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Journal of Lightwave Technology

A Mueller matrix formalism for modeling polarization effects in erbium-doped fiber

Jefferson L. Wagener, Dario G. Falquier, J.F. Digonnet, H. J. Shaw

Published Jan 1, 1998• 46 citations
Publisher

Abstract

The effects of erbium anisotropy in erbium-doped fiber lasers, sources, and amplifiers are examined. Starting from basic ion properties, inversion and gain equations are derived analytically to describe polarization dependencies. A novel matrix form of the Er/sup 3+/ rate equations is presented to propagate powers and polarization states. These equations are then numerically integrated and compared to experimentally observed polarization hole burning and polarization dependent gain. The theoretical predictions agree strongly with experiment in all cases.

DOI
10.1109/50.661010

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The effects of erbium anisotropy in erbium-doped fiber lasers, sources, and amplifiers are examined. Starting from basic ion properties, inversion and gain equations are derived analytically to describe polarization dependencies. A novel matrix form of the Er/sup 3+/ rate equations is presented to propagate powers and polarization states. These equations are then numerically integrated and compared to experimentally observed polarization hole burning and polarization dependent gain. The theoretical predictions agree strongly with experiment in all cases.
In Er-doped fiber amplifiers (EDFA), ASE polarized orthogonal to a saturating signal experiences more gain than ASE with the same polarization as the saturating signal.1 The accumulated enhancement of orthogonal ASE degrades the performance of long systems.1,2 This effect has been observed in single EDFAs using differential measurement techniques.3,4 A computer model of polarization hole-burning (PHB) has been presented.5 It postulates that each ion has an ellipsoid-like surface representing the emission and absorption cross-sections. The ratio of the major to minor cross-sections is the anisotropy parameter:
"Doping a part of the optical fiber core by (Er3+ ) ions in presence of external pumping power will lead to form the erbium-doped fiber amplifier (EDFA).The performance of this optical amplifier depends on (the power and the wavelength of the pumping laser, the power and wavelength of the input signal, amplifier length, ion concentration). These parameters will affect the characteristics of EDFA such as amplifier gain, gain saturation, noise figure and output power. However, these characteristics can be determined by solving the EDFA propagation and rate equations. The solution of these equations of two-level laser medium can be done numerically. In this paper, we are proposed a novel method to solve these equations. The reconstructed results are perfectly coincided the well known numerical results.
"Theoretical evaluations of polarization degree of the fluorescence excited in erbium doped fibers (EDF) dependence on the excitation light power are presented. In calculations we use the model of randomly oriented and not interacting Er3+ ions. Assumption of the reduced optical anisotropy of the individual ions (with the absorption/emission cross-sections described with the ellipsoids) is shown to be necessary to get a reasonable agreement with the existing experimental data. Similar values of the anisotropy parameters (0.6-0.7) are also utilized to explain the experimental data on polarization hole burning in EDF earlier."
One component of polarization-dependent gain (PDG) in optical amplifiers has been shown to originate from polarization hole burning (PHB) in the erbium fibers.1 In this paper we quantify its magnitude for copumped amplifiers under operating conditions typical of those used in long-haul amplified systems. We find that PDG can be significant, even when the polarization state of the signal is circular, and that hole burning due to the polarization of the 1480-nm pump laser contributes significantly to the overall polarization-dependent gain of the fiber.
Polarization hole burning (PHB) has been observed in individual erbium-doped amplifiers.1 PHB means that a polarized saturating signal causes anisotropic saturation in an erbium- doped fiber (EDF). The resulting gain measured with a weak probe is maximum when the probe state of polarization (SOP) is orthogonal to the signal SOP and is minimum for the same SOP. The absorption is also anisotropic and is the compliment of the gain; i.e., where the gain is maximum the absorption is minimum and vice versa. The saturation anisotropy is characterized by the difference (in dB) between extrema for gain δG or the absorption δA. If the same order of subtraction is maintained, δG is positive and δA is negative.