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

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.

General framework for ultrafast nonlinear photonics: unifying single and multi-envelope treatments [Invited]

Numerical modeling of ultrashort pulse propagation is important for designing and understanding the underlying dynamical processes in devices that take advantage of highly nonlinear interactions in dispersion-engineered optical waveguides. Once the spectral bandwidth reaches an octave or more, multiple types of nonlinear polarization terms can drive individual optical frequencies. This issue is particularly prominent in χ(2) devices where all harmonics of the input pulse are generated and there can be extensive spectral overlap between them. Single-envelope approaches to pulse propagation have been developed to address these complexities; this has led to a significant mismatch between the strategies used to analyze moderate-bandwidth devices (usually involving multi-envelope models) and those used to analyze octave-spanning devices (usually involving models with one envelope per waveguide mode). Here we unify the different strategies by developing a common framework, applicable to any optical bandwidth, that allows for a side-by-side comparison between single- and multi-envelope models. We include both χ(2) and χ(3) interactions in these models, with emphasis on χ(2) interactions. We show a detailed example based on recent supercontinuum generation experiments in a thin-film LiNbO3 on sapphire quasi-phase-matching waveguide. Our simulations of this device show good agreement between single- and multi-envelope models in terms of the frequency comb properties of the electric field, even for multi-octave-spanning spectra. Building on this finding, we explore how the multi-envelope approach can be used to develop reduced models that help build physical insights about new ultrafast photonics devices enabled by modern dispersion-engineered waveguides, and discuss practical considerations for the choice of such models. More broadly, we give guidelines on the pros and cons of the different modeling strategies in the context of device design, numerical efficiency, and accuracy of the 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.

Nonlinear refraction and absorption measurements of thin films by the dual-arm Z-scan method

We extend the recently developed dual-arm Z-scan to increase the signal-to-noise ratio (SNR) for measuring the nonlinear refraction (NLR) of thin films on thick substrates. Similar to the case of solutes in solution, the phase shift due to NLR in a thin film can often be dominated by the phase shift due to NLR in the much thicker substrate. SNR enhancement is accomplished by simultaneously scanning a bare substrate and the film plus substrate in two separate but identical Z-scan arms. The subtraction of these signals taken simultaneously effectively cancels the nonlinear signal from the substrate, leaving only the signal from the film. More importantly, the SNR is increased since the correlated noise from effects such as beam-pointing instabilities cancels. To show the versatility of the dual-arm Z-scan method, we perform measurements on semiconductor and organic thin films, some less than 100 nm thick and with thicknesses up to 4 orders of magnitude less than the substrate.

All-solid-state multipass spectral broadening to sub-20 fs

In this work, we present a nonlinear spectral broadening and compression scheme based on self-phase modulation in bulk media inside a Herriott-type multipass cell. With this reliable approach, we achieved a spectral broadening factor of 22 while maintaining an efficiency of over 60% at an average input power of 100 W, and an excellent output beam quality with M²=1.2. The output pulses were compressed to 18 fs, with the broadest spectrum supporting a Fourier-transform limit of 10 fs. The high efficiency and approximately four-optical-cycle pulse duration mark an important milestone towards the realization of a compact, high power oscillator-based driver for XUV frequency combs and other nonlinear processes.

Filamentation-free self-compression of mid-infrared pulses in birefringent crystals with second-order cascading-enhanced self-focusing nonlinearity

We experimentally demonstrate virtually lossless, filamentation-free and energy-scalable more than three-fold self-compression of mid-infrared laser pulses at 2.1 μm in a birefringent medium (β-BBO crystal), which stems from favorable interplay between the second-order cascading-enhanced self-phase modulation and anomalous group velocity dispersion. By choosing an appropriate input beam diameter and intensity, the self-compression down to sub-30 fs pulse widths with gigawatt peak power is achieved without the onset of beam filamentation and associated nonlinear losses due to the multiphoton absorption, yielding the energy throughput greater than 86%.

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.

