Self-frequency Shift Research Articles

Nonlinear effects-based 1.7 μm fiber lasers: A review and prospect

The nonlinear effects in the fiber lasers have always been explored and studied as people are pursuing higher quality fiber lasers in different wavelengths for profound applications. In recent years, 1.7 μm band fiber lasers have received the tremendous attention due to their unique spectral properties in biological imaging, organic gases detection, material processing and other fields. In this paper, the research progress of nonlinear effects-based 1.7 μm fiber lasers is thoroughly reviewed. Meanwhile, the four nonlinear effects applied in 1.7 μm fiber lasers included stimulated Raman scattering (SRS), super-continuum (SC), four-wave mixing (FWM), soliton self-frequency shift (SSFS) are introduced, as well as the principle, characteristics and advantages of each method. In addition, the latest researches on the 1.7 μm fiber lasers based on the hybrid gain are summarized in detail. Finally, the conclusion included the obstacles and adversities is given and the future development tendency of nonlinear effects-based 1.7 μm fiber lasers is prospected.

Temporal Self-Compression and Self-Frequency Shift of Submicrojoule Pulses at a Repetition Rate of 8 MHz

We combine soliton dynamics in gas-filled hollow-core photonic crystal fibers with a state-of-the-art fiber laser to realize a turn-key system producing few-fs pulses at 8 MHz repetition rate at pump energies as low as 220 nJ. Furthermore, by exploiting the soliton self-frequency shift in a second hydrogen-filled hollow-core fiber, we efficiently generate pulses as short as 22 fs, continuously tunable from 1100 nm to 1474 nm.

Characterization of Multimode Soliton Self-Frequency Shift

Optical solitons in multimode fibers exhibit complex dynamics, and peculiar characteristics in terms of pulse duration and energy, which distinguish them from their single-mode counterparts. We propose a theory for Raman-induced soliton self-frequency shift in multimode fibers, that is compared against experimental data of 1-km multimode soliton propagation. Specific values of pulsewidth and energy are found, at which solitons show long-distance stability and better correspondence with the theory of self-frequency shift; those values depend on the input wavelength, but are not related to the duration of the input pulse. Raman delay is affected by a jitter, characterized by a Gaussian statistical distribution, whose standard deviation tends to stabilize to a constant value for increasing pulse energies.

Numerical demonstration of mid-infrared soliton self-frequency shift in chalcogenide microstructured fiber

Compact optical devices with an output wavelength range of more than 3 μm are limited due to the requirements of proper material and structural design. In this study, the phenomenon of a soliton self-frequency shift pumped by a femtosecond pulse in a chalcogenide microstructured fiber is investigated numerically. The structural parameters of the fiber are optimized to obtain far-separated zero-dispersion wavelengths at 2.24 µm and 5.34 µm with low confinement loss. A femtosecond tunable soliton with a frequency shifted up to 3.7 µm is achieved from a 10-cm long fiber with a conversion efficiency above 38.6 %, consuming a pump pulse energy of no more than 200 pJ at 2.8 µm, which is available from Er-doped fluoride fibers. Our work can provide an effective way to construct compact, all-fiber femtosecond tunable mid-infrared laser sources with low operation power.

Generation of all-fiber ultrafast pulses at 2 μm by soliton self-frequency shift in highly nonlinear silica fiber

An efficient and straightforward method to obtain all-fiber pulsed sources at 2 μm is presented and experimentally demonstrated. It is based on the soliton self-frequency shift effect in a highly nonlinear fiber. The output power of a supercontinuum source is previously increased by an optimized homemade thulium-doped fiber amplifier. By coupling the amplified output power in a highly nonlinear fiber, the spectrum is shifted toward 130 nm and the spectral peak is located at 2014 nm. The power conversion factor reaches values as high as 0.93, without employing additional amplifiers. The mean spectral power of the 2 μm source reaches −4.6 dBm nm−1 (0.35 mW nm−1), its output power is 38 mW and the peak power of each pulse is higher than 27 kW.

Label-free measurement of wall shear stress in the brain venule and arteriole using dual-wavelength third-harmonic-generation line-scanning imaging.

