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Journal of Optics

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

Serguei I. Stepanov, Liliana O. Martínez-Martínez, E H Hernandez, Peter M. Agruzov, Alexander V. Shamray

Published Jun 10, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1088/2040-8978/17/7/075401

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•Apr 28, 2017•0 citations
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.
"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."
The contribution of the spatially uniform variation of average optical absorption to the dynamics of the transient two-wave mixing (TWM) response is considered. It is shown theoretically and confirmed experimentally that this transient effect, via dynamic population gratings in erbium-doped fibers (EDFs) can ensure a response nearly two times faster in such gratings as compared to the growth rate of fluorescence uniformly excited under similar conditions, and can also result in an additional overshot in the tail of the TWM response. This additional ‘accelerating’ contribution is of even type, and does not influence the odd transient TWM response for the refractive index component of such gratings in the EDFs reported earlier. It is also shown that this effect can be utilized to monitor the formation of the dynamic grating with an auxiliary probe wave of the essentially different non-Bragg wavelength.
The influence of spatial migration of excitation among neighboring Er3+ ions on the dynamics of population grating formation in Er-doped optical fibers is reported. The effect manifests itself in an additional increment in the grating formation rate compared with the fluorescence growth rate observed for the same spatially uniform average light power. The experiments, performed at lambda=1549 nm in the configuration of transient two-wave mixing with two similar single-mode Er-doped fibers with significantly different erbium concentrations (approximately 640 and approximately 5600 parts in 10(6)), demonstrated the essential contribution of this effect to the grating formation rate in the latter fiber. The evaluated diffusion coefficient proved to be approximately 2.3 x 10(-9) cm2/s, which ensures effective migration of the excitation by approximately 48 nm, i.e., by approximately 18 average inter-ion distances in this fiber.
"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."
Results of investigation of transient two-wave mixing via dynamic population gratings in Yb-doped fibers with saturable absorption are reported. The recorded gratings are characterized by submillisecond formation times and at wavelength lambda = 1064 nm need cw recording light power of 1 - 10 mW scale. What is important for different applications, the dynamic gratings were found to be predominantly of a phase type with an admixture of a significantly weaker amplitude component only. As in Er-doped fibers, the amplitude grating component proved to be essentially inferior to the theoretical estimation based on the fiber optical density and saturation power.
Dynamic population Bragg gratings can be recorded in the rare-earth-doped (e.g. doped with erbium or ytterbium) optical fibers with mWatt-scale cw laser power. Two-wave mixing (TWM) via such gratings is utilized in single-frequency fiber lasers and in adaptive interferometric fiber sensors with automatic stabilization of the operation point. Slow and fast light propagation can also be observed in the vicinity of narrow (~20-200Hz) spectral profile of stationary no-degenerate TWM. In particular, slow light propagation is observed for the purely amplitude grating, recorded in the erbium-doped fiber in spectral range 1510-1550nm. In its turn, in ytterbium-doped fibers at 1064nm (or in erbium-doped fiber at the wavelength below 1500nm) the dynamic grating has significant contribution of the phase component, the TWM profile has essentially asymmetric form, and both slow and fast (superluminal) light propagation is possible at different frequency off-sets between the counter-propagating interacting waves.