Optical Control of Spatial Riemann Waves and Burgers' Equation Dynamics
Bibliographic record
Abstract
Simple Riemann waves (RWs), solutions of the Inviscid Burgers' Equation (IBE), are of fundamental importance to study shock formation in different physical frameworks beyond hydrodynamics [1]. Recently, RW signatures in time domain have been reported in the context of nonlinear optical fibres [2-4]. Nevertheless, only limited control was demonstrated on the propagation of these peculiar optical pulses [5]. Here, we describe a method to control the nonlinear dynamics of their spatial counterpart, i.e., Riemann beams (RBs). Such RBs can be theoretically generated with arbitrary trajectories, by properly engineering an external potential and the application of an initial phase profile on the beam. In particular, we study shifted RBs, whose transversal shock position can be controlled, even in the absence of any external potential. Figures 1 (a,b) illustrate the dynamical control achievable for two different cases of RBs. During propagation, a pre-chirped Gaussian beam maintains a constant peak intensity, and undergoes a progressive steepening of its trailing edge up to a near-vertical front at z =10 mm (shock distance). Figure 1(a) shows a shifted Gaussian RB, generated by the inclusion of a linear phase shift α. In Fig. 1(b), the external potential function and the initial phase are designed to guide the Gaussian RB along a sinusoidal path T(z) - as detailed in caption. Numerical simulations with the nonlinear Schrodinger equation (NLSE) of nonlinear beam evolution show a good agreement with IBE predictions. Experimentally, we report the first observation of shifted RBs, obtained by injecting an input Gaussian RB into a 1cm-long cuvette filled with m-cresol/nylon thermal solution as shown in the setup of Fig. 1(c). The experimental results illustrated in Fig. 1(d) are in a good agreement with analytical predictions. Our work open up new possibilities for the control and tailoring of nonlinear beams as well as the study of spatial RWs dynamics in general.
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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".