A pure silica holey fiber with $\beta_2$ of 0.44 ps$^2$/km at 1.55 $\mu$m and less than 1 ps$^2$/km from 1.3 to 1.75 $\mu$m was engineered and drawn. It is numerically shown to generate a flat coherent spectrum, pumped by a 2 kW peak power, 250 fs pulse propagating 20 m.

A remarkable feature about the temporal optical soliton is that it can be phase-matched to new frequencies, emitting so-called resonant radiation (RR). This constitutes an efficient source of ultrafast pulses in emerging wavelength regimes, and plays a vital role in coherently extending the supercontinuum bandwidth [1]. RR waves are usually invoked by four-wave mixing (4WM) through the self-phase modulation (SPM) term A|A|2, or more recently through the conjugate SPM term A∗|A|2, or the third-harmonic generation (THG) term A3 [2, 3]. We here show with theoiy and experiments that three-wave mixing (3 WM) also supports soliton-induced RR waves [4].

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.

Pumping a quadratic nonlinear crystal in the mid-IR we observe octave-spanning mid-IR supercontinua. A self-acting cascaded process leads to the formation of a self-defocusing nonlinearity, allowing formation of filament-free octave-spanning supercontinua in the 2.0-7.0 μm range with 10s of μJ pulse energies, much higher than filament-based techniques. This allows to use the supercontinuum as ultra-broadband excitation pulses in nonlinear optical applications.

We experimentally observe widely tunable mid-IR femtosecond pulses by resonant radiation, generated by direct three-wave-mixing from a soliton in PPLN. The poling pitch gives a parametrically tunable resonant radiation, a feature absent in Kerr media.

We experimentally demonstrate efficient mid-infrared pulse generation by dispersive wave radiation in bulk lithium niobate crystal. Femtosecond mid-IR pulses centering from 2.8–2.92 mm are generated using the single pump wavelengths from 1.25–1.45 mm.

We experimentally demonstrate efficient mid-infrared pulse generation by dispersive wave radiation in bulk lithium niobate crystal. Femtosecond mid-IR pulses centering from 2.8-2.92 μm are generated using the single pump wavelengths from 1.25-1.45 μm.

The third order optical nonlinearities are often used to broaden the spectral bandwidth of ultrafast pulses for supercontinuum generation or pulse compression [1]. The self-focusing nature of cubic Kerr nonlinearity usually limits the applicable pulse energy. An alternative way is using the second order optical nonlinearity, for instance the nonlinearity generated with cascaded second harmonic generation process. In this case, the nonlinearity is controllable in both magnitude and sign through Δk. It could become a desirable self-defocusing nonlinearity if a positive Δk is chosen. However, there are only a handful of reports about the harness of cascaded nonlinearity. The Kerr-like cascading nonlinearity scales as n 2, casc ∝ -d 2 eff /Δk. For a successful implementation, focus has been on having the birefringent phase matching first and then tune to small Δk to overcome the material Kerr nonlinearity and have overall negative nonlinearity. The dillema is in most such cases, the d eff is small and quite low Δk values are needed. Such low Δk gives cascading response that is resonant due to the group-velocity mismatch (GVM), and therefore cannot support ultrafast interaction. Practically by this solution only very limited wavelength regimes support this kind of interaction, as done in e.g. [2].

Effects based on the χ(3)-nonlinearity are arguably the most commonly discussed nonlinear interactions in photonics. In the description of pulse propagation, however, the generation of the third harmonic (TH) is commonly neglected, because it is strongly phase mismatched in most materials and waveguide geometries and thus of negligible influence to the overall dynamics. This mismatch is characterized by a very short coherence length, calculated by the inverse of the wave-number mismatch Δβ = 3β(ω) - β(3ω). Thus the coherence length is much smaller than any other dynamic length of the system and the generation of TH can be neglected.

We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions.

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.

We show that effective soliton compression can be realized in strongly phase-mismatched quadratic media. Sub-15 fs pulses are experimentally generated directly from 10-mm-long bulk lithium niobate crystal by 120-fs input pulses at 1300 nm.

We theoretically investigate properties of individual bright spatial solitons and their interaction in nonlocal media with competing focusing and defocusing nonlinearities. We consider the general case with both nonlinear responses characterized by different strengths and degrees of nonlocality. We employ a variational approach to analytically describe soliton properties. In particular, we prove analytically that the interplay of focusing and defocusing nonlocal nonlinearities leads to attraction or repulsion of solitons depending on their separation distance. We then study the propagation and interaction of solitons using numerical simulations of the full model of beam propagation. The numerical simulations fully confirm our analytical results.

