| Summary: | Actively mode-locked fiber ring lasers (AMLLs) with loss modulators are used to generate approximately <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>100</mn><mspace width="0.166667em"></mspace><mi>ps</mi></mrow></semantics></math></inline-formula> pulses with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>100</mn><mspace width="0.166667em"></mspace><mi>MHz</mi></mrow></semantics></math></inline-formula> repetition. RF detuning around the fundamental frequency, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>f</mi><mn>0</mn></msub></semantics></math></inline-formula>, causes a loss in phase lock (unlocking) of cavity modes and partial mode locking. Multiple RF inputs are shown, theoretically, to relock and extend the locking range of cavity modes in a detuned partially mode-locked AMLL. A custom-built Yb<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula>-doped AMLL with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>f</mi><mn>0</mn></msub><mo>=</mo><mn>26</mn><mspace width="0.166667em"></mspace><mi>MHz</mi></mrow></semantics></math></inline-formula>, and operating wavelength of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1064</mn><mspace width="0.166667em"></mspace><mi>nm</mi></mrow></semantics></math></inline-formula>, was used to experimentally verify the theoretical predictions. Two RF sinusoidal signals with constant phase and equal amplitude resulted in an extension of the range by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>X</mi><mi>n</mi></msub><mo>=</mo><mn>6.4</mn><mspace width="3.33333pt"></mspace><mi>kHz</mi></mrow></semantics></math></inline-formula> in addition to the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mi>n</mi></msub><mo>=</mo><mn>14.34</mn><mspace width="0.166667em"></mspace><mi>kHz</mi></mrow></semantics></math></inline-formula> with single input for the mode <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>10</mn></mrow></semantics></math></inline-formula>. An increase in locking range was also observed for higher modes. Pulsewidth reduction to approximately <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>205</mn><mspace width="0.166667em"></mspace><mspace width="4.pt"></mspace><mi>ps</mi></mrow></semantics></math></inline-formula> from about <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mspace width="0.166667em"></mspace><mspace width="4.pt"></mspace><mi>ns</mi></mrow></semantics></math></inline-formula> was also observed in the AMLL.
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