Absorption nonlinear optics

Rao reported measurement of third-order optical non-linearity in the nanosecond and picosecond domains for phosphorus tetratolyl porphyrins bearing two hydroxyl groups in apical position [89]. Strong nonlinear absorption was found at both 532 nm and 600 nm. The high value of nonlinearity for nanosecond pulses is attributed to higher exited singlet and triplet states. Time resolved studies indicate an ultra-fast temporal evolution of the nonlinearity in this compound. 

For the application of QDs to three-dimensional biological imaging, a large two-photon absorption cross section is required to avoid cell damage by light irradiation. For application to optoelectronics, QDs should have a large nonlinear refractive index as well as fast response. Two-photon absorption and the optical Kerr effect of QDs are third-order nonlinear optical effects, which can be evaluated from the third-order nonlinear susceptibility, or the nonlinear refractive index, y, and the nonlinear absorption coefficient, p. Experimentally, third-order nonlinear optical parameters have been examined by four-wave mixing and Z-scan experiments. 

The term nonlinear optical property refers to an optical property, which can be modified by exposing the material to intense light irradiation. In this section, we focus on the cascaded first- (/ 1 ) and third-order ( / ) susceptibilities describing nonlinear absorption (ESA and 2PA) and nonlinear refraction (n2) processes. Z-scan, pump-probe, and two-photon upconverted fluorescence techniques are among the most used experimental methods for determining optical nonlinearities. 

For 2PA or ESA spectral measurements, it is necessary to use tunable laser sources where optical parametric oscillators/amplifiers (OPOs/OPAs) are extensively used for nonlinear optical measurements. An alternative approach, which overcomes the need of expensive and misalignment prone OPO/OPA sources, is the use of an intense femtosecond white-light continuum (WLC) for Z-scan measurements [71,72]. Balu et al. have developed the WLC Z-scan technique by generating a strong WLC in krypton gas, allowing for a rapid characterization of the nonlinear absorption and refraction spectra in the range of 400-800 nm [72]. 

In terms of beam delivery, the DLW method is based on optical microscopy, confocal microscopy [4,6,13] and laser tweezers [14] (for reviews on laser tweezers see [ 15,16]). These techniques allow for a high spatial 3D resolution of a tightly focused laser beam with optical exposure of micrometric-sized volumes via linear and nonlinear absorption. In addition, mechanical and thermal forces can be exerted upon objects as small as 10 nm molecular dipolar alignment can be controlled by polarization of light in volumes of with submicrometric cross-sections. This circumstance widens the field of applications for laser nano- and microfabrication in liquid and solid materials [17-22]. 

Applications making use of the nonlinear absorption of dyes are passive Q-switching in solid-state lasers, pulse shaping, pulse intensity measurements of high-power ultrashort pulses, optical isolation between amplifier stages of high power solid-state lasers, and pulse width measurements of ultrashort pulses by the two-photon-fluorescence (TPF) method. 

Nonlinear optical studies were carried out using a combination of nonlinear absorption, self-focusing and degenerate four wave mixing measurements. The measurements were made using a Quantel Nano-Pico system that permits operation at either 10 ns or 100 ps pulse lengths at 1064 nm. The 10 ns pulses were TEM mode and temporally smoothed to a near gaussian (H). 

There is a close relation between NLO and optical limiting (OL) properties. The main mechanisms to achieve OL are nonlinear absorption (NLA) and nonlinear refraction (NLR), but other effects such as nonlinear scattering can also contribute to OL. Materials with a positive NLA coefficient exhibit reverse saturable absorption (RSA), causing a decrease in transmittance at high intensity levels, and so operate as optical limiters [14]. 

The nonlinear absorption of Ptn acetylide chromophores has also continued to retain the interest of many researchers. Malmstrom and coworkers have recently investigated Pt-acetylide chromophores blended with solid-state polymer matrices [94], An example of such a complex is 4.7. They found that the photoluminescence properties of the blends agreed well with that of dilute THF solutions containing the Pt-acetylides. Optical power limiting experiments showed that the clamping levels for dyes nonbonded to the polymer host were about half that for dyes in the highly cross-linked solids at similar concentrations. 

Two-photon excited fluorescence (TPEF) is one of the most useful ways to quantify TPA in optical materials competing with nonlinear absorption. While nonlinear transmission yields absolute quantities describing TPA, TPEF requires knowledge of the collection efficiency if absolute data must be acquired. Thus, the use of standards is the method of choice to determine 5 in case of TPEF. 

One representative example of a covalently bound chromophore is the polymer 124. This material was subjected to nonlinear absorption measurements using the neat film. The TPA coefficient was 7 cm/GW [524], which can be considered large. Furthermore, this polymer shows a reduction of the photon-number noise of 0.1 dB (4.6%) during nonlinear transmission. This is important in order to minimize the optical loss at the laser wavelength. 

Optical bistability is a nonlinear process where for the same optical input intensity in a material, there are two possible output intensities and it is a consequence of nonlinear saturable absorption. Optical bistability allows the design of optical logical circuits and will play a fundamental role in the development of optical communication and optical computing [16-18]. 

We now focus on the main subject of this contribution, namely the optical Kerr effect. Depending on the material characteristics and experimental conditions - that is, on laser wavelength and power as well as on metal and matrix kinds and relative amounts - the nonlinear absorption coefficient (3 is found to be either negative or positive. The influence of each of these parameters on the nonlinear response will be examined in details in forthcoming sections. 

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