Generation Of Ultrashort Pulses Research Articles

Optical Soliton Solutions for the Nonlinear Schrödinger Equation with Higher-Order Dispersion arises in Nonlinear Optics

Abstract Optical solitons and traveling wave solutions for the higher-order dispersive extended nonlinear Schrödinger equation are studied. Ultrashort pulse propagation in optical communication networks is described by this equation. To find exact solutions to the model, the unified Riccati equation expansion approach and the Jacobi elliptic function expansion method are successfully applied. The optical solutions includes various solitary wave solutions, such as kink, dark, bright, combined dark-bright, singular, combined periodic, periodic, Jacobian elliptic, and rational functions. Three-dimensional and two-dimensional graphs of solutions are presented. Also, the dynamical behavior of waves and the impact of time on solutions by selecting appropriate parameters are illustrated.

Analysis of high-quality ultrashort pulse generation based on a dual-drive Mach-Zehnder modulator and chirp compensation

This study reports on high-quality picosecond pulse generation using a single-stage dual-drive Mach-Zehnder modulator (DDMZM) and chirp compensation. Sinusoidal microwave signals with different amplitudes are sent to two RF ports of the DDMZM to form a pulse train and pulse compression is achieved by compensating for the linear frequency chirp with a single-mode fiber (SMF). Three parameters encompassing the power difference between two RF signals, the power of RF signals, and the bias point of the DDMZM that affect the pulse formation have been numerically studied. The optimum length of SMF used for chirp compensation is obtained by simulating the temporal propagation and evolution of the pulse in SMF and 3.56-ps chirp-compensated ultrashort pulses are realized at 1.55 µm with a 25-GHz repetition rate experimentally. Modulator-based flexible ultrashort pulse generation can be achieved easily by tuning the RF generator and light source, and customized high-quality pulses according to practical applications can be expected.

Interlayer engineered bilayered V₂O₅ NPs as saturable absorbers for infrared ultrashort pulse generation

Interlayer engineering offers a promising approach to modifying the structure of layered vanadium-based oxides, enhancing their saturable absorption effect and making them a desirable choice for developing infrared wavelength-range photonics devices. This experimental work synthesizes interlayer vanadium pentoxide (V2O5) using hydrothermal techniques to produce an excellent saturable absorber (SA). The interlayer engineering strategy enhances strong saturable absorption and self-defocusing effects in V2O5-based SA, enabling the generation of ultrashort pulses in the infrared region. Their superior nonlinear optical characteristics are demonstrated by a modulation depth of 13.9 % and saturation intensity of 0.42 GW cm−1, respectively. By utilizing a transmission coupling fiber-based V2O5-SA inside an Er-doped fiber laser cavity, a passively Q-switched (PQS) laser with a narrow pulse width of 2.78 μs and signal-to-noise ratio (SNR) ∼50 dB is realized for the first time. Furthermore, we explore a V2O5 NPs-SA long-term stability and high damage threshold. The results not only offer additional proof of the capable potential of interlayer V2O5 as a photo-bleaching absorber for realizing pulsed lasers in the NIR band but also cover the method for advancing their probable applications in optoelectronic devices.

The multi-positon and breather positon solutions for the higher-order nonlinear Schrödinger equation in optical fibers

Under investigation in this paper is the higher-order nonlinear Schrödinger equation, which can imitate the ultrashort pulses propagation in optical fibers. The modulation instability is analyzed based on the plane-wave solution. With the help of the generalized Darboux transformation, the second-, third- and fourth-order positon solutions are constructed. Furthermore, the second-, third- and fourth-order breather positon solutions are obtained, and the influences of parameters for the characteristics of solutions are analyzed.

Polarization-diverse soliton transitions and deterministic switching dynamics in strongly-coupled and self-stabilized microresonator frequency combs

Dissipative Kerr soliton microcombs in microresonators have enabled fundamental advances in chip-scale precision metrology, communication, spectroscopy, and parallel signal processing. Here we demonstrate polarization-diverse soliton transitions and deterministic switching dynamics of a self-stabilized microcomb in a strongly-coupled dispersion-managed microresonator driven with a single pump laser. The switching dynamics are induced by the differential thermorefractivity between coupled transverse-magnetic and transverse-electric supermodes during the forward-backward pump detunings. The achieved large soliton existence range and deterministic transitions benefit from the switching dynamics, leading to the cross-polarized soliton microcomb formation when driven in the transverse-magnetic supermode of the single resonator. Secondly, we demonstrate two distinct polarization-diverse soliton formation routes – arising from chaotic or periodically-modulated waveforms via pump power selection. Thirdly, to observe the cross-polarized supermode transition dynamics, we develop a parametric temporal magnifier with picosecond resolution, MHz frame rate and sub-ns temporal windows. We construct picosecond temporal transition portraits in 100-ns recording length of the strongly-coupled solitons, mapping the transitions from multiple soliton molecular states to singlet solitons. This study underpins polarization-diverse soliton microcombs for chip-scale ultrashort pulse generation, supporting applications in frequency and precision metrology, communications, spectroscopy and information processing.

