Fig. 1. Optical microscopy image of the chip. Free-space light is coupled into waveguides by means of two grating couplers. Subsequently, the signal is processed by passive on-chip interferometers. The on-chip interferometers consist of passive phase shifters and Y-branch combiners. In each interferometer, the phase shifters introduce a fixed phase difference between the waveguide modes. This is achieved by asymmetrically varying the waveguide widths in the two waveguides before the modes are combined in the Y-branch. Finally, the processed light is coupled out of the chip via grating couplers again. To simplify experiments, the chip layout was designed with some distances intentionally increased, resulting in a total footprint of 3285  μm×325  μm.

Fig. 2. Illustration of the experimental setup. A Gaussian beam is weakly focused on the input section of the chip structure. The light is coupled to waveguide modes and subsequently processed by the on-chip architecture. The transmitted intensities of the outputs are monitored by means of an imaging system, which consists of a camera and an objective.

Fig. 3. Relative intensity and phase of a Gaussian beam as a function of the relative shift of the beam center with respect to the center of the input of the chip. (a) Measurements are performed with a beam at the design wavelength of the waveguides, λD=658  nm. (b) Measurements are taken using a beam with a wavelength λOD=580  nm, far from the design wavelength of the waveguides.

Fig. 4. Relative phase of Gaussian beams of different wavefront curvatures R. All measurements were conducted at the design wavelength of λD=658  nm.

Fig. 5. (a) Optical microscope image of the chip featuring a five-pixel input interface for demonstration of scalability. The input interface consists of five grating couplers functioning as input pixels, arranged in a square configuration with four corner pixels and one central pixel. The on-chip architecture is designed such that each corner pixel is connected to the central pixel via a phase and intensity measurement unit. This design facilitates the complete characterization of a Gaussian beam and its parameters through a single-shot intensity measurement at the outputs. The chip layout was designed to simplify experiments, with some distances intentionally increased, resulting in a total footprint of 6650  μm×1450  μm. (b) Retrieved parameters of a Gaussian beam as a function of the relative displacement of the center of the beam with respect to the center of the input section.

Fig. 6. Illustration of the coordinate transformation.

Fig. 7. (a) Effective index of fundamental and first order TE modes at three different wavelengths within the visible spectrum as a function of the waveguide width in our SiN platform. (b) Effective index of fundamental and first order TE and TM modes as a function of wavelength for a waveguide width of 500 nm.

Fig. 8. Optical microscopy image of a chip featuring an alternative architecture. The on-chip interferometers consist of directional couplers.

Fig. 9. (a) SEM image of etched SiN waveguide with residual HSQ mask. (b) SEM image of the fabricated Y-branch. (c) SEM image of the fabricated surface grating coupler.