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A novel wavelength combiner using non-uniform refractive index distribution within a multimode interference device is proposed and simulated. The refractive index step creates separate localized modes with different effective refractive indices and two modes are strongly excited which form the basis of an interferometer. We applied the concept to 1.30/1.31 μm and 1.31/1.55 μm wavelength combiners on an InP substrate. The lengths of the devices are 1272 μm and 484 μm with simulated insertion losses of 0.6 dB and 0.67 dB respectively.
© 2014 Optical Society of America
1. Introduction
Wavelength combiners are essential components for wavelength division multiplexing (WDM) optical communications systems. There has been interest in InP-based photonic integrated circuits where multiple lasers, modulators and beam combiners can be monolithically integrated on a single chip for WDM optical communications systems. It is therefore desirable to design wavelength combiners on InP substrates.
Several device concepts have been utilized to realize wavelength combiners such as arrayed waveguide devices (AWG) [1], Y branch devices [2], Mach-Zehnder interferometer (MZI) devices [3, 4] and multimode interference (MMI) devices [5] to name a few important ones.
For general power splitters or combiners, MMI devices are particularly attractive as they offer several advantages such as robust fabrication tolerances, ease of fabrication, compact size and low excess loss. However, MMI-based wavelength combiners which are based on the theory of self-imaging will lead to very long devices especially when combining wavelengths which are 10 nm apart due to the fact that the device length needs to equal several odd and even multiples of the beat lengths for both wavelengths. The conventional theory of MMI devices requires that for an MMI device to split two wavelengths λ1 and λ2, the length of the device L must satisfy the condition [5],
where Lπ(λ) is the wavelength-dependent beat length [5] and M is a positive integer. The beat length for an MMI device of width W can be approximated by Lπ = 4neffW2/3λ. For 10 nm wavelength spacing one can see that with W = 6μm, L would be over 10 mm long. Although novel MMI-based wavelength combiners have been proposed for InGaAsP/InP and silicon-on-insulator (SOI), they have typically targeted very large wavelength spacings of 240 nm such as 1.31/1.55 μm where it is much easier to design shorter devices [6, 7, 8].Recently, we proposed to use up to sixteen pieces of relatively small patches of different refractive index within MMI, and used a computer optimization algorithm to design efficient two beam and four beam wavelength combiners [9]. One important finding of the paper was that computer algorithms can optimize the device structure with tens of parameters with good performance. By closely looking at the beam propagation patterns of the two beam combiner, it was deduced that the collective refractive index pattern acted as an interferometer. So the next logical step would be to build an interferometric wavelength combiner using a few very long enough refractive index steps. In this paper, we propose a novel MMI device concept in which non-uniform refractive index forms two distinct modes and its middle section acts as an interferometer. Unlike typical MZI-based wavelength combiners, this device does not rely on the length difference of two arms, so it can be made as a straight and narrow device. This may be an important feature for many applications. In order to demonstrate that the concept works for a wide range of wavelengths, we designed two types of wavelength combiners, one for 1.30/1.31 μm and another for 1.31/1.55 μm. Although the results presented in this paper are for specific wavelength spacings of 10 nm and 240 nm, combiners for other wavelength spacings can be readily designed using our proposed device concept. Although all our simulation results are based on a wavelength combiner it is straightforward to extend them to act as wavelength splitters with slightly different optimization criteria such as maximizing the extinction ratio.
2. Principle and design
The top view of the proposed device is shown in Fig. 1(a), where the lighter green part shows the lower refractive index region, and the rest constitute the higher refractive index regions.
The functional diagram of the proposed device is depicted in Fig. 1(b) and it can be divided into three sections. The 2 × 2 coupler (leftmost section) splits the input field into two and excites the two main modes in the unbalanced interferometer section whose detail will be explained later. The outputs of the unbalanced interferometer are combined into the output port by a 2 × 1 coupler. The taper sections smoothly guide the modes with different waveguide heights.
The cross-sectional view of the interferometer section is shown in Fig. 2. An In1−xGaxAs1−yPy (y = 0.4) core layer sandwiched between an InP substrate and InP cladding layer. The core layer is etched by a small constant thickness Tg at a pre-determined rectangular plus taper shape creating a groove. In order to precisely control Tg, it is possible to insert a thin etch-stop layer which has different In1−xGaxAs1−yPy composition, such as InP. The groove is then filled with an InP regrown layer. This creates nearly-localized propagation modes with distinct effective refractive indices in the MMI, unlike conventional uniform MMIs. Figures 3(a) and 3(b) show the lowest TE mode and the third lowest TE mode respectively, when the total MMI width is W = 6.0 μm, the patch width is W1 = 3.6 μm, core layer thickness is Tcore = 0.5 μm, and groove thickness is Tg = 0.2 μm. The effective high and low refractive indices are 3.3001 and 3.2671 respectively at 1.30 μm and 3.29554 and 3.26303 at 1.31 μm.
