Experimental Validation of a Black Box Model for L-band Erbium Doped Fiber Amplifiers

We experimentally validate a black box model for long-wavelength erbium doped fiber amplifiers. The agreement between the model and the experiments is closer than in the case of conventionalwavelength erbium amplifiers. Introduction Several models have been proposed to predict gain spectral changes of Erbium Doped Fiber Amplifiers (EDFA) under different saturation conditions [1-3]. Most of these models rely on accurate values of absorption and emission crossection spectra or, equivalently, the intrinsic saturation power at all wavelengths, the geometry and doping characteristics of the doped fiber, and insertion losses of all optical components inside the EDFA (such as isolators, couplers, and background loss of the doped fiber). These parameters are seldom available and extremely difficult to measure in an assembled device by non-destructive methods. An alternative approach is the “black box” model (BBM), i.e., a model based only on external measurements of the complete optical amplifier. Several variants of BBMs have been proposed and refined along the years [4-6]. Instead of crossections, fiber geometry parameters and insertion loss data, a typical BBM uses an empirical formula to predict the gain and noise starting from non destructive measurements in the assembled EDFA. The lack of a theoretical foundation in an empirical model greatly reduces its practical utility, since one is never sure about its accuracy when the EDFA operates under unusual conditions, or whether the model is valid in a different optical amplifier (e.g., Thulium or Praseodymium doped fiber amplifiers, semiconductor amplifiers, and so on). Recently, however, a non-empirical BBM has been developed that is deduced from the rate and propagation equations under the assumption of homogeneously broadened transition [6].In this paper we shall restrict to this particular BBM. This BBM uses two “tilting functions” (i.e., functions of wavelength) for the gain (and two other tilting functions for the noise) which can be measured easily without dismounting the EDFA. In ref [6] this model has been validated in a Conventional-band (C-band, defined as 1525-1560 nm) EDFA. In this paper we present an experimental validation of this BBM in a long wavelength (L-band, 1560-1610 nm) EDFA. Validating the BBM in the L-band is important from the fundamental point of view since this type of EDFA operates in a quite different manner than the C-band EDFA. In the L-band case, the population of a substantial fraction of the ions is inverted not by pump laser directly (as in the case of a C-band EDFA) but by the amplified spontaneous emission (ASE). The theory presented in ref. [6] does not take into account this possibility. Furthermore, it was suggested in ref. [7] that inhomogenously broadening plays an important role in the L-band EDFA. Consequently, it is a priori dubious that the BBM would work in the L-band EDFA. In this paper we present a new theoretical derivation of the BBM and an experimental test for two EDFAs, one operating in the L band and the other in the C-band. Our results validate the BBM in both cases and show that, in fact, agreement with measurements is better in the L-band case. The theory developed suggests that the BBM is, in fact, more general than previously presumed and it should be valid in any single mode waveguide optical amplifier based on homogenously broadened quasi-two level system with single photon transitions. Theory In the frame of homogeneous saturation, the amplifier gain and noise figure are determined by the averaged distribution of the population inversion, which is directly related to the balance between the exc itation of erbium ions by the pump power and the deactivation by the signal lasers. In other words, we can achieve the same saturation conditions using different combinations of pump and signal powers. Therefore, the gain is defined by a wavelength independent scalar, describing the population inversion, and can be interpolated from two different OPTICS XXV ENFMC ANNALS -2002 gain measurements under two different saturation conditions. The gain can be expressed analytically as a linear combination of two tilt ing-functions T(λ,λref) and R(λ,λref) [6]: ) , ( ) ( ) , ( ) ( ref ref dB ref dB R G T G λ λ + λ λ λ = λ (1) The gain in expression (1) is given in decibels . The wavelength independent scalar defining the population inversion is G(λref) and is the gain at an arbitrarily chosen reference (λref) that the amplifier would have if a signal laser at λref were entering the amplifier alone with an input power such that it produces the same average inversion than the case being studied. The tilt ing functions are easily determined from two different gain spectra measured at two different saturation conditions (A and B): ) ( ) ( ) ( ) ( ) , ( ref dB B ref dB A dB B dB A ref G G G G T λ − λ λ − λ = λ λ (2)