The most general form of noise figure of the EDFA can be noted from Page no. 363, Equation no. 5.40, chapter 5 of book on EDFA  Devices and System by Desurvire (old book). The assumption is that Gain is large enough to dominate shot and beat noise over the detector's thermal noise.  No exact formula is available for the prediction of EDFA noise figure in the saturation region.Fundamental limit of EDFA noise figure is 3 dB. The NF is equal to twice the spontaneous emission factor in the high gain regime.

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Desurvire's "Erbium-Doped Fiber Amplifiers", suggested by Subhash, is an excellent reference.  It includes both quantum and classical descriptions of noise, and discusses lower gain regimes where the simple formula is inadequate.

Hermann Haus noted in 1998 that the definition of noise figure used for optical amplifiers differs from that adopted for radio frequency amplifiers, although the differences are small in the high gain regime.  He proposed an alternative definition which avoids problems with low level signals and the treatment of cascaded amplifiers.

Haus' 2000 paper offers a more detailed discussion of quantum effects which are negligible at RF and microwave frequencies, and proposes alternative definitions of noise figure which apply in both classical and optical domains.

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=726763

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=847759

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471589772.html

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471266272.html

Thanks to all you guys.

Let me more specify my question. Actually, what I would like to confirm or determine is the criteria to use the equation NF = 1/G(2Pase/hν+1). This equation requires to apply on the linear gain region. To quantify that region, people usually define it when the G > 10 dB or 20 dB? Is that true? I do remember I saw relative contents in some books, such as P.C. Becker's, but I could not find out again any more.

Desurvire presents a derivation of the formula which assumes:

There is no constraint on the gain.

The definition you specify ignores signal-dependent terms associated with ASE beat noise and ASE shot noise.  It is conventional to assume that NF is measured with sufficiently high signal powers for these terms to be ignored.

The signal level dependence is referred to by Desurvire, and discussed in more detail in the 1998 and 2000 papers by Haus.

The definition proposed by Haus is independent of signal level, is compatible with the IEEE definition applied at radio frequencies, and obeys a simple cascading formula for concatenated amplifiers or attenuators.  It approaches the same 3 dB limit for high gain fully-inverted amplifiers, but differs when the inversion is incomplete or when passive losses are present at the amplifier input.  For practical amplifiers, Haus' definition will typically give different values to the conventional formula.