Scientific Sources — Case10
References
Samuel Schöpa, Lina Bielke, Falk-Erik Wiechmann, Franziska Fennel, and Dieter Bauer. 2026. Phase structure of below-threshold harmonics in aligned molecules: A few-level model system. Physical Review Research, 8, L022022. Source
Phase structure of below-threshold harmonics in aligned molecules: A few-level model system
Samuel Schopa, Lina Bielke, Falk-Erik Wiechmann, Franziska Fennel, and Dieter Bauer. 2026. Supplemental Material: Analytical derivation for the phase of the below-threshold harmonics in a two-level model system, accompanying Physical Review Research 8, L022022. Source
Analytical dipole/population equations and adiabatic monochromatic harmonic recurrence.
Criterion-to-source crosswalk
Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
| Criteria | Source locations, scientific use and limits |
|---|---|
| F1 | Schopa et al. (2026), article pp.L022022-1-2, Eqs.(1)-(6): TLS dynamics, dipole, complex transform and finite Gaussian pulse; pp.L022022-3-4, Eqs.(8)-(11) for the orthogonal four-level extension. |
| F2, M1 | Schopa et al. (2026), article p.L022022-3, Eq.(7) and denominator-sign explanation; Supplemental Material pp.1-4, Eqs.(10),(12),(16)-(22): monochromatic adiabatic weaker-successive-harmonic recurrence and nonresonant phase organization. |
| F3, M4 | Schopa et al. (2026), article pp.L022022-3-4, Eqs.(8)-(11), Fig.5 and paragraph defining linear polarization from relative 0/pi component phase. A normalized coherent equal-weight lower-state preparation and modulo-pi line axis are task-explicit conventions. |
| O1, O2, I1, M2, M3 | Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence. |
| O3, I2, M5 | Schopa et al. (2026), article p.L022022-4, Fig.5 lower odd family (orders 1-7), Fig.4 and same-phase subsystem discussion: co-rotating polarization with nonlinear amplitude-dependent axis, not necessarily equal to the driver angle. |
| O4, I3, M6 | Schopa et al. (2026), article p.L022022-4, Fig.5 higher family (beginning at 9), Fig.3 reference frequency lines and counterrotation paragraph: relative pi phase mirrors the harmonic line axis. |
| M7, M8, V1, V2 | Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains. |
Formula and convention notes
The System-A recurrence and System-B line-axis formula are tied respectively to article p.L022022-3, Eq.(7), and the complex-vector interpretation of Eqs.(10),(11)/Fig.5. The latter is a derived Stokes-axis representation, not a separately printed article equation. For $D_x,D_y$ at one harmonic, line polarization requires a negligible ellipticity invariant $2\Im(D_xD_y^*)$ relative to total power; an axis cannot be assigned physical certainty at vanishing amplitude. The shared real component phases $0/\pi$ cause co-rotation/mirroring, while unequal nonlinear amplitudes mean the lower-family axis need not exactly equal the driver angle. No particular angle grid or line-axis display branch is required.
Scope of the source anchors
The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.