Noise equivalent power (NEP)

Noise-equivalent power is the optical input power at which a detector's signal equals its noise, a signal-to-noise ratio of one, when the output is observed in a 1 Hz bandwidth. It is the detector's noise expressed in optical units: the RMS noise current spectral density $i_n$ at the output, referred back through the responsivity $\mathcal{R}$,

$$\text{NEP}=\frac{i_n}{\mathcal{R}}[\text{W}\mathrm{/}\sqrt{\text{Hz}}]$$

with $i_n$ in A/√Hz. A lower NEP means a more sensitive detector. The unit W/√Hz reflects the fact that white noise current grows as the square root of the bandwidth, so the power that gives SNR = 1 in a bandwidth $B$ is

$$P_{\text{min}}=\text{NEP}\sqrt{B}$$

which at 10 pW/√Hz is 1.0 µW, or $-30.0$ dBm, in 10 GHz, and 32 nW, or $-45.0$ dBm, at 1 pW/√Hz in 1 GHz.

The noise terms

For a photodiode read out by a load resistor $R_L$ or a transimpedance amplifier, the noise present with no light is the sum of three independent current densities,

$$i_n^2=2e{I}_d+\frac{4k_{B}T}{R_L}+i_{\text{amp}}^2$$

where $I_d$ is the dark current and $2e{I}_d$ its shot noise, $4k_{B}T\mathrm{/}{R}_L$ the thermal noise of the load or feedback resistor at temperature $T$, and $i_{\text{amp}}$ the amplifier's input-referred noise current density. For an avalanche photodiode with gain $M$ and excess noise factor $F(M)$, the multiplied part of the dark current $I_{dm}$ adds $2e{M}^{2}F(M)I_{dm}$, and the responsivity in the denominator becomes $M{\mathcal{R}}_0$, so

$${\text{NEP}}_{\text{APD}}=\frac{i_n}{M{\mathcal{R}}_0}$$

which falls with gain for as long as the amplifier and resistor terms dominate $i_n$.

A worked case: an InGaAs photodiode at 1550 nm with $\eta =0.8$ has $\mathcal{R}=1.000$ A/W. With 5 nA of dark current (40 fA/√Hz of shot noise) and a 3 pA/√Hz amplifier, the amplifier term dominates by a factor of 75 and the NEP is 3.0 pW/√Hz. In a 10 GHz bandwidth that is a minimum detectable power of 0.30 µW, $-35.2$ dBm. The signal's own shot noise reaches the 3 pA/√Hz floor at a photocurrent of 28 µA, or $-15.5$ dBm; above that power the receiver is shot-noise limited and the NEP no longer describes its noise.

Values for common front ends

The NEP of a photodiode is almost always set by what reads it out. The values below are computed at 300 K for $\mathcal{R}=1$ A/W from the expression above, with amplifier voltage noise and 1/f noise neglected; they are floors that a real circuit approaches but does not beat.

The table is also a statement about bandwidth. A large feedback resistor has low current noise but, with the photodiode capacitance, a low bandwidth, so the femtowatt NEPs belong to instruments measuring slowly varying light, while receivers at gigahertz bandwidths live in the picowatt range and reach lower powers only with avalanche gain or optical preamplification.

Reading and measuring NEP

Three conventions cause most misreadings. NEP is defined at a stated modulation frequency and is only white where the noise is: below the 1/f corner of the amplifier the NEP rises, which is why weak signals are chopped and recovered with a lock-in amplifier. Some older and infrared literature quotes NEP in watts for a 1 Hz bandwidth, or for a 0.5 s integration time, rather than in W/√Hz; the numbers look the same and are not. And NEP describes the noise with no signal present: at SNR = 1 the signal's own shot noise is negligible only while it is small against the fixed floor, and with no fixed noise at all SNR = 1 would still require $P=2h\nu B\mathrm{/}\eta$, which at 1550 nm with $\eta =1$ is $2.6\times {10}^{-19}$ W per hertz of bandwidth. For infrared detectors whose noise scales with area $A$, the specific detectivity $D^{\ast }=\sqrt{A}\mathrm{/}\text{NEP}$ in cm·√Hz/W is used to compare devices of different size.

NEP is measured by recording the output noise spectral density with the input blocked, dividing by the responsivity measured at the same gain and frequency, and checking that the result does not depend on the analyzer's resolution bandwidth; the photodetector characterization article gives the procedure. For digital links the relevant figure is receiver sensitivity, the power that holds a target error ratio, which is several times the SNR = 1 power and includes the penalties of a real signal. Photon-counting detectors such as the SNSPD are specified by detection efficiency and dark count rate instead.

The Photodiode Noise Calculator computes the NEP from the dark current, load resistor, temperature and amplifier noise, and for an APD from the gain and ionization ratio, and reports the minimum detectable power as SNR = 1 in the chosen bandwidth.

The measurement itself, with a worked example in which the amplifier rather than the detector sets the NEP, is in How to Measure a Detector's NEP and D*.

References: G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010), chapter 4. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019). P. Horowitz and W. Hill, The Art of Electronics, 3rd ed. (Cambridge University Press, 2015), chapter 8.