Relative intensity noise (RIN)

Relative intensity noise (RIN) characterizes the random fluctuations of a laser's output power, normalized so that the result is independent of absolute power level:

$$\text{RIN}(f)=\frac{S_{\delta P}(f)}{⟨P{⟩}^2},$$

where $⟨P⟩$ is the average optical power and $S_{\delta P}(f)$ is the one-sided power spectral density of the power fluctuation $\delta P(t)=P(t)-⟨P⟩$. Units are 1/Hz; values are conventionally reported in dB/Hz as $10{\log }_{10}(\text{RIN})$.

The RIN spectrum of a typical semiconductor laser shows characteristic frequency-dependent structure:

Typical floor RIN values:

The shot-noise limit at detected DC photocurrent $I_{\text{dc}}$ corresponds to a RIN floor of ${\text{RIN}}_{\text{shot}}=2q\mathrm{/}{I}_{\text{dc}}$. For $I_{\text{dc}}=1$ mA this is $-155$ dB/Hz, for 10 mA $-165$ dB/Hz; the floor falls 10 dB per decade of detected current, which is why a laser specified at $-160$ dB/Hz cannot be measured at 1 mA of photocurrent. Laser RIN is bounded below by the shot-noise limit for the chosen detection power, and a measurement reports the sum of the two unless the shot term is subtracted.

Shape and scaling from the rate equations

The small-signal rate equations give the spectrum its shape. Above the $1\mathrm{/}f$ region the RIN of a single-mode laser is a second-order resonance,

$$\text{RIN}(f)\propto \frac{a+b{f}^2}{{(f_r^2-f^2)}^2+{\left(\gamma f\mathrm{/}2\pi \right)}^2}$$

peaking at the relaxation oscillation frequency $f_r$ with a width set by the damping rate $\gamma$. Above the peak it falls as $f^{-4}$ while $a$ dominates the numerator, and as $f^{-2}$ once $b{f}^2$ does. Because $f_r^2$ grows linearly with the power above threshold and the peak height falls with it, the low-frequency RIN of a semiconductor laser drops rapidly with bias, roughly as $P^{-3}$ in the simplest treatment (Coldren, Corzine, and Mašanović, chapter 5), which is why RIN specifications are quoted at a stated bias and why a laser run near threshold is a poor analog source. The same resonance is what optical feedback drives into chaos: in the coherence-collapse regime the RIN rises by tens of dB with structure at $f_r$ and at the external-cavity free spectral range, so a RIN spectrum is often the first place a bad connector shows up (optical feedback regimes).

For an analog link the consequence is direct. For a sinusoidal signal with modulation depth $m$, the electrical signal-to-noise ratio set by the source alone is $\text{SNR}=m^2\mathrm{/}(2\text{RIN}\cdot B)$, so at $m=1$ a $-155$ dB/Hz laser in a 1 GHz bandwidth gives 62 dB, and a $-150$ dB/Hz laser 57 dB, before shot and thermal noise are counted.

RIN matters for analog optical links (where it sets the SNR floor independent of received power), for coherent communication (where it contributes to phase noise via amplitude-to-phase coupling), and for any system using lasers as a precision reference. Measurement procedure is in Relative Intensity Noise Measurement of Semiconductor Lasers.

In a coherent receiver the local oscillator's RIN is suppressed by the balanced detector's common-mode rejection; the numbers, including how much rejection is needed to put the RIN below the shot noise, are worked in Common-mode rejection in balanced detectors.

References: L. A. Coldren, S. W. Corzine, and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), chapter 5. G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010), section 3.5. K. Petermann, Laser Diode Modulation and Noise (Kluwer, 1988), chapter 7.