1. Introduction

Multimode Interference (MMI) couplers [1] are important building blocks for power splitting in Photonics Integrated circuits (PICs). Compared to typical synchronous directional couplers [2], they have smaller footprint, better tolerances to fabrication errors and significantly wider operation bandwidth. In terms of bandwidth they are outperformed only by adiabatic couplers [3], which, anyway, are typically much longer. Two additional advantages of MMIs are that their fabrication doesn’t require expensive high resolution tools and that they can be accurately designed also based on analytic models [1]. On the other hand, the main drawback of adopting 2 x 2 MMIs as generic devices for power splitting is that they cannot in general achieve any wanted splitting ratio (here defined as the ratio between the bar power and the cross power) but just 5 discrete non-trivial values, namely 15/85, 28/72, 50/50, 72/28 and 85/15 [4,5]. Many different approaches have been proposed and demonstrated to overcome this significant limitation [5–10]. Electro-optic effects can be exploited to achieve tunable slitting ratios in suitable materials [5], but completely passive approaches are preferable when a given fixed splitting-ratio is wanted. Passive approaches are based on inducing a certain phase shift in the MMI section for example with suitably designed tilts [6], or suitably designed butterfly shapes [7], cuts [8] or holograms [9]. A somewhat different approach is based on cascading two MMIs connected by two waveguides of same length and different width [10]. This idea has been originally proposed and simulated for many different types of MMIs. However, the use of just two identical 50/50 splitters is definitely enough to achieve any wanted splitting ratio through a Mach-Zehnder Interferometer (MZI) configuration. The main drawback of this solution is that the connecting waveguides have different widths compared to the input/output waveguides, inducing significant extra-loss. In this paper we propose a simple solution to this limitation and, for the first time, we demonstrate experimentally this MZI approach to work. We also study in details the tolerance of the proposed solution to fabrication errors as well as its wavelength dependence.

2. The proposed solution

The proposed structure is shown in Fig. 1(a). Instead of using connections of constant width, we gradually change their widths by the same amount but in opposite directions. This keeps constant the gap between the two branches, helping the optimization of the fabrication process. Compared to the solution proposed in [10], using our approach allows a smooth low-loss transition from the field image size in the MMI, which clearly matches the Input/Output (I/O) waveguide width, to the narrowed/enlarged waveguide. The taper function can be chosen freely. It can be for example linear, like in Fig. 1(a), or sinusoidal, like in the simulated structure Fig. 1(c). In all the presented simulations and experiments we have used a sine taper function. Our simulations assume through-etched strip waveguides and MMIs in 4 µm thick Silicon on Insulator (SOI) wafers. A cross section of a typical waveguide is shown in Fig. 1(b). Simulations were done using the commercial software FIMMPROP, which is based on fully vectorial local mode expansion. We found the 2D simulations based on the effective index method to perfectly match the 3D simulations when set to have the same number of modes (for the 3D case we counted only the modes with a single lobe in the vertical direction). Results reported in this paper are all based on 2D simulations, because they have the advantage to allow for a much higher number of modes with minor computational effort, so carefully modeling also possible back reflections in non-ideal working conditions. As 50/50 splitter we have chosen 2x2 MMIs based on general interference, both because of their smaller size and higher tolerance to fabrication errors. The MMI width is 5 µm, the I/O waveguide width is 1.875 µm and the gap between the waveguides is 1.25 µm in order to enable safe lithographic resolution in our UV fabrication process (which includes also 225 nm consumption of silicon after thermal oxidation). The optimal MMI length at 1.55 µm wavelength has been simulated to be 112 µm. Hence, the total length of the device in Fig. 1 is 259.5 μm. All reported results assume TE polarization and 1.55 µm wavelength, unless otherwise stated. In fact, the polarization dependence of the designed MMIs is quite significant, resulting in more than 80 nm wavelength shift of the optimal working point. Bigger MMIs can be used to relax polarization issues. For example 14 µm wide MMIs would result in less than 20 nm wavelength shift, i.e. 10% of the bandwidth at 1 dB of the MMI.

 

Fig. 1 (a) Top view of the proposed MZI configuration to get any wanted splitting ratios. The two connecting waveguides are tapered by the same amount but with opposite sign. (b) Cross section of a micron-scale SOI strip waveguide. (c) Simulated intensity pattern of a 70/30 splitter based on a 35.5 µm long sinusoidal taper. The width change is 500 nm. Light is launched in port 1. (d) Same as previous, when light is launched in port 2. Percentages indicate the relative output powers coupled to the fundamental modes of the output waveguides.

