| Abstract [eng] |
Polarization of an arbitrary order can be calculated by expanding density operator in powers of interaction with the excitation field. The resulting optical response theory is not only useful for precise calculations, but also allows one to discover and describe various processes with the help of Feynman diagrams. The lowest order optical signal that is generated in isotropic media is third order. At this order, the one exciton states and excited state energy transfer can be observed. When excitation dynamics are followed at the lowest (third) power of interaction to excitation field, dependence on excitation intensity is often ignored. This dependence can be important as laser pulse intensity is one of parameters that is tuned for better signal-noise ratio. At high excitation intensity exciton-exciton annihilation (EEA) takes place. The EEA process in molecular aggregates has the effect of limiting the number of excitations, and can be used to observe exciton migration. Nonlinear exciton equations (NEE) were used for calculations in this work. In previous work spectra were calculated with these equations with EEA terms, but the relaxation model was too primitive and the system of equations was too small. Therefore in this work NEE system of equations is expanded beyond the third order. Secular relaxation and phenomenologic EEA terms were added to the equations. Also pump-probe spectra at various excitation intensities were calculated by numerically solving NEE. The goal of this work is to expand the nonlinear exciton equations: include higher than third order terms and include exciton relaxation and EEA effects and calculate pump-probe spectra. The results are: (1) The NEE system of equations was expanded: higher than third order and secular relaxation and EEA terms were added. Expanded equations can be used for calculations of spectra at arbitrary excitation intensity; (2) Calculated pump-probe spectra for molecular complex show expected relaxation and EEA dynamics: at low excitation intensity pump-probe spectra show excitation transfer, at high excitation intensity spectra amplitudes decay non-exponentially; (3) application of third order variable „full entropy“ factorization gives pump-probe spectra that look like J aggregate spectra, but actually introduce a nonphysical shift for excited state bands and are misleading. Application of „pure state“ factorization gives pump-probe spectra that is very similar to correct calculations - this factorization could be very useful to computer based spectra modeling. |
