Mode-locked Regions Research Articles

Mode-locking and wavelength-tuning of a NPR fiber laser based on optical speckle.

Passively mode-locked fiber lasers based on nonlinear polarization rotation (NPR) have been widely used due to their ability to produce short pulses with high peak power. Nevertheless, environmental perturbations can influence the mode-locked state, making it a challenge for the practical implementation. Therefore, researchers are searching for assessment criteria to quickly assist and maintain mode-locking of NPR fiber lasers. Speckle patterns containing spectral information can be generated when the laser transmits through a scattering medium, which can serve as indicators of the mode-locked state. The mode-locked regions are confined to the area close to the minimum texture contrast of speckle patterns. Based on these characteristics, we manually simulate the automatic mode-locking (AML). In addition, we utilize convolutional neural networks (CNNs) to recognize speckle patterns of wavelength tunable lasers and determine the center wavelength.

Theoretical and experimental analysis of the complex dynamics of spectral RMS width of an erbium-doped figure eight fiber laser

There are a large number of different ultrashort light pulses; a particular case is called noise-like pulses (NLPs), which are ultrashort light pulses that have the characteristic that their electric field has a very complex internal structure. Due to this characteristic, the envelope can take various shapes (Gaussian, triangular, square, complex shape, etc.). Also its amplitude and temporal width vary with respect to the polarization within the cavity. In this work we carry out a theoretical and experimental study of the RMS widths of NLPs measured within the mode-locked regions generated with our laser cavity: an erbium-doped figure eight fiber laser (EDFEFL). The experimental measurements of the RMS widths of the NLPs were compared with the theoretical model of light intensity transmission based on Jones matrices and with the theoretical model of the NOLM. We find that the theoretical model partially fits with the experimental results. We analyze NLPs with a wavelength carrier of 960 nm, repetition rate of 60 MHz, and temporal profile with duration on the order of nanoseconds.

Density of mode-locking property for quasi-periodically forced Arnold circle maps

Abstract We show that the mode-locking region of the family of quasi-periodically forced Arnold circle maps with a topologically generic forcing function is dense. This gives a rigorous verification of certain numerical observations in [M. Ding, C. Grebogi and E. Ott. Evolution of attractors in quasiperiodically forced systems: from quasiperiodic to strange nonchaotic to chaotic. Phys. Rev. A 39(5) (1989), 2593–2598] for such forcing functions. More generally, under some general conditions on the base map, we show the density of the mode-locking property among dynamically forced maps (defined in [Z. Zhang. On topological genericity of the mode-locking phenomenon. Math. Ann. 376 (2020), 707–72]) equipped with a topology that is much stronger than the $C^0$ topology, compatible with smooth fiber maps. For quasi-periodic base maps, our result generalizes the main results in [A. Avila, J. Bochi and D. Damanik. Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Duke Math. J.146 (2009), 253–280], [J. Wang, Q. Zhou and T. Jäger. Genericity of mode-locking for quasiperiodically forced circle maps. Adv. Math.348 (2019), 353–377] and Zhang (2020).

The necessity of the sausage-string structure for mode-locking regions of piecewise-linear maps

Piecewise-smooth maps are used as discrete-time models of dynamical systems whose evolution is governed by different equations under different conditions (e.g. switched control systems). By assigning a symbol to each region of phase space where the map is smooth, any period-p solution of the map can be associated to an itinerary of p symbols. As parameters of the map are varied, changes to this itinerary occur at border-collision bifurcations (BCBs) where one point of the periodic solution collides with a region boundary. It is well known that BCBs conform broadly to two cases: persistence, where the symbolic itinerary of a periodic solution changes by one symbol, and a nonsmooth-fold, where two solutions differing by one symbol collide and annihilate. This paper derives new properties of periodic solutions of piecewise-linear continuous maps on Rn to show that under mild conditions BCBs of mode-locked solutions on invariant circles must be nonsmooth-folds. This explains why Arnold tongues of piecewise-linear maps exhibit a sausage-string structure whereby changes to symbolic itineraries occur at codimension-two pinch points instead of codimension-one persistence-type BCBs. But the main result is based on the combinatorical properties of the itineraries, so the impossibility of persistence-type BCBs also holds when the periodic solution is unstable or there is no invariant circle.

