High-energy pulse compression by use of negative phase shifts produced by the cascade chi((2)):chi((2)) nonlinearity

Peregrine solitons and resonant radiation in cubic and quadratic media

We present the fascinating phenomena of resonant radiation emitted by transient rogue waves in cubic and quadratic nonlinear media, particularly those shed from Peregrine solitons, one of the main wavepackets used today to model real-world rogue waves. In cubic media, it turns out that the emission of radiation from a Peregrine soliton can be attributed to the presence of higher-order dispersion, but is affected by the intrinsic local longitudinal variation of the soliton wavenumber. In quadratic media, we reveal that a two-color Peregrine rogue wave can resonantly radiate dispersive waves even in the absence of higher-order dispersion, subjected to a phase-matching mechanism that involves the second-harmonic wave, and to a concomitant difference-frequency generation process. In both cubic and quadratic media, we provide simple analytic criteria for calculating the radiated frequencies in terms of material parameters, showing excellent agreement with numerical simulations.

Resonant radiation emitted by solitary waves via cascading in quadratic media

We present a systematic investigation of the resonant radiation emitted by localized soliton-like wave-packets supported by second-harmonic generation in the cascading regime. We emphasize a general mechanism which allows for the resonant radiation to grow without the need for higher-order dispersion, primarily driven by the second-harmonic component, while radiation is also shed around the fundamental-frequency component through parametric down-conversion processes. The ubiquity of such a mechanism is revealed with reference to different localized waves such as bright solitons (both fundamental and second-order), Akhmediev breathers, and dark solitons. A simple phase matching condition is put forward to account for the frequencies radiated around such solitons, which agrees well with numerical simulations performed against changes of material parameters (say, phase mismatch, dispersion ratio). The results provide explicit understanding of the mechanism of soliton radiation in quadratic nonlinear media.

Quadratic Peregrine solitons resonantly radiating without higher-order dispersion

We show that two-color Peregrine solitary waves in quadratic nonlinear media can resonantly radiate dispersive waves even in the absence of higher-order dispersion, owing to a phase-matching mechanism that involves the weaker second-harmonic component. We give very simple criteria for calculating the radiated frequencies in terms of material parameters, finding excellent agreement with numerical simulations.

Photo-Switchable Nanoripples in Ti3C2Tx MXene

MXenes are two-dimensional materials with a rich set of chemical and electromagnetic properties, the latter including saturable absorption and intense surface plasmon resonances. To fully harness the functionality of MXenes for applications in optics, electronics, and sensing, it is important to understand the interaction of light with MXenes on atomic and femtosecond dimensions. Here, we use ultrafast electron diffraction and high-resolution electron microscopy to investigate the laser-induced structural dynamics of Ti₃C₂T_x nanosheets. We find an exceptionally fast lattice response with an electron-phonon coupling time of 230 fs. Repetitive femtosecond laser excitation transforms Ti₃C₂T_x through a structural transition into a metamaterial with deeply sub-wavelength nanoripples that are aligned with the laser polarization. By a further laser illumination, the material is reversibly photo-switchable between a flat and rippled morphology. The resulting nanostructured MXene metamaterial with directional nanoripples is expected to exhibit an anisotropic optical and electronic response as well as an enhanced chemical activity that can be switched on and off by light.

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.

Nonlinear pulse compression based on a gas-filled multipass cell

We demonstrate nonlinear temporal compression of a high-energy Yb-doped fiber laser source in a multipass cell filled with argon. The 160 μJ 275 fs input pulses are compressed down to 135 μJ 33 fs at the output, corresponding to an overall transmission of 85%. We also analyze the output beam, revealing essentially no space-time couplings. We believe this technique can be scalable to higher pulse energies and shorter pulse durations, enabling access to a wider parameter range for a large variety of ultrafast laser sources.

Efficient middle-infrared generation in LiGaS2 by simultaneous spectral broadening and difference-frequency generation

We report a surprisingly broadband and efficient midinfrared pulse generation in LiGaS₂ (Langasite, LGS) by invoking a simultaneous interplay of intrapulse difference-frequency generation, self-phase modulation, and dispersion. This cascaded mechanism expands the output bandwidth and output power at the same time. With 30-fs driving pulses centered at 1030-nm wavelength we obtain a broadband middle-infrared spectrum of 8-11 μm with an LGS crystal as thick as 4 mm, which is eight times longer than the walk-off length.

