High-harmonic emission from a one-dimensional periodic system
Background and research question
A coordinate-space finite-basis calculation can generate a smooth radiation spectrum without necessarily preserving all of the relevant physics of a periodic system. For the model and driving conditions below, assess whether a coordinate-space B-spline treatment provides a physically reliable account of high-harmonic emission and determine what physical conclusions are supported by your calculations.
Design the derivation, computation, tests, evidence and scientific argument needed to answer this question. Do not assume in advance that the method is reliable or that a single interpretation applies to the full response.
Physical system
Use atomic units unless stated otherwise. Treat one active electron in the one-dimensional periodic potential
under the electric-dipole approximation. The initial physical state belongs to band 2 at crystal momentum $k=0$.
Use a linearly polarized finite-support field
and set it to zero outside the support. The carrier-phase and time-origin convention is not fixed; declare one and use the same physical field in every calculation being compared.
| Case | Peak intensity | Wavelength |
|---|---|---|
| A | $8.087\times10^{11}\ \mathrm{W,cm^{-2}}$ | $3.2\ \mu\mathrm m$ |
| B | $4.5\times10^{11}\ \mathrm{W,cm^{-2}}$ | $3.2\ \mu\mathrm m$ |
Determine the field amplitude and carrier frequency using standard atomic-unit conversions and state the conventions used.
Research boundary
Use a coordinate-space B-spline TDSE as the primary method. Standard periodic-state, analytical or numerical methods may be used as needed. All other modelling, numerical, diagnostic and presentation choices are yours. Establish that the evidence supporting each retained claim is sufficiently reliable and reproducible. Absolute spectral yield is not a grading target.
Submission and resources
Submit one self-contained scientific report and an offline reproduction package containing the producing code, numerical data underlying the retained evidence, a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge, and concise run and environment information. No fixed scientific figure set, file tree or exploratory history is required.
The active examination resources and limits are defined in the companion
resource_limits.json. All retained production calculations must run
within that fixed allocation and active wall time. More expensive modelling
does not receive additional credit.
Reference and integrity policy
This examination is conducted without network access or live literature retrieval. You may rely on your existing general scientific knowledge and, if any are explicitly supplied with the examination, on those offline materials or software documentation. Record every such source actually consulted. For formulas, methods, constants, or conventions used from general knowledge rather than a consulted source, state enough of the method basis, definition, value, units, and convention to make the calculation auditable; do not invent a citation. You are not required to identify or prove a publication date or to retrieve literature during the examination.
The hidden target article and its identifying metadata, figures or captions, supplementary material, author code or data, target-specific reproduction code, solution or scoring material, online solutions, and worked reproductions of this case must not be used. All submitted scientific figures and numerical data must be generated by your own implementation of the stated problem.
See submission requirements for the common submission entry points.