Pumping intensity

Since there is a definite phase relation between the fiindamental pump radiation and the nonlinear source tenn, coherent SH radiation is emitted in well-defined directions. From the quadratic variation of P(2cii) with (m), we expect that the SH intensity 12 will also vary quadratically with the pump intensity 1 ... 

Applications Involving Nonlinear Absorption Phenomena. Saturable absorption (hole-burning) is a change (typically a decrease) in absorption coefficient which is proportional to pump intensity. For a simple two level system, this can be expressed as... 

Reverse saturable absorption is an increase in the absorption coefficient of a material that is proportional to pump intensity. This phenomenon typically involves the population of a strongly absorbing excited state and is the basis of optical limiters or sensor protection elements. A variety of electronic and molecular reorientation processes can give rise to reverse saturable absorption many materials exhibit this phenomenon, including fuUerenes, phthalocyanine compounds (qv), and organometaUic complexes. 

The dependence of the in-phase and quadrature lock-in detected signals on the modulation frequency is considerably more complicated than for the case of monomolecular recombination. The steady state solution to this equation is straightforward, dN/dt = 0 Nss — fG/R, but there is not a general solution N(l) to the inhomogeneous differential equation. Furthermore, the generation rate will vary throughout the sample due to the Gaussian distribution of the pump intensity and absorption by the sample... 

The energy threshold appears to be dependent on the excitation spot size at constant pump intensity, which indicates that amplification occurs over the whole illuminated area. It should be stated that, despite the large domains, the optical quality within the domains is lower than that of the annealed films. This gives rise to additional scattering losses which decrease the magnitude of the amplification. 

In a crystalline medium, the parametric gain (2) T2 is propor-tionnal to d2 Ip n-3 and the oscillation condition r2A2>aA where a is the signal residual absorption (dramatically increased by any crystalline defect), d the efficient phase-matched nonlinear susceptibility, n an average refractive index, Ip the pump intensity (limited by the optical damage threshold) and A the effective interaction length (also limited by any source of crystalline disorientation). 

Fig. 12.10 (a) SEM image of the circular Bragg nanocavity designed to support the m 0 mode in the 300 nm wide central pillar, (b) The evolution of the emitted spectrum from the device shown in Fig. 12.9a as a function of the pump intensity. Inset L L curve, indicating a lasing threshold of Pth 900 pW. (c) Calculated modal intensity profile of the nanocavity, (d) IR image of the emitted beam profile... 

When pure R6G is passed through the OFRR, the lasing emission is observed at 565 nm. By adding an acceptor dye (LDS722), while the pump intensity remains... 

Fig. 19.12 Characteristics of the nonradiative Forster transfer, (a) FRET spectra show that e 100%, 91%, and 63%, respectively, when the pump intensity is below, near, and above the R6G lasing threshold, (b) FRET spectra show a decreased s (61%, 41%, and 34%) when R6G concentration increases while LDS722 concentration and the pump power remain the same, (c) LDS722 emission as a function of its concentration. Reprinted from Ref. 20 with permission. 2008 International Society for Optical Engineering...

Figure 3.23. ASE of a 50-nm film of spiro-sexiphenyl. At pump intensities 40 pJ/cm2, the normal fluorescence spectrum collapses to a narrow line.

The absolute efficiency, rj (%), in the absence of depletion of the fundamental wave is defined hy rj = VoWfu d, where Wjund is the fundamental pulse energy in pj. At higher pump intensities, when the depletion of the fundamental is weak but essential, the corrected value for the absolute effieieney, p (%), can be found by ° ... 

We remind the reader that Eq. (12) is derived under conditions where the effects of pump depletion are neglected. In much the same way as it was described in section 2.2, we can expand the application of Eq. (12) for the range of higher pump intensities for which the depletion of the fundamental is weak but essential. The corrected value for the SHG efficiency,, which accounts for the effects of pump depletion is ... 

There are crystals which work between intermediate levels so that the pump intensity requirement is less severe, e.g., CaF2 with U doping (developed by IBM in I960) or Sa. By the end of 1962, Bell Labs used a crystal rod of CaWO doped with tervalent Nd to produce a continuous wave solid-state laser. 

