Fig. 1. Scheme of an eight-port error-tolerant interferometer architecture that consists 56 DCs and 56 tunable PSs. Each DC has an imbalanced splitting ratio shifted to a higher transmission 0.5–0.8 according to original proposal [19].

Fig. 2. Dependence of the transmission coefficients on the distance between the waveguides in the DC at different wavelengths. The black solid lines limit the transmittance range 0.5–0.8 that is required by the PMI architecture [19]. Inset schematically shows the DC structure.

Fig. 3. Statistics of the transmission coefficient for 40 DCs with d=7.8  μm at the 945 nm wavelength. Noticeable fluctuations in the absolute value of the transmission coefficient T are clearly visible. However, T falls in the required range 0.5–0.8 for all 40 directional couplers.

Fig. 4. Sketch of the experimental setup. The PMI was connected to a 64 channel current source capable of setting currents up to 60 mA in each of its channels individually with a step of 0.01 mA. The current source was connected to and fully controlled from a PC.

Fig. 5. Simulated numerical comparison of the performance of realizing port-to-port optical mode switching between BS-based error-tolerant PMI [19] and conventional MZI-based PMI [15] architectures. The colored regions show the transmissions of all the DCs of switching-capable PMI configurations. The PMI was considered capable of realizing the switching task if the optimization procedure converged to the infidelity values lower than 10−3 for switching to each of eight output ports from the particular input port. If the PMI comprising DCs with transmission coefficients T satisfied the criterion (for a particular input mode), a colored marker was put on the plot.

Fig. 6. (a) Illustration of the optimization principle used for programming the interferometer. (b) Results of VFSA optimization of the phaseshifts to realize optical port-to-port switching for three wavelengths: 920, 945, and 980 nm. Histograms of the power distribution in the output ports of the device optimized for 1 to 1 switching to the specific output are shown for each input port and for each wavelength. The fidelity of the observed distribution to the expected one is shown for each input port in the graphs on the right.

Fig. 7. Microscope images of the (a) top and (b) facet views of the waveguides. (c) Measured TE mode field profile at the 920 nm wavelength. (d) Refractive index contrast profile Δn(x,y) reconstructed from the measured near-field waveguide’s mode [39,40]. Estimated maximum refractive index change Δn≈4×10−3. (e) Photograph of the experimental setup and optical chip (PMI). Two CCD cameras are used to ease the alignment and visualize the fiber-to-chip and chip-to-fiber coupling at the input and output of the optical chip, respectively.

Fig. 8. Actual optical chip structure (view from the top). (a) Real scale scheme of the chip. Red and black dots represent the electrical and ground contacts with the PCB. Blue dots represent special markers on a fused silica sample needed for precise chip alignment before electrodes engraving. (b) Zoomed part of the waveguide structure and electrodes. Waveguides are depicted with black solid lines; engraved electrodes are depicted with blue solid lines. The thin metal film covers all the top surface of the chip—i.e., the whole white area on the figure is conducting—whereas blue lines represent the isolation trenches engraved between the electrodes.

Fig. 9. Comparison of the total lengths of eight-mode interferometers with different architectures with a curvature radius of R=60  mm and an input/output transverse distance between ports equal to 127 µm. (a) Scheme of an MZI-based interferometer, classic [15] (L=122.6  mm) with straight waveguides connecting individual directional couplers. (b) Scheme of the BS-based error-tolerant interferometer (L =89.7  mm) [19] demonstrated in this work including diagonally connected directional couplers. (c) Scheme of an MZI-based interferometer, hybrid (L =107.2  mm) with optimized directional coupler connections.

Fig. 10. Simulated numerical comparison of the performance of realizing port-to-port optical mode switching between BS-based error-tolerant PMI [19] and conventional MZI-based PMI [15] architectures. The colored regions show the mean values of normally distributed transmissions of DCs with standard deviation of 0.03 of switching-capable (with infidelity values lower than 10−3 for each of eight switchings from the particular input port) PMI configurations.

Fig. 11. Convergence of the infidelity value. Each figure contains information about 24 optimizations. These are the results of phaseshift optimizations that minimize the infidelity between the target and measured output vectors. For each of the four first input ports, eight optimization runs were performed to switch all radiation power to any of the output modes using laser light with three different wavelengths (920, 945, and 980 nm).

Fig. 12. Examples of achievable output power distributions of the studied optical chip with input radiation injected into the first port. (a) Uniform power distributions obtained using three different laser wavelengths, (b) power distributions replicating the shape of the main building of the Lomonosov Moscow State University (MSU), and (c) logo of the Lomonosov Moscow State University, which illustrates the main building.

Fig. 13. Measured times of reconfiguration of the fabricated optical chip. (a) Turning on and off the phaseshift π on a single heater. (b) Applying phase π on a single heater takes ≈100  ms. (c) Turning the phase π off on a single heater lasts no longer than 150 ms. (d) Switching the chips’ transformation from configuration where most of output power exits the third output port to configuration where most of the power exits from the sixth output port and back. (e) Switching from the third output to the sixth output takes ≈1  s. (f) Switching from the sixth output to the third output takes ≈2  s.

Fig. 14. Measured thermal crosstalk between heaters in the transverse direction. (a) Crosstalk measurement protocol: light was injected into first input mode of the optical chip and electrical current was applied to a single heater (h1, h2, or h3, each with resistance of 480 Ω) in the range from 0 to 28 mA with a 0.13 mA step. (b) and (c) Measured optical power during the current sweep through the heater h1 and the model fit of the data. The current corresponding to 2π phaseshift is equal to 26.1 mA, which yields the 0.33 W of dissipated heat. (d) and (e) Measured optical power during the current sweep through the heater h2 and the model fit of the data. (f) and (g) Measured optical power during the current sweep through the heater h3 and the model fit of the data. The phaseshift induced by a heater is ϕ(x)=αx2+ϕ0, where ϕ is the phase induced by the applied current x and ϕ0 is the constant phase offset.