Difference frequencies, nonlinear optics

Materials are also classified according to a particular phenomenon being considered. AppHcations exploiting off-resonance optical nonlinearities include electrooptic modulation, frequency generation, optical parametric oscillation, and optical self-focusing. AppHcations exploiting resonant optical nonlinearities include sensor protection and optical limiting, optical memory appHcations, etc. Because different appHcations have different transparency requirements, distinction between resonant and off-resonance phenomena are thus appHcation specific and somewhat arbitrary. 

Abstract Optical Parametric Oscillators provide a very efficient source of tunable coherent radiation. The principle of different kinds of OPOs are described. OPOs are used in astronomy for Laser Guide Star systems, and they may be used for other nonlinear optics applications in astrophysics, such as frequency conversion or parametric amplification. 

From the form of the polarization it is clear that in order to observe any nonlinear optical effect, the input beams must not be copropagating. Furthermore, nonlinear optical effects through the tensor y eee requires two different input frequencies (otherwise, the tensor components would vanish because of permutation symmetry in the last two indices, i.e., ytfl eee = Xijy ) For example, sum-frequency generation in isotropic solutions of chiral molecules through the tensor y1 1 1 has been experimentally observed, and the technique has been proposed as a new tool to study chiral molecules in solution.59,61 From an NLO applications point of view, however, this effect is probably not very useful because recent results suggest that the response is actually very low.62... 

We believe that our model can be extended even further to accurately describe other nonlinear optical interactions such as sum and difference frequency mixing, as well as higher-order harmonics generation. 

Another technological breakthrough in optical hber technology, however, allows one to upgrade established 100 fs-class laser systems for broadband applications and even surpass the bandwidth of dedicated short-pulse Ti sapphire lasers. Key to this is the use of novel microstructured optical hbers, which are designed to exhibit extremely high optical nonlinearities. If nanojoule femtosecond laser pulses are launched into such a hber, the combination of different nonlinear optical processes leads to the creation of new frequency components. Therefore, the laser bandwidth can be increased dramatically by orders of magnitude. 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

The experimental techniques adopted to measure linear and nonlinear optical properties are quite different and must be discussed separately. In broad terms, linear properties can be measured using low intensity probes and high spectral resolution. They are usually understood in the frequency domain. Nonlinear responses on the contrary need very large intensities, typically achieved in short pulses, and are discussed in the time domain. In addition to these physical considerations, we have to remember that time-resolved spectroscopy and optical characterization usually require good optical quality samples, so our understanding of the physics of these materials is closely linked to their quality. 

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