1. Introduction
Reconfigured and programmable photonic integrated circuits (PICs) are dedicated to discovering the general on-chip hardware configurations for versatile functions by customized programs [
1,
2]. Their network architectures are commonly formed by the cascaded Mach–Zehnder interferometers (MZIs), directional couplers (DCs), and micro ring resonators (MRRs), which can be programmed in real time through a series of optical phase shifters applied on the single-mode waveguide arms. Their cascaded mesh connectivity can determine the path of light routing, define the transmission matrix, and perform spectral filtering operations.
On the single-mode waveguide arms, the change of refractive index is translated to the optical phase change only. The cascaded systems can be well-represented by a set of analytical equations or a linear transfer matrix, and the required settings to reach the target output can then be readily calculated. However, there remain two problems. For one, the cascaded structure requires a large number of independent tuning units, which may pose a challenge for electronic wiring during integration and assembly [
3,
4]. Secondly, the phase tuning on a single-mode waveguide cannot efficiently introduce variable attenuation of light amplitude. In fact, the MZI and DC-based solutions all work under the theoretically lossless condition [
5], apart from the insertion loss in practice, i.e., if the power of one output is tuned down, the sum of the output power from the remaining ports is bound to go up.
To illustrate the second problem, let us consider the integrated power splitters, a fundamental PIC component that divides the input optical power into multiple streams. They can be realized by Y-branch structures [
6], directional couplers (DC) [
7], and QR code-like nanostructure [
8]. However, they often perform a fixed splitting ratio, as shown in
Figure 1a. The tunable power splitters can be realized by the cascaded MZI-based device [
9], as shown in
Figure 1b. By precisely tuning each phase shifter, the input light can be divided into arbitrary splitting ratios at the outputs. Note that in
Figure 1b, the phase tuning does not affect the overall power passing through the device. To implement extra attenuation, each output port needs to connect to a variable optical attenuator (VOA) [
10,
11]. The extra VOAs require more independent tuning elements plus methods to suppress the crosstalk among them, thereby increasing the device footprint and cost.
Multimode interference (MMI) devices have been long implemented as compact power splitters [
12]. However, most MMIs are used as fixed power splitters, e.g., the 3 dB coupler in a MZI network [
13]. Recently, thermally tunable MMIs have been demonstrated as programmable multi-functional PICs [
14,
15,
16]. For example, switching networks of large port counts can be realized with a minimal number of control units in a compact, non-cascaded structure [
14]. As shown in
Figure 1c, such device consists of only one multimode waveguide with a set of parallel microheater electrodes and input/output access waveguides. However, so far, only the “digital” switching function is achieved [
14]. Light can only go from zero to its respective maximum at a given logic output and cannot be tuned freely at any value in between.
The problem lies in the complexity of index tuning in the multimode waveguide. Unlike in the single-mode system, where only the optical phase changes, the tuned local refractive index in a multimode waveguide can simultaneously influence the multiple guided modes, including their total number, field profiles, and propagation constants, all of which can alter the multimode interference patterns as well as the coupling efficiencies to the output waveguides. Thus, under the multimode regime, the outputs cannot be calculated using simple, analytical equations. One can rely on numerical simulations to find the solution, e.g., translating the thermal power to the temperature gradient and further to index profile, obtaining the parameters for each supported mode, adding their respective phase delay over a propagation distance, and finally, calculating the combine optical fields at the output ports. However, such simulation would take a long time, and a substantial number of iterations are needed to sweep the parameters for a reasonably optimal output. This “forward” design method based on simulations is extremely time-consuming. As a result, only a small number of “digital” switching functions were demonstrated in [
14].
On the other hand, we believe that local index tuning on a multimode waveguide is a powerful tool, as it can simultaneously alter several factors of a light wave, steer the light interference in the confined space, and in turn dramatically change the amount of light flow at the output ports. Programmable photonic devices can be built with simpler structures, fewer microheaters, and more compact footprints. Therefore, we established a platform called function programmable waveguide engine (FPWE), on which we can apply a set of thermal powers to a MMI and obtain the optical readout directly from experiment without running tedious simulations, i.e., the FPWE itself works as a practical simulator [
15,
16]. Though similar engines can be built on other material platforms, such as the silicon multimode waveguide with embedded phase change material [
17,
18], the polymer platform is attractive, as the fabrication process is simple and low-cost, the integration technology with other materials/components is flexible [
19,
20], and multi-layer waveguide structures can be integrated [
20,
21], all of which can be well-managed within one small-sized laboratory.
In this work, we explored the FPWE system further and developed a truly flexible light flow controller beyond digital switching and with integrated VOA function. Some preliminary simulations were needed to confirm the size of the multimode waveguide and the microheaters under the constraints of the fabrication technology. The MMI-based chip was directly measured and defined in experiment. Understanding the complex nature of multimode tuning, an “online” search program was developed to drive the chip and collect the feedback like “instant messaging” between input and output. The results of each iteration were instantly analyzed to guide the setting of the next driver update. A levelled searching algorithm was implemented to jump over traps of local optima. We stress that the tuning element/electrodes on the multimode waveguide work collectively, i.e., they do not need to be isolated. The unwanted tuning crosstalk in the single-mode case is in fact a powerful tool in the multimode waveguide. Live light flow switching is demonstrated under various lossless and lossy targets (see
Supplementary Video S1). We hope this work may trigger interesting applications of multimode waveguide devices for advanced photonic applications.
3. Results
Figure 7 shows the captured output spots for four different targets. The bar figures under each spot photo denote the comparison between the experimental and target values.
