Search

Cascaded nonlinearities in quadratic nonlinear crystals underlie an immensely powerful control over the ultrafast nonlinear response, where it is possible at will to change the signof the nonlinearity and tune its strength seamlessly from weak to extremely strong. Here the physics behind the cascading nonlinearity is investigated in detail, especially withfocus on femtosecond energetic laser pulses being subjected to this nonlinear response. Analytical, numerical and experimental results are used to understand the cascading interaction and applications are demonstrated. The defocusing soliton is of particular interest here, since it is quite unique and provides the solution to a number of standing challenges in the ultrafast nonlinear optics community. It solves the problem of catastrophic focusing and formation of a filaments in bulk glasses, which even under controlled circumstances is limited to energies of a few µJ. In contrast, the defocusing soliton can sustain orders of magnitude larger energies. It also solves the challenge of using maturenear-IR laser technology to generate ultrashort, coherent and bright mid-IR radiation. The defocusing nonlinear effect that leads to intriguing observations with analogies in fiberoptics are observed numerically and experimentally, including soliton self-compression, soliton-induced resonant radiation, supercontinuum generation, optical wavebreaking andshock-front formation. All this happens despite no waveguide being present, thanks to the defocusing nonlinearity. Finally, the richness of the complex nonlinear system is immense, and as an example the first observation of parametrically tunable resonant radiation is shown, phase-matched to the defocusing soliton, and emitted in the mid-IR and the visible/near-IR.

We investigate numerically soliton-plasma interaction in a noble-gas-filled silica hollow-core anti-resonant fiber pumped in the mid-IR at 3.0 {\mu}m. We observe multiple soliton self-compression stages due to distinct stages where either the self-focusing or the self-defocusing nonlinearity dominates. Specifically, the parameters may be tuned so the competing plasma self-defocusing nonlinearity only dominates over the Kerr self-focusing nonlinearity around the soliton self-compression stage, where the increasing peak intensity on the leading pulse edge initiates a competing self-defocusing plasma nonlinearity acting nonlocally on the trailing edge, effectively preventing soliton-formation there. As the plasma switches off after the self-compression stage, self-focusing dominates again, initiating another soliton self-compression stage in the trailing edge. This process is accompanied by supercontinuum generation spanning 1-4 {\mu}m. The technique could be exploited to generate an ultrafast sequence of several few-cycle pulses., Comment: submitted

Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystal like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband supercontinuum generation in the visible, near-IR and short-wavelength mid-IR. Here we conduct an experiment where a mid-IR crystal pumped in the mid-IR gives multiple-octave spanning supercontinua. The crystal is cut for noncritical interaction, so the three-wave mixing of a single mid-IR femtosecond pump source leads to highly phase-mismatched second-harmonic generation. This self-acting cascaded process leads to the formation of a self-defocusing soliton at the mid-IR pump wavelength and after the self-compression point multiple octave-spanning supercontinua are observed (covering 1.6-$7.0~\mu$m). The results were recorded in a commercially available crystal LiInS$_2$ pumped in the 3-$4~\mu$m range, but other mid-IR crystals can readily be used as well., Comment: submitted to APL Photonics

We here derive the so-called Nonlinear Analytical Envelope Equation (NAEE) inspired by the work of Conforti et al. [M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, "Interaction between optical fields and their conjugates in nonlinear media," Opt. Express 21, 31239-31252 (2013)], whose notation we follow. We present a complete model that includes $\chi^{(2)}$ terms [M. Conforti, F. Baronio, and C. De Angelis, "Nonlinear envelope equation for broadband optical pulses in quadratic media," Phys. Rev. A 81, 053841 (2010)], $\chi^{(3)}$ terms, and then extend the model to delayed Raman effects in the $\chi^{(3)}$ term. We therefore get a complete model for ultrafast pulse propagation in quadratic nonlinear crystals similar to the Nonlinear Wave Equation in Frequency domain [H. Guo, X. Zeng, B. Zhou, and M. Bache, "Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media," J. Opt. Soc. Am. B 30, 494-504 (2013)], but where the envelope is modelled rather than the electrical field while still keeping a sub-carrier level resolution. The advantage of the envelope formation is that the physical origin of the additional terms that are included to model the physics at the carrier level becomes more clear, in contrast to the electric field equations that are more "black box" expansions of the electrical field. We also point out that by comparing our results to a very similar model and widely used model [G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, "Nonlinear envelope equation modeling of sub-cycle dynamics and harmonic generation in nonlinear waveguides," Opt. Express 15, 5382-5387 (2007)], the Raman terms presented there will most likely lead to an artificially lower Raman effect.

Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystals like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband supercontinuum generation in the visible, near-IR, and short-wavelength mid-IR. Here we conduct an experiment where a mid-IR crystal is pumped in the mid-IR. The crystal is cut for noncritical interaction, so the three-wave mixing of a single mid-IR femtosecond pump source leads to highly phase-mismatched second-harmonic generation. This self-acting cascaded process leads to the formation of a self-defocusing soliton at the mid-IR pump wavelength and after the self-compression point multiple octave-spanning supercontinua are observed. The results were recorded in a commercially available crystal LiInS2 pumped in the 3-4 µm range with 85 fs 50 µJ pulse energy, with the broadest supercontinuum covering 1.6-7.0 µm. We measured up 30 µJ energy in the supercontinuum, and the energy promises to scale favorably with an increased pump energy. Other mid-IR crystals can readily be used as well to cover other pump wavelengths and target other supercontinuum wavelength ranges

A method and a pulse compressor (1) for compressing an optical pulse, wherein the pulse compressor comprising a bulk quadratic nonlinear medium (2) adapted for generating a negative nonlinear phase variation on the optical pulse and having a negative group-velocity dispersion, and a dispersive unit (3) with a net positive dispersion. Furthermore, the net positive dispersion in the dispersive unit at least partially compensates for the negative nonlinear phase variation and the negative group-velocity dispersion produced by the bulk quadratic nonlinear medium when the optical pulse passes through the bulk quadratic nonlinear medium and subsequently through the dispersive unit thereby generating a temporally compressed optical pulse. For 1 micron lasers second-harmonic generation at high intensities yields spectral broadening due to self-defocusing by the Kerr-nonlinearity which can subsequently be compressed by providing normal dispersion. As KDP crystals can be glued together, large apertures of the pulse compressor are possible making this method suitable for pulse compression in Joule-class lasers.

