The Interpath Relation for Spatially-Discrete Traveling-Wave Modulated Structures

Traveling-wave modulation has been employed since the 1950s for amplification and frequency conversion, and more recently for beam-steering and breaking reciprocity. Typically, traveling-wave modulation is realized by applying a staggered bias/pump signal to an array of discrete unit cells. This is referred to as spatially-discrete traveling-wave modulation (SD-TWM). SD-TWM structures can prove challenging to simulate due to their often complex geometry and extreme temporal variation. Here, we examine a relation established within SD-TWM structures referred to as the interpath relation. The interpath relation reveals that the solution within a single unit cell (as opposed to an entire spatial period) is sufficient to determine the entire problem. The interpath relation is then incorporated into a method of moments solver to compute the scattered field produced by a representative SD-TWM metasurface. The presented method simplifies the computation of both physical patterned designs, as well as nearly continuous idealized structures.