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There are many advantages in using through etched waveguides instead of rib waveguides. First of all, the very high lateral index contrast makes the exponential tail in the cladding become negligible and the MMI response almost ideal. Furthermore I/O waveguides can be put close to each other without significant coupling between them, and the phase shifting waveguides can be tapered in a short distance without significant extra loss. All reported results correspond to a waveguide width change of Δw = 500 nm; the top waveguide is enlarged by Δw while the bottom waveguide is narrowed by the same amount. Figure 1(c) and 1(d) show the simulated intensity pattern in a 70/30 configuration, based on a 35.5 µm long phase shifter, when the input is in port 1 and 2 respectively. The noise in the output images comes from excitation of higher order modes, accounting for the missing 2.6% power (0.11 dB loss) in the first case and 1.6% (0.07 dB loss) in the second case. The advantages of the proposed phase shifter are that it is collinear (unlike those using bends or tilts [6] that change the propagation direction), compact, and can ensure 0th order phase shifts, i.e. with phasechange φ + 2kπ and k = 0, which corresponds to both minimum length and minimum wavelength dependence. Furthermore, its design is simple. Once a given value of Δw is chosen, different phase shifts φ are achieved by simply changing the length of the phase shifter. In fact φ scales linearly with the taper length L, as can be clearly seen from the sine like response of the simulations in Fig. 2(a).The same figure shows a slightly different bar response between the two ports of the device. Instead the two cross responses match perfectly. This is better highlighted by the simulated overall loss Fig. 2(b), showing different loss depending on the chosen input port, with differences as high as 0.1 dB. The port in line with the narrower arm of the phase shifter (conventionally port 1) performs better for $\text{π}<\varphi <2\text{π}$, whereas port 2 ensures lower losses for $\text{0}<\varphi <\text{π}$. We believe this behavior to be related with the different image formation in the second MMI, clearly visible when comparing Fig. 1(c) and 1(d). We have observed that lower losses always correspond, in the second MMI, to patterns with zero intensity in the middle axis along the propagation direction. The high frequency ripples in Fig. 2(b) come from back-reflections, and it takes a sufficiently high number (>30) of modes to find them in simulations. For the chosen value of Δw = 500 nm, phase shifters shorter than 10 µm result in higher losses, due to the non-adiabatic tapering of the waveguides, leading to significant coupling to higher order modes. We point out that we chose a relatively high Δw value, because we are aiming at the design of power splitters for ring resonators, i.e. having most of the power in the bar output port ($\text{π/2}<\varphi <\text{π}$). For different applications, like tap couplers, smaller values of Δw can be chosen, in order to ensure adiabatic transitions and low loss also in the range $\text{0}<\varphi <\text{π/2}$. In Fig. 3(a) we show the simulated relative phase between the outputs of the phase shifter alone, showing perfect linear behavior. Figure 3(b) is the relative output phase of the whole splitter, showing the standard behavior of MZIs, with abrupt π-jumps whenever the phase shifter equals an integer number of π-shifts, that can be easily understood in term of a suitable geometric representation of the operation of a MZI [11].

 

Fig. 2 (a) Simulated power splitting in the output fundamental modes vs phase shifter length L. Cross response T12 and T21 coincide perfectly, whereas the two bar responses T11 and T22 are slightly shifted. This is better seen in (b), showing the simulated total power in the fundamental modes of the output waveguides.

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Fig. 3 Simulated phase difference between port 2 and port 1 vs. phase shifter length, (a) in the phase shifter alone and (b) when the light is coupled in input port 1of the whole double-MMI splitter. The splitter is the same as in Fig. 2.