The same equations, albeit with damping and coherent external driving field, were studied by Drummond et al. [104] as a particular case of sub/second-harmonic generation. They proved that below a critical pump intensity, the system can reach a stable state (field of constant amplitude). However, beyond the critical intensity, the steady state is unstable. They predicted the existence of various instabilities as well as both first- and second-order phase transition-like behavior. For certain sets of parameters they found an amplitude self-modula-tion of the second harmonic and of the fundamental field in the cavity as well as new bifurcation solutions. Mandel and Erneux [105] constructed explicitly and analytically new time-periodic solutions and proved their stability in the vicinity of the transition points. 

The case of a frequency mismatch between laser pumps and cavity modes was investigated [83], and for the first time, chaos in SHG was found. When the pump intensity is increased, we observe a period doubling route to chaos for Ai = 2 = 1. Now, for/i = 5.5, Eq. (3) give aperiodic solutions and we have a chaotic evolution in intensities (Fig. 5a) and a chaotic attractor in phase plane (Imaj, Reai) (Fig. 5b). 

Cmax increases with increasing pumping intensity. At x = 3 m, Cmax reaches 2.5 ng L 1 (Regime II), but this is still only 5% of the concentration in the river (Cin = 50 ng L 1). Since dilution of the infiltrating river water with uncontaminated groundwater is disregarded, the real concentrations are even smaller. 

An additional piece of information can be obtained by studying a synthetic compound derived from the GFP chromophore (1-28) fluorescing at room temperature. In Fig. 3a we show the chemical structure of the compound that we studied in dioxan solution by pump-probe spectroscopy. If we look at the differential transmission spectra displayed in Fig. 3b, we observed two important features a stimulated emission centered at 508 nm and a huge and broad induced absorption band (580-700 nm). Both contributions appear within our temporal resolution and display a linear behavior as a function of the pump intensity in the low fluences limit (<1 mJ/cm2). We note that the stimulated emission red shifts with two characteristic time-scales (500 fs and 10 ps) as expected in the case of solvation dynamics. We conclude that in the absence of ESPT this chromophore has the same qualitative dynamical behavior that we attribute to the relaxed anionic form. 

The power dependence of the laser output was determined by plotting the relative output intensity vs. the relative pump intensity. In Figure 6 this function is clearly non-linear. Separate measurements show that the absolute threshold is 1 mJ, and the absolute output energy is 0.5 jiJ/pulse when the input energy is 2mJ/pulse. 

In this equation, d2u) represents the angle of the radiated SH light with respect to the surface normal, 7(co) is the pump intensity, and e(2co) is the polarization at the SH frequency. The vectors e(co) and e(2co) are related to the unit polarization vectors e(co) and e(2co) in medium 2 by Fresnel coefficients. The effective surface nonlinear susceptibility incorporates the surface nonlinear susceptibility x( and the bulk magnetic dipole contributions to the nonlinearity. The result simplifies since, for isotropic media, there are only three nonzero independent elements of xf These are x%, X% = X%.> and XsfL where 1 =... 

National Laboratory have optical switches like 75 based on PET that flip within picoseconds [48], Optical pumping of the porphyrin absorption band at low intensities produces the perylenetetracarboxydiimide radical anion (and the porphyrin radical cation). The absorbance of the radical anion naturally increases with increasing pump intensity but falls at still higher pump intensities. So the absorbance versus pump intensity profiles show off-on-off behavior. At these higher intensities the second porphyrin unit joins in to launch a PET process into the perylenetetracarboxydiimide radical anion which pushes the latter into the dianion state. Although our main interest here is in luminescent systems, this work has much to teach us. 

Figure 7. Decays of photoinduced absorption in sexithienyl at pump intensities Io and Io/2 (picosecond range). Bi-molecular exciton-exciton annihilation is evidenced [21].

Figure 9.9 (a) Temperature dependence of the transmitted pump intensity, (b) Temperature dependence of the total scattered intensity. Both data sets have been normalized to their maximum values, (c) Dependence of the intensity ratio R. 

Fig. 7. Excitation spectra of the 1 / (a) < - I Ml. 2,3) transitions in I r UMCUS nanocrystals at various temperatures from 2.2 to 66 K, with a pump intensity of 60 kW/cm2.

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