Power-Dependent Attenuation and Dynamic Grating of Un-Pumped EDF Sagnac Loop and Their Applications to Single Frequency Lasers

The un-pumped erbium-doped fiber (EDF) Sagnac loop (UESL) is an attractive com ponent for narrow line lasers due to the saturable absorption (SA). Its characteristics are analyzed in detail in this paper, including the power dependent attenuation (PDA) and the dynamic Bragg grating based on the optical standing wave in the loop. The former can be utilized to enhance the side mode suppression ratio (SMSR) of lasers, and the latter is useful to reduce the linewidth effectively. To describe their characteristics, two equations are deduced. One equation defines the averaged absorption of the loop as a function of the EDF length and input power. The other is the spectrum of dynamic grating in the medium with losses, illustrating how the peak reflectivity decreases with the loss. Both effects are related to the material properties, especially the absorption <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{{\bm{\alpha }}}_{\bm{0}}}$</tex-math></inline-formula> at the low power limit, the saturating power <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{{\bm{I}}}_{{\bm{sat}}}}$</tex-math></inline-formula>, and the coefficient of index change over the loss <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> based on the universal Kramers-Kronig (K-K) relations. The two effects were measured experimentally; by fitting the experimental data with the theoretical calculations, the typical values were given as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\alpha }_0} = 1.6{\bf }\,{{\mathrm{m}}^{ - 1}}$</tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{I}_{sat}}{\rm{ = 0}}{\rm{.91}}{\bf }\text{ mW}$</tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K = 1.0\times{{10}^{ - 7}} \, {\rm{ m}}$</tex-math></inline-formula> for the EDF used in this work. The UESL was connected in a fiber laser as a mode controller; the multiply modes was suppressed and a stable single longitudinal mode operation was obtained; the instantaneous linewidth was narrowed from 660 Hz to 190 Hz experimentally.