Compression of picosecond pulses from a thin-disk laser to 30fs at 4W average power

We investigate two approaches for the spectral broadening and compression of 1-ps long pulses of a thin-disk laser amplifier running at 50 kHz repetition rate at 1030 nm wavelength. We find that with a single, 2.66-m long stretched flexible hollow fiber filled with xenon gas, Fourier transform limited output pulse duration of 66 fs can be directly reached. For larger pulse shortening, we applied a hybrid cascaded approach involving a BBO-based pre-compressor and a long hollow fiber. We could achieve 33-times temporal shortening of 1-ps pulses down to a duration of 30 fs at an overall efficiency of ~29% with an output power level of 3.7 W. These results demonstrate the potential of stretched flexible fibers with their free length scalability for shortening laser pulses of moderate peak power.

Efficient High-Power Ultrashort Pulse Compression in Self-Defocusing Bulk Media

Peak and average power scalability is the key feature of advancing femtosecond laser technology. Today, near-infrared light sources are capable of providing hundreds of Watts of average power. These sources, however, scarcely deliver pulses shorter than 100 fs which are, for instance, highly beneficial for frequency conversion to the extreme ultraviolet or to the mid- infrared. Therefore, the development of power scalable pulse compression schemes is still an ongoing quest. This article presents the compression of 90 W average power, 190 fs pulses to 70 W, 30 fs. An increase in peak power from 18 MW to 60 MW is achieved. The compression scheme is based on cascaded phase-mismatched quadratic nonlinearities in BBO crystals. In addition to the experimental results, simulations are presented which compare spatially resolved spectra of pulses spectrally broadened in self-focusing and self-defocusing media, respectively. It is demonstrated that balancing self- defocusing and Gaussian beam convergence results in an efficient, power-scalable spectral broadening mechanism in bulk material.

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.

Parametric amplification of 100 fs mid-infrared pulses in ZnGeP2 driven by a Ho:YAG chirped-pulse amplifier

We report on the parametric generation of 100 fs sub-6-cycle 40 μJ pulses with the center wavelength at 5.2 μm using a 1 ps 2.1 μm pump laser and a dispersion management scheme based on bulk material. Our optically synchronized amplifier chain consists of a Ho:YAG chirped-pulse amplifier and white-light-seeded optical parametric amplifiers providing simultaneous passive carrier-envelope phase locking of three ultrashort longwave pulses at the pump, signal, and idler wavelengths corresponding, respectively, to 2.1, 3.5, and 5.2 μm. We also demonstrate bandwidth enhancement and efficient control over nonlinear spectral phase in the regime of cascaded χ² nonlinearity in ZnGeP₂.

Direct regenerative amplification of femtosecond pulses to the multimillijoule level

We present a compact femtosecond nonlinear Yb:YAG thin-disk regenerative amplifier delivering pulses carried at a wavelength of 1030 nm with an average power of >200  W at a repetition rate of 100 kHz and an energy noise value of 0.46% (rms) in a beam with a propagation factor of M²<1.4. The amplifier is seeded with bandwidth-limited subpicosecond pulses without temporal stretching. We give estimates for the nonlinear parameters influencing the system and show that chirped mirrors compress the 2 mJ pulses to a near-bandwidth-limited duration of 210 fs.

Spatiotemporal light bullets and supercontinuum generation in β-BBO crystal with competing quadratic and cubic nonlinearities

We experimentally study filamentation and supercontinuum generation in a birefringent medium [beta-barium borate (β-BBO) crystal] pumped by intense 90 fs, 1.8 μm laser pulses whose carrier wavelength falls in the range of anomalous group velocity dispersion of the crystal. We demonstrate that the competition between the intrinsic cubic and cascaded-quadratic nonlinearities may serve as a useful tool for controlling the self-action effects via phase matching condition. In particular, we found that spectral superbroadening of the ordinary polarization is linked to three-dimensional self-focusing and formation of self-compressed spatiotemporal light bullets that could be accessed within a certain range of either positive or negative phase mismatch. In the extraordinary polarization, we detect giant spectral shifts of the second harmonic radiation, which are attributed to a light bullet-induced self-phase matching.

