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Tolerant , Broadband Tunable 2 × 2 Coupler Circuit

We designed and demonstrated a coupler circuit with tunability for arbitrary coupling ratio and being tolerant to process errors. We also demonstrate that the circuit can be tuned to a uniform coupling spectrum over a 50 nm spectral bandwidth.


I. INTRODUCTION
In programmable photonic circuits [1], one of the essential building blocks is a tunable optical 2 × 2 coupler, that can change its coupling ratio from 0% to 100%, and preferably over a wide wavelength range. This is essential for linear transformations, switch fabrics or bandpass filters. To implement a static 2 × 2 coupler, the directional coupler (DC) is one of the simplest coupling structures. However, a DC implemented in silicon is very sensitive to process variations, and therefore difficult to make with an exact coupling ratio. Also, DCs usually have a very dispersive spectral response and cannot be tuned over a wide range. A common way of implementing a tunable 2 × 2 coupler is a balanced Mach-Zehnder interferometer (MZI). The MZI is constructed from two static 50:50 couplers (e.g. DCs), connected with two delay lines with integrated phase shifters (e.g. heaters). The coupling response of the MZI can be swept from minimum to maximum by tuning the phase delay from 0 to π. However, to obtain the full 0-100% coupling range, the two static couplers need to have a perfect 50:50 splitting balance, which is not easy to design over a wide wavelength range. In [2], it is suggested to replace the two couplers each with a 2 × 2 MZI coupler that can be tuned to a 50:50 ratio as long as the balance of the DCs is better than 15:85. Indeed, such a three-stage MZI enables a full tuning range, but requires at least 3 phase shifters to configure. In this paper, we simplify this concept and show that we can achieve similar performance with a two-stage MZI, as shown in Fig. 1, in a similar was as presented in [3]. This eases the control and lowers the power consumption, as we only need two phase shifters. We also show that this circuit can be tuned for a uniform coupling over a wide bandwidth of 50 nm, making it easier to construct wavelength filters or route broadband light through a programmable circuit [4].
The design of the two-stage is depicted in Fig. 1a lines with phase shifters. In our fabricated device we incorporated phase shifters in all arms of the circuit, so we have 4 phase shifters, but in practice it is possible to use only two. We can adjust the transmission by tuning the phase shift in the two stages. Compared to the three-stage design, the tuning algorithm becomes simpler and covers only a two-dimensional space [∆ϕ 1 , ∆ϕ 2 ]. The device can be tuned from 0% to 100% as long as the three directional couplers have a balance that is better than 25:75. This makes the circuit tolerant to fabrication imperfections and even local variability, as it is not required that all three DCs perform identically.
We fabricated our design on the IMEC iSiPP50G silicon photonics platform. Due to an unfortunate design error, we used the wrong length of the directional coupler, which means that they have a coupling strength that is way below 25% at our target wavelength of 1550 nm. However, for longer wavelengths, we find that the coupling increases, up to 27% at 1610 nm. While this is at the edge of the measurement range, it allows us to validate the operational principle of this circuit: Fig 2a shows the simulated circuit transmission in the [∆ϕ 1 , ∆ϕ 2 ] control space assuming 27% coupling for the DCs. Fig. 2b shows the measured transmission when controlling the tuning power of the heaters, for a wavelength of 1610 nm. We noticed a very good agreement between simulation and measurement.

III. TUNING FOR BROADBAND OPERATION
The tunable coupler can be operated to achieve any coupling ratio for a single wavelength. However, the directional couplers are dispersive, so we can expect that the coupling response    proposed a single stage MZI that has a flat response over 50 nm range, but with a tuning range limited to 10-70%. Using the circuit in Fig.1, we can achieve broadband operation for any arbitrary coupling ratio. As our fabricated circuit is already on the edge of our measurement range, we currently can only validate this in simulation. We assume the circuit consists of imperfect DCs of 40:60 coupling ratio at 1550nm. In Fig. 3, we plot the power coupling η at 1550 nm (white contours), and overlay it with the maximum deviation ∆η within the wavelength range of 1525-1575 nm. For any given desired coupling value, we can tune the two phase shifters such that we obtain this coupling value within 3% over the entire wavelength range for an almost uniform response. Figure 4 shows the simulated cross power transmission for the best operating point for coupling values of 0%,10%,40%,70%,90% and 100%. The maximum dispersion of coupling power is 3% between 1525 nm and 1575 nm.

IV. CONCLUSION
We designed and demonstrated a simplified tunable coupler circuit with 0-100% coupling range even under conditions of fabrication variations. We also show that we can bias the circuit to obtain a flat spectral response over a wavelength range of 50 nm.