We experimentally observe long-wavelength dispersive waves generation in a BBO crystal. A soliton was formed in normal GVD regime of the crystal by a self-defocusing and negative nonlinearity through phase-mismatched quatradic interaction. Strong temporal pulse compression confirmed the formation of soliton during the pulse propagation inside the crystal. Significant dispersive wave radiation was measured in the anomalous GVD regime of the BBO crystal. With the pump wavelengths from 1.24 to 1.4 $\mu$m, tunable dispersive waves are generated around 1.9 to 2.2 $\mu$m. The observed dispersive wave generation is well understood by simulations., Comment: in preparation

Efficient supercontinuum generation (SCG) requires excitation of solitons at the pump laser wavelength. Quadratic nonlinear waveguides may support an effective self-defocusing nonlinearity so solitons can directly be generated at common ultrafast laser wavelengths without any waveguide dispersion engineering. We here experimentally demonstrate efficient SCG in a standard lithium niobate (LN) waveguide without using quasi-phase matching (QPM). By using femtosecond pumps with wavelengths in the $1.25-1.5 \mu\rm m$ range, where LN has normal dispersion and thus supports self-defocusing solitons, octave-spanning SCG is observed. An optimized mid-IR waveguide design is expected to support even broader spectra. The QPM-free design reduces production complexity, allows longer waveguides, limits undesired spectral resonances and effectively allows using nonlinear crystals where QPM is inefficient or impossible. This result is important for mid-IR SCG, where QPM-free self-defocusing waveguides in common mid-IR nonlinear crystals can support solitons directly at mid-IR ultrafast laser wavelengths, where these waveguides have normal dispersion., Comment: To appear in Optics Letters

We interpret the forward Maxwell equation with up to third order induced polarizations and get so called nonlinear wave equation in frequency domain (NWEF), which is based on Maxwell wave equation and using slowly varying spectral amplitude approximation. The NWEF is generalized in concept as it directly describes the electric field dynamics rather than the envelope dynamics and because it concludes most current-interested nonlinear processes such as three-wave mixing, four-wave-mixing and material Raman effects. We give two sets of NWEF, one is a 1+1D equation describing the (approximated) planar wave propagation in nonlinear bulk material and the other corresponds to the propagation in a waveguide structure., Equation Derivations

We interpret the forward Maxwell equation with up to third order induced polarizations and get so called nonlinear wave equation in frequency domain (NWEF), which is based on Maxwell wave equation and using slowly varying spectral amplitude approximation. The NWEF is generalized in concept as it directly describes the electric field dynamics rather than the envelope dynamics and because it concludes most current-interested nonlinear processes such as three-wave mixing, four-wave-mixing and material Raman effects. We give two sets of NWEF, one is a 1+1D equation describing the (approximated) planar wave propagation in nonlinear bulk material and the other corresponds to the propagation in a waveguide structure.

We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (��-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant $��^{(3)}$ cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments in the literature are analyzed and we correct the data from some of the experiments for contributions from cascading as well as for updated material parameters. We find that the Kerr nonlinear tensor component responsible for self-phase modulation in cascading is considerably larger than what has been used to date. We evaluate the impact of using such a cubic anisotropic response in ultrafast cascading experiments., Updated version, comments on experiments from the literature welcome

We review measurements in the literature regarding Kerr nonlinearity of lithium niobate. Of particular interest is to separate the value of the electronic Kerr nonlinearity and the strength of the delayed Raman nonlinearity. The spectral shape of the Raman response in LN is discussed and we restrict ourselves to the case where the pump is polarized along the optical axis. This configuration is important for so-called type 0 noncritical interaction, which is used in QPM devices and in recent supercontinuum generation and few-cycle soliton compression experiments., Comment: in progress, comments welcome

The output of a high-power femtosecond fiber laser is typically 300 fs with a wavelength around $\lambda=1030-1060$ nm. Our numerical simulations show that cascaded quadratic soliton compression in bulk LiNbO$_3$ can compress such pulses to below 100 fs.

A model is proposed where two chi((2)) nonlinear waveguides are contained in a cavity suited for second-harmonic generation. The evanescent wave coupling between the waveguides is considered as weak, and the interplay between this coupling and the nonlinear interaction within the waveguides gives rise to quantum violations of the standard quantum limit. Pronounced twin-beam behavior is observed as almost complete noise suppression in the difference as well as the sum of the waveguide intensities close to bistable transitions, self-pulsing instabilities as well as the transition from symmetric to asymmetric states. The correlations imply strong correlations and anticorrelations induced by the coupling. The violations of the standard quantum limit are particularly strong when two instabilities are competing. The results are based on the full quantum Langevin equations derived from the boson operator Hamiltonian and including cavity damping effects. The intensity correlations of the output fields are calculated semianalytically using a linearized version of the Langevin equations derived through the positive-P representation. Confirmation of the analytical results are obtained by numerical simulations of the nonlinear Langevin equations derived using the truncated Wigner representation.