dorsal/arxiv
View SchemaPump and Probe nonlinear processes: new modified sum rules from a simple oscillator model
| Authors | Franco Bassani, Valerio Lucarini |
|---|---|
| Categories | |
| ArXiv ID | physics/9904056 |
| URL | https://arxiv.org/abs/physics/9904056 |
| DOI | 10.1007/s100510051011 |
Abstract
The nonlinear oscillator model is useful to basically understand the most important properties of nonlinear optical processes. It has been shown to give the correct asymptotic behaviour and to provide the general feature of harmonic generation to all orders, in particular dispersion relations and sum rules. We investigate the properties of Pump and Probe processes using this model, and study those cases where general theorems based on the holomorphic character of the Kubo response function cannot be applied. We show that it is possible to derive new sum rules and new Kramers-Kronig relations for the two lowest moments of the real and imaginary part of the third order susceptibility and that new specific contributions become relevant as the intensity of the probe increases. Since the analitic properties of the susceptibility functions depend only upon the time causality of the system we are confident that these results are not model depemdent and therefore have a general validity, provided one substitutes to the equilibrium values of the potential derivatives the density matrix expectation values of the corresponding operators.
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"abstract": "The nonlinear oscillator model is useful to basically understand the most\nimportant properties of nonlinear optical processes. It has been shown to give\nthe correct asymptotic behaviour and to provide the general feature of harmonic\ngeneration to all orders, in particular dispersion relations and sum rules. We\ninvestigate the properties of Pump and Probe processes using this model, and\nstudy those cases where general theorems based on the holomorphic character of\nthe Kubo response function cannot be applied. We show that it is possible to\nderive new sum rules and new Kramers-Kronig relations for the two lowest\nmoments of the real and imaginary part of the third order susceptibility and\nthat new specific contributions become relevant as the intensity of the probe\nincreases. Since the analitic properties of the susceptibility functions depend\nonly upon the time causality of the system we are confident that these results\nare not model depemdent and therefore have a general validity, provided one\nsubstitutes to the equilibrium values of the potential derivatives the density\nmatrix expectation values of the corresponding operators.",
"arxiv_id": "physics/9904056",
"authors": [
"Franco Bassani",
"Valerio Lucarini"
],
"categories": [
"physics.optics",
"physics.atom-ph"
],
"doi": "10.1007/s100510051011",
"title": "Pump and Probe nonlinear processes: new modified sum rules from a simple oscillator model",
"url": "https://arxiv.org/abs/physics/9904056"
},
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