Second-order cascading-assisted filamentation and controllable supercontinuum generation in birefringent crystals

We experimentally investigate filamentation and supercontinuum generation in a birefringent medium (BBO crystal), in the self-focusing regime where intrinsic cubic nonlinearity is either enhanced or reduced by the second-order cascading due to phase-mismatched second harmonic generation. We demonstrate that the supercontinuum spectral extent is efficiently controlled by varying the phase mismatch parameter. In the range of negative phase mismatch, we achieve full control of the blue-shifted spectral broadening, which is very robust and independent on the input pulse energy. In the range of positive phase mismatch, both the blue-shifted and the red-shifted spectral broadenings are controlled simultaneously, however showing a certain dependence on the input pulse energy. The results are interpreted in terms of complex interplay between the self-phase-matched second harmonic generation, which is a process inherent to narrow ultrashort pulsed laser beams and concurrent self-steepening processes which arise from cubic and cascaded-quadratic nonlinearities.

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.

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.

Mid-IR femtosecond frequency conversion by soliton-probe collision in phase-mismatched quadratic nonlinear crystals

We show numerically that ultrashort self-defocusing temporal solitons colliding with a weak pulsed probe in the near-IR can convert the probe to the mid-IR. A near-perfect conversion efficiency is possible for a high effective soliton order. The near-IR self-defocusing soliton can form in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between λ=2.2-2.4  μm as a resonant dispersive wave. This process relies on nondegenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation.

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.

Measurements of the third- and fifth-order optical nonlinearities of water at 532 and 1064 nm using the D4σ method

The nonlinear response of liquid water was investigated at 1064 and 532 nm using a Nd:YAG laser delivering pulses of 17 ps and its second harmonic. The experiments were performed using the D4σ method combined with the Z-scan technique. Nonlinear refractive indices of third- and fifth-order were determined, as well as the three-photon absorption coefficient, for both wavelengths. A good agreement was found between theory and experiment.

Highly coherent mid-IR supercontinuum by self-defocusing solitons in lithium niobate waveguides with all-normal dispersion

We numerically investigate self-defocusing solitons in a lithium niobate (LN) waveguide designed to have a large refractive index (RI) change. The waveguide evokes strong waveguide dispersion and all-normal dispersion is found in the entire guiding band spanning the near-IR and the beginning of the mid-IR. Meanwhile, a self-defocusing nonlinearity is invoked by the cascaded (phase-mismatched) second-harmonic generation under a quasi-phase-matching pitch. Combining this with the all-normal dispersion, mid-IR solitons can form and the waveguide presents the first all-nonlinear and solitonic device where no linear dispersion (i.e. non-solitonic) regimes exist within the guiding band. Soliton compressions at 2 μm and 3 μm are investigated, with nano-joule single cycle pulse formations and highly coherent octave-spanning supercontinuum generations. With an alternative design on the waveguide dispersion, the soliton spectral tunneling effect is also investigated, with which few-cycle pico-joule pulses at 2 μm are formed by a near-IR pump.

Intense sub-two-cycle infrared pulse generation via phase-mismatched cascaded nonlinear interaction in DAST crystal

Octave-spanning, 12.5 fs, (1.9 cycle) pulses with 115 μJ energy in the short-wavelength mid-infrared spectral range (1-2.5 μm) have been generated via phase-mismatched cascaded nonlinear frequency conversion using organic DAST (4-N, N-dimethylamino-4'-N'-methylstilbazolium tosylate) crystal. Such ultrafast cascading effect is ensured by the interaction of a pump pulse with the exceptionally large effective nonlinearity of the DAST crystal and experiencing nonresonant, strongly phase-mismatched, Kerr-like negative nonlinearity.

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.

Coherent anti-Stokes Raman spectroscopy utilizing phase mismatched cascaded quadratic optical interactions in nonlinear crystals

We experimentally investigated the nonlinear optical interaction between the instantaneous four-wave mixing and the cascaded quadratic frequency conversion in commonly used nonlinear optical KTP and LiNbO3 with the aim of a possible background suppression of the non-resonant background in coherent anti-Stokes Raman scattering. The possibility of background-free heterodyne coherent anti-Stokes Raman scattering microspectroscopy is investigated at the interface formed by a liquid (isopropyl alcohol) and a nonlinear crystal (LiNbO3).

Higher-order Kerr effect and harmonic cascading in gases

The higher-order Kerr effect (HOKE) has recently been advocated to explain measurements of the saturation of the nonlinear refractive index in gases. Here we show that cascaded third-harmonic generation results in an effective fifth-order nonlinearity that is negative and significant. Higher-order harmonic cascading will also occur from the HOKE, and the cascading contributions may significantly modify the observed nonlinear index change. At lower wavelengths, cascading increases the HOKE saturation intensity, while for longer wavelengths cascading will decrease the HOKE saturation intensity.