How to calculate two photon absorption cross section and two photon emission cross section of dyes?
There isn't really a trivial way to do this. A good starting point is probably the perturbation calculations in Boyd Ch. 5, or you can delve into some computational methods in quantum chemistry.
I think in practice, most of these spectra are measured empirically.
For given wave length you can obtain the 2PA either by density matrix method or by rate equation approach. these two methods we can used in z-scan or or single beam transmittance to obtain the absorption cross section. emission cross sections can be obtained by some multi-photon spectroscopy.
here I am giving some references, they may helpful for you
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8. Fischer A., Cremer C. S. E. H. K. and Stelzer E. H. K., “Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titanium–sapphire laser.” App. Opt. 34 (12) 1989 (1995).
9. Xu C. and Webb W. W., “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm.” JOSA B 13 (3) 481 (1996).
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11. Rumi M. and Perry J. W., “Two-photon absorption: an overview of measurements and principles.” Adv. Opt. Photon. 2 (4) 451 (2010).
12. Boitier F., Godard A., Rosencher E. and Fabre C., “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors.” Nature Phys. 5 (4) 267 (2009).
13. Gu B., Sun Y. and Ji W., “Two-photon-induced excited-state nonlinearities.” Opt. Exp. 16 (22) 17745 (2008).
14. Sperber P. and Penzkofer A., “S0-Sn two-photon absorption dynamics of rhodamine dyes.” Opt. Quant. Electron. 18 (5) 381 (1986).
15. Wang J., Gu B., Ni X. W. Wang H. T., “Z-scan theory with simultaneous two-and three-photon absorption saturation.” Opt. Laser Techn. 44 (2) 390 (2012).
16. Boudebs G., Cherukulappurath S., Guignard M., Troles J., Smektala F. and Sanchez F., “Experimental observation of higher order nonlinear absorption in tellurium based chalcogenide glasses.” Opt. commun. 232 (1) 417 (2004).
17. Gu B. and Ji W., “Two-step four-photon absorption. Optics express” 16 (14) 10208 (2008).
18. Ganeev R. A., Ryasnyansky A. I., Ishizawa N., Baba M., Suzuki M., Turu M., Sakakibara S. and Kuroda H., “Two-and three-photon absorption in CS2.” Opt. commun. 231 (1) 431 (2004).
This article will help to master the TPA techniques.
https://www.osapublishing.org/view_article.cfm?gotourl=https%3A%2F%2Fwww%2Eosapublishing%2Eorg%2FDirectPDFAccess%2F639A4B73-9304-D445-AB4F5EFDE2BCA591_205399%2Faop-2-4-451%2Epdf%3Fda%3D1%26id%3D205399%26seq%3D0%26mobile%3Dno&org=National%20Inst%20of%20Science%20Ed%20%26%20Research
Please, look in to this journal...
A. Nag, D. Goswami / Journal of Photochemistry and Photobiology A: Chemistry 206 (2009) 188–197 I think this would be helpful to your question.
Hi, you can using this research
https://www.nature.com/articles/srep17712
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