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A novel layout is presented to minimize the size of an arrayedwaveguide grating (AWG) demultiplexer based on Si nanowire waveguides, in particular when a high diffraction order is required. A series of microbends are inserted in the middle of arrayed waveguides to increase the lightpath difference while keeping small separation between arrayed waveguides. A designed ultrasmall AWG with a narrow channel spacing of 0.8nm has a total size of only about 0.505mm×0.333mm (0.165mm2).
©2006 Optical Society of America
1. Introduction
In recent years, Si nanowire waveguides have become very attractive since the large difference between the refractive indices of the core (Si) and the cladding/insulator (air or SiO2) makes it possible to realize ultra-small photonic integrated devices [1–3]. An arrayed waveguide grating (AWG) (de)multiplexer, which can realize various functionalities, is one of the mot important components in a dense wavelength division multiplexing (DWDM) system [4]. It is very attractive to develop a Si-nanowire-waveguide-based AWG (de)multiplexer, which has an ultra-small size [5–7]. In some papers published earlier, the channel spacing Δλch is relatively large, e.g., Δλch=11nm in [5, 6]. Recently a compact wavelength router with a smaller channel spacing of 2nm has been presented [7]. When a high diffraction order m is desired in e.g. a dense AWG (de)multiplexer or wavelength router with a narrow channel spacing, a large path difference (several tens of microns) between two adjacent arrayed waveguides is required. In order to achieve the required large path difference, the separation between two adjacent arrayed waveguides will be much larger than the decoupling separation (~2µm) for Si nanowire waveguides when a standard layout is used (This can be seen clearly from the design shown in [7]). In this case, the size of an AWG is determined by the separation of arrayed waveguides instead of the bending radius. Therefore, a conventional design will not be suitable to minimize the size of an AWG based on Si nanowire waveguides.
In this paper we present a novel layout for a very compact AWG including arrayed waveguides with a series of microbends, which enable a large lightpath difference in a small occupied area (with a small separation), and consequently minimize the total size.
2. Layout
Our novel layout is shown in Fig. 1, where the two FPRs (free propagation regions) are overlapped and a series of microbends are inserted at the middle of arrayed waveguides.
For an AWG, a constant lightpath difference between two adjacent optical paths (instead of geometrical length) is required, i.e.
where Pl is the lightpath of the l-th arrayed waveguide, m is the diffraction order, λc is the central wavelength. It is well known that there is a difference between the effective indices of the straight and bending sections ([8]; also see Fig. 3 below). This is considered in our design since a very small bending radius (~5µm) is usually chosen for Si nanowire waveguides. The lightpath Pl is given as follows (see Fig. 1):
where n S, n B1, n B2 and n B3 are the effective indices in the straight and bending sections, R 3l, θ 3l, and Ql are the bending radius, the arc angle, and the total number of the microbends, respectively, S 1l, S 2l and S 3l are the lengths of straight waveguides, R 1l and R 2l are the curvature radii of the bending sections, θ 1l and θ 2l are the corresponding arc angles, θ 1l=π/2-αl (here αl is the radial angle), and θ 2l=π/2 (see Fig. 1). The radial angle αl is given by αl=α 0-lΔα, where α 0 is the radial angle for the shortest (l=0) arrayed waveguide, Δα=dg/L FPR (here d g is the end separation between two adjacent arrayed waveguides, L FPR is the FPR length). One can rewrite Eq. (2) as follows:
where η 1=n B1/n S, η 2=n B2/n S, η 3=n B3/n S. In this paper, we use a full-vectorial finite-difference method (FV-FDM) [8] to calculate the effective index n B of a bent Si nanowire and obtain a fitting function η=f(R) to give the relation between the ratio η(=n B/n S) and the radius R, which makes the design convenient especially when one chooses different bending radii for different arrayed waveguides. From Fig. 1, one also has the following relations:
where L io is the distance between the vertexes (O and O′) of two FPRs, Xl is the position for the second straight waveguide in x direction, Yl is the height of the third straight waveguide, ΔXl=Xl-Xl-1 and ΔYl=Yl-Yl -1. We choose ΔXl=ΔYl=Δxy and then obtain the following formulas
where
In order to avoid any geometrical cross between arrayed waveguides, we add a constraint that each period of microbend has the same stretch L MB(l) in the x direction, i.e., L MB(l)=4R 3lsinθ3l=L MB(l-1). Then one can obtain the geometrical parameters for the l-th arrayed waveguide from those for the (l-1)-th arrayed waveguide. From Eq. (3)–(6), we have the following relevant equations for the shortest arrayed waveguide (l=0), which will be used as the initial in the recursion.,
From the above equations, one sees that parameters (S 10, S 20, S 30, R 10, R 20, α 0, L FPR, R 30, θ 30, and Q 0) should be chosen first in a design, and the whole structure of the AWG is then determined accordingly. The initial value of the bending radii for the l-th arrayed waveguides are chosen (according to the allowable bending loss) with a constant R min, i.e., R 1l=R 2l=R 3l=R min. R 3l and θ 3l will be adjusted below in order to avoid negative value for S 3l. First, we preset Ql=Ql -1 for the calculation of S 1l, S 2l and S 3l. If S 3l>L MB(l), we let Ql=Ql -1+1 and recalculate all the parameters for the l-th arrayed waveguide. When S 3l<0, we adjust R 3l to a new value R′ 3l=(1+γ)R 3l (where γ is a small quantity), and consequently θ′ 3l=sin-1[L MB/(4R′ 3l)], η′ 3=f(R′ 3l). Generally speaking, the calculated bending radii R 3l will be different from R 30 for a few arrayed waveguides according to the chart flow of Fig. 2.
