Limits to compression with cascaded quadratic soliton compressors

Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity

The modulational instability (MI) phenomenon is addressed in a nonlocal medium under controllable saturation. The linear stability analysis of a plane-wave solution is used to derive an expression for the growth rate of MI that is exploited to parametrically discuss the possibility for the plane wave to disintegrate into nonlinear localized light patterns. The influence of the nonlocal parameter, the saturation coefficient, and the saturation index are mainly explored in the context of a Gaussian nonlocal response. It is pointed out that the instability spectrum, which tends to be quenched by the high nonlocality parameter, gets amplified under the right choices of the saturation parameters, especially the saturation index. Via direct numerical simulations, confirmations of analytical predictions are given, where competing nonlocal and saturable nonlinearities enable the emergence of trains of patterns as manifestations of MI. The comprehensive parametric analysis carried out throughout the numerical experiment reveals the robustness of the obtained rogue waves of A- and B-type Akhmediev breathers, as the nonlinear signature of MI, providing the saturation index as a suitable tool to manipulate nonlinear waves in nonlocal media.

Vector solitons in nonlocal optical media with pseudo spin-orbit-coupling

We numerically investigate the existence and stability of nonlocal vector solitons with pseudo spin-orbit-coupling (SOC). The pseudo SOC is realized by a framework based on the spatial-domain copropagation of two beams with mutually orthogonal polarizations and opposite transverse components of the carrier wave vectors in nonlocal optical media. The numerical results show that there are two kinds of solutions for vector solitons, one is central symmetric, and the other is noncentral symmetric. The solitons may exist below a certain threshold value of the effective SOC strength in the system.

Exploiting optical nonlinearities for group delay dispersion compensation in femtosecond optical parametric oscillators

A wavelength tunable femtosecond optical parametric oscillator pumped by the second harmonic of a Yb: KGW solid state oscillator was investigated. The intracavity group delay dispersion was positive, and soliton condition was satisfied by introducing negative nonlinearity from cascaded quadratic nonlinearity (CQN). Two different approaches were investigated - CQN induced by the same amplifying nonlinear crystal or CQN induced by an additional second harmonic generating nonlinear crystal inside the same resonator. The second crystal was shown to correct the resonator misalignment induced by the rotation of the amplifying crystal as the wavelength was tuned in the range of 770-970 nm. It simultaneously compensated positive resonator GDD offsets of +/- 1000 fs² with +/- 5% SHG power losses, simulating a method for compensation of GDD ripples in a broadband mirror.

Generalized nonlinear Schrödinger equations describing the Second Harmonic Generation of femtosecond pulse, containing a few cycles, and their integrals of motion

An interaction of laser pulse, containing a few cycles, with substance is a modern problem, attracting attention of many researches. The frequency conversion is a key problem for a generation of such pulses in various ranges of frequencies. Adequate description of such pulse interaction with a medium is based on a slowly evolving wave approximation (SEWA), which has been proposed earlier for a description of propagation of the laser pulse, containing a few cycles, in a medium with cubic nonlinear response. Despite widely applicability of the frequency conversion for various nonlinear optics problems solutions, SEWA has not been applied and developed for a theoretical investigation of the frequency doubling process until present time. In this study the set of generalized nonlinear Schrödinger equations describing a second harmonic generation of the super-short femtosecond pulse is derived. The equations set contains terms, describing the pulses self-steepening, and the second order dispersion (SOD) of the pulse, a diffraction of the beam as well as mixed derivatives. We propose the transform of the equations set to a type, which does not contain both the mixed derivatives and time derivatives of the nonlinear terms. This transform allows us to derive the integrals of motion of the problem: energy, spectral invariants and Hamiltonian. We show the existence of two specific frequencies (singularities in the Fourier space) inherent to the problem. They may cause an appearance of non-physical absolute instability of the problem solution if the spectral invariants are not taken into account. Moreover, we claim that the energy preservation at the laser pulses propagation may not occur if these invariants do not preserve. Developed conservation laws, in particular, have to be used for developing of the conservative finite-difference schemes, preserving the conservation laws difference analogues, and for developing of adequate theory of the modulation instability of the laser pulses, containing a few cycles.

