Polarization extinction ratio (PER)

PER quantifies how purely polarized a light source or how well a polarization-maintaining component preserves polarization. It is defined for a linearly polarized signal as:

$$\text{PER} \;=\; 10 \log_{10}\!\left(\frac{P_\text{principal}}{P_\text{orthogonal}}\right),$$

where $P_\text{principal}$ is the power along the dominant polarization axis and $P_\text{orthogonal}$ is the power along the perpendicular axis. Higher PER indicates purer polarization.

PER is sometimes confused with extinction ratio (ER), which describes the on/off contrast of a modulator. The two are distinct: PER is about polarization purity (axes orthogonal in space), while ER is about temporal modulation contrast (states differing in intensity over time).

Typical PER specifications:

Source / component	PER (typical)
Free-space HeNe laser	$>$ 1,000:1 ($>$ 30 dB)
Telecom DFB pigtailed in PM fiber	18 – 25 dB
External cavity diode laser, polarized output	30 – 50 dB
Premium PM fiber (single span, controlled environment)	25 – 35 dB
Long PM fiber link (deployed)	15 – 25 dB
Standard polarization beam splitter	25 – 30 dB
High-extinction PBS	35 – 50 dB
Polarizing sheet (cheap polarizer)	10 – 25 dB
Quarter-wave plate (cross-coupling)	$>$ 35 dB (off-design wavelength reduces this)

PER degradation mechanisms.

For PM fiber transport, PER drops as the fiber experiences:

Disturbance	Effect on PER
Temperature variation	Random walk: PER degrades by $\sim$ 0.5 dB per K excursion (depends on fiber type)
Bending	Each tight bend ($<$ 30 mm radius) adds $\sim$ 1 – 5 dB PER degradation
Connector mating	Each connector adds $\sim$ 5 – 15 dB degradation (angular alignment limit)
Lateral stress	$\sim$ 0.3 dB / N lateral force
Aging	$<$ 1 dB / decade for high-quality PM fiber in stable environment

PER vs PDL relationship. PER characterizes polarization purity of a signal. PDL characterizes polarization-dependent insertion loss of a device. The two interact: a device with finite PDL reduces the PER of a transmitted signal by an amount that depends on the input polarization orientation relative to the device's principal axes.

If the input PER is $r_\text{in}$ and the device PDL is $p$, the output PER (worst case, polarization aligned with high-loss axis) is:

$$r_\text{out} \;\approx\; r_\text{in} \cdot p^{-2}.$$

So a 30 dB PER input through a device with 0.5 dB PDL exits with $\sim$ 27 dB PER in the worst case orientation.

PER measurement. Standard PER measurement uses a rotating linear polarizer (or fixed polarizer with rotating sample) and a power meter. The minimum and maximum measured powers give PER = $10 \log_{10}(P_\text{max}/P_\text{min})$. Care must be taken to:

• Use a polarizer with much higher extinction (typically 40+ dB) than the PER being measured
• Stabilize temperature during the measurement
• Apply consistent fiber routing (PER varies with fiber arrangement)

For high-PER measurements ($>$ 35 dB), specialized polarization analyzers (Stokes-vector measurement) provide better accuracy than simple polarizer rotation.

PER is particularly critical in:

• Coherent telecom receivers — local oscillator polarization stability
• Atomic-physics experiments — laser cooling and trapping require well-defined polarization
• Interferometric sensors — polarization drift would otherwise produce false signals
• Polarization-multiplexed transmission — channel-to-channel isolation