3. Design example
Here we give a design example to demonstrate the size minimization of an AWG with a small channel spacing (Δλch=0.8nm) when the present layout is used. We choose a 500nm×300nm Si nanowire waveguide with an air cladding. The refractive indices for the core and insulator layers are 3.455 and 1.460, respectively. The other parameters are given as follows: λc=1545.32nm, m=80, L FPR=50µm, dg=1.0µm, the total channel number N ch=8, and the total number of arrayed waveguides N WG=34. For this design, the free spectral range is about 19nm. We calculate the effective index n B of a bent Si nanowire by using a FV-FDM. Fig. 3 shows the ratio η(=n B/n S) for different core widths, which is fitted numerically with a power function of η=f(R)=1+0.0149R (-2.0011). From this figure, one sees that the change of η due to the variation of the core width is small and thus the performance of the AWG will not degrade much when the width of the fabricated microbends deviates slightly from the designed value.
We choose S 10=6µm, S 20=6µm, S 30=10µm, R 10=R 20=R 30=5µm, and α0=55.48° for the shortest waveguide. Since the diffraction order is large, we choose the arc-angle θ 30=80°. According to the flow chart shown in Fig. 2, the parameters for all the arrayed waveguides are obtained and shown in Fig. 4. From Fig. 4(a), one sees that the total period number (2Ql) of the microbends in the l-th arrayed waveguide does not increase linearly (they are obtained automatically from the algorithm shown in Fig. 2). Nevertheless, the lightpaths of the arrayed waveguides (each arrayed waveguide consists of many microbends and six straight waveguides) increase linearly [see Eq. (1)], as the basic principle of an AWG for (de)multiplexing. The calculated bending radius R 3l and arc-angle θ 3l are shown in Fig. 4(b), from which one sees that the bending radius and arc-angle for most microbends are the same as the initial value, i.e., R min=5µm and θ 3l=80°. Fig. 4(c) shows the distance Δxy (in x or y direction) between the arrayed waveguides. One sees the separation is smaller than 10µm and the smallest separation is larger than 4µm. This minimizes the total size and in the mean time makes the coupling negligible between arrayed waveguides.
Fig. 4. The parameters for different arrayed waveguides in the designed AWG. (a) total period number (2Ql) of the microbends; (b) bending radius R 3l and arc angle θ3l; (c) distance Δxy.
The designed AWG with the present layout is shown in Fig. 5(a). One sees that with the present novel design the device size is only about 0.165mm2. For this layout, the minimal distance Δxy is about 4.0µm [see Fig. 4(c)] and the corresponding minimal separation between arrayed waveguides is about 1.35µm, which is large enough for a negligible coupling between arrayed waveguides [3]. In order to check this, we use a FDTD to simulate the light propagation in the microbends of the arrayed waveguides [see Fig. 5(b)]. From this figure one sees that the coupling between arrayed waveguides is negligible and will introduce little phase error. In fact, the coupling is still very small even when the distance Δxy is reduced to 3µm.
Fig. 5. (a) The present AWG layout; (b) light propagation in the microbends simulated with a FDTD; (c) the calculated spectral response.
Fig. 5(c) shows the calculated spectral response (which does not include the coupling loss between the input/output waveguides and the fibers). In a sharply bending section the hybrid modes exhibit varying scattering losses for different initial polarizations and this introduces a polarization-dependent loss (PDL). In our cases, the calculated PDL is small (as the bending radius R=5µm is large enough) [3]. From Fig. 5(c), one sees that the calculated crosstalk is smaller than -30dB. The excess loss due to the inserted microbends in the arrayed waveguides is very small when the bending radius is large enough (e.g., 5µm in our design). Generally speaking, an AWG based on Si nanowire waveguides is highly polarization-sensitive [6] and consequently one should use some polarization-compensation method, e.g., optimize the height and width of the core [9] (this does not increase the total size of an AWG). Therefore, theoretically speaking, our design can give good performances while keeping the total size very small.
We also give a design of an AWG with the same parameters as the AWG presented in Ref. [7] for comparison. In this example, the diffraction order is very large (m=113) and thus the separation between two adjacent arrayed waveguides will be much larger than the decoupling separation when a conventional layout is used (e.g., the separation is about 30µm in Ref. [7]. Fig. 6 shows our designed AWG with the present layout and the size is about 0.2mm×0.144mm, which is smaller than half of the size of the AWG presented in Ref. [7]. For this layout, the minimal distance Δxy is about 6.5µm and the corresponding minimal separation between arrayed waveguides (see position P in Fig. 6) is about 1.4µm (the coupling between arrayed waveguides is negligible). From the above example, one sees that the proposed layout is preferred for a reduction of the total size, especially when the diffraction order is quite high.
4. Conclusion
In this paper, we have proposed a novel layout design for an ultra-small AWG demultiplexer based on Si nanowire waveguide especially when a high diffraction order is required. The arrayed waveguides with a series of microbends have been introduced to reduce the separation between arrayed waveguides, which minimizes the total size of the AWG. The difference between the effective indices of the straight and bending sections of waveguides has been considered. As an example, an ultrasmall AWG with a narrow channel spacing (Δλch=0.8nm) has been designed and the total size is only about 0.505mm×0.333mm=0.165mm2.
Acknowledgment
This project was supported by China Postdoctoral Science Foundation and research grants (No. 20044131095 and R104154) of the provincial government of Zhejiang Province of China.
References and links
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