Analysing the temporal amplitude and average output power distribution in the mode-locked regions of an erbium-doped figure-eight fibre laser (theoretical and experimental results)

The noise like pulses (NLPs) are ultrashort light pulses that present very complex dynamics, they are a particular case of the multiple light pulses generated by the partial mode-locked regime. These ultrashort light pulses exhibit very complex behaviour in amplitude and width, in the temporal domain and subsequently in the frequency domain. In this paper we present a theoretical and experimental analysis of temporal amplitude distribution of NLPs within the mode-locked regions of an erbium-doped figure-eight Fibber laser. The mode-locked regions were studied at different settings of the four polarization controllers (HWR1, QWR1) in the ring section and in the nonlinear optical loop mirror (HWR2, QWR2, NOLM) of the fibre laser cavity. We found a wide variety of values of the temporal amplitude of NLPs. The experimental results of the temporal amplitude are compared with simulations generated with the theoretical model based on the theory of polarization of light and the theoretical model of the NOLM. Also, we discovered experimentally that the theoretical model performs well in predicting the complex dynamics of the temporal distribution of amplitude. Finally, we experimentally discovered that the average power output distribution of the cavity has a behaviour which is close to proportional to the temporal amplitude distribution. We analyse NLPs with a carrier wavelength of 1562 nm with typical duration of ns and a repetition rate of 0.9 MHz.

Stable mode-locking region analysis of all normal dispersion optical fiber laser by measuring polarization state inside a resonator

Stable mode-locking region analysis of all normal dispersion optical fiber laser by measuring polarization state inside a resonator

Time-bandwidth product of noise-like pulses within the mode-locked regions of a figure-eight fiber laser: theoretical and experimental analysis

We present for the first time, to the best of our knowledge, a theoretical and experimental analysis of the time-bandwidth product (TBP) of noise-like pulses (NLPs) within the mode-locked regions of an erbium-doped figure-eight fiber laser (EDFEFL). The tuning of the mode-locked regions was carried out by varying and recording the values of the angle of the polarization controllers in the ring section and in the nonlinear optical loop mirror (NOLM). Within the mode-locked regions, we obtained a large variability of the TBPs. We found that the variability of the temporal profile is greater than that of the spectral profile in all mode-locked regions; for this reason, the TBPs of all mode-locked regions have a behavior proportional to the temporal profile. We also identify the temporal and spectral profiles corresponding to the maximum and minimum TBP. Finally, among all the NLPs within the mode-locked regions, we identify and study the one that is Fourier-transform-limited. We analyze NLPs with a carrier wavelength of 1562 nm with duration in the order of nanoseconds and a repetition rate of 0.9 MHz.

Ultrafast Photonics of Ternary RexNb(1-x)S2 in Fiber Lasers.

Two-dimensional (2D) transition metal chalcogenides (TMCs) become more attractive upon addition of a third element owing to their unique structure and remarkable physical and chemical properties, which endow these materials with considerable potential for applications in nanoscale devices. In this work, a RexNb(1-x)S2-based saturable absorber (SA) device for ultrafast photonics applications is studied. The device is assembled by placing RexNb(1-x)S2 nanosheets with a thickness of 1-3 nm onto a microfiber to increase their compatibility with an all-fiber laser cavity. The prepared RexNb(1-x)S2-based device exhibits a modulation depth of 24.3%, a saturation intensity of 10.1 MW/cm2, and a nonsaturable loss of 28.5%. Furthermore, the RexNb(1-x)S2-based device is used to generate ultrashort pulses in an erbium-doped fiber (EDF) laser cavity. At a pump power of 260 mW, the EDF laser operates in a conventional soliton mode-locked region. The pulse width is 285 fs, and the repetition frequency is 61.993 MHz. In particular, the bound-state soliton mode-locking operation is successfully obtained in a pump power range of 300-900 mW. The bound-state pulses are formed by doubling identical solitons with a temporal interval of 0.8 ps. The output power is as high as 47.9 mW, and the repetition frequency is 123.61 MHz. These results indicate that the proposed RexNb(1-x)S2-based SAs have comparable properties to currently used 2D SAs and provide a basis for their application in the field of ultrafast photonics.

Experimental evolution of the temporal and spectral profiles of noise-like pulses within the mode-locked regions of a figure-eight fiber laser.

