Relative Intensity Noise (RIN): How to Measure It

Scope

Relative intensity noise (RIN) is the spectral density of a laser's power fluctuations divided by the square of its mean power, quoted in dB/Hz. This article describes the procedure for measuring the RIN of a single-mode or near-single-mode semiconductor laser via direct detection and electronic spectrum analysis. Coverage includes the standard photodiode-plus-spectrum-analyzer configuration, shot-noise reference calibration, electronic noise floor subtraction, and the dominant measurement errors. Balanced-detector and self-homodyne RIN measurement variants used at the quantum-noise limit are outside scope.

RIN definition and typical values

Relative intensity noise quantifies the random fluctuations in optical power normalized to the average power. The standard definition is the one-sided power spectral density (PSD) of relative power fluctuations:

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

where $⟨P⟩$ is the average optical power and $S_{\delta P}(f)$ is the PSD of the power fluctuation $\delta P(t)=P(t)-⟨P⟩$. The units are 1/Hz, conventionally expressed in dB/Hz as $10{\log }_{10}(\text{RIN})$.

The RIN spectrum of a typical semiconductor laser has three regions:

Typical RIN values for telecom semiconductor lasers:

The shot-noise limit at $\lambda =1550$ nm and detected photocurrent $I_{\text{dc}}$ corresponds to a RIN floor of ${\text{RIN}}_{\text{shot}}=2q\mathrm{/}{I}_{\text{dc}}$, where $q$ is the electron charge. For 1 mA detected DC photocurrent, this is ${\text{RIN}}_{\text{shot}}=3.2\times {10}^{-16}$ Hz${}^{-1}=-155$ dB/Hz.

Measurement principle

The intensity noise of the laser is detected by a photodiode and converted to a photocurrent fluctuation. The AC component of the photocurrent is separated from the DC bias by a bias-tee, amplified to overcome instrument noise, and analyzed on an electronic spectrum analyzer (ESA).

The measured noise PSD on the ESA $S_V(f)$ (in V${}^2$/Hz, often displayed in dBm/Hz) contains contributions from three sources that add as variances:

$$S_V(f)=S_V^{\text{laser}}(f)+S_V^{\text{shot}}(f)+S_V^{\text{elec}}(f),$$

where $S_V^{\text{laser}}$ is the laser intensity noise of interest, $S_V^{\text{shot}}$ is the photodetector shot noise, and $S_V^{\text{elec}}$ is the combined electronic noise floor of the photodetector, amplifier, and ESA.

The shot noise floor at DC photocurrent $I_{\text{dc}}$ is

$$S_I^{\text{shot}}=2q{I}_{\text{dc}}{\text{(in A}}^2\text{/Hz)}\mathrm{.}$$

Translating to RIN:

$${\text{RIN}}_{\text{measured}}(f)=\frac{S_I^{\text{laser}}(f)}{I_{\text{dc}}^2}$$ $$=\frac{S_V^{\text{measured}}-S_V^{\text{shot}}-S_V^{\text{elec}}}{G^2{R}^2{I}_{\text{dc}}^2},$$

where $R$ is the photodiode transimpedance load resistance (typically 50 Ω) and $G$ is the cumulative amplifier gain.

Correct RIN extraction requires subtracting both the electronic noise and the shot-noise floor from the measured spectrum, then normalizing by the squared DC photocurrent.

Equipment

The photodetector bandwidth must comfortably exceed the highest frequency of interest. For RIN measurements up to the relaxation oscillation peak of a typical DFB ($\sim 10$ GHz), a 20 GHz detector is appropriate. Bandwidth-limited detection produces a roll-off in the measured spectrum that is mistaken for laser RIN roll-off.

The detector responsivity at the test wavelength and the absolute optical power must be known with $<5\mathrm{\%}$ accuracy to convert photocurrent to optical power and to verify the shot-noise reference.

RIN measurement procedure

1. Configure the measurement chain

Connect the laser output to the photodetector via a calibrated optical attenuator. The photodetector AC output passes through a bias-tee (the DC arm goes to the current meter) and through the LNA to the ESA input. The photodiode bias voltage is supplied through the bias tee's DC arm.

