Telecommunication technologies

Diagram:
A typical waveguide path consists of a series of straight sections, bends, and transitions. The figure below shows a diagram of a waveguide path with a rectangular-to-circular transition, an E-plane bend, and two straight sections.
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1. 
   Simulation of transverse spatial modes in a multi-mode waveguide. (b) Schematic shows interference between two indistinguishable photons incident on the two input ports (or modes) of a beamsplitter, where the two input ports are the two spatial modes of a waveguide (TE0 and TE2). The four cases of probability amplitudes, in which TE0 and TE2 are reflected (R) or transmitted (T) are added or subtracted based on the unitary transformation of a beamsplitter. The arrows indicate whether the photons remain in the same mode or convert to the other mode. The destructive interference of the two cases that result in coincidences (RR and TT) leads to the characteristic HOM interference. (c) Schematic showing chip implementation of spatial mode multiplexing (asymmetric directional coupler) and spatial mode beamsplitter (nanoscale grating). The colours indicate the mode order within the multi-mode region of the device (red is TE0, green is TE2). The colour also shows the path that transfers single-mode inputs and outputs to the different spatial modes within the multi-mode waveguide. Wavelength (808 nm) and polarization (TE) are identical within each path. The inset shows a microscope image of the device. Scale bar is 160 μm.
   

The key building blocks required to demonstrate HOM interference are a spatial mode multiplexer for generating the different spatial modes and a spatial mode beamsplitter for interfering the spatial modes, which both rely on selective mode coupling by phase matching in our design. The spatial mode multiplexer allows us to generate orthogonal spatial modes within the multi-mode waveguide without cross talk between the modes, which would reduce the interference visibility. We couple pairs of photons from a spontaneous parametric down conversion (SPDC) source into single-mode silicon nitride waveguides that couple into a multi-mode waveguide (Methods; Fig. 1c). Finally, the photons are sent to the spatial mode beamsplitter where they are equally split between the two modes, coupled into single-mode output waveguides, and the fundamental mode fields are detected as coincidences. We use a silicon nitride platform because the high-core-cladding (Si₃N₄/SiO₂) index contrast allows one to strongly vary the propagation constants of different spatial modes by varying the waveguide dimensions, which is essential for selective mode coupling. The silicon nitride platform is attractive for integrated quantum information processing because its transparency window spans the visible to mid-infrared wavelength range and has been used to demonstrate non-classical light sources.

Selective mode coupling by phase matching

To demonstrate the spatial mode multiplexer, we use an asymmetric directional coupler to selectively couple the fundamental mode in a single-mode waveguide to a specific higher-order mode in an adjacent multi-mode waveguide. The asymmetric directional coupler uses two different waveguide widths to phase match light propagating in different modes within adjacent waveguides, allowing for efficient coupling24^,25^,26^,27. In Fig. 2a, the horizontal red line indicates where the effective indices of different higher-order modes in waveguides of different widths match. For example, to excite the TE2 mode in the multi-mode waveguide using the TE0 mode in a single-mode waveguide with 420 nm width, we choose the multi-mode waveguide width of 1.6 μm (Methods).