A numerical study suggests that waveguides can be designed, at least in simulation, to move light between two chosen patterns while keeping a third pattern almost out of the exchange. In the higher-confinement design, a vertical modulation gave near-equal endpoint power in 1S and 2Pᵧ, while 2Pₓ remained below 10⁻¹² in normalized power.
The study treats a mode as a distinct light pattern supported by the guide, then asks whether the symmetry of a disturbance can be matched to one modal pair and mismatched to another. Its intended conversion pair was 1S–2Pᵧ; the 2Pₓ channel was tracked as the possible leakage route.
How the model set the modes
The calculations used a custom scalar split-step Fourier beam-propagation model at 640 nm. They compared a lower-confinement design, or LC, with an index contrast of 2.5 × 10⁻³ and 4.0 µm horizontal width, with a higher-confinement design, or HC, at 3.0 × 10⁻³ and 4.5 µm; both had ellipticity of 1.60.
Before testing conversion, the calculation checked that its numerical window captured the relevant modes. Cropped field-overlap power exceeded 99.996%, while changes in the calculated propagation constant stayed below 0.25 rad per metre. LC had converged 1S and 2Pᵧ states but no converged 2Pₓ; all three states converged in HC.
The validated modal spectra gave 1S–2Pᵧ beat periods—the modeled distances associated with their power exchange—of 0.752 mm in LC and 0.647 mm in HC. After vertical modulation was tuned to those scales, the optimized beam-propagation periods differed from coupled-mode predictions by 1.0% and 0.5%, respectively.
At the optimized settings, a 1S launch ended with nearly equal normalized power in the pair: LC produced 0.495 in 1S and 0.490 in 2Pᵧ, while HC produced 0.492 and 0.490. Reversing the launched mode reproduced cross-converted power within 2 × 10⁻⁵, showing reciprocity in the converted component.
The exchange was not identical in total transmission. With a 2Pᵧ launch, total output was 0.951 for LC and 0.939 for HC, compared with 0.989 and 0.986 for 1S launches.
Routing favored the intended channel
The same selection rule was tested during horizontal routing. In a modeled 4 mm cosine S-bend, LC retained 0.814 of cleaned 2Pᵧ power at a 40 µm displacement, whereas HC retained 0.810 at 150 µm.
At 150 µm in HC, a 1S launch retained 0.986 in 1S and sent 0.0060 to 2Pₓ; 2Pᵧ stayed below 3.5 × 10⁻¹². Total output was 0.993, with 0.0007 unresolved. In the model, the small tracked transfer therefore went to 2Pₓ rather than 2Pᵧ.
A separate thermo-optic calculation used an assumed heater and swept the reference drive to 160 mW. At that setting, the two resolved powers were 0.468 and 0.466 for HC, compared with 0.368 and 0.420 for LC. The heater profile and conversion from drive to refractive-index change were illustrative model assumptions.
The weak point was broken symmetry
The clearest leakage appeared when the model introduced writing-position noise that broke horizontal symmetry. Vertical-only noise left HC 2Pₓ at the 10⁻¹³ numerical floor. Adding x-direction noise with an RMS of 0.05 µm produced HC 2Pₓ power of 0.018 at the largest tested y-direction RMS, 0.15 µm; the corresponding HC 1S and 2Pᵧ powers were 0.852 and 0.084.
Other parameter sweeps found the flattest response for core-width errors, a broader nominal crossing for ellipticity, and the strongest equal-power detuning from index contrast. The same qualitative pattern appeared in LC and HC.
The authors frame confinement and symmetry as joint design variables and say implementation requires writing-position control below 100 nm.
A design rule, not yet a device
These are outputs from a scalar beam-propagation model, not a fabricated-device demonstration. The bend, thermal and writing-error results apply to the specified model geometries, assumptions and finite stochastic scans; the reported leakage floors and power balances should not be read as universal device specifications.
The study therefore supports a component-level design idea: use vertical symmetry matching for deliberate 1S–2Pᵧ conversion and horizontal symmetry mismatch to limit that transition during routing. Whether the rule survives fabrication conditions remains an experimental question.
Paper data and sources
Original title: Symmetry-guided modal control in elliptical femtosecond-laser-written photonic waveguides
Authors: Tadas Paulauskas, Ubaid Ur Rehman, Eimantas Dermauskas, Valdemar Stankevic
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
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