Mode partition noise (MPN)

Mode partition noise is the noise that appears when the light of a laser running on several longitudinal modes passes through a dispersive medium. In a Fabry-Perot laser the modes draw on the same carrier population, so when one mode takes more power another takes less. The total output is nearly constant and its relative intensity noise can be low, but the power in each individual mode fluctuates strongly and the fluctuations of different modes are anticorrelated. A detector that receives all modes at once sees the fluctuations cancel. After a length of fiber with chromatic dispersion, each mode is delayed by a different amount, the cancellation fails, and the partition becomes intensity noise on the received signal. Because this noise scales with the signal rather than with the receiver noise, it produces an error floor that more received power cannot remove. It confines Fabry-Perot lasers to short links, a few kilometers at 1550 nm at gigabit rates.

Observing it

The total-power RIN of a Fabry-Perot laser, measured with a fast photodiode and an electrical spectrum analyzer, is usually low. Passing the beam through a monochromator or a narrow tunable filter that selects one mode raises the measured RIN substantially, most visibly at low frequencies, which is the signature of partition. In a transmission experiment the effect shows up as a bit-error-rate curve that bends over and flattens as the fiber is lengthened, and as a spread of amplitudes on the eye diagram that a back-to-back measurement does not show. Direct modulation makes it worse, since the mode distribution is rebuilt from spontaneous emission at every turn-on.

The power penalty

Agrawal's textbook treatment, following Ogawa, characterizes the laser by its rms spectral width $\sigma_\lambda$ and a mode partition coefficient $k$ between 0 and 1, which measures how strongly the mode powers fluctuate. Measured values of $k$ are usually quoted in the range of about 0.5 to 0.8 and are hard to predict for a given device. The relative noise level after the fiber is

$$r_\text{mpn} = \frac{k}{\sqrt{2}}\left[1 - e^{-(\pi B L D \sigma_\lambda)^2}\right],$$

where $B$ is the bit rate, $L$ the length and $D$ the dispersion parameter. The resulting power penalty is

$$\delta_\text{mpn} = -5\log_{10}\!\left(1 - \tfrac{1}{2} Q^2 r_\text{mpn}^2\right)\ \text{dB},$$

with $Q = 6$ for a bit error rate near $10^{-9}$. The penalty depends on the single dimensionless product $x = B L D \sigma_\lambda$, the dispersive spread expressed as a fraction of the bit period. With $Q = 6$ it is:

Beyond this the penalty climbs steeply, and it becomes infinite (an error floor at $10^{-9}$) when $r_\text{mpn}$ reaches $\sqrt{2}/Q = 0.236$, at $x = 0.23$ for $k = 0.8$ and $x = 0.33$ for $k = 0.5$. Because $k$ is uncertain and the formula approximate, a common design rule keeps $B L D \sigma_\lambda$ below about 0.1, which holds the penalty near 0.1 dB even at $k = 0.8$ and leaves margin for dispersive intersymbol interference.

Worked link. A 2.5 Gb/s signal from a Fabry-Perot laser with $\sigma_\lambda$ = 2 nm, in standard fiber at 1550 nm with $D$ = 17 ps/(nm·km), has $x$ = 0.085 per kilometer. The rule $x < 0.1$ gives a maximum length of about 1.2 km, where the modes spread by about 40 ps against a 400 ps bit period. With the formula above the error floor arrives between 2.7 km ($k = 0.8$) and 3.9 km ($k = 0.5$). At 1310 nm, where $D$ in standard fiber is near zero, the same laser reaches much farther, which is why Fabry-Perot transmitters are used in the O-band.

Single-mode lasers

A DFB laser with a high side-mode suppression ratio carries so little side-mode power that partition is negligible in most links. Under fast direct modulation a side mode can still build up occasionally during a turn-on transient, and at very low target error rates such rare events can set an error floor. This is one reason telecom DFB lasers are specified with an SMSR of 35 dB or more under modulation as well as CW, and why poor SMSR at some operating points is treated as a failure.

Pitfalls

The penalty formula assumes a Gaussian spectral envelope and small noise; for lasers with only two or three dominant modes, or with $\sigma_\lambda$ that changes under modulation, it is an estimate. Partition noise should not be confused with the pulse broadening caused by dispersion acting on the full spectral width; both grow with $B L D \sigma_\lambda$, but broadening closes the eye deterministically while partition adds random amplitude noise. Feedback and temperature changes alter $k$.

Common questions

Why does mode partition noise not appear back-to-back?

Without dispersion all modes arrive together, and the detector sums their anticorrelated fluctuations into a nearly constant total.

Can more received power fix it?

No. The noise is proportional to the signal, so raising the power raises the noise equally, and the error floor remains. Reducing dispersion, spectral width or bit rate, or changing to a single-mode laser, are the remedies.

References: K. Ogawa, "Analysis of mode partition noise in laser transmission systems," IEEE J. Quantum Electron. QE-18, 849 (1982); G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010); G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).