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.

The role of spatial and temporal modes in pulsed parametric down-conversion

We explore spatial correlations created by stimulated pair emission in frequency degenerate parametric down-conversion from a periodically poled KTP crystal pumped by ∼2 ps duration laser pulses. The ratio of stimulated pairs over spontaneous pairs reaches as high 0.8 in the experiment. This ratio is a direct measure of the total number of modes relevant to the down-conversion process. We identify a universal curve for this ratio that accounts for the effect of the focused pump, introducing a coherence diameter r(0) related to the diffraction limited size of the pump beam in the far-field. Measurements of the spatial correlations of the PDC light for longer crystals and tight focusing conditions show that the description given in terms of a universal curve is surprisingly robust and breaks down only for a laser beam focussed to a waist smaller than 40 μm in a 2 mm long PPKTP crystal.

SESAM modelocked Yb:CaGdAlO4 laser in the soliton modelocking regime with positive intracavity dispersion

We demonstrate femtosecond SESAM modelocking in the near-infrared by using cascaded quadratic nonlinearities (phase-mismatched second-harmonic generation, SHG), enabling soliton modelocking in the normal dispersion regime without any dispersion compensating elements. To obtain large and negative self-phase modulation (SPM) we use an intracavity LBO crystal, whose temperature and angles are optimized with respect to SPM, nonlinear losses, and self-starting characteristics. To support femtosecond pulses, we use the very promising Yb:CaGdAlO(4) (CALGO) gain material, operated in a bulk configuration. The LBO crystal provides sufficient negative SPM to compensate for its own GDD as well as the positive GDD and SPM from the gain crystal. The modelocked laser produces pulses of 114 fs at 1050 nm, with a repetition rate of 113 MHz (average output power 1.1 W). We perform a detailed theoretical study of this soliton modelocking regime with positive GDD, which clearly indicates the important design constraints in an intuitive and systematic way. In particular, due to its importance in avoiding multi-pulsed modelocking, we examine the nonlinear loss associated with the cascading process carefully and show how it can be suppressed in practice. With this modelocking regime, it should be possible to overcome the limits faced by current state of the art modelocked lasers in terms of dispersion compensation and nonlinearity management at high powers, suppression of Q-switching in compact GHz lasers, and enabling femtosecond soliton modelocking at very high repetition rates due to the high nonlinearities accessible via cascading combined with eliminating the need for intracavity dispersion compensation.

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.

Design of quasi-phasematching gratings via convex optimization

We propose a new approach to quasi-phasematching (QPM) design based on convex optimization. We show that with this approach, globally optimum solutions to several important QPM design problems can be determined. The optimization framework is highly versatile, enabling the user to trade-off different objectives and constraints according to the particular application. The convex problems presented consist of simple objective and constraint functions involving a few thousand variables, and can therefore be solved quite straightforwardly. We consider three examples: (1) synthesis of a target pulse profile via difference frequency generation (DFG) from two ultrashort input pulses, (2) the design of a custom DFG transfer function, and (3) a new approach enabling the suppression of spectral gain narrowing in chirped-QPM-based optical parametric chirped pulse amplification (OPCPA). These examples illustrate the power and versatility of convex optimization in the context of QPM devices.

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.

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.

Supercontinuum generation in quasi-phasematched waveguides

We numerically investigate supercontinuum generation in quasi-phase-matched waveguides using a single-envelope approach to capture second and third order nonlinear processes involved in the generation of octave-spanning spectra. Simulations are shown to agree with experimental results in reverse-proton-exchanged lithium-niobate waveguides. The competition between χ((2)) and χ((3)) self phase modulation effects is discussed. Chirped quasi-phasematched gratings and stimulated Raman scattering are shown to enhance spectral broadening, and the pulse dynamics involved in the broadening processes are explained.