Verify the chain by injecting a known optical power and measuring the DC photocurrent. The relation $I_{\text{dc}}=\mathcal{R}\cdot P$ (where $\mathcal{R}$ is the responsivity at the test wavelength) confirms detector calibration. Discrepancy indicates either responsivity drift or path loss.

2. Measure the electronic noise floor

With the optical input fully attenuated or the laser turned off (DC photocurrent verified as zero), measure the spectrum on the ESA across the full frequency range of interest. This is $S_V^{\text{elec}}(f)$: the combined detector dark, amplifier, and ESA noise floor.

Record this spectrum for later subtraction. The electronic noise floor is fixed for a given detector + amplifier + ESA configuration; small drift between calibration and measurement is acceptable.

3. Verify shot-noise-limited operation

The signal arm of any RIN measurement must be shot-noise-limited at the operating photocurrent: $S_V^{\text{shot}}\gg S_V^{\text{elec}}$. To verify, illuminate the detector at the same DC photocurrent as the laser measurement with a source whose own intensity noise lies well below the shot noise, and check that the measured spectrum is approximately flat versus frequency and matches the calculated shot-noise level $2q{I}_{\text{dc}}$. A tungsten lamp or an LED shining directly onto a large-area photodiode qualifies, since its excess noise averages out over many spatial modes. A fiber-coupled LED or amplified spontaneous emission source does not: confined to one spatial mode, its beat noise gives a RIN of about $1\mathrm{/}\mathrm{\Delta }\nu$ for an unpolarized source of optical bandwidth $\mathrm{\Delta }\nu$, about $-127$ dB/Hz for 5 THz, far above the shot noise at milliamp photocurrents. For a fiber-pigtailed detector the calibration sweep below is the practical route.

If the measured spectrum is dominated by the electronic noise floor (within $\sim 3$ dB), the shot noise is not adequately above the electronic floor. Reduce the LNA noise figure, increase optical power (and therefore $I_{\text{dc}}$), or improve detector responsivity to recover headroom.

Alternative: calibrate the absolute gain $G$ of the chain by measuring the noise at multiple DC currents (using a variable attenuator) and fitting $S_V(I_{\text{dc}})-S_V^{\text{elec}}=G^2{R}^2(2q{I}_{\text{dc}}+\text{RIN}{I}_{\text{dc}}^2)$: the term linear in photocurrent is the shot noise and fixes $G^2{R}^2$, and the quadratic term is the laser's own noise. This is the shot-noise calibration sweep and is the standard absolute calibration method for RIN measurements.

4. Acquire the laser spectrum

Turn on the laser at the operating point of interest (typically biased $\ge 2I_{\text{th}}$). Measure $S_V^{\text{measured}}(f)$ on the ESA across the full frequency range, with the same resolution bandwidth (RBW) and video bandwidth as the noise floor measurement. Record the DC photocurrent $I_{\text{dc}}$ simultaneously.

Optical power into the detector should be set so that $I_{\text{dc}}$ is in the linear range of the detector (typically 0.1–10 mA) and so that shot noise comfortably exceeds the electronic floor.

5. Compute RIN

For each frequency point:

$$\text{RIN}(f)=\frac{S_V^{\text{measured}}(f)-S_V^{\text{elec}}(f)-S_V^{\text{shot}}(I_{\text{dc}})}{G^2{R}^2{I}_{\text{dc}}^2}\mathrm{.}$$

Equivalently, in decibels, with the noise readings in dBm/Hz at the 50 Ω input of the ESA:

$$\text{RIN [dB/Hz]}=S_{\text{laser}}-P_{\text{dc}}$$ $$P_{\text{dc}}=10{\log }_{10}\frac{I_{\text{dc}}^2\cdot 50\cdot G^2}{{10}^{-3}},$$

where $S_{\text{laser}}$ is the measured noise after the electronic floor and the shot noise have been subtracted in linear units, and $P_{\text{dc}}$ is the DC carrier power referred to the same point. Dividing by ${10}^{-3}$ W expresses the carrier in milliwatts, so it comes out in dBm like the noise readings.

For high-RIN regions (e.g., the relaxation oscillation peak), the shot-noise correction is negligible. For low-RIN regions (the floor between $1\mathrm{/}f$ corner and the relaxation peak), the shot-noise correction is essential.

