Transverse momentum as the counter-diabatic generator in bent waveguide couplers
Abstract
Bending the axis of a mode-evolution coupler suppresses the nonadiabatic coupling between its supermodes, and bent couplers of this kind were recently shown to realize the counter-diabatic (CD) protocol. Here we identify the operator responsible. Rigid lateral displacement of a waveguide structure is generated by the transverse momentum p̂x, whose diagonal matrix elements vanish in a real supermode basis and whose off-diagonal element is purely imaginary; in a two-mode system such an operator is proportional to sy. The CD term of a two-waveguide coupler is itself proportional to sy, while the detuning and the coupling, the two parameters set by the waveguide widths and spacing, lie in the σz--σx plane and cannot produce it. The transverse momentum is therefore the CD generator of the bent coupler, by necessity rather than by design. Equating the term it supplies to the nonadiabatic coupling gives the axis slope in closed form as a ratio of two matrix elements of the unperturbed supermodes at a single cross section, which a commutator identity recasts in coupled-mode variables as xȯ=θ̇/(γdbeta2). The expression agrees with the numerical offset search to 0.3% and requires no search. Beam propagation simulations confirm the design and compare it, for the first time, with the CD protocol realized by unitary transformation in a straight coupler built from the same reference structure. The two devices reach $0.994$ and $1.000$ supermode fidelity where the untreated coupler reaches $0.886$, and agree in bandwidth and fabrication tolerance, while their internal trajectories differ by exactly the frame transformation that relates them.
Related
- Broadband transverse mode directional couplers using partial Euler bends
- Typed Transverse Momentum Parton distribution function computations
- Gravitational transverse momentum dependent distributions for the gluons
- Energy-momentum tensor at small x from gravitational transverse-momentum distributions
- Transverse momentum correlations and QED effects in TMD determinations
BibTeX
@misc{lee2026transverse,
title = {{Transverse momentum as the counter-diabatic generator in bent waveguide couplers}},
author = {Yu-kai Lee and Shuo-Yen Tseng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.36431},
eprint = {2609.36431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36431},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Transverse momentum as the counter-diabatic generator in bent waveguide couplers
AU - Yu-kai Lee
AU - Shuo-Yen Tseng
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2609.36431
UR - https://arxiv.org/abs/2609.36431
AB - Bending the axis of a mode-evolution coupler suppresses the nonadiabatic coupling between its supermodes, and bent couplers of this kind were recently shown to realize the counter-diabatic (CD) protocol. Here we identify the operator responsible. Rigid lateral displacement of a waveguide structure is generated by the transverse momentum p̂_x, whose diagonal matrix elements vanish in a real supermode basis and whose off-diagonal element is purely imaginary; in a two-mode system such an operator is proportional to sy. The CD term of a two-waveguide coupler is itself proportional to sy, while the detuning and the coupling, the two parameters set by the waveguide widths and spacing, lie in the σ_z--σ_x plane and cannot produce it. The transverse momentum is therefore the CD generator of the bent coupler, by necessity rather than by design. Equating the term it supplies to the nonadiabatic coupling gives the axis slope in closed form as a ratio of two matrix elements of the unperturbed supermodes at a single cross section, which a commutator identity recasts in coupled-mode variables as xȯ=θ̇/(γdbeta^2). The expression agrees with the numerical offset search to 0.3% and requires no search. Beam propagation simulations confirm the design and compare it, for the first time, with the CD protocol realized by unitary transformation in a straight coupler built from the same reference structure. The two devices reach $0.994$ and $1.000$ supermode fidelity where the untreated coupler reaches $0.886$, and agree in bandwidth and fabrication tolerance, while their internal trajectories differ by exactly the frame transformation that relates them.
ER -