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Noise Specifications

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Definition: specifications for the noise properties of lasers, for example

German: Rauschspezifikationen

Category: fluctuations and noise

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The strength of noise e.g. of the output of a laser often needs to be quantified – particularly in the context of applications such as frequency metrology, sensitive spectroscopic measurements, or optical fiber communications, where the performance of devices or systems is limited by noise.

Examples of Noise Specifications of Lasers and Optical Amplifiers

Intensity noise is often measured by analyzing the laser output with a photodiode and related electronic equipment such as an electronic spectrum analyzer. It can be specified with a power spectral density of the relative intensity noise as a function of noise frequency. For some purposes, a root-mean-square (r.m.s.) value, essentially the square root of the integral of the power spectral density over some frequency range (e.g. 1 Hz – 1 MHz), is sufficient. However, r.m.s. values without specification of the measurement bandwidth are nonsensical. That bandwidth is determined as follows:

Optical phase noise can be quantified by the power spectral density (PSD) of the phase fluctuations. Alternatively, the PSD of the fluctuations of the instantaneous frequency can be specified. Such power spectral densities often diverge for zero frequency, so that integration down to zero frequency is not possible. For simple random-walk processes, the specification of a coherence time or coherence length or of a linewidth value can be appropriate. Note that linewidth values often depend on the measurement time.

Frequency noise is directly related to phase noise; it is the noise of the instantaneous frequency, the latter being related to the temporal derivative of the phase.

Timing jitter of a pulse train can be quantified as the power spectral density of the timing deviation (e.g. from some noiseless reference) or the timing phase. It is also common to specify an r.m.s. value for a certain range of noise frequencies.

In frequency metrology, the use of a Allan deviation or Allan variance as a function of time is common. These quantities can be calculated from a power spectral density, whereas the opposite calculation is ambiguous.

The noise figure of an electronic or optical amplifier quantifies the amplifier excess noise.

In frequency metrology, it is common to use normalized phase fluctuations x(t) = δφ(t) / (2πν0), i.e., phase fluctuations divided by the mean angular frequency. The time derivative of the normalized phase fluctuations then delivers the normalized frequency fluctuations y(t), i.e., the fluctuations of the instantaneous frequency relative to the mean frequency. For a comparison of the phase noise of sources with different mean frequencies, it is appropriate to compare the power spectral densities Sx(f) of normalized phase fluctuations or Sy(f) of normalized frequency fluctuations, rather than of the phase or frequency excursions themselves, because these normalized fluctuations are what determines the precision and accuracy e.g. of a clock.

Ambient Conditions

Laser noise often depends on ambient conditions. Therefore, it is obviously essential to know what are the ambient conditions for which certain specifications apply. In particular:

The latter is particularly important for specifications of beam pointing fluctuations.

It is not easy to specify laser noise under the influence of ambient noise sources such as vibrations, since it is difficult to quantify these influences. Also, their impact may strongly depend e.g. on the noise frequency: a mechanical setup may have some resonances, making the device very sensitive to vibrations at certain frequencies.

Common Problems

For various reasons, correct noise specifications are often not achieved:

See also: laser noise, intensity noise, relative intensity noise, phase noise, frequency noise, power spectral density, linewidth, coherence, coherence time, narrow-linewidth lasers, laser specifications, Spotlight article 2006-10-09
and other articles in the category fluctuations and noise

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