6. Report

Report:

• RIN as a function of frequency, in dB/Hz
• Operating point: bias current, optical power, temperature
• Frequency range and resolution bandwidth
• Shot-noise calibration method (sweep or reference source) and verified shot-noise floor
• Electronic noise floor in dBm/Hz across the frequency range
• DC photocurrent $I_{\text{dc}}$ during the measurement

Worked example: RIN of a 1550 nm DFB laser

A 1550 nm DFB laser is biased at 50 mA ($I_{\text{th}}=8$ mA) and coupled to an InGaAs PIN photodiode with responsivity $\mathcal{R}=0.9$ A/W via an optical attenuator. The optical power at the detector is set to give $I_{\text{dc}}=1$ mA.

Detector + LNA + ESA gain calibration via shot-noise sweep: $G=23$ dB (a voltage factor of $\approx 14.1$, so $G^2\approx 200$), with 50 Ω load. Shot-noise level at $I_{\text{dc}}=1$ mA:

$$S_V^{\text{shot}}=2q{I}_{\text{dc}}{R}^2{G}^2$$ $$=2\cdot 1.6\times {10}^{-19}\cdot {10}^{-3}\cdot {50}^2\cdot 200$$ $$=1.6\times {10}^{-16}{\text{ V}}^2\text{/Hz},$$

which across the ESA's 50 Ω input is $3.2\times {10}^{-18}$ W/Hz, or $-145$ dBm/Hz. The DC carrier referred to the same point is $I_{\text{dc}}^{2}R{G}^2=10$ mW, or $+10$ dBm, so shot noise alone sets a RIN floor of $2q\mathrm{/}{I}_{\text{dc}}=-155$ dB/Hz.

Electronic noise floor (laser off): $-162$ dBm/Hz across the band, comfortably below shot noise.

Measured spectrum with laser on at $I_{\text{dc}}=1$ mA:

Subtracting shot noise and electronic noise (all in linear units), then normalizing by the carrier $I_{\text{dc}}^{2}R{G}^2$ (+10 dBm):

The relaxation oscillation peak appears near 8 GHz, with a peak RIN of $-140$ dB/Hz. The off-peak RIN of $\sim -150$ dB/Hz is typical of a well-designed telecom DFB laser. The shot-noise correction is significant near the off-peak floor (where the laser RIN is only $\sim 5$ dB above shot noise) and negligible at the relaxation peak.

Sources of measurement error

Electronic noise floor not subtracted. The dominant error in low-RIN measurements. Without subtraction, the apparent floor RIN is artificially elevated and frequency-dependent following the electronic noise profile.

Shot noise not subtracted. For laser RIN within 10 dB of shot noise, omitting the shot-noise subtraction produces a systematic overestimate of laser RIN. The error becomes severe as the laser RIN approaches the shot-noise limit.

Detector bandwidth roll-off mistaken for laser roll-off. The product of detector responsivity and load impedance has a frequency response that rolls off at high frequencies. Without correction by the calibrated chain gain $G(f)$, the measured RIN above the detector 3-dB bandwidth is systematically low. Standard mitigation: measure $G(f)$ via the shot-noise sweep at each frequency.

Photodetector nonlinearity at high optical power. PIN photodiodes saturate above a power-dependent current limit, producing apparent excess noise that scales with optical power but is not laser intrinsic. Verify operation in the linear regime by checking that the shot-noise floor scales as $I_{\text{dc}}$, not slower.

RF pickup and 50/60 Hz line noise. External RF interference at telecom or wireless bands (cellular, Wi-Fi, instrument cooling fans) appears as discrete spurs in the RIN spectrum. Shielding the photodetector and using a Faraday cage if needed eliminates most pickup. Spurs that persist should be excluded from reported RIN.

Polarization-induced fluctuation in the optical path. If the photodetector responsivity is polarization-dependent, polarization drift in the fiber path produces fluctuations interpreted as RIN. Verify polarization stability over the measurement duration or use a polarization-insensitive detector.

