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Revista Mexicana de Física

On polarization of the fluorescence in erbium-doped fibers

Liliana O. Martínez-Martínez, E. Hernández-Hernández, Serguei I. Stepanov

Published Jan 1, 2013• 2 citations
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Abstract

"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."

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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:

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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.

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"Experimental results on formation dynamics of population gratings in erbium-doped fiber (EDF) investigated via two-wave mixing (TWM) are reported. It is shown that at all three utilized essentially different recording wavelengths 1492, 1526 and 1568nm the transient TWM response in EDF with low erbium concentration (¼ 640 ppm) has the characteristic rate significantly larger than that of the population of the Er3+ meta-stable level evaluated from the fluorescence dynamics. Additionally in EDF with high erbium concentration (¼ 5600 ppm) the TWM response is faster (even at low recording power) and the relative TWM amplitude is lower than that in EDF with low concentration. General increase of the TWM response rate is explained by contribution of a transient decrease of the fiber average absorption level, while above-mentioned differences observed in heavily doped EDF - by spatial migration of the excited states. The spectral dependence of the later effect is attributed to the difference in the absorption/emission cross-section ratio of the Er3+ ions at the utilized wavelengths."

Revista Mexicana de Física•Dec 1, 2015•1 citation

Fluorescence depolarization in erbium-doped fibers excited in 1490-1570 nm spectral range

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Depolarization of the fluorescence excited at 1492, 1526, and 1568nm in EDF with concentrations 600-5600ppm proved to be in good qualitative agreement with earlier reported reduction in population gratings recorded via saturation of absorption.

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Population gratings in saturable optical fibers with randomly oriented rare-earth ions

Serguei I. Stepanov, Liliana O. Martínez-Martínez, E H Hernandez +2 more

Formation of the dynamic population gratings in optical fibers with randomly oriented rare-earth ions is analyzed with a special interest to the grating component for readout with the orthogonal light polarization. It is shown that as compared with a simple model case of the collinearly oriented dipole-like centers their random orientation leads to approximately 2-times growth of the effective saturation power P sat when it is estimated from the incident power dependence of the fiber absorption or from that of the fluorescence intensity. An optimal incident power, for which the maximum of the dynamic population grating amplitude for collinear light polarization is observed, also follows this change in P sat , while formation of the grating for orthogonal polarization needs essentially higher light power. The reduced anisotropy of the active centers, which is in charge of the experimentally observed weakening of the polarization hole burning (PHB) and of the fluorescence polarization, compensates in some way the effect of random ion orientation. The ratio between the maximum conventional (i.e. for the interacting waves collinear polarizations) two-wave mixing (TWM) amplitude and the initial not saturable fiber optical density proves to be, however, nearly the same as in the model case of collinearly oriented dipoles. The ratio between the PHB effect and the amplitude of the anisotropic grating, which is responsible for TWM of the orthogonally polarized waves, is also not influenced significantly by the reduced anisotropy of ions.

Journal of Optics•Jun 10, 2015•2 citations
"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."
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:
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.
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.
"Experimental results on formation dynamics of population gratings in erbium-doped fiber (EDF) investigated via two-wave mixing (TWM) are reported. It is shown that at all three utilized essentially different recording wavelengths 1492, 1526 and 1568nm the transient TWM response in EDF with low erbium concentration (¼ 640 ppm) has the characteristic rate significantly larger than that of the population of the Er3+ meta-stable level evaluated from the fluorescence dynamics. Additionally in EDF with high erbium concentration (¼ 5600 ppm) the TWM response is faster (even at low recording power) and the relative TWM amplitude is lower than that in EDF with low concentration. General increase of the TWM response rate is explained by contribution of a transient decrease of the fiber average absorption level, while above-mentioned differences observed in heavily doped EDF - by spatial migration of the excited states. The spectral dependence of the later effect is attributed to the difference in the absorption/emission cross-section ratio of the Er3+ ions at the utilized wavelengths."
Formation of the dynamic population gratings in optical fibers with randomly oriented rare-earth ions is analyzed with a special interest to the grating component for readout with the orthogonal light polarization. It is shown that as compared with a simple model case of the collinearly oriented dipole-like centers their random orientation leads to approximately 2-times growth of the effective saturation power P sat when it is estimated from the incident power dependence of the fiber absorption or from that of the fluorescence intensity. An optimal incident power, for which the maximum of the dynamic population grating amplitude for collinear light polarization is observed, also follows this change in P sat , while formation of the grating for orthogonal polarization needs essentially higher light power. The reduced anisotropy of the active centers, which is in charge of the experimentally observed weakening of the polarization hole burning (PHB) and of the fluorescence polarization, compensates in some way the effect of random ion orientation. The ratio between the maximum conventional (i.e. for the interacting waves collinear polarizations) two-wave mixing (TWM) amplitude and the initial not saturable fiber optical density proves to be, however, nearly the same as in the model case of collinearly oriented dipoles. The ratio between the PHB effect and the amplitude of the anisotropic grating, which is responsible for TWM of the orthogonally polarized waves, is also not influenced significantly by the reduced anisotropy of ions.