Edwin Ding

Dissipative soliton resonance in a passively mode-locked fiber laser

The phenomenon of dissipative soliton resonance (DSR) predicts that an increase of pulse energy by orders of magnitude can be obtained in laser oscillators. Here, we prove that DSR is achievable in a realistic ring laser cavity using nonlinear polarization evolution as the mode-locking mechanism, whose nonlinear transmission function is adjusted through a set of waveplates and a passive polarizer. The governing model accounts explicitly for the arbitrary orientations of the waveplates and the polarizer, as well as the gain saturation in the amplifying medium. It is shown that DSR is achievable with realistic laser settings. Our findings provide an excellent design tool for optimizing the mode-locking performance and the enhancement of energy delivered per pulse by orders of magnitude.

Operating regimes, split-step modeling, and the Haus master mode-locking model

We develop an iterative (averaging) method to characterize the mode-locking dynamics in a laser cavity mode locked with a combination of wave plates and a passive polarizer. The model explicitly accounts for the effects of self- and cross-phase modulation, an arbitrary alignment of the fast- and slow-axes of the fiber with the wave plates and polarizer, fiber birefringence, saturable gain, and chromatic dispersion. The general averaging scheme results in the cubic-quintic Ginzburg-Landau equation at the leading order and the Swift-Hohenberg equation at the next order. An extensive comparison between the full model and the averaged equations shows a quantitative agreement that allows for characterizing the stability and operating regimes of the laser cavity.

Generalized Master Equation for High-Energy Passive Mode-Locking: The Sinusoidal Ginzburg–Landau Equation

A generalized master mode-locking model is presented to characterize the pulse evolution in a ring cavity laser passively mode-locked by a series of waveplates and a polarizer, and the equation is referred to as the sinusoidal Ginzburg-Landau equation (SGLE). The SGLE gives a better description of the cavity dynamics by accounting explicitly for the full periodic transmission generated by the waveplates and polarizer. Numerical comparisons with the full dynamics show that the SGLE is able to capture the essential mode-locking behaviors including the multi-pulsing instability observed in the laser cavity and does not have the drawbacks of the conventional master mode-locking theory, and the results are applicable to both anomalous and normal dispersions. The SGLE model supports high energy pulses that are not predicted by the master mode-locking theory, thus providing a platform for optimizing the laser performance.

Scaling Fiber Lasers to Large Mode Area: An Investigation of Passive Mode-Locking Using a Multi-Mode Fiber

The mode-locking of dissipative soliton fiber lasers using large mode area fiber supporting multiple transverse modes is studied experimentally and theoretically. The averaged mode-locking dynamics in a multi-mode fiber are studied using a distributed model. The co-propagation of multiple transverse modes is governed by a system of coupled Ginzburg-Landau equations. Simulations show that stable and robust mode-locked pulses can be produced. However, the mode-locking can be destabilized by excessive higher-order mode content. Experiments using large core step-index fiber, photonic crystal fiber, and chirally-coupled core fiber show that mode-locking can be significantly disturbed in the presence of higher-order modes, resulting in lower maximum single-pulse energies. In practice, spatial mode content must be carefully controlled to achieve full pulse energy scaling. This paper demonstrates that mode-locking performance is very sensitive to the presence of multiple waveguide modes when compared to systems such as amplifiers and continuous-wave lasers.

Dual transmission filters for enhanced energy in mode-locked fiber lasers.

We theoretically demonstrate that in a laser cavity mode-locked by a set of waveplates and passive polarizer, the energy performance can be increased by incorporating a second set of waveplates and polarizer in the cavity. The two nonlinear transmission functions acting in combination can be engineered so as to suppress the multi-pulsing instability responsible for limiting the single pulse per round trip energy in a myriad of mode-locked cavities. In a single parameter sweep, the energy is demonstrated to double. It is anticipated that further engineering and optimization of the transmission functions by tuning the eight waveplates, fiber birefringence, two polarizers and two lengths of transmission fiber can lead to further significant increases. Moreover, the analysis suggests a general design and engineering principle that can potentially realize the goal of making fiber based lasers directly competitive with solid state devices. The technique is feasible and easy to implement without requiring a new cavity design paradigm.