In order for the combiner to have maximum efficiency, the following relationship needs to hold,
where Δβ1 and Δβ2 are the differences in the propagation constant of the two modes at λ1 and λ2 respectively, and L0 is the length of the interferometer section. In our case of 10 nm wavelength difference, L0 becomes 893 μm.Since the interferometer is not symmetric in terms of mode positions, instead of using symmetric 2 × 2 and 2 × 1 couplers, we use an optimization algorithm to design the asymmetric 2 × 2 and 2 × 1 couplers. Multiple parameters were optimized to maximize the output power when λ1 was injected into input port 1 and the output power when λ2 was injected into input port 2 [9]. For the optimization algorithm, we used a covariance matrix adaptation evolutionary strategy (CMA-ES) [9, 10]. We optimized widths and offsets of input/output waveguides and the lengths of the 2 × 2 coupler, unbalanced interferometer, 2 × 1 coupler and taper sections simultaneously. Considering the fabrication repeatability, the width of the tip of the taper is set to 0.2 μm. In the following two sections, we present simulation results for a 1.30/1.31 μm and 1.31/1.55 μm wavelength combiner.
3. Simulation results − 1.30/1.31 μm wavelength combiner
The proposed device is simulated using the commercial software FIMMWAVE [11] which uses the eigenmode expansion method to solve the propagation problem. A 3-dimensional finite difference mode solver has been employed as a mode solver in all sections. The optimized lengths of the four sections were found to be L1 = 197.9 μm, L2 = 849.1 μm, L3 = 44.9 μm, and Lt = 89.9 μm. The optimized waveguide widths are Wport = 2.8 μm. The offsets for the input and output ports are Oin = 0.50 μm, Oout1 = 1.50 μm and Oout2 = 1.63 μm.
Figures 4(a) and 4(b) show propagation patterns for 1.30 μm input to port 1, and 1.31 μm input to port 2, respectively. In the interferometer section, two beams are confined into each section. However, since the two modes as shown in Figs. 3(a) and 3(b) are not totally spatially separated, there are interference patterns as can be seen in the interferometer section. The wavelength-dependent transmission for this device is shown in Fig. 5. Since this device was optimized at 1.30 μm and 1.31 μm, the transmittance (ratio of the output power to the input power) is as high as 0.870 (0.6 dB loss).
Fig. 4: Propagation patterns for a 1.30/1.31 μm wavelength combiner. The total MMI length is 1271.7 μm
We also optimized a device without taper sections. In this case, the transmittance was 0.798, which was 7.2% lower than the case with taper sections. Therefore, taper sections play an important role in guiding beams smoothly between sections with different vertical confinement. Also, the optimized interferometer length was 873.0 μm, which is close to the optimum length L0 = 893 μm calculated from Eq. (2). Note that L2 = 849.1 μm when taper sections are used. So the difference between 873.0 μm and 849.1 μm shows the effective length of taper section as part of an interferometer. To the best of our knowledge, no attempt has been made at using MMI-based devices for targeting such a small wavelength spacing to date. The high transmittance achieved using our proposed device concept is promising.
A common device for wavelength splitters or combiners is an AWG. For an InP-based AWG, Barbarin et al. [1] reported very small size of 230 μm × 330 μm. On the other hand, our 1.30/1.31 μm wavelength combiner has a size of 6 μm × 1272 μm. For photonic integrations circuit applications, there may be situations where latter is more favorable than the other.
4. Simulation results − 1.31/1.55 μm wavelength combiner
Another important application of wavelength combiner is for the 1.31 μm/1.55 μm wavelength spacing. For this application, we re-optimized the device parameters. In this case, MMI width is W = 8.0 μm, patch width is W1 = 4.5 μm, input and output waveguide widths of Wport = 3.0 μm were used. We then optimized section lengths and found L1 = 253.5 μm, L2 = 11.7 μm, L3 = 52.9μm, and Lt = 83.1 μm. The offsets for the input and output ports are Oin = 1.46 μm, Oout1 = 1.16 μm and Oout2 = 2.58 μm. The total MMI length is 484.3μm.
Figures 6(a) and 6(b) show propagation patterns for 1.31 μm input to port 1, and 1.55 μm input to port 2, respectively. These show the effective combining effect clearly. Note that lower refractive index part is on the lower side of the arm.