Multi-pass-cell-based nonlinear pulse compression to 115 fs at 7.5 µJ pulse energy and 300 W average power

We demonstrate nonlinear pulse compression by multi-pass cell spectral broadening (MPCSB) from 860 fs to 115 fs with compressed pulse energy of 7.5 µJ, average power of 300 W and close to diffraction-limited beam quality. The transmission of the compression unit is >90%. The results show that this recently introduced compression scheme for peak powers above the threshold for catastrophic self-focusing can be scaled to smaller pulse energies and can achieve a larger compression factor than previously reported. Good homogeneity of the spectral broadening across the beam profile is verified, which distinguishes MPCSB among other bulk compression schemes.

Parametrically Tunable Soliton-Induced Resonant Radiation by Three-Wave Mixing

We show that a temporal soliton can induce resonant radiation by three-wave mixing nonlinearities. This constitutes a new class of resonant radiation whose spectral positions are parametrically tunable. The experimental verification is done in a periodically poled lithium niobate crystal, where a femtosecond near-IR soliton is excited and resonant radiation waves are observed exactly at the calculated soliton phase-matching wavelengths via the sum- and difference-frequency generation nonlinearities. This extends the supercontinuum bandwidth well into the mid IR to span 550-5000 nm, and the mid-IR edge is parametrically tunable over 1000 nm by changing the three-wave mixing phase-matching condition. The results are important for the bright and broadband supercontinuum generation and for the frequency comb generation in quadratic nonlinear microresonators.

Dispersive waves induced by self-defocusing temporal solitons in a beta-barium-borate crystal

We experimentally observe dispersive waves in the anomalous dispersion regime of a beta-barium-borate (BBO) crystal, induced by a self-defocusing few-cycle temporal soliton. Together the soliton and dispersive waves form an energetic octave-spanning supercontinuum. The soliton was excited in the normal dispersion regime of BBO through a negative cascaded quadratic nonlinearity. Using pump wavelengths from 1.24 to 1.4 μm, dispersive waves are found from 1.9 to 2.2 μm, agreeing well with calculated resonant phase-matching wavelengths due to degenerate four-wave mixing to the soliton. We also observe resonant radiation from nondegenerate four-wave mixing between the soliton and a probe wave, which was formed by leaking part of the pump spectrum into the anomalous dispersion regime. We confirm the experimental results through simulations.

Energetic mid-IR femtosecond pulse generation by self-defocusing soliton-induced dispersive waves in a bulk quadratic nonlinear crystal

Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO(3) cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm(-1)) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily by using large-aperture crystals. The technique can readily be implemented with other crystals and laser wavelengths, and can therefore potentially replace current ultrafast frequency-conversion processes to the mid-IR.

Supercontinuum generation in quadratic nonlinear waveguides without quasi-phase matching

Supercontinuum generation (SCG) is most efficient when the solitons can be excited directly at the pump laser wavelength. Quadratic nonlinear waveguides may induce an effective negative Kerr nonlinearity, so temporal solitons can be directly generated in the normal (positive) dispersion regime overlapping with common ultrafast laser wavelengths. There is no need for waveguide dispersion engineering. Here, we experimentally demonstrate SCG in standard lithium niobate (LN) waveguides without quasi-phase matching (QPM), pumped with femtosecond pulses in the normal dispersion regime. The observed large bandwidths (even octave spanning), together with other experimental data, indicate that negative nonlinearity solitons are indeed excited, which is backed up by numerical simulations. The QPM-free design reduces production complexity, extends the maximum waveguide length, and limits undesired spectral resonances. Finally, nonlinear crystals can be used where QPM is inefficient or impossible, which is important for mid-IR SCG. QPM-free waveguides in mid-IR nonlinear crystals can support negative nonlinearity solitons, as these waveguides have a normal dispersion at the emission wavelengths of mid-IR ultrafast lasers.

Few-cycle solitons and supercontinuum generation with cascaded quadratic nonlinearities in unpoled lithium niobate ridge waveguides

Formation and interaction of few-cycle solitons in a lithium niobate ridge waveguide are numerically investigated. The solitons are created through a cascaded phase-mismatched second-harmonic generation process, which induces a dominant self-defocusing Kerr-like nonlinearity on the pump pulse. The inherent material self-focusing Kerr nonlinearity is overcome over a wide wavelength range, and self-defocusing solitons are supported from 1100 to 1900 nm, covering the whole communication band. Single cycle self-compressed solitons and supercontinuum generation spanning 1.3 octaves are observed when pumped with femtosecond nanojoule pulses at 1550 nm. The waveguide is not periodically poled, as quasi-phase-matching would lead to detrimental nonlinear effects impeding few-cycle soliton formation.

