A novel design for a polarization-independent SOI-based 2 × 2 3-dB adiabatic splitter with sub-micron-scale dimensions is proposed and modeled. To achieve slow and smooth mode evolution, a structure with simultaneous tapering of velocity and coupling is used. To reduce the adiabatic region length by adjusting the gap separation, the coupling strengths of TE and TM polarizations as a function of the gap value are analyzed. For both polarizations, a high uniformity within ± 0.2dB over a broad bandwidth from 1520 to 1650 nm is achieved with a 300-μm-long adiabatic region.
© 2013 Optical Society of America
Photonics based on the silicon-on-insulator (SOI) platform are compatible with commercial complementary metal–oxide–semiconductor (CMOS) processes and offer a promising solution to the present bottlenecks of traditional electrical interconnects . In many multi-port optical devices based on SOI, such as optical switches, 2 × 2 optical power splitters are one of the fundamental components [2–5]. Currently, multimode interference (MMI) couplers [3,6,7], and adiabatic couplers [4,7,8], with their broad bandwidth and relaxed fabrication tolerances, are widely used as 2 × 2 optical splitters. In order to achieve high integration density, high speed, and low power consumption, SOI-based waveguides with sub-micron dimensions are typically used in silicon photonics. However, since SOI-based waveguides are strong restrictive waveguides (large index contrast 3.5/1.5), these two kinds of optical splitters are highly polarization-dependent when the waveguide size reaches the sub-micron-scale [9,10].
The principle of MMI couplers is based on self-imaging, resulting in different imaging positions for the quasi-transverse-electric (TE) polarization and the quasi-transverse-magnetic (TM) polarization. Thus, MMI couplers have an intrinsic polarization-dependence, which is then difficult to completely remove. Although a polarization-insensitive 1 × 2 MMI splitter has been proposed theoretically in , this design strongly relies on the value of the refractive index of the cover layer.
An SOI-based 2 × 2 3-dB adiabatic splitter has been shown to be fabrication-tolerant on the scale of a coupling length, given an adequately long coupling length . Although different values of the adiabatic region length (L) are required for TE and TM polarizations, using a longer length will render the adiabatic splitter polarization-independent. In this paper, an SOI-based polarization-independent design of a 2 × 2 3-dB adiabatic splitter with a sub-micron-scale waveguide is proposed. The coupling strengths of TE and TM polarizations as a function of the gap value will be analyzed. By balancing the coupling strength of the two polarizations, the required L to realize polarization-independence is strongly reduced. To the best of our knowledge, this is the first reported design of a polarization-independent adiabatic splitter based on a sub-micron-scale SOI platform.
The adiabatic splitter analyzed here is based on a coupled-waveguide system, as shown in Fig. 1(b). This splitter consists of two SOI-based waveguides, waveguide 1 and waveguide 2, which are placed close to each other in the same plane. According to coupled-mode theory [11,12], there will be two system modes for both TE and TM polarizations, an even mode and an odd mode. The normalized system modes, denoted as Ee and Eo, are expressed as column vectors with their components being the amplitudes of the two individual waveguide modes,
The operating principle of the splitter is based on the adiabatic evolution of the position of the even (odd) mode in waveguide 1 (2) to each mode being equally divided amongst the two waveguides. At the input port, when |δ| >> κ,8]. However, according to Ref , the difference in coupling strength between the TE and TM polarizations is quite large, leading to a large difference in the required L values. Thus, we will focus on reducing the value of L required by balancing the coupling strength of the two polarizations.
To study the coupling strength, two parallel SOI-based coupled waveguides with a 340-nm rib height, a 160-nm slab height, and a typical 500-nm width are used as an example, as shown in Fig. 1(a). Figure 2 shows the coupling strength of the two polarizations as a function of the gap between the two waveguides. Compared to the TE polarization, the coupling strength of the TM polarization is more sensitive to the gap value. Taking a gap value of 120 nm as the point at which the coupling is equal for both polarizations, when the gap is smaller (larger), the coupling strength of the TM polarization is stronger (weaker) than that of the TE polarization.
As shown in Fig. 1(b), the gap value between the two waveguides at the input port of the adiabatic splitter should be large enough to make the coupling strength approach zero. However, according to Fig. 2, different minimum gap values of 1000 nm and 500 nm are required for the TE and TM polarizations, respectively. As a result, a gap value of 1000 nm is chosen for the input port to reduce polarization sensitivity. In the adiabatic region, the gap is then linearly tapered to the narrowest value (G). In this way, it is possible to make the coupling of the two polarizations more balanced by choosing an appropriate G value.
Considering the difficulty of fabrication, G = 50 nm is chosen as an example. Theoretically, at the input port, the difference between the widths of the two waveguides should also be large enough to realize adiabatic light input. Meanwhile, single-mode operation and low propagation loss should also be ensured [13,14]. As a result, widths of 600 nm and 400 nm are chosen and are linearly tapered respectively to the typical waveguide width of 500 nm in the adiabatic region. When L = 300 μm, Fig. 3 shows the effective index and the coupling strength as a function of the propagation position in the adiabatic region at a wavelength of 1550 nm for both polarizations. These quantities are calculated with a mode solver based on a full-vectorial finite-difference method. The coupling of the TM polarization has been enhanced by reducing the G value, while the evolution of the effective index evolutions for both polarizations is maintained in a slow and smooth fashion.
A three-dimensional semi-vectorial beam propagation method with transparent boundary conditions is used in the following simulations. The grid spacing for x and y directions and the step size for z are 10 nm. In order to demonstrate how our analysis works, splitting performance of input port 1 (I1) is simulated as an example. When G = 50 nm, the simulated uniformity of both polarizations as a function of L is shown in Fig. 4(a). Taking the uniformity within ± 0.2dB as a standard, an L of 170 μm is adequate for the TE polarization, while a much longer L of 280 μm is required for the TM polarization. This simulation is repeated for G = 100 nm in Fig. 4(b). The L values required for the TE and TM polarizations become 190 μm and 360 μm, respectively. Thus, when G is changed from 100 to 50 nm, the value of L required for the TM polarization decreases much more quickly, indicating a rapid enhancement of the coupling strength. These simulation results support the idea that reducing the required L value can be achieved by balancing the coupling strength of the two polarizations with a small G.
To study the behavior of the proposed splitter as a function of wavelength, a G of 50 nm and an L of 300 μm is considered. As shown in Fig. 5(a), the simulated uniformity for both polarizations is within ± 0.2dB from 1520 to 1650 nm. The simulated excess loss of both polarizations per splitter is only about 0.01dB over the whole simulated wavelength range. More importantly, as shown in Fig. 5(b) the proposed splitter maintains a high uniformity within ± 0.2dB for both polarizations when G varies from 10 to 70 nm, which can be reliably fabricated by using one step of electron-beam lithography and one step of inductively coupled plasma etching.
In conclusion, a new design of a polarization-independent 2 × 2 3-dB adiabatic splitter based on a sub-micron-scale SOI platform is proposed and theoretically demonstrated. The design of simultaneous tapering of velocity and coupling is used to realize a slow and smooth evolution of the effective index. The imbalance between the TE and TM polarizations with respect to the L value is reduced by decreasing G to 50 nm. For both TE and TM polarizations, an L of 300 μm is adequate to achieve a high uniformity within ± 0.2dB over a broad bandwidth. An experimental demonstration will be reported in future works.
This work is supported by the National Basic Research Program of China (Grant No. 2011CB301701), the High Technology Development Project (Grant No. 2012AA012202), and the National Natural Science Foundation of China (Grant Nos. 61107048 and 61275065).
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