Insufficient averaging at low frequencies. Low-frequency RIN ($<1$ kHz) requires long acquisition times to resolve. Standard frequency-domain measurements with $\sim$Hz-level RBW and adequate averaging are required. For $1\mathrm{/}f$-region characterization, time-domain measurement and FFT analysis is often more efficient than direct RF spectrum measurement.

Ground loops and microphonic noise. Mechanical vibration coupling into the photodetector or amplifier produces low-frequency excess noise. Mitigation: isolated power supply, vibration isolation table, short cables.

ESA resolution bandwidth not noted. Reported RIN values must be normalized by 1 Hz (the conventional unit). ESA spectrum readings in dBm at finite RBW must be corrected by subtracting $10{\log }_{10}(\text{RBW}\mathrm{/}1\text{ Hz})$.

Validation

The measured shot-noise level should scale linearly with $I_{\text{dc}}$ across at least one decade. Deviation from linear scaling indicates either detector saturation, electronic-noise-dominated operation, or calibration error.

Repeating the measurement at a second photocurrent, set with the attenuator, checks the shot-noise correction: attenuation leaves the laser's own RIN unchanged while the shot-noise floor $2q\mathrm{/}{I}_{\text{dc}}$ moves with the photocurrent, so the corrected RIN should agree at the two settings. A laser biased below threshold is not a shot-noise reference: its spontaneous emission, confined to one spatial mode and to the cavity resonances, carries beat noise far above the shot-noise level.

The off-peak RIN level for a known device should agree with published values for that device type within $\pm 3$ dB. Disagreement by $>10$ dB indicates calibration error rather than novel device behavior.

When the laser under test is the local oscillator of a coherent receiver, the RIN measured here is suppressed by the receiver's common-mode rejection; how much, and how to measure that rejection, is in Common-mode rejection in balanced detectors.

Common questions

What is relative intensity noise (RIN)?

RIN describes how strongly a laser's optical power fluctuates: it is the one-sided power spectral density of the power fluctuations, normalized to the square of the mean power. Its unit is 1/Hz, and it is normally quoted in dB/Hz as $10{\log }_{10}(\text{RIN})$, so a more negative value means a quieter laser.

What causes RIN in a semiconductor laser?

Different mechanisms dominate different parts of the spectrum: carrier and current noise below about 100 kHz, the spontaneous-emission floor from there up to the relaxation oscillation frequency, and the resonance between carriers and photons, which produces a peak at that frequency. Above the relaxation oscillation the noise rolls off.

How do you measure RIN?

Detect the laser on a photodiode with a bandwidth of at least twice the relaxation oscillation frequency, split off the AC part of the photocurrent with a bias tee, amplify it with a low-noise amplifier and record its spectrum on an electronic spectrum analyzer. Subtract the electronic noise floor, recorded with the laser off, and the shot noise, then divide by $G^2{R}^2{I}_{\text{dc}}^2$, where $R$ is the load resistance and $G$ the chain gain, calibrated from shot noise measured at several photocurrents.

What is a typical RIN value for a laser diode?

In the flat region below the relaxation oscillation, telecom DFB lasers typically reach $-150$ to $-160$ dB/Hz, while multimode 1310 nm lasers and 850 nm VCSELs sit at $-130$ to $-145$ dB/Hz. The DFB laser in the worked example measures about $-150$ dB/Hz between 100 MHz and 5 GHz and $-140$ dB/Hz at its relaxation oscillation peak near 8 GHz.

What is the shot-noise limit of RIN?

Shot noise sets a floor of $2q\mathrm{/}{I}_{\text{dc}}$ that depends only on the detected DC photocurrent: $-155$ dB/Hz at 1 mA, and 10 dB lower for each tenfold increase in photocurrent. Laser RIN within 10 dB of this floor must be corrected for the shot-noise contribution, or the result overestimates the laser's noise.

References

For the foundational treatment of laser intensity noise including the shot-noise floor and the quantum origin of RIN, see Coldren, Corzine, and Mašanović (2012), chapter 4. For the relaxation oscillation contribution to RIN in semiconductor lasers, see Petermann (1991), Laser Diode Modulation and Noise. For shot-noise calibration procedures and modern RIN measurement automation, see Yariv and Yeh (2007), Photonics: Optical Electronics in Modern Communications.