Generation and evolution dynamics of gain-guided dissipative solitons in a Tm-doped fiber laser

The generation of dissipative solitons from a mode-locked fiber laser can enhance emission energy, while the insertion of a bandwidth filter exposes the system to complexity. This study presents the first generation and evolution dynamics of gain-guided dissipative solitons (GGDSs) in Tm-doped fiber lasers exploiting the finite gain bandwidth. The results highlight the intricate interplay of finite gain bandwidth with dispersion and nonlinearity in governing the dynamics of GGDSs. An increase in pump power significantly broadens the emission spectrum, which in turn introduces the finite gain bandwidth to the generation of GGDSs. Consequently, linear chirp accumulates, promoting high-energy ultrashort pulse generation after external compression. However, an increase in round-trip group delay dispersion leads to a narrower spectral bandwidth, which can weaken the influence of the finite gain bandwidth, resulting in decreased soliton energy and broader pulse duration. The investigation of GGDS evolution dynamics within the cavity also provides us with a deeper insight into the characteristics of GGDS. Overall, this research offers important guidance for designing high-performance Tm-doped fiber lasers with simple structures that fully exploit the finite gain bandwidth.

H 2-solutions for an Ostrosky–Hunter type equation

The Ostrosky–Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth, for the evolution of nonlinear propagation of optical pulses of a few oscillations duration in dielectric media, and for the evolution of the propagation of ultra-short light pulses in silica optical fibers. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.

Modelling of long-wave mid-infrared ultrashort pulse generation via difference frequency generation

In this paper, a model of generating mid-infrared (MIR) ultrashort laser pulse through difference frequency generation (DFG) is established. The pulse evolution relationship among the pump, signal, and idler pulses during the DFG process, as well as the effects of crystal length, pulse energy of the pump and signal lights, pulse width, and other factors on the characteristics of the MIR pulse are explored. Furthermore, through simulations from the time domain to the frequency domain, the spectral characteristics and angular distribution of MIR were analyzed. DFG experimental data are also presented to support the model.

Exploring the impact of multiplicative white noise on novel soliton solutions with the perturbed Triki–Biswas equation

This study examines the effects of multiplicative white noise on soliton perturbations governed by the Triki–Biswas equation for the first time. Triki–Biswas equation advances research on ultrashort pulse propagation in optical fibers. It modifies the nonlinear Schrödinger equation to describe the behavior of femtosecond pulses more accurately in optical media, becoming a critical tool in the field. The paper employs two innovative methods, the enhanced direct algebraic method and the new projective Riccati equations method to uncover a broad range of soliton solutions, including bright, dark, and singular solitons. The solutions are expressed in terms of Jacobi elliptic functions and exhibit a transition to soliton-type solutions as the elliptic modulus approaches unity. This investigation is the first of its kind to explore the effects of multiplicative white noise within this context, providing new perspectives and methodologies for future research in the field. The study sheds light on previously unexplored aspects of multiplicative white noise and contributes significantly to the body of knowledge in soliton theory and its application to optical fiber technology.

Dynamics of fractional optical solitary waves to the cubic–quintic coupled nonlinear Helmholtz equation

This work investigates the dynamics of optical waves to the generalized coupled nonlinear fractional Helmholtz equation with quintic and cubic nonlinear effects. The evolution of broad multicomponent self-trapping beams in Kerr-type nonlinear media is described by the coupled Helmholtz equation, which also take into account spatial dispersion due to non-paraxial effects. This phenomena is particularly relevant to the progressive miniaturization of optics, where the optical wavelength is similar to the beam width. It is essential to integrate non-Kerr terms, such as the self-steepening and the self frequency shift, into the coupled Helmholtz system in order to investigate the propagation of ultrashort optical pulses in the non-paraxial domain. For optical wave solutions, nonlinear ordinary equation of the governing model is achieved by applying the fractional transformation. The different types of the solutions like bright, dark, singular and mixed type solitons are extracted by applying advanced integration methods, namely modified Sardar subequation method and new Kudryashov method. These solutions provide very useful information on how the system operates. The applied approaches are highly efficient and have significant computational capability to efficiently tackle the nonlinear systems. Additionally, we include a diverse array of graphs to demonstrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. In the context of the proposed model, these visualizations assist with a comprehensive understanding of the solution’s behavior and characteristics. It is anticipated that these solutions may be significant in the study of wave propagation and related fields.

