 interface and the discontinuity in the Ey field at the Si-SiO2 interface. This is a key advantage of this configuration because of its significance for various applications such as active devices  and nonlinear effects . Moreover, it is notable that in MSHPW, although the high-index dielectric layer is not patterned to form a dielectric core waveguide as the common case in other hybrid plasmonic waveguides [10, 12], the residual power guided in the high-index silicon slab still has a finite modal width. The lateral confinement is obtained by the metal strip which generates an effective index difference between areas with metal and without metal along the direction.
3.2 Dependence on the geometrical parameters
Geometrical parameters may have significant influence on waveguide performance, as discussed in [29,30], which also refer to metal strips for surface plasmon. Here we carried out a detailed study about the effects of and on the effective index and propagation loss, and results are shown in Fig. 3 . One sees that rises as w increases or decreases. The qualitative explanation is that dimensions affect the energy distribution in different areas of the structure. Specifically, when more power is confined in the area with high index, the corresponding will be larger, and when smaller area of electromagnetic field interacts with the metal, will be smaller. Figure 3(b) suggests that can be made very low by reducing and enlarging simultaneously.
However, it is considerable whether the ability of confinement becomes weaker when decreasing waveguide width for lower losses. There are a few figures of merit to measure a mode’s confinement [31–33].9, 17, 18, 33]. In addition, it is inversely proportional to the spontaneous emission rate enhancement . This is also a reason why this measurement has been widely used, and it may be useful for our future work on active applications. and versus the waveguide width at a fixed of 70nm are shown in Fig. 4 . When goes down from 500nm to 50nm, experiences a gradual decrease from 0.00596dB/μm to 0.00179dB/μm while increases from 0.17434μm2 to 0.29207μm2. Therefore, a trade-off between loss and confinement exists here. However, it is notable that when reaches around 350nm and increases further, levels off at 0.175μm2, whereas keeps rising continually. Therefore, the point = 350nm is an optimum value for both low propagation loss and compact confinement. Accordingly, for different applications, we can effectively control the waveguide performance by tuning waveguide dimensions.
3.3 Overlap with the active region
Substantial mode confinement in the active region is necessary for effective loss compensation [34, 35]. In order to further describe the power distribution that paves the way to introduce gain materials in the next subsection, we calculated the power confinement factor for different regions. is defined as the ratio of the power confined in a certain region to the total power. Illustrated in Fig. 5 inset, the structure is divided into several regions: regions covered by metal strip are called “center” while other regions are called “side”. Figure 5 shows the power confinement factor of the high-index Si layer in center (center) and side (side) regions, and the low-index SiO2 gap in center (center) and side (side) regions. There are two remarkable points. First, as increases, center and center go up while side and side go down. These trends indicate that more power is confined in the center region for wider metal strips,resulting in a stronger confinement at larger width, which is in accordance with the trend of in Fig. 4. Secondly, is always larger than though there is a strong electric field enhancement in the SiO2 gap as mentioned before. Overall, mode power is confined in the low-index region and the high-index region separately, which provides the possibility to utilize gain materials with low or high refractive index.
3.4 Loss compensation in MSHPW
A gain material is introduced either in the low-index gap or in the high-index layer to compensate the propagation loss or even obtain net gain. For simplicity, it is assumed that the gain obtained in the active region is uniform. The gain coefficient of the bulk material is written in terms of the imaginary part of the refractive index as . By doing so, we are able to treat the gain as a perturbation to the modal effective refractive index and thus the modal propagation loss (or gain).
First, we introduce gain in the low-index dielectric gap. Figure 6(a) shows the propagation loss (or gain) versus at varying widths. One sees that for a certain width, the modal loss decreases (or gain increases) linearly as increases. When is large enough, the modal propagation loss can be fully compensated, i.e. = 0. This special point of bulk material gain is defined as critical material gain . When increases further to be larger than , net modal gain is obtained, which corresponds to the region above the dashed line in Fig. 6(a). For different widths, the modal gain (or loss) and are all in linear relationship. However, slopes of these lines are different—larger slope at larger width. This can be partly expained by the power distribution in Fig. 5. As goes up, center rises and begins to lead the trend of the total power in the gap. Therefore, when the metal strip is wider, a larger overlap between the electromagnetic field and the low-index gain material apears and results in a more effective loss compensation. In consequence, a competetion exsits for the net propagation loss (or gain): on one hand, the intrinsic modal propagation loss is larger for wider waveguides; on the other hand, the gain material works more effectively when the width increases.
In order to provide a merit for the final competetion result, we calculated the critical material gain for varying widths. As shown by the blue curve in Fig. 6(c), for the case of introducing a low-index gain material, undergoes an increase as rises, from 33.73cm−1 ( = 50nm) to 59.09 cm−1 ( = 500nm).
In the next place, we fill the high-index layer with a gain material. Figure 6(b) presents the propagation loss (or gain) for varying material gain coefficients when is 100, 300, and 500nm, respectively. Trends in Fig. 6(b) are similar to those in Fig. 6(a). A more interesting fact is that loss compensation from the high-index gain material is much more effective than that from the low-index gain material. For example, when is 40.5 cm−1 and w is 100nm, the propogation loss is 3.18e−4dB/μm for the case of introducing gain in the low index gap, while a pure gain of 1.67e−2dB/μm is obtained if gain is introduced in the high-index layer. One reason account for this phenomenon is that much more power is confined in the high-index layer than the low-index gap, which means there will be a larger overlap and stronger interaction between the electricmagentic field and the gain material if gain is introduced in the high-index layer. The critical material gain of the high-index gain material is also shown in Fig. 6(c). Its trend is similar to that of the low-index gain material but with a much lower level of values. For instance, when = 50nm, of the high-index gain material is only 3.8cm−1, and around a ninth of the value (33.7 cm−1) for the low-index gain material. When rises to 500nm of the high-index gain material is still as low as 14.1 cm−1. It is notable that the critical gain values discussed above could be easily obtained by many current gain materiels such as quantum dots , III-V semiconductors , and dyes .
In conclusion, we have proposed and investigated an active metal strip hybrid plasmonic waveguide. The extremely simple fabrication procedure not only avoids extra losses from fabrication but also widens the scale of gain material selection. The propagation loss and mode confinement of the waveguide are effectively controlled by tuning waveguide dimensions. This is beneficial to meet various demands of applications. In the passive case, an optimum value of the metal strip width is demonstrated to be 350nm for both low-loss propagation and compact confinement. In the active case, gain materials could be introduced either in the low-index gap or the high-index layer for loss compensation. Specifically, the high-index gain material works more effectively than the low-index gain material. For one configuration simulated, the critical material gain for the high-index gain material is as low as 3.8cm−1. Consequently, apart from providing an active waveguide with loss compensation, the results from this investigation also facilitate the designing of other plasmonic devices for active applications such as amplifiers, sources and modulators.
This work was partially supported by the Peking University 985 startup fund and the National Natural Science Foundation of China under Grant No. 61036011.
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