In this paper, the authors extend the theory of cascaded Kerr to the case of pulses propagating in a dispersion tuned optical fibre generating a strongly mismatched third harmonic wave. This model includes the nonlocal response due to group velocity mismatch and different levels of dispersion for the fundamental and the third harmonic. The nonlocal harmonic approximation was applied to the system of coupled equations and derive a perturbed nonlinear Schrodinger equation for the fundamental wave only. The perturbation was shown to have the functional structure of a 5th order Kerr effect with a phase shift dependent on the square of the intensity. The dispersion features of the system create a non-instantaneous response of the perturbation, which can act similarly to a higher order Raman response with a mean time delay of tuneable magnitude and sign.

Access to energetic μJ-multi-mJ ultra-short fs laser pulses is crucial for many research topics today and in the future. Typically, laser amplifier pulses are an order of magnitude longer that the single-cycle limit making pulse compression desirable. We use soliton compression using cascaded quadratic nonlinearities to compress energetic pulses towards few-cycle duration. Specifically, we obtain sub-20 fs solitons by launching 0.25 mJ 55 fs pulses at 1300 nm in a lithium niobate (LN) crystal as short as 1 mm. The solitons are formed by phase-mismatched (cascaded) second-harmonic generation (SHG): upon propagation little second harmonic (SH) is generated, but the fundamental wave (FW) will instead experience a strong Kerr-like nonlinear phase shift. The total FW refractive index is n1+ncubicII1 where ncubicI = nSHGI +nKerrI. It includes contributions from the material Kerr nonlinearity nKerrI >; 0 and the cascaded quadratic nonlinearities nSHGI ≃ - 4πdeff2/cε0λ1n12n2Δk. The goal is to achieve a self-defocusing nonlinearity ncubicI <; 0 through a large phase mismatch Δk ≫ 0. In this case, solitons can be formed with normal dispersion, which means anywhere in the visible and near-IR. Moreover it is possible to compress multi-mJ pulse-energies because there are no self-focusing problems.

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.

We investigate analytically and numerically propagation and spatial localization of light in nonlocal media with competing nonlinearities. In particular, we discuss conditions for the modulational instability of plane waves and formation of spatial solitons. We show that the competing focusing and defocusing nonlinearities enable coexistence of dark or bright spatial solitons in the same medium by varying the intensity of the beam.

We investigate analytically and numerically propagation and spatial localization of light in nonlocal media with competing nonlinearities. In particular, we discuss conditions for the modulational instability of plane waves and formation of spatial solitons. We show that the competing focusing and defocusing nonlinearities enable coexistence of dark or bright spatial solitons in the same medium by varying the intensity of the beam.

We show that ultra-short few-cycle pulses can be generated through soliton compression of energetic femtosecond pulses from a Ti:Sapphire regenerative amplifier. The compression relies on cascaded type 0 second-harmonic generation in mm-length lithium niobate crystals.

We show through theory and numerics that when few-cycle femtosecond solitons are generated through cascaded (phase-mismatched) second-harmonic generation, these broadband solitons can emit optical Cherenkov radiation in the form of linear dispersive waves located in the red part of the spectrum. The beating between the dispersive wave and the soliton generates trailing temporal oscillations on the compressed soliton. Insertion of a simple short-wave pass filter after the crystal can restore a clean soliton. On the other hand, bandpass filtering around the dispersive wave peak results in near-transform-limited ultrashort mid-IR pulses with pulse durations much shorter than the input near-IR pulse. The Cherenkov radiation for the crystal considered (β-barium borate) is found for pump wavelengths in the range λ = 0.95‐1.45 µm, and is located in the regime λ = 1.5‐3.5 µm. For shorter pump wavelengths, the phase-matching point is located in the absorption region of the crystal, effectively absorbing the generated dispersive wave. By calculating the phase-matching curves for typically used frequency conversion crystals, we point out that the mid-IR absorption in the crystal in many cases automatically will filter away the dispersive wave. Finally, an investigation of recent experimental results uncovers a four-wave-mixing phenomenon related to Cherenkov radiation that is an additional generation mechanism of long-wavelength radiation that can occur during soliton compression. We discuss the conditions that lead to this alternative dynamics rather than generation of Cherenkov radiation.