One, two and three photon absorption of two level system in femto-second laser excitation

Nonlinear behavior of the population dynamics of three-level systems in the presence of single photon absorption

“…For example, organic dye molecules [2] in the presence of their singlet and triplet states, while they act as noncascade energy level systems in the presence of long pulse excitation (Section 2), [4] in the presence of short pulse excitation become cascade systems (Section 3). [30] While non-cascade systems are good nonlinear optical materials in the cw and ns due to their large triplet lifetimes, cascade systems can be used as efficient optical nonlinear media in ultra-fast time scale absorptions. Depending upon the material's spectroscopic parameters with respect to laser beam parameters, one has to choose a proper medium as saturable absorber/optical limiter for a given laser.…”

“…It is inferred that to accurately measure the second excited state spectroscopic parameters, we have to use low repetition rate and high peak power ultra-short laser pulses while avoiding thermal damage; i.e., single shot laser pulse excitation. [30] Fast decay allows cascade systems to use efficient optical limiters and saturable absorbers in ultra-short time scale laser pulses.…”

“…where, I 0 is the peak intensity, w is beam spot size, and τ FWHM is the full width at half maximum (FWHM) of the laser pulse. The time-dependent populations can be studied with the rate equation technique [27][28][29][30] under the non-steady state condition. The photon flux intensity used in this article is 10 17 photons/s • cm 2 .…”

Nonlinear absorption study in four and five energy level systems

“…Because of low repetition rate and short pulse nature, the contribution of triplet states on the ultra shortpulses can be successfully neglected [22]. Under low repetition rate ultra short-laser excitation, noncascade system transforms to cascade system and the transmittance profile becomes as like we discussed in the sections three and four.…”

“…Four level cascade system Absorption takes place through three stimulated absorption cross-sections (σij, j=i+1) in the cascade way and the downward transitions carried through stimulated emission cross-sections (σji, j=i+1) and decay time of energy levels (τ ji, j=i+1). According to Einstein stimulated excitation theory, stimulated absorption cross-section is equal to the stimulated emission cross-section i.e., Wij=Wji [22]. Thus the rate equations have the form as…”