Second harmonic frequency

Figure 15. Fourier analysis of an asymmetric polarization wave showing that it is comprised of components at the fundamental frequency, second harmonic frequency, and zero frequency (DC).

Equation (2) can be expanded to a form that more directly shows the existence of high frequency (second harmonic generation or frequency doubling - f= 2go) and low frequency (electro-optic - f=0) phenomena. 

The curve is elevated relative to zero by a constant amount (0.125) and has a contribution of 2o), double the modulation frequency (+, second harmonic). Both these contributions are not included in the experimental reversing heat flow which contains only the contribution to the first harmonic ( , see Sect. 4.4.3). Accepting the present analysis, it is possible to determine y and x from the reversing heat capacity by matching the last term of the equation in Figs. 6.118 and 4.131, and then use the paramters describing the match to compute (A), the actual response of the TMDSC to the quasi-isothermal temperature modulation. 

Optical second-harmonic generation (SHG) has recently emerged as a powerful surface probe [95, 96]. Second harmonic generation has long been used to produce frequency doublers from noncentrosymmetric crystals. As a surface probe, SHG can be caused by the break in symmetry at the interface between two centrosymmetric media. A high-powered pulsed laser is focused at an angle of incidence from 30 to 70° onto the sample at a power density of 10 to 10 W/cm. The harmonic is observed in reflection or transmission at twice the incident frequency with a photomultiplier tube. 

SHG Optical second-harmonic generation [95, 96] A high-powered pulsed laser generates frequency-doubled response due to the asymmetry of the interface Adsorption and surface coverage rapid surface changes... 

Shen Y R 1989 Surface-properties probed by second-harmonic and sum-frequency generation Nature 337 519-25... 

Ohihoff C, Lupke G, Meyer C and Kurz H 1997 Static and high-frequency electric fields in silicon MOS and MS structures probed by optical second-harmonic generation Phys. Rev. B 55 4596-606... 

DeLong K W, Trebino R, Hunter J and White W E 1994 Frequency-resolved optical gating with the use of second-harmonic generation J. Opt. Soc. Am. B 11 2206-15... 

Pumping is with a flashlamp, as in the case of the ruby laser, and a pulse energy of the order 1 J may be achieved. Frequency doubling (second harmonic generation) can provide tunable radiation in the 360-400 nm region. 

One of the foremost potential appHcations of LB films is in the generation of second harmonic radiation at optical frequencies. 

The second term on the right-hand side, a component oscillating at frequency 2co, represents the second harmonic of the incident beam. This component of the polarization vector can radiate light at the frequency 2co. Observation of the second harmonic generation was demonstrated in the early 1960s using mby lasers (59). 

Materials for Frequency Doubling. Second-order NLO materials can be used to generate new frequencies through second harmonic generation (SHG), sum and difference frequency mixing, and optical parametric oscillation (OPO). The first, SHG, is given in equation 3. 

Barium sodium niobium oxide [12323-03-4] Ba2NaNb 02, finds appHcation for its dielectric, pie2oelectric, nonlinear crystal and electro-optic properties (35,36). It has been used in conjunction with lasers for second harmonic generation and frequency doubling. The crystalline material can be grown at high temperature, mp ca 1450°C (37). 

Torsional criticals should be at least 10% away from the first or second harmonics of the rotating frequency. Torsional excitations can be excited by some of the following ... 

Unlike linear optical effects such as absorption, reflection, and scattering, second order non-linear optical effects are inherently specific for surfaces and interfaces. These effects, namely second harmonic generation (SHG) and sum frequency generation (SFG), are dipole-forbidden in the bulk of centrosymmetric media. In the investigation of isotropic phases such as liquids, gases, and amorphous solids, in particular, signals arise exclusively from the surface or interface region, where the symmetry is disrupted. Non-linear optics are applicable in-situ without the need for a vacuum, and the time response is rapid. 

In a second kind of infrared ellipsometer a dynamic retarder, consisting of a photoelastic modulator (PEM), replaces the static one. The PEM produces a sinusoidal phase shift of approximately 40 kHz and supplies the detector exit with signals of the ground frequency and the second harmonic. From these two frequencies and two settings of the polarizer and PEM the ellipsometric spectra are determined [4.316]. This ellipsometer system is mainly used for rapid and relative measurements. 

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. 

Many electrical problems, or problems associated with the quality of the incoming power and internal to the motor, can be isolated by monitoring the line frequency. Line frequency refers to the frequency of the alternating current being supplied to the motor. In the case of 60-cycle power, monitoring of the fundamental or first harmonic (60 Hertz), second harmonic (120 Hz), and third harmonic (180 Hz) should be performed. 

The shift in vibration profile is the result of the linear motion of the pistons used to provide compression of the air or gas. As each piston moves through a complete cycle, it must change direction two times. This reversal of direction generates the higher second harmonic (2x) frequency component. 

There is a potential for unstable flow through pumps, which is created by both the design-flow pattern and the radial deflection caused by back-pressure in the discharge piping. Pumps tend to operate at their second-mode shape or deflection pattern. This mode of operation generates a unique vibration frequency at the second harmonic (2x) of running speed. In extreme cases, the shaft may be deflected further and operate in its third (3x) mode shape. Therefore, both of these frequencies should be monitored. 

Rolling-element bearings The ability to monitor rolling-element or anti-friction bearing defects requires the inclusion of multiples of their rotating frequency. For example, with ball-pass inner-race bearings, the bandwidth should include the second harmonic (2x). 

Internal (i.e., bearing) and offset misalignment also excite the second (2x) harmonic frequency. Two high spots are created by the shaft as it turns though one complete revolution. These two high spots create the first (lx) and second harmonic (2x) components. 

Friedly (F4) expanded the theoretical analysis of Hart and McClure and included second-order perturbation terms. His analysis shows that the linear response of the combustion zone (i.e., the acoustic admittance) is not sign-ficantly altered by the incorporation of second-order perturbation terms. However, the second-order perturbation terms predict changes in the propellant burning rate (i.e., transition from the linear to nonlinear behavior) consistent with experimental observation. The analysis including second-order terms also shows that second-harmonic frequency oscillations of the combustion chamber can become important. 

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