Glossary entry

Extinction ratio (ER)

The ratio of the maximum to minimum transmitted optical power of a device or signal, in dB. Quantifies on/off contrast for modulators, filters, and switches.

Fiber & telecom Integrated photonicsUpdated October 2026

The extinction ratio in decibels is

ER = 10 \log_{10} ⁣ (\frac{P_{max}}{P_{min}}) .

For a modulator or switch, ER measures the contrast between fully-on and fully-off states. Higher ER produces sharper switching and lower crosstalk in WDM systems.

For a ring resonator filter, ER is the extinction depth at the resonance wavelength. The depth depends on the coupling regime:

Coupling regime	Extinction at resonance
Critical coupling ( $Q_{i} = Q_{c}$ )	Full extinction (in theory, $\infty$ dB)
Under-coupled ( $Q_{i} < Q_{c}$ )	Partial extinction
Over-coupled ( $Q_{i} > Q_{c}$ )	Partial extinction

Real ring resonators reach 20–40 dB ER at critical coupling; achieving $> 50$ dB requires careful control of coupling gap, propagation loss, and absence of stray feedback.

Typical ER values:

Device	Typical ER
Mach–Zehnder modulator (telecom)	20 – 30 dB
Electro-absorption modulator	12 – 20 dB
Ring resonator filter	15 – 30 dB
Optical switch (MEMS)	40 – 60 dB
Polarization-maintaining components	25 – 30 dB (between principal axes)
Critically-coupled high- $Q$ ring	$> 40$ dB

For digital optical communications, ER also describes the modulated signal: $ER = P_{one} / P_{zero}$ . Standard telecom NRZ-OOK transmitters typically specify ER $> 8.2$ dB; higher ER improves receiver sensitivity but reduces average optical power.

Distinguishable from insertion loss: IL is the loss in the "on" state relative to input, while ER is the on-to-off contrast.

What finite extinction ratio costs a link depends on the reference convention: measured against average power it carries a classic power penalty, while OMA-referenced metrics such as TDECQ do not see it at all, a distinction the fourth experiment in the PAM4 Eye & TDECQ Explorer demonstrates.

Referenced to average power, the penalty for a linear extinction ratio $r$ is $10 \log_{10} [(r + 1) / (r - 1)]$ , the ratio of the average power that carries a given eye opening at finite $r$ to the power that would carry it at infinite $r$ :

ER (dB)	$r$	Penalty (dB)
4	2.5	3.7
6	4.0	2.2
8	6.3	1.4
9	7.9	1.1
10	10	0.9
12	15.8	0.6
15	31.6	0.3
20	100	0.1

The same expression applies to PAM4 with $r$ taken as the outer extinction ratio (top level to bottom level), and PAM4 pays a further $10 \log_{10} 3 = 4.8$ dB relative to NRZ at the same outer OMA because each of its three eyes is one third of the outer opening. Both penalties disappear from OMA-referenced specifications, which is why a PAM4 transmitter is specified by OMA and TDECQ and a low extinction ratio shows up only as a higher average power for the same OMA, as the explorer's experiment shows.