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Relative Intensity Noise

Acronym: RIN

Definition: noise of the optical intensity (or actually power), normalized to its average value

More general term: intensity noise

German: relatives Intensitätsrauschen

Categories: laser devices and laser physics, fluctuations and noise

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URL: https://www.rp-photonics.com/relative_intensity_noise.html

In the context of intensity noise (optical power fluctuations) of a laser, it is common to specify the relative intensity noise (RIN), which is the power noise normalized to the average power level. The optical power of the laser can be considered to be

power fluctuations

with an average value and a fluctuating quantity δP with zero mean value. The relative intensity noise is then that of δP divided by the average power; in the following, this quantity is called I. The relative intensity noise can then be statistically described with a power spectral density (PSD):

power spectral density of relative intensity noise

which depends on the noise frequency f. It is essentially the Fourier transform of the autocorrelation function of the normalized power fluctuations, and can be measured e.g. with a photodiode and an electronic spectrum analyzer.

The factor of 2 in the formula above leads to a one-sided PSD as usually used in the engineering disciplines. The units of this RIN PSD are Hz−1, but it is common to specify 10 times the logarithm (to base 10) of that quantity in dBc/Hz (see also: decibel). The PSD may also be integrated over an interval [f1, f2] of noise frequencies to obtain a root mean square (r.m.s.) value of relative intensity noise

r.m.s. value of relatively intensity noise

which is then often specified in percent.

Note that it is not sensible to specify relative intensity noise in percent (e.g. as ±0.5%) without clarifying whether this means an r.m.s. value or something else. See the article on noise specifications for more such details.

relative intensity noise spectrum of a laser
Figure 1: Simulated relative intensity noise spectrum of a 1064-nm Nd:YAG laser with 100 mW average output power. The shot noise level of −174 dBc/Hz is reached above 5 MHz. There is also a pronounced peak from relaxation oscillations, and excess noise at low frequencies introduced by the pump source.

RIN from Shot Noise

It might be expected that the amount of RIN of a laser beam will remain constant when the beam is subject to linear attenuation. This is not true, however, when the RIN is limited by shot noise. In that case, the RIN is given by

shot-noise-limited relative intensity noise

As an example, a 1-mW laser beam at 1064 nm with intensity noise at the shot noise limit has a RIN of 3.73 × 10−16 Hz−1 or −154 dBc/Hz.

That PSD is independent of noise frequency (white noise), and it increases with decreasing average power. This can be understood as the introduction of additional quantum noise in the attenuation process.

Quantum-limited RIN measurements should be done by detecting the entire laser power e.g. with a photodiode, while minimizing the influence of excess noise (e.g. thermal noise) from the electronics. For high power levels, it can be challenging to find a sufficiently fast photodetector with high power handling capability, while electronic noise issues are more critical at low power levels.

Questions and Comments from Users

2021-03-08

What is the difference between frequency noise and relative intensity noise?

Answer from the author:

Frequency noise is noise of the instantaneous frequency, which in optics means noise of the optical frequency. That is related to phase noise.

2021-06-04

How to normalize the intensity fluctuations of a HeNe laser, measured with a photodiode?

Answer from the author:

This simply means that you divide the fluctuating power by the average power, obtaining a dimensionless quantity fluctuating around 1. You can then further process that, for example estimate the power spectral density.

2021-07-21

How to convert RIN data with 1/sqrt(Hz) unit into a result with % units?

Answer from the author:

Multiply it with the square root of the detection bandwidth, and with 100 to get percent. The fluctuations of power will of course not fully remain within that percent value, but often go somewhat beyond it.

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See also: intensity noise, noise specifications, quantum noise
and other articles in the categories laser devices and laser physics, fluctuations and noise

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