Phase noise spectral density

Fig. 2.15. (a) Cross correlation trace of the synchronized titanium sapphire lasers (averaging time 1 s) obtained by SHG in an LBO crystal with cross correlation width AtcToss = 2.4 ps. The pulse widths of the lasers are both 1.4ps. (b) Phase noise spectral density Sj (/) for open and closed servo loop. Note the break in the scale of Sj (/). The figures are taken from [223]... 

The frequency noise power spectral density of a SL typically exhibits a 1/f dependence below 100 kHz and is flat from 1 MHz to well above 100 MHz. Relaxation oscillations will induce a pronounced peak in the spectrum above 1 GHz. The "white" spectral component represents the phase fluctuations that are responsible for the Lorentzian linewidth and its intensity is equal to IT times the Lorentzian FWHM.20 xhe 1/f component represents a random walk of the center frequency of the field. This phase noise is responsible for a slight Gaussian rounding at the peak of the laser field spectrum and results in a power independent component in the linewidth. Figure 3 shows typical frequency noise spectra for a TJS laser at two power levels. 

A typical layout of a squeezing experiment based on a Mach-Zehnder interferometer (Sect. 4.2.3) is shown in Fig. 14.64. The output of a well-stabilized laser is split into two beams, a pump beam bi and a reference beam b2. The pump beam with the frequency co] generates by nonlinear interaction with a medium (e.g., four-wave mixing or parametric interaction) new waves at frequencies o l /. After superposition with the reference beam, which acts as a local oscillator, the resulting beat spectrum is detected by the photodetectors D1 and D2 as a function of the phase difference A0, which can be controlled by a wedge in one of the interferometer arms. The difference between the two detector output signals is monitored as a function of the phase difference A0. Contrary to the situation in Fig. 14.62, the spectral noise power density p(/, 0) (= Pnep per frequency interval d/ = 1 s ) shows a periodic variation with 0. This is due to the nonlinear interaction of one of the beams with the nonlinear medium, which preserves phase relations. At certain values of 0 the noise power density Pn(/, 0) drops below the photon noise limit... 

Noise analysis has been particularly fruitfiil in characterizing various aspects of hydrodynamics, as noted above for the specific case of corrosion processes. First of all, multiphase flows were investigated, either gas/water [78], solid/liquid [79, 80], oil/water [81] or oil/brine [82]. In these flows, fluctuations are due primarily either to fluctuations in transport rates to an electrode or to fluctuations in electrolyte resistance. If one phase preferentially wets the electrode, then there may be fluctuations due to variation in the effective electrode area. Each of these phenomena has a characteristic spectral signature. Turbulent flows close to a wall have been investigated by means of electrochemical noise by using electrochemical probes of various shapes, by measuring the power spectral density of the limiting diffusion current fluctuations [83-86],... 

Another method that uses the random phases, but has no complete control over the spectral characteristics, is called the random complex spectrum method. Its synthesis procedure is as follows. A Gaussian distributed white noise complex spectrum, with a standard deviation of 1, is first generated and then filtered using the amplitude spectrum derived from the target spectral density. Subsequent inverse Fourier transform results in a time series of desired record length. Unlike the previous method, the waves produced by this technique will not match exactly the desired spectral density. Obviously, this method does not also exercise control on the time domain characteristics. However, both these synthesis methods based on random phases have their own proponents. Funke and Mansard describe the rationale associated with each of these methods. 

Moreover, in recent years broad band lasers have appeared which lack any frequency modal structure, at the same time retaining such common properties of lasers as directivity and spatial coherence of the light beam at sufficiently high spectral power density. The advantages of such a laser consist of fairly well defined statistical properties and a low noise level. In particular, the authors of [245] report on a tunable modeless direct current laser with a generation contour width of 12 GHz, and with a spectral power density of 50 /xW/MHz. The constructive interference which produces mode structure in a Fabry-Perot-type resonator is eliminated by phase shift, introduced by an acoustic modulator inserted into the resonator. 

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