Wall shear stress (WSS) is of fundamental physiological and pathological significance. Current measurement technologies suffer from poor spatial resolution or cannot measure instantaneous values in a label-free manner. Here we demonstrate dual-wavelength third-harmonic-generation (THG) line-scanning imaging, for instantaneous wall shear rate and WSS measurement in vivo. We used the soliton self-frequency shift to generate dual-wavelength femtosecond pulses. Simultaneous acquisition of dual-wavelength THG line-scanning signals extract blood flow velocities at adjacent radial positions for instantaneous wall shear rate and WSS measurement. Our results show the oscillating behavior of WSS in brain venules and arterioles at micron spatial resolution in a label-free manner.

Chirped localized pulses in a highly nonlinear optical fiber with quintic non-Kerr nonlinearities

We study the existence and propagation properties of chirped localized pulses in a highly nonlinear fiber medium exhibiting self-steepening, self-frequency shift, and quintic non-Kerr nonlinearities. Pulse evolution in such fiber system is governed by a higher-order nonlinear Schrödinger equation incorporating the derivative Kerr and non-Kerr nonlinear terms. We show that bright, dark and kink type solitary waves exist in the presence of all physical processes. A special ansatz is introduced to analyze the existence of solitary waves on a continuous-wave background in the optical fiber medium. It is shown that the obtained localized pulses exhibit a nonlinear chirp which has a quadratic dependence on light intensity. We also find that the magnitude of the associated frequency chirp can be controlled effectively by varying the parameters of self-steepening, self-frequency shift, and derivative non-Kerr nonlinearity effects. The restrictions on the optical fiber parameters are also extracted for the existence of these nonlinearly chirped solitary waves. Results in this study may be useful for experimental realization of shape-preserved pulses in optical fibers and further understanding of their optical transmission properties.

Propagation of periodic and solitary waves in a highly dispersive cubic–quintic medium with self-frequency shift and self-steepening nonlinearity

We study the dynamics of femtosecond light pulse propagation in a cubic–quintic medium exhibiting dispersive effect up to the fourth order as well as self-frequency shift and self-steepening nonlinearity. A rich variety of periodic and solitary wave solutions are derived for the governing generalized higher-order nonlinear Schrödinger equation in the presence of self-frequency shift and self-steepening effects. It is found that the frequency shift, inverse velocity, amplitude and wave number of both periodic and solitary waves depend on dispersion coefficients and nonlinearity parameters as well. The conditions on optical fiber parameters for the existence of these structures are presented. The stability of these periodic and solitary wave solutions is studied numerically by adding white noise. It is proved by using the numerical split-step Fourier method that the derived exact solutions are stable by Lyapunov criteria.

Femtosecond tunable solitons up to 4.8 µm using soliton self-frequency shift in an InF3 fiber

A tunable ultrashort soliton pulse source reaching up to 4.8 µm is demonstrated based on a 2.8 µm femtosecond fiber laser coupled to a zirconium fluoride fiber amplifier followed by a small core indium fluoride fiber. This demonstration is extending by 300 nm the long wavelength limit previously reported with soliton self-frequency shift (SSFS) sources based on fluoride fibers. Our experimental and numerical investigation highlighted the spectral dynamics associated with the generation of highly redshifted pulses in the mid-infrared using SSFS enhanced by soliton fission. This study is intended at providing a better understanding of the potential and limitations of SSFS based tunable femtosecond fiber sources in the 3–5 µm spectral range.

Chirped self-similar localized pulses on a continuous wave background in presence of cubic–quintic nonlinearity and self-frequency shift

We investigate the nonlinear pulse propagation through an inhomogeneous single-mode optical fiber where the evolution dynamics is governed by the generalized higher-order nonlinear Schrödinger equation with varying group velocity dispersion, cubic and quintic nonlinearities, self-frequency shift arising from stimulated Raman scattering, and linear gain or loss. A new class of soliton pulse solutions for a wave field is constructed based on the similarity transformation connecting with the constant-coefficient Kundu–Eckhaus equation. This class describes soliton structures that propagate self-similarity on a continuous-wave (cw) background, and acquires a nonlinear chirp as it propagates in the inhomogeneous fiber medium. It is found that the nonlinear chirp associated with these self-similar pulses originates essentially from the self-frequency shift effect. The conditions on fiber parameters for the existence of those nonlinearly chirped self-similar localized pulses are also given. As a practical example, we studied their evolution dynamics in a specified soliton control system. The solution stability against perturbation is checked by direct numerical simulation.

