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Physical Review A

Slow and fast light via two-wave mixing in erbium-doped fibers with saturable absorption

Serguei I. Stepanov, Marcos Plata Sánchez

Published Nov 30, 2009• 17 citations
Publisher

Abstract

We report experimental observation of slow or fast light in configuration of counterpropagating saturating and probe waves in erbium-doped fibers with saturable absorption. The delayed or accelerated probe light propagation is shown to be associated with two-wave mixing (TWM) between these two waves via dynamic population grating. As compared with recording at 1526 nm from the central region of ${\text{Er}}^{3+}$ fundamental absorption spectrum, at 1485 nm, the population grating has significant admixture of the refractive index component. This results in a significant asymmetry of the TWM-induced transmittance of the probe wave as a function of the frequency offset $\ensuremath{\Delta}\ensuremath{\Omega}$ between the waves and shifts position of the maximum group delay from zero $\ensuremath{\Delta}\ensuremath{\Omega}$. The same reason ensures appearance of a significant group advancement for the frequency offset of the opposite sign.

DOI
10.1103/physreva.80.053830

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Abstract Experimental results on effective two-wave mixing (TWM) via dynamic population gratings in saturable erbium doped fibers (EDFs) at liquid nitrogen temperature (77 K) are reported. It is shown that formation of the spectral holes (SHs) by the recording coherent waves in the wavelength region 1500–1540 nm results in a complex dynamics of the transient TWM response. In addition to conventional slow, even-type response due to amplitude grating formation via spectrally uniform EDF absorption saturation we also observed a dominating contribution due to SH formation. In particular, at the recording wavelength 1527 nm the relaxation time of the SH contribution to the TWM process was significantly shorter (< 4.7 ms) and with the effective recording power ∼4 times lower than that for conventional EDF population grating.

Journal of Optics•Jun 11, 2020•5 citations
We report experimental observation of slow or fast light in configuration of counterpropagating saturating and probe waves in erbium-doped fibers with saturable absorption. The delayed or accelerated probe light propagation is shown to be associated with two-wave mixing (TWM) between these two waves via dynamic population grating. As compared with recording at 1526 nm from the central region of Er3+{\text{Er}}^{3+}Er3+ fundamental absorption spectrum, at 1485 nm, the population grating has significant admixture of the refractive index component. This results in a significant asymmetry of the TWM-induced transmittance of the probe wave as a function of the frequency offset \ensuremathΔ\ensuremathΩ\ensuremath{\Delta}\ensuremath{\Omega}\ensuremathΔ\ensuremathΩ between the waves and shifts position of the maximum group delay from zero \ensuremathΔ\ensuremathΩ\ensuremath{\Delta}\ensuremath{\Omega}\ensuremathΔ\ensuremathΩ. The same reason ensures appearance of a significant group advancement for the frequency offset of the opposite sign.
Detailed experimental data on the efficiency of two-wave mixing via population dynamic grating in erbium-doped fiber (EDF) with saturable optical absorption are presented. The measurements were performed for spectral region 1490–1560 nm of the EDF absorption/gain spectrum, both for absorption and for phase (refractive index) components of the dynamic grating. The reported data confirm the earlier results published for some particular recording wavelengths. In particular, the amplitude gratings recorded in EDF in the central part of this region (1520–1560 nm) are significantly less efficient (by more than 1 order of magnitude) than it can be estimated from measurements of a spatially uniform fiber absorption saturation. It is shown, however, that this effect cannot be explained by spatial migration of the Er3+ excited state. At the short-wavelength spectrum side around 1490 nm, the disagreement between the experimentally observed and the evaluated grating amplitude is minimum (∼0.3) and can, probably, be attributed to the polarization mismatch in the counterpropagating recording waves.
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.
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.
We report controllable (slow or fast) propagation of low-intensity probe-light pulses through erbium-doped fiber periodically saturated by the synchronized master-pulse sequence. These two pulse sequences could have significantly different carrier wavelengths within the fundamental absorption spectrum 1470-1570 nm of Er(+3) ions. The effect of fractional delay or advancement grew with the fiber optical absorption at the probe wavelength and could be significantly stronger than that at the saturating wavelength. The probe-pulse advancement was observed in the case when the saturating and probe waves were modulated approximately in antiphase. The observed effects are explained in the framework of a simple model of a periodically saturated homogeneously broadened absorption line.
We present experimental results of two-wave mixing in single-mode Er-doped optical fibers for which dynamic Bragg reflectance gratings are formed as a result of saturation of fiber-optic absorption (i.e., by means of the effect of spatial hole burning). The gratings are probed by the same recording waves at lambda approximately = 1549 nm and are detected as periodic changes of the intensity of light reflected from a Sagnac interferometer (with a piece of the doped fiber included) observed when periodic phase modulation is induced in one of the waves. Both rectangular and sinusoidal modulation were used, which permitted evaluation of the grating recording time (tau(g) approximately = 3 ms for OFS-Fitel EDF-HG980 fiber) and the grating amplitude, which proved to be approximately 6-7 times lower than expected from measurements of saturation of fiber-optic absorption by one wave only.
Abstract Experimental results on effective two-wave mixing (TWM) via dynamic population gratings in saturable erbium doped fibers (EDFs) at liquid nitrogen temperature (77 K) are reported. It is shown that formation of the spectral holes (SHs) by the recording coherent waves in the wavelength region 1500–1540 nm results in a complex dynamics of the transient TWM response. In addition to conventional slow, even-type response due to amplitude grating formation via spectrally uniform EDF absorption saturation we also observed a dominating contribution due to SH formation. In particular, at the recording wavelength 1527 nm the relaxation time of the SH contribution to the TWM process was significantly shorter (< 4.7 ms) and with the effective recording power ∼4 times lower than that for conventional EDF population grating.