We present an experimental analysis of the pulse profile variability within the mode-locked regions of an erbium-doped figure-eight fiber laser (EDFEFL). The tuning of the mode-locked regions was carried out by varying and recording the values of the angle of the polarization controllers in the ring section and in the nonlinear optical loop mirror (NOLM). Within the mode-locked regions, we obtained a large variability of the temporal profile, specifically amplitude and width of the noise-like pulses (NLPs). Subsequently, we recorded and studied the changes in the spectral domain. We identified the mode-locked regions where the temporal profile of the pulse remains constant (stationary state), and where it expels sub-packets (non-stationary state). Finally, a theoretical analysis of the power transmission through the polarizing in the ring section and in the NOLM switching characteristic as a function of wave plate angles is also performed, which allows an understanding of the existence of the multiple mode-locked regions and pulse profile adjustability. We analyze NLPs with a carrier wavelength of 1560 nm with duration of the order of nanoseconds and a repetition rate of 0.9 MHz.

Approach to high pulse energy emission of the self-starting mode-locked figure-9 fiber laser.

The figure-9 fiber laser exhibits excellent performance, but improvement of its output pulse energy is restricted by the laser structure design that ensures self-starting mode-locking. In this paper, we propose and verify a novel method to increase the pulse energy of the self-starting figure-9 fiber laser. By reducing the linear phase shift step-by-step in a self-starting figure-9 laser and synchronously increasing the pump power, the output pulse energy can be increased while the laser can always operate in the single-pulse mode-locking region. Using a 112-MHz dispersion-managed soliton figure-9 fiber laser, the effectiveness of our proposed method is verified, and the laser output pulse energy has been successfully increased to 1.4 nJ, which is 5.6 times the pulse energy before the boost. The entire self-starting mode-locking of the laser including the program-controlled joint adjustment is less than 1s with 100% success rate of more than 100 tests. This method can in principle solve the limitation on the output pulse energy caused by the self-start of the figure-9 laser.

Multistate passively mode-locked thulium-doped fiber laser with nonlinear amplifying loop mirror.

In this paper, a multistate passively mode-locked thulium-doped fiber laser with nonlinear amplifying loop mirror is reported. An ultra-high numerical aperture fiber is employed to compensate the cavity abnormal dispersion, and the net cavity dispersion value is fixed at -0.046 ps2. By changing the pump power, three different mode-locked regions, namely Q-switched mode-locking operation, mode-locking operation, and dual-wavelength mode-locking operation, are observed sequentially. When the pump power is raised to the threshold of 1.60W, the transition state of the Q-switched mode locking begins to be observed. When the pump power increases from 2.88W to 8.75W, stable single-wavelength mode-locking operation is obtained. And the center wavelength is 1988.73nm corresponding to the 3dB spectral bandwidth of 11.21nm. As the pump power is raised beyond 8.75W, dual-wavelength mode-locking operation is developed, where the dual wavelengths are 1969.70nm and 1984.12nm with the 3dB spectral bandwidth of ∼4.11 nm and ∼6.14 nm, respectively.

The structure of mode-locking regions of piecewise-linear continuous maps: II. Skew sawtooth maps

In two-parameter bifurcation diagrams of piecewise-linear continuous maps on , mode-locking regions typically have points of zero width known as shrinking points. Near any shrinking point, but outside the associated mode-locking region, a significant proportion of parameter space can be usefully partitioned into a two-dimensional array of annular sectors. The purpose of this paper is to show that in these sectors the dynamics is well-approximated by a three-parameter family of skew sawtooth circle maps, where the relationship between the skew sawtooth maps and the N-dimensional map is fixed within each sector. The skew sawtooth maps are continuous, degree-one, and piecewise-linear, with two different slopes. They approximate the stable dynamics of the N-dimensional map with an error that goes to zero with the distance from the shrinking point. The results explain the complicated radial pattern of periodic, quasi-periodic, and chaotic dynamics that occurs near shrinking points.

Electronic initiation and optimization of nonlinear polarization evolution mode-locking in a fiber laser

We describe a system for automated modelocking and optimization of a fiber laser oscillator employing nonlinear polarization evolution. Using four liquid crystal variable retarders, we fully control the fiber launch and output polarization states, enabling compensation for mechanical and environmental perturbations to the fiber cavity. We demonstrate mapping of the modelocking regions for an ANDi fiber oscillator and demonstrate that local and global optimization algorithms can be used to maintain the laser in the same operating state. This technique enables robust operation of nonlinear polarization evolution modelocked fiber lasers, rivaling the stability of PM fiber lasers while maintaining the advantages of the NPE modelocking mechanism.

