Nonlinear photoconductivity in pump-probe spectroscopy. I. Optical coefficients
Bibliographic record
Abstract
We analyze the optical pump-probe reflection and transmission coefficients when the photoinduced response depends nonlinearly on the incident pump intensity. Under these conditions, we expect the photoconductivity depth profile to change shape as a function of the incident fluence, unlike the case when the photoinduced response is linear in the incident intensity. We consider common optical nonlinearities, including photoconductivity saturation and two-photon absorption, and we derive analytic expressions for the photoconductivity depth profile when one or more is present. We review the theory of the electromagnetic transmission and reflection coefficients in a stratified medium, and we derive general expressions for these coefficients for a medium with an arbitrary photoconductivity depth profile. For several photoconductivity profiles of importance in pump-probe spectroscopy, we show that the wave equation can be transformed into one of three standard differential equations$\unicode{x2014}$the Bessel equation, the hypergeometric equation, and the Heun equation$\unicode{x2014}$with analytic solutions in terms of their associated special functions. From these solutions, we derive exact analytic expressions for the optical coefficients in terms of the photoconductivity at the optical interface, and we discuss their limiting forms in various physical limits. Our results provide a systematic guide for analyzing pump-probe measurements over a wide range of pump intensities, and establishes a framework for constraining the systematic uncertainty associated with nonlinear photoconductivity profile distortion.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".