Stabilization of nonlocal solitons by boundary conditions

We discovered that boundary conditions can stabilize nonlocal solitons with an oscillatory periodic response function. These solitons are the equivalent of quadratic solitons consisting of fundamental waves and oscillatory second harmonics, which are unstable unless subject to boundary confinement.

Formation of localized structures in bistable systems through nonlocal spatial coupling. I. General framework

The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in one-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear dependence on the field. Leveraging spatial dynamics we provide a general framework to understand the effect of the nonlocality on the shape of the fronts connecting two stable states. In particular we show that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts. In parameter space the region where fronts are oscillatory is limited by three transitions: the modulational instability of the homogeneous state, the Belyakov-Devaney transition in which monotonic fronts acquire spatial oscillations with infinite wavelength, and a crossover in which monotonically decaying fronts develop spatial oscillations with a finite wavelength. We show how these transitions are organized by codimension 2 and 3 points and illustrate how by changing the parameters of the nonlocal coupling it is possible to bring the system into the region where localized structures can be formed.

Formation of localized structures in bistable systems through nonlocal spatial coupling. II. The nonlocal Ginzburg-Landau equation

We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-dimensional real Ginzburg-Landau equation. While for local coupling the fronts are always monotonic and therefore the dynamical behavior leads to coarsening and the annihilation of pairs of fronts, nonlocal terms can induce spatial oscillations in the front, allowing for the creation of localized structures, emerging from pinning between two fronts. We show this for three different nonlocal influence kernels. The first two, mod-exponential and Gaussian, are positive definite and decay exponentially or faster, while the third one, a Mexican-hat kernel, is not positive definite.

Temporal switching induced by cascaded third order nonlinearity

We investigate the impact of cascaded third harmonic generation and the intrinsic n4 material nonlinearity on the propagation of ultrashort pulses in noble-gas filled Kagome fibers. We show that the pressure tunability of the cascade allows for the implementation of temporal switching. We also investigate the relative strengths of both effects and show their ratio to be pressure tunable.

Ultrafast and octave-spanning optical nonlinearities from strongly phase-mismatched quadratic interactions

Cascaded nonlinearities have attracted much interest, but ultrafast applications have been seriously hampered by the simultaneous requirements of being near phase matching and having ultrafast femtosecond response times. Here we show that in strongly phase-mismatched nonlinear frequency conversion crystals the pump pulse can experience a large and extremely broadband self-defocusing cascaded Kerr-like nonlinearity. The large cascaded nonlinearity is ensured through interaction with the largest quadratic tensor element in the crystal, and the strong phase mismatch ensures an ultrafast nonlinear response with an octave-spanning bandwidth. We verify this experimentally by showing few-cycle soliton compression with noncritical cascaded second-harmonic generation: Energetic 47 fs infrared pulses are compressed in a just 1-mm long bulk lithium niobate crystal to 17 fs (under 4 optical cycles) with 80% efficiency, and upon further propagation an octave-spanning supercontinuum is observed. Such ultrafast cascading is expected to occur for a broad range of pump wavelengths spanning the near- and mid-IR using standard nonlinear crystals.

Solitons in nonlocal nonlinear Kerr media with exponential response function

In this paper, we find some exact analytical solutions including bright soliton solution, dipole-mode soliton solution, double soliton solution and periodic solution when a slit laser beam propagates in Kerr-type nonlinear, nonlocal media with exponential response function. Furthermore, we address the energy flow is a monotonically growing function of d₂ and the Hamiltonian decreases while the energy flow increases. And we also obtain an Airy-like soliton by numerical method.

Optical Cherenkov radiation by cascaded nonlinear interaction: an efficient source of few-cycle energetic near- to mid-IR pulses

When ultrafast noncritical cascaded second-harmonic generation of energetic femtosecond pulses occur in a bulk lithium niobate crystal optical Cherenkov waves are formed in the near- to mid-IR. Numerical simulations show that the few-cycle solitons radiate Cherenkov (dispersive) waves in the λ = 2.2 - 4.5 μm range when pumping at λ₁ = 1.2 - 1.8 μm. The exact phase-matching point depends on the soliton wavelength, and we show that a simple longpass filter can separate the Cherenkov waves from the solitons. The Cherenkov waves are born few-cycle with an excellent Gaussian pulse shape, and the conversion efficiency is up to 25%. Thus, optical Cherenkov waves formed with cascaded nonlinearities could become an efficient source of energetic near- to mid-IR few-cycle pulses.