Ultrafast temporal pulse shaping via phase-sensitive three-wave mixing

It is well-known that the process of optical parametric amplification (OPA) can be sensitive to the phases of the incident waves. In OPA realized by three-wave mixing, injection of all three waves into the same mode with appropriate phase relationship results in amplification of the signal phase, with an associated deamplification of the signal energy. Prospects for the use of this technique in the temporal domain for shaping ultrashort laser pulses are analyzed using a numerical model. Several representative pulse shaping capabilities of this technique are identified, which can significantly augment the performance of common passive pulse shaping methods operating in the Fourier domain. It is found that the use of phase-sensitive OPA shows a potential for significant compression of approximately 100 fs pulses, steepening of the rise time of ultrashort pulses, and production of pulse doublets and pulse trains. It is also shown that the group velocity mismatch can assist the shaping process. Such pulse shaping capabilities are found to be within reach of this technique in common nonlinear optical crystals pumped by pulses available from compact femtosecond chirped-pulse amplification laser systems.

Energy transfer from wide-band supercontinuum to narrow-band second harmonic generation

We present an experimental and theoretical study of energy transfer from a wide-band supercontinuum to narrow-band second harmonic light during propagation of a femtosecond pulse in a MgO:LiNbO(3) crystal. The energy removed from the supercontinuum at 1038 nm by phase-matched second harmonic generation is compensated by energy transfer from other wavelengths within the supercontinuum by self phase modulation via the Kerr effect.

Excitation of two-colored temporal solitons in a segmented quasi-phase-matching structure

We conducted a numerical study on the excitation of a two-colored temporal soliton in a segmented quasi-phase-matching (QPM) structure. The device has three parts: a periodic QPM grating for second-harmonic generation, a single domain for phase shift, and a periodic QPM grating for soliton evolution. The second harmonic pulse generated in the first grating works as a seed in the cascaded up-and-down conversions in the second grating. The numerical results showed that the second harmonic seeding enables the excitation of soliton pulses with an improved spatio-temporal intensity profile in a broad bandwidth of the wave-vector mismatch.

Broadband and high power terahertz pulse generation beyond excitation bandwidth limitation via chi2 cascaded processes in LiNbO3

We proposed a novel THz generation technique beyond the limitation of the input optical pulse width, based on phase modulation via cascaded chi((2)) process. When intense THz electric field generated by optical rectification lies in electro-optic (EO) crystal, emitted THz field gives phase modulation to the optical excitation pulse. The phase modulation causes excitation pulse narrowing and consequently gives rise to the enhancement of conversion efficiency and THz wave bandwidth broadening. We experimentally realize this generation technique with high chi((2)) EO crystal LiNbO(3) and with subpicosecond pulse from Yb-doped fiber laser. It opens new concept of THz technologies.

Soliton compression in quadratic media: high-energy few-cycle pulses with a frequency-doubling crystal

We present a soliton effect pulse compression technique that uses self-defocusing cascaded-quadratic nonlinearities, with no fundamental limit to its scalability to high pulse energies and the capability of generating few-cycle pulses with only a frequency-doubling crystal. The conditions for which group-velocity mismatch causes an acceptable perturbation to soliton compression are analyzed and underlie optimization of the compressor. Calculations predict compression to near-single-cycle durations, with compression ratios as high as 100. Initial experiments closely agree with calculations, demonstrating compression to durations under three optical cycles (12 fs) and generation of 600 nm bandwidths.

Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity

Using the numerical solution of the nonlinear Schrödinger equation and a variational method, it is shown that ( 3+1 ) -dimensional spatiotemporal optical solitons, known as light bullets, can be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.

Direct measurement of wave-front distortion induced during second-harmonic generation: application to breakup-integral compensation

The wave-front distortion of femtosecond laser pulses recorded with a Shack-Hartmann analyzer makes it possible to retrieve the nonlinear index of refraction of different glasses and the nonlinear phase shift induced during second-harmonic generation in beta-barium borate (BBO) crystal versus the phase mismatch. It is shown that the nonlinear phase shift induced in a 2-mm-thick BBO crystal allows compensation for up to a 2pi breakup-integral induced in a 4-cm fused-silica glass. The stability of the compensation is reported to be from 10 to 100 GW cm(-2).

Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities

We experimentally demonstrate that one can exploit nonlinear phase shifts produced in type I phase-mismatched second-harmonic generation to produce intensity-dependent polarization evolution with 100-fs pulses. An amplitude modulator based on nonlinear polarization rotation provides passive amplitude-modulation depth of up to ~50%. Applications of the amplitude and phase modulations to mode locking of femtosecond bulk and fiber lasers are promising and are discussed.