UV 30 fs laser pulse generation using a multi-pass cell.

Ultrashort ultraviolet (UV) pulses are pivotal for resolving ultrafast electron dynamics. However, their efficient generation is strongly impeded by material dispersion and two-photon absorption, in particular, if pulse durations around a few tens of femtoseconds or below are targeted. Here, we present a new (to our knowledge) approach to ultrashort UV pulse generation: using the fourth-harmonic generation output of a commercial ytterbium laser system delivering 220 fs UV pulses, we implement a multi-pass cell (MPC) providing 5.6 µJ pulses at 256 nm, compressed to 30.5 fs. Our results set a short-wavelength record for MPC post-compression while offering attractive options to navigate the trade-off between upconversion efficiency and acceptance bandwidth for UV pulse production.

The integrability and infinite conservation laws of a variable coefficient higher-order Schrödinger equation

In this paper, a variable coefficient high-order Schrödinger equation is studied to describe the propagation of ultrashort optical pulses in dispersion reducing fibers. It has third-order dispersion, self steepening and stimulated Raman scattering effects. Using the Bell polynomial method, the integrability of the variable coefficient higher-order Schrödinger equation is discussed. And the bilinear Bäcklund transformation, Lax pair, and infinite conservation laws of the equation are derived. It can be obtained that the variable coefficient higher-order Schrödinger equation is integrable in the sense of Lax pair. The soliton solutions are constructed from the obtained bilinear Bäcklund transformation and the bilinear form. The obtained results are analyzed in the initial–boundary value problem. It is worth mentioning that this paper, based on the angle of increasing the order, obtained the bilinear Bäcklund transformation of the third order variable coefficient Schrödinger equation by using the Bell polynomial method. On this basis, relevant properties such as Lax pair and infinite conservation laws are also obtained, and analyzed the application in the initial–boundary value problem. This has not been studied in existing literatures.

Second-harmonic generation of ultrashort pulses in refractive index linearly modulating quantum dot structure

While other works use segments of nonlinear crystal to compensate for walk-off, this work utilizes a quantum dot (QD) nanostructure for such compensation. Such nanocrystal structures allow two benefits: the high nonlinear susceptibility in these nanocrystals and the high surface density of QDs in the structure. Good results are obtained for pre-chirping and modulation parameters. The results are computed at 10 and 100 kV/cm applied electric fields. Compared to ordinary nonlinear crystals, the pulse width, intensity, and efficiency of the second harmonic (SH) pulse are all higher in QD nanocrystals, even with a low electric field applied. Higher applied fields give higher results.

Transverse mode switchable mode-locked laser with narrow bandwidth

Transverse mode switchable ultrashort optical pulses with narrow bandwidths can create potential for exploring what we believe are new physical effects. We demonstrate the generation of transverse mode switchable ultrashort pulses with narrow bandwidths in an all-fiber mode-locked laser by exploring a mode-selective photonic lantern (MSPL). The laser cavity serves not only as a ring resonator but also as an intrinsic spectral filter. For mode-locking with the LP01, LP11a, and LP11b modes, the bandwidths are 3.0 nm, 86.7 pm and 101.7 pm, respectively. The narrowband pulses with higher-order modes are generated by an intrinsic spectral filter due to the spectral-domain intermodal interference. Mode-locked pulses with a signal-to-noise ratio better than 60 dB for LP01, LP11a, and LP11b modes are independently generated, i.e., transverse mode switchable by changing the input port of the MSPL. The mode-locked wavelength can be tuned for the LP11a mode and LP11b mode by adjusting the state of polarization. Furthermore, our experimental results also show that, the slope efficiency of LP11a and LP11b modes can be improved, by the use of LP11 mode pump scheme. We anticipate that, narrowband pulses with complex mode profiles can be generated by simultaneously phase-locked transverse and longitudinal modes.

Generation of soliton molecules in a 1.5-μm ultrafast fiber laser based on Zinc 2,5-dihydroxyterephthalate saturable absorber

Two-dimensional (2D) Zinc 2,5-dihydroxyterephthalate (Zn-MOF-74) is a kind of metal–organic framework (MOF), which has been intensively studied in gas adsorption, gas storage, and catalysis. However, the potential applications of Zn-MOF-74 in the fields of optics, especially in the areas of nonlinear optical response and ultrafast optics need further exploration. Here, the nonlinear optical properties of Zn-MOF-74 are systematically investigated. In this work, we demonstrate that it gradually becomes saturated with the increase of the intensity of the incident pulse, which makes Zn-MOF-74 an effective saturable absorber in a mode-locked Er-doped fiber laser for ultrashort pulse generation. Our experiments yield stable single solitons as well as soliton molecules with tunable characteristics. When the pump power is 126 mW, conventional solitons with an output power of 2.35 mW and a pulse width of 0.93 ps are obtained. The generated pulses characterize a central wavelength of 1554.84 nm and a 3-dB bandwidth of 3.07 nm. By adjusting the pump power and polarization appropriately, the center wavelength of the soliton molecules is tunable from 1532.76 nm to 1554.24 nm. The experimental observations further proves that Zn-MOF-74 has great potential in ultrafast optics.

