MMI Couplers and the Talbot Effect, Symmetries and Golden Ratio
Bibliographic record
Abstract
The Talbot effect concerns the periodic self-imaging along an optical axis of a free-space optical field that is periodic in an initial transverse plane. It may be modeled by a shift-invariant linear system, fully characterized by the convolution of its impulse response. Self-imaging at integer and fractional Talbot distances of point sources on a regular grid in free space may then be represented by a transmission matrix that is circulant, symmetric, and persymmetric. The free-space Talbot effect may be mapped to the Talbot effect in a multimode waveguide by imposing the anti-symmetry of the mirror-like sidewalls created by the tight confinement of light within a high-index contrast multimode waveguide. The position of the anti-symmetry axis controls the distribution of discrete lattice points in a unit cell. For different distributions, interesting features such as conditional flexibility in the placement of access ports without altering amplitude and phase relationships, omitting ports without power penalty, closed form uneven splitting ratios, and offset access ports can be derived from the MMI coupler. As a specific example, a simple 2×2 MMI coupler is shown to provide a power-splitting ratio related to the golden ratio φ. The structure is amenable to planar photonic integration on any high-index contrast platform. The predictions of the theory are confirmed by simulation and verified by experimental measurements on a golden ratio MMI coupler fabricated using an SOI process.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".