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3. Experimental results

We have fabricated the designed structures on 4 µm thick SOI wafers based on the well assessed VTT silicon waveguide technology. The devices were fabricated using smart-cut silicon-on-insulator wafers from SOITEC. Initial SOI layer thickness was increased with epitaxial silicon growth. FilmTek 4000 spectrophotometer was used to measure the thicknesses of the SOI layer (4.20 ± 0.04 µm) and the underlying buried oxide (2.998 ± 0.002 µm). A 0.5 µm thick Tetraethyl orthosilicate (TEOS) layer was deposited on the wafer in LPCVD diffusion furnace to work as a hard mask in silicon etching. Waveguide fabrication was done using our standard double-masking multi-step process [12]. In the process, two mask layers are passively aligned with respect to each other, and two separate silicon etch-steps form the rib and strip waveguide structures and waveguide facets. Lithography steps were done using FPA-2500i3 i-line wafer stepper from Canon Inc. and pattern transfer to oxide hard mask was done using LAM 4520 reactive ion etcher with CF4 and CHF3 chemistry. Waveguides were etched into silicon using Aviza ICP etcher from SPTS Technologies. The etching was done with a modified Bosch process [13] using SF6 and C4F8 as etch and passivation gases, respectively, and O2 as an etch gas to break passivation polymer formed by C4F8. After silicon etching, TEOS hard mask was removed with buffered oxide etch (BOE). Hard mask removal was followed by wet thermal oxidation consuming 225 nm of silicon, and thermal oxide removal with BOE. This was done to smoothen the etched surfaces, and to thin the SOI-layer to its final thickness of approximately 4 µm. A 0.17 µm thick silicon nitride layer was then deposited on the wafer with LPCVD as an antireflection coating and to prevent the etching of buried oxide in later oxide wet etch process steps. This layer was patterned in hot phosphoric acid using a hard mask made of 0.25 µm thick LPCVD TEOS patterned with BOE. Another 0.5 µm thick LPCVD TEOS layer was then deposited to form a cladding oxide, and locally removed from waveguide facets with BOE before dicing the wafer into chips.

We adopted a sinusoidal taper shape and we varied the phase shifter length from 28 µm to 46 µm in steps of 2 µm. The experimental characterization of the fabricated splitters at 1.55 µm wavelength is shown in Fig. 4.Transmission at 1.55 µm wavelength were measured with a Fabry-Perot laser (HP 81554SM) coupled into waveguides through a polarization-maintaining fibre and a polarization controller. All measurements correspond to TE polarization. The transmitted light from the output waveguide was coupled into an optical power meter via single-mode fibre. The use of both single-mode fibres and on chip input/output single-mode rib waveguides ensured suppression of any power fraction coupled to the higher order modes of the strip waveguides. The reported transmission values are normalized with respect to the losses of a single mode rib waveguide. Bars in Fig. 4(a) and 4(b) are the experimental results when light is coupled to the first port and to second port respectively. Both plots show the capability of the designed splitter to achieve arbitrary splitting ratios. The solid lines in Figs. 4(a) and 4(b) are the results of 2D propagation simulations. In order to best fit the experimental data we assumed a systematic width error in the fabricated waveguides as a degree of freedom. The reported curves correspond towaveguides that are 40 nm narrower than the designed ones. In fact, in the next section it will be clearly shown that a drawback of the proposed solution is its sensitivity to width errors. As a final remark, when comparing the simulated curves with the experimental data, it should be taken into account that the experimental losses are expected to exceed the simulated ones. In fact the best way to fit the data is rather to focus on the power imbalance, that is the splitting ratio in dB scale. A comparison between experimental and simulated imbalance is shown in Fig. 5, highlighting their remarkable match. For the sake of clarity we also show the normalized power percentage in both outputs of the double-MMI splitters. Figures 5(c) and 5(d) show the total losses when the power is launched in port 1 and port 2 respectively. The found overall losses ranged between 0.2 dB and 0.6 dB with an average of about 0.4 dB, that is in the same order of magnitude as the 0.5 dB uncertainty of our measurements. Accurate estimation of the splitter losses is beyond the scope of this work, and it would require cascades of a significant number of identical couplers.

 

Fig. 4 (a) Transmitted power from input port 1 to output ports 1 and 2. The solid lines are the simulated fit corresponding to 40 nm narrower waveguides, and the experimental data are shown with ± 0.5 dB error bars. (b) Same as (a) when light is launched in port 2. (c) Optical microscope image of a fabricated double-MMI splitter.

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Fig. 5 (a) Comparison of simulated and experimental power imbalances. The red solid line and the black dashed line are the simulations when the input is port 1 and port 2 respectively. The experimental data are shown with ± 1 dB error bars. (b) Simulated (solid lines) and experimental (crosses and circles) normalized power percentage in the two outputs of the splitters. (c) and (d) Measured total loss with ± 0.5 dB error bars.

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4. Tolerance analysis

We have already mentioned that, in order to fit the experimental data with numerical simulations, we had to assume that fabricated waveguides are 40 nm narrower than targeted. Indeed, in our process we expect width variations in the order of tens of nanometers both across a single wafer and from wafer to wafer, although we presently miss a proper tool to precisely measure such small width variations on micron-scale waveguides. Unfortunately these variations turn out to be the weak point of our solution. In Fig. 6(a) we simulated how uniform and systematic width changes affect the phase shifter length L_π required to get a π shift, i.e. complete bar coupling. The simulation clearly shows that if for example the designedphase shifter has 100 nm narrower waveguides, then L_π becomes about 10 µm shorter, i.e. 18% shorter. Figure 6(b) shows the shift between the nominal design and the assumed fabricated device. Highlighted is the impact of 40 nm narrowing the waveguide width on a splitter as in Fig. 1(d): the bar transmission changes from 69.4% to 75.4%.

