Unified design of short mode-evolution couplers

Abstract

Short mode-evolution couplers have been designed with several seemingly different approaches, including fast quasi-adiabatic dynamics (FAQUAD), counter-diabatic (CD) driving realized by tailoring waveguide widths and spacing, CD driving realized by axis bending, and numerical optimization of the coupler geometry. Using exact two-mode coupled-mode theory in the Kramers--Henneberger frame of the bent coupler, we show that these approaches belong to the same design space. The three geometric parameters, width difference, spacing, and axis tilt, act on the light through two functions only: the coupling strength, set by the spacing, and an effective detuning, set by the width difference and the axis curvature. The gauge, bent, and mixed realizations of a CD coupler are therefore the same device and have the same bandwidth. The bandwidth is set by the angle $χ$ between the light and the field that steers it on the Bloch sphere, integrated along the device as $\int\sin^2χdz$, and for a CD coupler this integral is set by the reference alone. This leads to a lithography-aware design rule: make the reference as adiabatic as the minimum gap allows, by narrowing its spacing at the anticrossing, and let exact CD suppress the remaining nonadiabatic coupling. In beam propagation method (BPM) simulations on a polymer platform, a 500\um{} coupler designed this way, without numerical optimization, maintains ${>}99\%$ transfer over 274~nm at a minimum edge gap of 1.05\um, compared with 150~nm for the CD coupler of a fixed-spacing reference at nearly the same gap. Particle swarm optimization of the geometry with BPM in the loop does not exceed the design rule. Three-dimensional BPM of the BCB channel waveguides also confirms these conclusions.