Scientific sources - Case28
References
Takuya Ikemachi, Yasushi Shinohara, Takeshi Sato, Junji Yumoto, Makoto Kuwata-Gonokami, and Kenichi L. Ishikawa. 2017. Trajectory analysis of high-order-harmonic generation from periodic crystals. Physical Review A, 95, 043416. Source.
Field-dependent solid HHG plateaus/cutoffs, Brillouin-zone-edge multiband climbing and time-energy trajectory tests. Approximate onsets and estimator-dependent cutoffs are robust structural anchors, not fixed numerical thresholds.
Criterion-to-source crosswalk
Locations refer to the article or named preprint/manuscript page, not a figure-file index. Source examples establish scientific identity and robust structure; the task defines required reporting, case coverage and risk-triggered validation. No original source images are reproduced.
| Criteria | Source locations, scientific use and limits |
|---|---|
| F1 | article pp. 043416-2-3, Eqs. (1)-(5), Fig. 1, Fig. 2 and pulse paragraph The periodic independent-electron crystal begins with two filled valence bands; finite-pulse support follows the stated task convention. |
| F2 | article p. 043416-3, Eqs. (6)-(7) and following spectral paragraph A coherent occupied-state/BZ total current, not incoherent band powers, defines the HHG spectrum. |
| F3 | article pp. 043416-4-6, Eq. (8), Eq. (10), Sec. IV steps (i)-(iii) and Figs. 4-6 Momentum displacement, repeated interband passage and particle-hole gaps define a computable multiband trajectory model. |
| O1, I1 | article pp. 043416-3-4, Fig. 3(a,b) and adjacent transition discussion Low-field single-plateau response changes into several high-energy plateau families as field increases. |
| O2, I2, M2, M3 | article pp. 043416-3-6, Fig. 3(b), Eqs. (9), (12)-(14), and Fig. 7 Major branch openings track vector-potential excursion relative to Brillouin-zone scales; source onset coordinates and display cutoffs are not exact task thresholds. |
| O3, I3, M6 | article p. 043416-5, Fig. 6(a-f), especially time-frequency panels (c,d) and trajectory panels (e,f) Low/high-field time-energy diagnostics test multiband emission timing; another physically discriminating time-resolved representation is allowed. |
| M1, M5 | article pp. 043416-4-5, Eqs. (8)-(12), Figs. 4(c,d), 5(c,d) Before reaching the zone edge the first-conduction-band particle-hole gap limits the branch; recombination energies track instantaneous gaps to the initial hole. |
| M4 | article pp. 043416-4-6, Sec. IV, Fig. 5 and Eq. (14) Repeated interband excitation and intraband displacement allow band climbing; one two-band cutoff cannot explain all high-field plateaus. |
| M7, M8, V3 | article pp. 043416-6-7, timing/approximation discussion, Fig. 7 and Conclusion Field-domain and finite-pulse trajectory conclusions remain independent-electron, single-cell and one-dimensional; pulse-duration behavior is context, not a mandatory extra scan. |
| V1, V2 | article pp. 043416-3-6, spectral construction, Fig. 6 and discussion of trajectory timing and pulse-duration effects Truncation, display thresholds, windowing and a concrete simpler-model alternative can threaten specific branch claims. Source grids and Gabor windows are examples, not required validation procedures. |
Formula and convention notes
Source-numbered identities below are paraphrased mathematically. Explicit algebraic consequences and accepted model-conditioned representations are identified as such; they do not add a required solver, plot or validation recipe.
$V(x)=-V_0[1+\cos(2\pi x/a)]$ and $H_k(t)=\tfrac12[-i\partial_x+k+A(t)]^2+V(x)$ act on cell-periodic states with both valence bands initially filled (Eqs. (3)-(5)). $j(t)\propto\sum_{n\in\mathrm{VB}}\int_{\rm BZ}dk\langle u_{nk}|-i\partial_x+k+A|u_{nk}\rangle$ and $S(\omega)\propto|\int w(t)j(t)e^{i\omega t}dt|^2$ (Eqs. (6)-(7)); use one consistent normalization.
The acceleration theorem gives $k(t)=k_0+A(t)$; for excitation at the zone center, $k(t)=A(t)-A(t_0)$ (Eq. (10)). Emitted energy is $\Delta\varepsilon_{n,n_0}[k(t)]=\varepsilon_n[k(t)]-\varepsilon_{n_0}[k(t)]$ (Eq. (8), Sec. IV). The source peak-to-valley excursion $A_{\rm peak}$ reaching $\pi/a$ and then $2\pi/a$ organizes new branches, but its finite-pulse band-climbing/cutoff relations are approximate and not hidden exact onset coordinates.
Scope of the source anchors
Figure panels, displayed source coordinates, curve multipliers, numerical grids and named controls are reference examples, not compulsory submission layouts or hidden pointwise targets. Equivalent evidence must preserve the actual physical observable, case, relative scale and discriminating function. Correct data, candidate identification, causal explanation and risk resolution are separate evidential acts. Existing branch-local dependencies, applicability/N/A and descriptive Research Closure rules remain in the case rubric.