Generation of single solitons tunable from 3 to 3.8 μm in cascaded Er3+-doped and Dy3+-doped fluoride fiber amplifiers

High-power tunable femtosecond mid-infrared (MIR) pulses are of great interest for many scientific and industrial applications. Here we demonstrate a compact fluoride-fiber-based system that generates single solitons tunable from 3 to 3.8 μm. The system is composed of an Er:ZBLAN fiber oscillator and amplifier followed by a fusion-spliced Dy:ZBLAN fiber amplifier. The Er:ZBLAN fiber amplifier acts as a power booster as well as a frequency shifter to generate Raman solitons up to 3 μm. The Dy:ZBLAN fiber amplifier transfers the energy from the residual 2.8 μm radiation into the Raman solitons using an in-band pumping scheme, and further extends the wavelength up to 3.8 μm. Common residual pump radiation and secondary solitons accompanying the soliton self-frequency shift (SSFS) are recycled to amplify Raman solitons, consequently displaying a higher output power and pulse energy, a wider shifting range, and an excellent spectral purity. Stable 252 fs pulses at 3.8 μm with a record average power of 1.6 W and a pulse energy of 23 nJ are generated. This work provides an effective way to develop high-power widely tunable ultrafast single-soliton MIR laser sources, and this method can facilitate the design of other SSFS-based laser systems for single-soliton generation.

W-shaped profile and breather-like soliton of the fractional nonlinear Schrödinger equation describing the polarization mode in optical fibers

We use the fractional nonlinear Schrödinger equation (FNLSE) to describe the polarization mode in optical fiber with Self-Steepening, Self-Frequency Shift, and Cubic-quintic terms to analyze the effects of the fractional time parameter (FTP) on bright and dark solitons as well as breather-like solitons. We use the transformation hypothesis and auxiliary equations method to obtain three families of solutions such as combined bright soliton, dark solitons, and rational solitons. We have shown the effects of the fractional parameter (FP) on the W-shaped profile, bright and dark optical soliton solutions as well as the corresponding chirp component. It is observed that for small values of the FP, optical soliton shape is affected and the soliton is unstable. Moreover, one observes the effects of fraction time on Modulation Instability (MI) gain spectra and MI bands. For certain values of the FP, it is formed sides lobes and for specific small values of the FP, both stability zone increases and amplitude of the MI gain increase while the stability zones increase. To confirm the robustness of the analytical results, we have used a numerical investigation. One exhibits the formation of breathers-like soliton with stable amplitude for small values of the FTP. It results from this study that the FP is efficient and can be used as an energy source where soliton or breathers-like soliton are involved for communication in optical fibers.

Optical solitons and qualitative analysis of nonlinear Schrodinger equation in the presence of self steepening and self frequency shift

In this manuscript, the optical solitons of nonlinear Schrödinger equation (NLSE) with cubic–quintic law nonlinearity, in the presence of self-frequency shift and self-steepening, has been studied. The ultrahigh capacity propagation and transit of laser light pulses in optical fibres were described using this form of equation. To extract new results, two strong methodologies has been used. To extract the exact solution unified method has been employed. The solutions obtained by this analytical method, are in form of polynomial and rational function solution. Moreover, the validity of non-singular solutions has guaranteed by a limitation condition that is graphically illustrated in 3D. The 2D graphical representation are also used to demonstrate the influence of parameters on the predicted non-singular solutions. The other technique, used for qualitative analysis, is bifurcation. The system has been transformed into a planer dynamical system, which has been transformed into a hamiltonian system. All the possible phase portrait has been plotted by complete discrimination method. The acquired results are novel and have not been recorded before and they indicate that the proposed methodologies may be used to investigate innovative soliton solutions and phase portraits for any NLSE.

Quantum model for supercontinuum generation process

A quantum theory is established for the propagation of electromagnetic waves in highly nonlinear dispersive optical fibers. By applying the method recently presented dispersion terms and retarded response of the medium are included for the propagation of light in a fiber in this work. A coupled stochastic generalized nonlinear Schrödinger equation (GNLSE) is obtained via the coherent positive-P representation to describe the supercontinuum generation process. This coupled quantum-stochastic equation is applied to obtain the linearized fluctuation equation for studying quantum noise and the fluctuation in the vicinity of the formed solitons in the supercontinuum generation process in the region of anomalous dispersion. Also, these equations can be used to study the soliton self-frequency shift quantum mechanically. Finally, we simulate the obtained coupled stochastic generalized nonlinear Schrödinger in the mean case and compare our simulation results with experimental results.

