Computer modeling supports a design in which two light patterns can be exchanged inside a glass waveguide while horizontal routing uses a separate symmetry channel. It pairs a vertically elliptical set of modes with perturbations of matching parity, or symmetry: vertical modulation targets the 1S↔2P_y pair, while horizontal routing is intended to avoid that pair.
The work is an arXiv preprint based on scalar split-step Fourier beam-propagation calculations rather than an experiment. Here, a mode means a recurring pattern of light inside the guide; the researchers extracted and checked those patterns, then separated power in tracked modes from power that was unresolved or removed by an absorber.
Two designs test the idea
Researchers compared two vertically elliptical numerical guides at a wavelength of 640 nanometres: one designed to hold light less tightly, called lower confinement or LC, and one designed to hold it more tightly, called higher confinement or HC. LC used an index contrast of 2.5 × 10⁻³ and a 4.0-micrometre horizontal width; HC used 3.0 × 10⁻³ and 4.5 micrometres. Both had ellipticity of 1.60 and a cladding index of 1.507.
As a basis check, the model was run with a transverse computational window widened from 80 micrometres on a 512² grid to 120 micrometres on a 768² grid. Cropped field-overlap power stayed above 99.996%, and the change in propagation constant stayed below 0.25 rad m⁻¹. The LC 1S and 2P_y states passed the convergence test, no LC 2P_x trial did, and all HC states passed.
Vertical modulation matched the intended pair
For deliberate vertical conversion, the estimated phase-matching periods—the spacings expected to keep the exchange in step—were 0.752 millimetres for LC and 0.647 millimetres for HC. Direct beam-propagation optimization gave 0.744 and 0.644 millimetres, respectively, with a reported difference of up to 1.0%, including 0.5% for HC.
After a 1S launch, the endpoint powers in the two intended modes were nearly even: 0.495 and 0.490 in LC, and 0.492 and 0.490 in HC. The resolved pairs accounted for 0.985 and 0.982, respectively, while HC 2P_x stayed below 10⁻¹² in the splitter test. Reversing the launch reproduced the cross-converted power within 2 × 10⁻⁵, but total output remained launch dependent: 1S launches gave 0.989 in LC and 0.986 in HC, compared with 0.951 and 0.939 for 2P_y launches.
The higher-confinement design carries a trade-off
The horizontal-routing test used a 4-millimetre cosine S-bend and cleaned 2P_y input. LC retained 0.814 at a 40-micrometre displacement, while HC retained 0.810 at 150 micrometres, indicating a larger modeled retention range for the higher-confinement design.
The same HC design also exposed the cost of its additional guided channel. At 150 micrometres with a 1S launch, 0.986 remained in 1S and 0.0060, or 0.6%, reached 2P_x; 2P_y stayed below 3.5 × 10⁻¹². Total output was 0.993, with 0.0007 unresolved. The paper attributes the small allowed transfer to strong modal detuning of about 1.31 × 10⁴ rad m⁻¹ and a nearly adiabatic trajectory.
Heat offers another compromise
The thermal test revealed another trade-off. Under an imposed, surface-localized thermo-optic profile, the model’s 160 mW heater setting left HC near an equal resolved split, at 0.468 and 0.466, whereas LC shifted to 0.368 and 0.420 and had the larger unresolved-loss fraction. Straight-guide controls remained mode preserving. The authors interpret the pattern as lower HC sensitivity to the imposed profile but a larger modeled trimming range for LC, with more loss.
Small horizontal errors activate the weak point
The writing-error tests made the symmetry condition explicit. With vertical-only noise, HC 2P_x stayed at the 10⁻¹³ numerical floor. When the modeled noise included an x-direction root-mean-square displacement of 0.05 micrometres alongside a y-direction value of 0.15 micrometres, HC 2P_x reached 0.018, while LC had no tracked 2P_x channel.
The simulations represented these errors as stationary Ornstein–Uhlenbeck centerline trajectories and used 25 realizations per point for beam-pointing and servo-loop tests, and 15 for vectorial noise. At the largest servo-loop error, y-RMS 0.15 micrometres, mean 1S power was 0.920 for LC and 0.895 for HC, while 2P_y power was 0.055 and 0.087. These figures are finite-ensemble means from model runs, not measurements from fabricated guides.
A design rule still awaiting a device test
The result remains a modeling study, not a device demonstration. The calculations used a scalar, selected-polarization model, so birefringence and device-specific thermal transport still require experimental calibration. The proposed path–mode circuit combines path couplers, vertically modulated sections and surface trim heaters, but it is a component-level architecture outlook rather than an end-to-end simulation.
Taken together, the calculations support symmetry as a design variable for modal control while leaving the practical balance between confinement and leakage to experimental testing.
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
Original paper · Full text