Figure 7a–c show three different splitting powers under the lossless scenario.
Figure 7d shows the lossy adjustment when a 3 dB attenuation is intended in the target total power. Further experiments show that all power splitting targets, lossless or lossy, can be optimized with
CF > 0.9 within 300 iterations. More splitter configurations and their iteration processes can be found in the
Video S1 in the Supplementary Materials.
Figure 8 shows the
CF progress for the
[0.33:0.33:0.33] case over the iterations, in which the device transforms from the initial 3 dB two-port splitter to an even three-port splitter. The
CF rises to 0.969 after 166 iterations. The insets of
Figure 8 are the captured photos of the output spots for the iteration No. 6, 90, 99, and 166, respectively. The heat power configurations of these four iterations are summarized in
Table 1. The resistances of H
1 to H
4 at room temperature are measured as 163.8 Ω, 175.8 Ω, 176.1 Ω, and 163.1 Ω, respectively. The current (mA) configurations (H
1 to H
4) over the iterations are summarized in
Figure 9. For comparison, a simple sweeping method without feedback mechanism, e.g., from 0 to 10 mA in step of 0.5 mA for all the four microheaters subsequently, leads to a total iteration number as high as 1.6×10
5, while our program can already find the target settings within a few hundred iterations. The iteration process under the target
[0.33:0.33:0.33] can be viewed in the
Video S2 in the Supplementary Materials.
In
Figure 8, the cost functions oscillate dramatically over the iterations. This is mainly caused by the coarse adjustment of level-1: when the adjacent iterations are both out of the target range, the reinitialized configurations cause a large difference on the output fields. When the present total output power is out of the target range while the last iteration is inside, large jumps can still happen, such as the iterations from No. 30 to 40. If the actual total power in consecutive iterations all stays within the target range, it shows a continuous gradient descent under the fine adjustment of level-2, such as the iterations from No. 61 to 78, in which the current values also change smoothly, as shown in
Figure 9a–d.
It must be pointed out that the comparison between the actual and target total output power is necessary in each iteration. If the difference of the total output powers becomes large without being noticed, the iteration in the fine adjustment of level-2 can be easily trapped in the time-consuming loops within the local optima. It may also lead to wrong directions, e.g., results with the same relative splitting ratio but with different absolute splitting powers, such as [0.33:0.33:0.33] and [0.10:0.10:0.10].
The coarse adjustment by level-1 brings a specific uncertainty that completely discards the previous configuration. Although this may increase the total number of the iterations, it brings robustness in finding better solutions beyond local optima. The simultaneous adjustments by the microheaters allow the target to be reached with possibly different configurations, i.e., the solution may not be unique. The vastly different heat power configurations between No. 90 (
CF90 = 0.846) and No. 166 (
CF166 = 0.969), shown in
Table 1, have demonstrated the program’s ability to jump over locally optimized solutions, and the
CF can be further improved along the increasing iterations.
4. Discussion
In our current technology, each iteration takes 1 s to complete, considering the response time of the camera, synchronization, and processing in MATLAB. There are a few ways to speed up the process. Firstly, high-speed PDs can be integrated on the FPWE instead of camera shot to record monitor the output power. The receiver response time can be shorted to sub-nanosecond. A tap coupler can be added to the input waveguide and divert part of light to a monitor diode for a more accurate reference to evaluate the lossless/lossy conditions. Thirdly, the thermo-optic tuning mechanism can be replaced by the ultrafast electro-optic (EO) effect using EO polymers [
26] or by carrier injection method on junction semiconductor structures. The modulation time can also be shorted to sub-nanosecond scale. As only simple computation without matrix operation is performed in the optimization, the processing time for each iteration can be short. The computation takes roughly 0.1 millisecond on our lab PC (Intel Core i7-11700 @ 2.5GHz, 64 GB RAM, Windows 10) through the MATLAB program. The computation can be performed more efficiently by a customed MCU/FPGA system. With high-speed driver circuits integrated to transmit, receive, and process the data, we estimate the entire process to reach the target output can be improved to hundreds of microseconds for 300 iterations, which is comparable with the speed from the state-of-the-art MEMS-based switches.
The search program can also be improved in our future work, especially when developing a light flow controller with a large number of output ports and control electrodes. Firstly, the iteration configurations can be partially reserved with specific rules based on the target functions. For example, when CF already approaches a high value, a counter can be set so that the adjustment level-1 should be trigged less frequently in order to examine the local optima more closely. Secondly, each microheater can be applied with independent adjustment levels based on their contributions for different targets. For example, H2 and H3 may influence the light path to output Port2 more prominently than H1 and H4 because they are physically placed closer to the output port. In this case, the adjustment levels of H2 and H3 can be made finer to hit the sweet spot. The electrodes can be grouped based on their locations and contributions to the target. The comparison between the present and the previous values can be extended to a block of consecutive values, which can provide a balanced information for the next configuration.
Furthermore, an “offline” program can be developed as the first-round “coarse” search to limit the range of input variations so as to speed up the “online” search process. An equivalent AI-based neural network can be introduced to represent the MMI as the black box to map the input and output. To do so, a large dataset must be collected, followed by subsequent modelling and training. This equivalent network can then be solved reversely to find the closest input under a given output. In the end, the “online” search program can narrow in on the suggested values and perform the “fine” search. While the online search program is generic, the offline approach must be repeated each time the MMI structure or the electrode layout is changed. Depending on the specific applications, one may choose online, offline, or hybrid approach.