The Proper Orthogonal Decomposition for Dimensionality Reduction in Mode-Locked Lasers and Optical Systems

The onset of multipulsing, a ubiquitous phenomenon in laser cavities, imposes a fundamental limit on the maximum energy delivered per pulse. Managing the nonlinear penalties in the cavity becomes crucial for increasing the energy and suppressing the multipulsing instability. A proper orthogonal decomposition (POD) allows for the reduction of governing equations of a mode-locked laser onto a low-dimensional space. The resulting reduced system is able to capture correctly the experimentally observed pulse transitions. Analysis of these models is used to explain the sequence of bifurcations that are responsible for the multipulsing instability in the master mode-locking and the waveguide array mode-locking models. As a result, the POD reduction allows for a simple and efficient way to characterize and optimize the cavity parameters for achieving maximal energy output.

High-Energy Passive Mode-Locking of Fiber Lasers

Mode-locking refers to the generation of ultrashort optical pulses in laser systems. A comprehensive study of achieving high-energy pulses in a ring cavity fiber laser that is passively mode-locked by a series of waveplates and a polarizer is presented in this paper. Specifically, it is shown that the multipulsing instability can be circumvented in favor of bifurcating to higher-energy single pulses by appropriately adjusting the group velocity dispersion in the fiber and the waveplate/polarizer settings in the saturable absorber. The findings may be used as practical guidelines for designing high-power lasers since the theoretical model relates directly to the experimental settings.

Rogue waves for a system of coupled derivative nonlinear Schrödinger equations.

Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics, plasmas, etc., exhibits RWs only in the regime of modulation instability (MI) of the background. For a system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI and RWs, even if each component has dispersion and cubic nonlinearity of opposite signs. A similar effect is demonstrated here for a system of coupled derivative NLSEs (DNLSEs) where the special feature is the nonlinear self-steepening of narrow pulses. More precisely, these additional regimes of MI and RWs for coupled DNLSEs depend on the mismatch in group velocities between the components, and the parameters for cubic nonlinearity and self-steepening. RWs considered in this paper differ from those of the NLSEs in terms of the amplification ratio and criteria of existence. Applications to optics and plasma physics are discussed.

Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity

We introduce a system with one or two amplified nonlinear sites (‘hot spots’, HSs) embedded into a two-dimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain applied to selected HS cores. The subject of the analysis is discrete solitons pinned to the HSs. The shape of the localized modes is found in quasi-analytical and numerical forms, using a truncated lattice for the analytical consideration. Stability eigenvalues are computed numerically, and the results are supplemented by direct numerical simulations. In the case of self-focusing nonlinearity, the modes pinned to a single HS are stable and unstable when the nonlinearity includes the cubic loss and gain, respectively. If the nonlinearity is self-defocusing, the unsaturated cubic gain acting at the HS supports stable modes in a small parametric area, whereas weak cubic loss gives rise to a bistability of the discrete solitons. Symmetric and antisymmetric modes pinned to a symmetric set of two HSs are also considered.

Symmetric and antisymmetric nonlinear modes supported by dual local gain in lossy lattices

We introduce a discrete lossy system, into which a double “hot spot” (HS) is inserted, i.e., two mutually symmetric sites carrying linear gain and cubic nonlinearity. The system can be implemented as an array of optical or plasmonic waveguides, with a pair of amplified nonlinear cores embedded into it. We focus on the case of self-defocusing nonlinearity and cubic losses acting at the HSs. Symmetric localized modes pinned to the double HS are constructed in an implicit analytical form, which is done separately for the cases of odd and even numbers of intermediate sites between the HSs. In the former case, some stationary solutions feature a W-like shape, with a low peak at the central site, added to tall peaks at the positions of the embedded HSs. The special case of two adjacent HSs is considered too. Stability of the solution families against small perturbations is investigated in a numerical form, which reveals stable and unstable subfamilies. The instability generated by an isolated positive eigenvalue leads to a spontaneous transformation into a co-existing stable antisymmetric mode, while a pair of complex-conjugate eigenvalues gives rise to persistent breathers. This article is a contribution to the volume dedicated to Professor Helmut Brand on the occasion of his 60th birhday.