Fig. 6: Propagation patterns for a 1.31/1.55 μm wavelength combiner. The total MMI length is 484.3μm.
The wavelength-dependent transmission for this device is shown in Fig. 7. This device was optimized at 1.31 μm and 1.55 μm and the peak transmittance is as high as 0.856 (0.67 dB loss) which is comparable to the 0.87 transmittance acheived for the 10 nm wavelength spacing. This illustrates the suitability of our device concept for a wide range of wavelength spacings.
In order to evaluate the tolerance to fabrication error, we first changed the groove thickness Tg. Its nominal value is 0.20 μm and is changed by ±0.01μm which is 5% deviation from the nominal value. As discussed in Section 2, this can be achieved if we use etch-top layer and selective etching, for example. Figure 8(a) shows that the peak wavelength and height are slightly affected. We then calculated the transmittance as a function of wavelength when the groove width W1 was changed by ±0.05μm which can be achieved by the current state-of-theart lithography and etching technologies. The result is shown in Fig. 8(b), and the device still performs satisfactorily as a 1.31/1.55 μm wavelength combiner. Device optimization technique by taking the fabrication error into account has been discussed in [9], and if we had used this scheme for this device, the device would have been better optimized taking into account such fabrication errors.
The proposed device concept has thus been shown to perform satisfactorily against variations in its groove thickness and width as can be observed by observing the transmittances for varying groove thickness and width in Fig. 8(a) and Fig. 8(b) respectively.
A previous attempt at using InP-based 1.31/1.55 μm MMI wavelength splitters and combiners had device lengths longer than 960 μm and simulated insertion loss of about 1.4 dB (worst of the two wavelengths) was obtained [6]. So, our proposed device is a factor of two improvement in terms of device length and our device has nearly identical insertion loss for both wavelengths unlike the device in [6] where there was a large difference of about 0.8 dB in the insertion losses between the two wavelengths. An alternative approach for a 1.31/1.55 μm splitter or a combiner is a cascaded Mach-Zehnder Interferometer made of silica waveguides [12]. This demonstrates excellent performance with fiber-to-fiber insertion loss less than 1dB and crosstalk of −50dB. However, the device size is 60 mm × 0.6 mm.
5. Discussions
With λ = 1.30 μm input to port 1, the relative power (with input power as 1.0) of the lowest TE mode (the lower arm in Fig. 4(a)) is 0.6171, while that of the third lowest TE mode (the lower arm in Fig. 4(b)) is 0.3125. The other modes have a few percent or less. Therefore, these two modes form the basis for the interferometer. Note that our device was optimized such that the transmittance for λ = 1.30 μm input to port 1 and λ = 1.31 μm input to port 2 are maximized simultaneously. If we designed the device as a wavelength splitter, where transmittances for λ = 1.30 μm input to port 2 and λ = 1.31 μm input to port 1 are minimized (in reality the device is used in the reverse direction), we would have different device parameters, and more balanced power for the two MMI modes will be obtained. The maximum transmittance in the current design is limited to 0.87. This can be partly explained by observing that the mode shown in 3(b) has a small distribution in the right hand side, and it is not completely spatially separated from lowest TE mode. Hence the interferometer suffers a small loss.
Conventional AWGs or MZIs need to create large path difference (tens of microns, depending on the wavelength separation), so the device size (area) is typically larger than several hundred square microns. One difference of the proposed MMI-based wavelength combiners over AWGs or MZIs is that they are narrow and straight devices (W < 10 μm) which can be placed next to each other and will be beneficial when many similar devices need to be integrated on a single chip.
Even though we have focused on the InP material system in this paper, the device concept could readily be extended to other material systems such as SOI by adjusting the effective refractive index within an MMI. The concept of nonuniform refractive index distribution can potentially be extended to N × 1(N > 2) combiner or splitter. For that, one would need to create a structure with modes having multiple (> 2) effective refractive indices by the combination of different core layer thickness and width of the waveguides.
6. Conclusion
A novel device concept for designing compact MMI-based wavelength combiners has been proposed. A refractive index step in the cross-section of the MMI creates two distinct modes, which can be used for an unbalanced interferometer. Wavelength combiners were designed with 1.30/1.31 μm and 1.31/1.55 μm wavelength spacings as examples. Simulations show that the devices have insertion losses in the range of 0.6 − 0.67 dB. These devices are significantly shorter than conventional MMI-based wavelength combiners. Since their width is much smaller than conventional AWGs and MZIs, they may have a potential for high density integration on a chip.
References and links
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