 

Fig. 6 (a) Simulated impact of systematic uniform waveguide narrowing on the length of the phase shifter corresponding to π phase shift. (b) Simulated impact of 40 nm waveguide width change on the transmission in the bar port. Highlighted is the impact on the splitter of Fig. 1(d).

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It is also important to analyze the wavelength response of the proposed double-MMI splitters. The single MMIs have a 1 dB bandwidth of about 200 nm. We collected in the top rows of Fig. 7 and Fig. 8 the simulated spectral response of two different double-MMI splitters with 32 µm long and 46 µm long phase shifter respectively, corresponding to about 3 dB power imbalance (i.e. 67/33 splitting ratio) and about 14 dB power imbalance (96/4 splitting ratio). In the first case the bandwidth at 1 dB is about 124 nm (highlighted in red in Fig. 7(c)).

 

Fig. 7 Simulated wavelength response (top row) of a splitter with 32 µm long phase shifter and corresponding experimental results (bottom row). (a) and (d) are the spectral response of all ports, (b) and (e) the power imbalance vs. wavelength, and (c) and (f) the overall losses in the fundamental mode over the considered spectral range.

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Fig. 8 Simulated wavelength response (top row) of a splitter with 46 µm long phase shifter and corresponding experimental results (bottom row). (a) and (d) are the spectral response of all ports, (b) and (e) the power imbalance vs. wavelength, and (c) and (f) the overall losses in the fundamental mode over the considered spectral range.

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Within this band the power imbalance ranges from 2.5 dB to 4.3 dB. Instead in the 135 nm wide band of the second splitter the power imbalance goes from 11.2 dB to 16.0 dB.

The bar port responses of the two splitters are comparably flat, whereas the cross port response of the second splitter is more sensitive to wavelength changes, affecting also the power imbalance. The bottom rows of Fig. 7 and Fig. 8 are the corresponding experimental results. In the spectral measurements, an HP 83437A was used as a broadband light source. Output spectrum with range from 1450 nm to 1650 nm was measured with an optical spectrum analyser (ANDO AQ-6315A). The reported transmission values are normalized with respect to the losses of a single mode rib waveguide. The found experimental results match well the simulations, except for the significantly higher wavelength dependence of the power imbalance. However this is significantly affected by the experimental uncertainties, including the non-negligible experimental spectral oscillations of up to 0.3 dB amplitude. These oscillations have in both cases a free spectral range (FSR) of about 12 nm. In silicon this would correspond to a cavity of about 30 µm length. We have found oscillations with the same FSR not only in all the 10 tested phase shifter lengths, but also in the reference straight waveguides. Hence, they cannot originate from the devices, but rather from some spurious reflections in the experimental setup. The noise at longer wavelengths comes from the low power of the broadband source in that spectral range.

5. Conclusion

We have introduced a novel power splitter that can be simply designed to get unconstrained splitting ratios. Compared to previous solutions, the proposed double-MMI splitters have the advantage of being simple to design and to fabricate with low cost fabrication tools. They are also relatively compact in size, with a footprint not exceeding 5 µm × 300 µm. The characterization of the fabricated devices is in very good agreement with the simulations, provided that 40 nm narrower waveguides are assumed in the fabricated phase shifter. The simulations highlighted some significant (up to 0.1 dB) asymmetry between the two input ports of the splitters, which were too small to be detected in the measurements ( ± 0.5 dB accuracy). For the same reason it was not possible to give an accurate estimation of the overall losses. However, at the central wavelength of 1.55 µm, they were simulated to be lower than 0.12 dB and found to be in the range 0.4 ± 0.5 dB in experiments. A possible limitation of the proposed splitters has been found to be its sensitivity to waveguide width errors. A possible solution is to use wider waveguides and/or smaller values of Δw (waveguide width change). We also highlighted in-band variations of the power imbalance in the order of ± 1 dB for lower imbalance values, and reaching up to about ± 2 dB for higher imbalance values (in agreement with the slope of Fig. 5(a)). The experimental results clearly prove the ability to continuously change the splitting ratio by simply changing the phase shifter length. The demonstrated solution adds a key functionality to MMI splitters, and in a practical way. It can be effectively exploited for example as coupler for ring resonators, as waveguide tap, or to design complex interferometric filters requiring unconstrained splitting ratios [14].