Second/third harmonic generation

Electric field-induced second harmonic generation, f Third-harmonic generation. 

Second harmonic generation THG Third harmonic generation) [27]. 

Optical harmonic generation (second and third order) Nonlinear coefficients, orientation 26,27... 

Sipe J E, Moss D J and van Driel H M 1987 Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals Phys. Rev. B 35 1129-41... 

Because the second term in the brackets contains 3v in the sine function, radiation at a frequency which is three times that of the incident radiation is generated. This is referred to as third harmonic generation. The first term in brackets indicates that some radiation of unchanged frequency also results. 

The Nd YAG rod is a few centimetres long and contains 0.5 to 2.0 per cent by weight of Nd. In pulsed operation the peak power of each pulse is sufficiently high for generation of second, third or fourth harmonics at 533 nm, 355 nm and 266 nm, respectively, using suitable crystals. 

Almost every unique frequency contained in the vibration signature of a machine-train can be directly attributed to a corresponding mechanical motion within the machine. For example, the constant endplay or axial movement of the rotating element in a motor-generator set generates elevated amplitude at the fundamental (lx), second harmonic (2x), and third harmonic (3x) of the shaft s true running speed. In addition, this movement increases the axial amplitude of the fundamental (lx) frequency. 

Table 1 Coefficients for 7[ (a ) for third harmonic generation (THG), degenerate four wave mixing (DFWM), electric field induced second harmonic generation (ESHG), and Kerr effect in methane at the experimental geometry rcH = 2.052 a.u. A CCSD wavefunction and the t-aug-cc-pVDZ basis were used. (Results given in atomic units, the number in parentheses indicate powers of ten.)...

Fig. 8. Examples of some of the donor-acceptor substituted TEEs prepared for the exploration of structure-property relationships in the second- and third-order nonlinear optical effects of fully two-dimensionally-conjugated chromophores. For all compounds, the second hyperpolarizability y [10 esu], measured by third harmonic generation experiments in CHCI3 solution at a laser frequency of either A = 1.9 or 2.1 (second value if shown) pm is given in parentheses. n.o. not obtained...

Schaller, R. D., Johnson, J. C Wilson, K R., Lee, L. F., Haber, L. H. and Saykally, R. J. (2002) Nonlinear chemical imaging nanomicroscopy from second and third harmonic generation to multiplex (broad-bandwidth) sum frequency generation near-freld scanning optical microscopy. 

The first term in constant phase of E(r. z) that arises from the refractive index of the medium through which the beams propagate. The second term vanishes because of conservation of momentum in the harmonic generating medium. The third term is the Gouy phase, which changes by (n — m) n as the beams pass through a focal point. 

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

These effects Q.2) are all driven by the same third-rank frequency dependent nonlinear susceptibility x2(-u>3 w,, u>2).d is sometimes preferred for second-harmonic generation (SHG). 

Figure 2.20 The spectral range covered by the fundamental radiation of a Ti-sapphrre laser and the various harmonic generation processes second, third, and fourth harmonic generation (SHG, THG, and FHG, respectively) (courtesy of Quantronix).

We have listed the hrst three of the six experiments (a-c) below. Arrange them in order of complexity (and, hence, the order in which they will be performed), identifying the correct ordinal language (hrst, second, third) where indicated. (SHG = second harmonic generation SAM = self-assembled monolayer.)... 

Lasers and LEDs. Dye lasers pumped by Ar ion, Cu ion and frequency doubled Nd YAG solid state lasers. LEDs operating at 635-652, diode lasers at 635 (AlGalnP), 652 (InGaAlP) and 730 mn (AlGaAs). Solid state pulsed lasers, (e.g. Nd YAG, Nd YLF) operating at second, third and fourth harmonic generation. 

Where P is the polarisation and the others the linear (1) and non-linear, second (2) and third order (3) terms. Examples of important second order effects are frequency doubling and linear electro-optic effects (Pockles effect), third order effects are third-harmonic generation, four-wave mixing and the quadratic electro-optic effect (Ken-effect). 

---