This is a review of fiber-optic soliton propagation and of methods to determine the soliton content in a pulse, group of pulses or a similar structure. Of central importance is the nonlinear Schrödinger equation, an integrable equation that possesses soliton solutions, among others. Several extensions and generalizations of this equation are customary to better approximate real-world systems, but this comes at the expense of losing integrability. Depending on the experimental situation under discussion, a variety of pulse shapes or pulse groups can arise. In each case, the structure will contain one or several solitons plus small amplitude radiation. Direct scattering transform, also known as nonlinear Fourier transform, serves to quantify the soliton content in a given pulse structure, but it relies on integrability. Soliton radiation beat analysis does not suffer from this restriction, but has other limitations. The relative advantages and disadvantages of the methods are compared.
We report a simple and compact design of a dispersion compensated mode-locked Yb:fiber oscillator based on a nonlinear amplifying loop mirror (NALM). The fully polarization maintaining (PM) fiber integrated laser features a chirped fiber Bragg grating (CFBG) for dispersion compensation and a fiber integrated compact non-reciprocal phase bias device, which is alignment-free. The main design parameters were determined by numerically simulating the pulse evolution in the oscillator and by analyzing their impact on the laser performance. Experimentally, we achieved an 88 fs compressed pulse duration with sub-fs timing jitter at 54 MHz repetition rate and 51 mW of output power with 5.5 × 10 −5 [20 Hz, 1 MHz] integrated relative intensity noise (RIN). Furthermore, we demonstrate tight phase-locking of the laser's carrierenvelope offset frequency (fceo) to a stable radio frequency (RF) reference and of one frequency comb tooth to a stable optical reference at 291 THz.
We consider the evolution of fiber-optic solitons in the presence of loss. Localized power reduction can be cast into a well-known form for which changes of all parameters are known explicitly. We proceed to a sequence of such perturbations with the same total loss, so that still all parameters are known, and eventually take the limit to infinitely many steps. This establishes the connection with distributed loss, and in the limit of vanishing loss reproduces the known results from perturbation theory. Outside this adiabatic limit the mechanism becomes clear that causes deviations: interference between solitons and radiation upsets the balance of dispersive and nonlinear effects characteristic of solitons; as one consequence the soliton continually sheds energy, which goes into radiation. We derive an expression for the radiation production rate in a lossy fiber, and predict quantitatively the distance until the soliton finally decays. Our approach provides quantitative results for fibers with loss small or strong, localized or distributed, and numerical results confirm predictions. It can be generalized to gain rather than loss.
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