On-chip deterministic arbitrary-phase-controlling

Abstract

The stable on-chip deterministic arbitrary-phase-controlling of signal light in micro/nanometer spatial scale is an extremely important basis for large-scale and high-density integrated photonic information processing chips. Conventional phase-controlling methods face with serious limitation of unavoidable crosstalk, length distortion, and fabrication error. To date, it is still a great challenge to achieve deterministic and wide-range on-chip arbitrary-phase-controlling. Here, we report an effective strategy of three-waveguide coupled configuration to realize on-chip deterministic arbitrary-phase-controlling (ranging from 0 to 2π) by combing the dynamic phase and the geometric phase. Based on this strategy, quantum gate operations in an optical permutation-group circuit are successfully realized in femtosecond-laser direct writing sample. To extend the feasibility of this method, on-chip silicon-based deterministic arbitrary-phase-controlling in the optical communication range is also experimentally verified. Our work not only paves the way for fundamental research in chip-scale novel optical devices but also promotes the study of topological quantum computing.

Keywords: deterministic arbitrary-phase-controlling; optical chip; optical permutation circuit; three-waveguide configuration.

Figure 1:

The Schematic diagram of waveguide coupling system. (a) The dual-waveguide configuration composed of two identical waveguides. I, II, III show that the coupling coefficient changes with the distance between waveguides. No matter what the coupling coefficient is, the dual-waveguide configuration can only realize π/2 phase controlling; (b) the two identical dual-waveguide configurations. For the coupling shown by I and II, the two identical dual-waveguide configurations can only realize π phase controlling; (c) the three-waveguide configuration, the structure parameter d represent the distance between the waveguide P and the plane determined by the waveguide O and waveguide Q. The coupling coefficient κ ₁ decreases with the increase of d, then the arbitrary-phase-controlling can be achieved; (d) the optical field intensities in waveguide O, waveguide Q, and the phase distributions in waveguide Q of the three-waveguide configuration, which is obtained by solving the Schrodinger equation in the waveguide configuration and angling the function. Corresponding to each coupling, the phase platforms are obvious.

Figure 2:

The theoretical and experimental results of the three-waveguide configuration. (a) The distribution of output optical field intensity of waveguide Q with respect to changes in the O–P–Q three-waveguide configuration when κ ₁ = 1, the line at a = 1 is the area where the singularity appears in the theory in the O–P–Q three-waveguide configuration when a = 1. (b) The distribution of output optical field phase of waveguide Q with respect to changes in the O–P–Q three-waveguide configuration when κ ₁ = 1, the line at a = 1 is the area where the singularity appears in the theory in the O–P–Q three-waveguide configuration when a = 1. (c) The different phase changes caused by varying parameters a when κ ₁ = 1; (d) the designed circuits for experimental verification of the arbitrary phase value controlling capability of the O–P–Q three-waveguide configuration. The red box shows the cross section of the phase controller, which consists of a three-waveguide configuration and a dual-waveguide configuration with the same length; (e) the output optical field intensity distribution in experiments for the O–P–Q three-waveguide configuration.

Figure 3:

The permutation lines and experimental results. (a) The controlling of light in the permutation circuit. All four configurations Couple1, Couple2, Couple3, and Couple4 are shown; (b) the 3D structure of the permutation circuit; (c), (d) the experimental results of the permutation circuit shown in Figure 3(a), with input light from the waveguide α and β, respectively; (e), (f) the experimental results of the permutation structure with the auxiliary waveguide ξ; (g) the experimental results of single-photon incident the permutation circuit with input light from the waveguide α or β, which demonstrates the circuit can still realize the permutation function when the single photon is injected with different structure parameter d.

Figure 4:

The arbitrary phase controller and quantum gate chip based on permutation circuits. (a) The permutation circuit. The number ①②③④ represents the four configurations Couple1, Couple2, Couple3, and Couple4; (b) the 3D structure of the permutation circuit; (c) the experimental results with input light from the waveguide α1 and β2 at the same time. Different phase controlling results can be obtained with different structural parameters d when light outputs from the waveguide α2 and β1 at the same time.

Figure 5:

The on-chip silicon-based three-waveguide configuration phase controller. (a) The on-chip silicon phase controller based on the three-waveguide configuration. The circuit of the waveguides is shown by the blue line in the figure, and the three-waveguide configuration is shown by the red short line. The interlayer coupling coefficient between the top and bottom waveguide layer is determined by the thickness d of the silicon oxide layer. All three waveguides are buried in a silicon oxide layer. (b) The optical microscope image of the three-waveguide structure. (c) The scanning electron microscope image of the three-waveguide structure. (d), (e) The simulation and experimental result of the on-chip silicon phase controller based on the three-waveguide configuration when d = 0.25 µm and d = 0.4 µm. The parameter d corresponds to phases controlling in the three-waveguide configuration.