Harmonically mode-locked Yb:CALGO laser oscillator.

We present a passively mode-locked Yb:CALGO oscillator with harmonic repetition rate operation up to the third order. It is operated in the solitary regime with a fundamental roundtrip rate of 94 MHz and pulse durations between 200 fs and 600 fs. Harmonic operation was observed being stable for several days. The harmonic mode-locking regions are analyzed depending on intra-cavity dispersion. The transient pulsing dynamics converging to the stable harmonic modes is tracked and a theoretical model describing the pulse moving mechanisms is presented.

The structure of mode-locking regions of piecewise-linear continuous maps: I. Nearby mode-locking regions and shrinking points

The mode-locking regions of a dynamical system are subsets of parameter space within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a distinctive chain structure with points of zero width called shrinking points. In this paper a local analysis about an arbitrary shrinking point is performed. This is achieved by studying the symbolic itineraries of periodic solutions in nearby mode-locking regions and performing an asymptotic analysis on one-dimensional centre manifolds in order to build a comprehensive theoretical framework for the local dynamics. The main results are universal quantitative descriptions for the shape of nearby mode-locking regions, the location of nearby shrinking points, and the key properties of these shrinking points. The results are applied to the three-dimensional border-collision normal form, a model of an oscillator subject to dry friction, and a model of a DC/DC power converter.

Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy.

The effect of barrier width in coupled asymmetric double quantum well structure on passive mode-locking region of existence

Semiconductor two-sectional laser diodes with active region, consisting of two InGaAs quantum wells of different width separated with GaAs barrier are investigated. At barrier thickness of 2 nm quantum wells are coupled and diagonal optical transition originates between them. Peak in absorption spectra of lasing structure related to this diagonal transition is observed. An additional region of passive mode-locking due to this absorption peak takes place at low reverse biases on absorber section.

Bistability and resonance in the periodically stimulated Hodgkin-Huxley model with noise

We describe general characteristics of the Hodgkin-Huxley neuron's response to a periodic train of short current pulses with Gaussian noise. The deterministic neuron is bistable for antiresonant frequencies. When the stimuli arrive at the resonant frequency the firing rate is a continuous function of the current amplitude I(0) and scales as (I(0)-I(th))(1/2), characteristic of a saddle-node bifurcation at the threshold I(th). Intervals of continuous irregular response alternate with integer mode-locked regions with bistable excitation edge. There is an even-all multimodal transition between the 2 : 1 and 3 : 1 states in the vicinity of the main resonance, which is analogous to the odd-all transition discovered earlier in the high-frequency regime. For I(0)<I(th) and small noise the firing rate has a maximum at the resonant frequency. For larger noise and subthreshold stimulation the maximum firing rate initially shifts toward lower frequencies, then returns to higher frequencies in the limit of large noise. The stochastic coherence antiresonance, defined as a simultaneous occurrence of (i) the maximum of the coefficient of variation and (ii) the minimum of the firing rate vs the noise intensity, occurs over a wide range of parameter values, including monostable regions. Results of this work can be verified experimentally.

Transition state to mode locking in a passively mode-locked erbium-doped fibre ring laser

The transition state between the continuous wave region and the mode-locked region in a passively mode-locked erbium-doped fibre ring laser has been experimentally observed by utilizing the nonlinear polarization rotation technique. When the pump power reaches the mode-locked threshold, the metastable pulse train with a tunable repetition rate is obtained in the transition from the continuous wave state to the passive mode-locked state via proper adjustment of the polarization controller. A simple model has been established to explain the experimental observation.

Resonance near border-collision bifurcations in piecewise-smooth, continuous maps

Mode-locking regions (resonance tongues) formed by border-collision bifurcations of piecewise-smooth, continuous maps commonly exhibit a distinctive sausage-like geometry with pinch points called ‘shrinking points’. In this paper we extend our unfolding of the piecewise-linear case [Simpson and Meiss (2009 Nonlinearity 22 1123–44)] to show how shrinking points are destroyed by nonlinearity. We obtain a codimension-three unfolding of this shrinking point bifurcation for N-dimensional maps. We show that the destruction of the shrinking points generically occurs by the creation of a curve of saddle-node bifurcations that smooth one boundary of the sausage, leaving a kink in the other boundary.