Optical linewidth of soliton microcombs

Soliton microcombs provide a versatile platform for realizing fundamental studies and technological applications. To be utilized as frequency rulers for precision metrology, soliton microcombs must display broadband phase coherence, a parameter characterized by the optical phase or frequency noise of the comb lines and their corresponding optical linewidths. Here, we analyse the optical phase-noise dynamics in soliton microcombs generated in silicon nitride high-Q microresonators and show that, because of the Raman self-frequency shift or dispersive-wave recoil, the Lorentzian linewidth of some of the comb lines can, surprisingly, be narrower than that of the pump laser. This work elucidates information about the physical limits in phase coherence of soliton microcombs and illustrates a new strategy for the generation of spectrally coherent light on chip.

Breather-like soliton, M-shaped profile, W-shaped profile, and modulation instability conducted by self-frequency shift of the nonlinear Schrödinger equation

Breather-like soliton, M-shaped profile, W-shaped profile, and modulation instability conducted by self-frequency shift of the nonlinear Schrödinger equation

Heteronuclear soliton molecules with two frequencies

Bound states of optical solitons represent ideal candidates to investigate fundamental nonlinear wave interaction principles and have been shown to exhibit intriguing analogies to phenomena in quantum mechanics. Usually, such soliton molecules are created by a suitable balance of phase-related attraction and repulsion between two copropagating solitons with overlapping tails. However, there exists also another type of compound state, where strong binding forces result directly from the Kerr nonlinearity between solitons at different center frequencies. The physical mechanisms as well as the properties of these objects are quite different from those of usual soliton molecules, but are hardly known. Here we characterize and investigate these compound states in greater detail. We demonstrate unique propagation dynamics by investigating the robustness of the compound states under perturbations, such as third-order dispersion and the Raman effect. The constituents are individually affected by the perturbations, but the impact on the compound state is not a mere superimposition. One observes complex dynamics resulting from a strong entanglement between the subpulses. For example, in the case of the Raman effect both subpulses are subject to a cancellation of the self-frequency shift, although only one subpulse is approaching a zero-dispersion frequency. We extend the concept of the molecule states to three and more constituents by adopting appropriate propagation constants. These multicolor soliton molecules open up further perspectives for exploring the complex physics of photonic molecules, but also show great potential for application resulting from their robustness and the possibility to control their properties.

Analytical study of perturbed chirped solitons with triple-power law nonlinearity

In this work, a novel class of analytical chirped soliton solutions of the triple-power law nonlinear Schrödinger equation with perturbations are constructed. This model is used to describe the propagation of light waves in a nonlinear medium with the higher-order nonlinear optical effects including the triple-power law nonlinearity, self-frequency shift and self-steepening. The results shown that exact chirped plane wave, bright and kink solitons can exist in this physical setting when the degree of nonlinearity satisfy 2m=3n.

Perturbation of chirped localized waves in a dual-power law nonlinear medium

We investigate the transmission of localized waves through a dual-power law medium exhibiting the perturbations including the inter-modal dispersion, self-steepening, and self-frequency shift effects. A novel class of nonlinear waves that are periodic wave, kink soliton, algebraic soliton and bright soliton, along with the corresponding chirping, are reported. We found the nonlinear contribution chirp is proportional to n power of the light intensity, which is arising from the perturbations. Finally, the influence of degree of nonlinearity on the dynamical properties of the obtained chirped structures is presented.

Gigahertz-repetition rate, high power, ultrafast Tm-doped fiber laser source

The gigahertz (GHz)-pulse repetition rate, 2-μm harmonic mode-locking (HML) Tm-doped fiber oscillator is realized with the nonlinear polarization rotation method. The fundamental pulse repetition rate is 95.8 MHz, which is further increased to 1.25 GHz at 1962 nm, 1.63 GHz at 1982 nm, and 1.05 GHz at 2005 nm with a high super-mode suppression above 37 dB respectively. It is believed to be the first report on the GHz Tm-doped fiber oscillators, which can optionally operate in < 2000-nm or > 2000-nm region. The HML fiber oscillator delivers maximum output powers of 480 mW, 538 mW and 340 mW and at each wavelength, which are the largest output powers never reported from previous GHz 2-μm fiber oscillators. The pulse durations in each wavelength are all < 500 fs. The laser pulse with the highest pulse repetition rate is further scaled up to ∼ 4 W. The observed spectral narrowing and soliton self-frequency shift in the fiber amplifier are further analyzed with a theoretical model, which matches well with the experimental results.