Crystal growth, polarized spectral properties, and 2.3 µm laser performance of Tm:LuVO4 crystal

We report on the Czochralski crystal growth, polarized optical spectroscopy, and the first continuous-wave laser operation of 1.5 at.% Tm:LuVO4 crystal on the 3H4 → 3H5 transition. The polarized absorption and stimulated-emission properties of Tm3+ ions in LuVO4 were revised and the crystal-field splitting of the Tm3+ multiplets was determined by low-temperature (12 K) spectroscopy. The maximum stimulated-emission cross-section for the 3H4 → 3H5 transition is 2.48 × 10−20 cm2 at 2363 nm for π-polarization corresponding to an emission bandwidth of 28 nm. Evidence of phonon-assisted emissions of Tm3+ ions above 2 µm is presented. The broadband emission properties of the Tm:LuVO4 crystal make it promising for ultrashort pulse generation. Additionally, pumped by a 796 nm fiber-coupled laser diode, the Tm:LuVO4 laser generated a Watt-level output power at 2279-2295 nm with a slope efficiency of 9.2% and linearly polarized emission (π-polarization).

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Frequency Conversion of Femtosecond Ti:Sapphire Laser Pulse to the Long-Wave Mid-IR Range with BaGa2GeSe6 Crystal

Generation of ultrashort mid-IR pulses spanning from 8.5 to 10.5 μm with high energy (up to 4.5 μJ) was experimentally demonstrated through difference frequency generation in BaGa2GeSe6 crystal pumped by 100-fs 0.95-μm Ti:sapphire laser pulses. Optical damage threshold and two-photon absorption coefficient were determined for this pump pulses. Frequency conversion efficiency reached 0.24% at 1.85 mJ pump pulse energy and was decreased at higher one. Estimations indicate that application of 15 mm in diameter wide-aperture BaGa2GeSe6 sample will allow one to increase pump pulse energy up to ~10 mJ, and to increase the mid-IR pulse energy up to 24 μJ at the same efficiency.

Analytical solution to second-harmonic generation of ultrashort laser pulse

We present an analytical method to evaluate the second-harmonic generation (SHG) process of ultrashort laser pulses in a nonlinear medium within the small-signal regime. Building upon the broadband nonlinear coupled wave theory, we derive an analytical solution that allows one to investigate the fundamental physics and detailed dynamics of the nonlinear interaction between ultrashort laser pulses. We find that SHG for ultrashort laser pulses in a nonlinear crystal arises from a series of self-SHG and self sum-frequency generation processes involving different frequency components. We have applied the analytical method to investigate specific pulse profiles with Gaussian and sech functions and found good agreement between analytical theory and numerical simulations, validating the accuracy of the analytical approach. The analytical method enables one to explore the evolution of the second-harmonic wave under various pulse profiles, pulse widths, and crystal thicknesses, and offers a more efficient and insightful approach to study the nonlinear optical dynamics of ultrashort laser pulses.

Ultrafast nonlinear optical response of layered violet phosphorus for femtosecond noise-like pulse generation

As a new member of two-dimensional (2D) phosphorene, 2D layered violet phosphorus (VP) has unique optoelectronic properties and good environmental stability, showing its huge advantages in optoelectronic applications. In this paper, the ultrafast nonlinear optical (NLO) properties of layered VP nanosheets at 1 µm band were explored, which exhibit an obvious saturable absorption response with a modulation depth of ∼1.97%. Meanwhile, the fast and slow carrier lifetimes of VP nanosheets at 1µm band were also determined as 295.9 fs and 2.36 ps, respectively, which are much shorter than that of most reported 2D materials. The excellent saturable absorption response combined with ultrashort carrier lifetimes indicate the prospect of layered VP nanosheets as a fast saturable absorber (SA) for ultrafast laser modulation. Then we demonstrated a Yb-doped fiber laser based on the VP-deposited taper-shaped fiber (TSF) SA, which delivers stable Q-switched mode-locked (QSML) pulses, dual-wavelength mode-locked pulses and 404-fs noise-like pulses. This work fully demonstrates the great potential of 2D VP materials for 1 µm ultrashort laser pulse generation.