Observation of quadratic spatial solitons in periodically poled lithium niobate

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

High-energy, near- and mid-IR picosecond pulses generated by a fiber-MOPA-pumped optical parametric generator and amplifier

We report a high-energy picosecond optical parametric generator/amplifier (OPG/A) based on a MgO:PPLN crystal pumped by a fiber master-oscillator-power-amplifier (MOPA) employing direct amplification. An OPG tuning range of 1450-3615 nm is demonstrated with pulse energies as high as 2.6 μJ (signal) and 1.2 μJ (idler). When seeded with a ~100 MHz linewidth diode laser, damage-limited pulse energies of 3.1 μJ (signal) and 1.3 μJ (idler) have been achieved and the signal pulse time-bandwidth product is improved to ~2 times transform-limited. When seeded with a 0.3 nm-bandwidth filtered amplified spontaneous emission source, crystal damage is avoided and maximum pulse energies of 3.8 μJ (signal) and 1.7 μJ (idler) are obtained at an overall conversion efficiency of 45%.

Exact cascading nonlinearity in quasi-phase-matched quadratic media

The evolution of light pulses and beams in a quasi-phase-matched (QPM) quadratic medium is usually described by considering only the spatial harmonic of the QPM grating that minimizes the residual phase-mismatch. I show that, for strongly phase-mismatched interactions (the cascading regime), several harmonics need to be accounted for in order to obtain the correct value of the effective cubic nonlinearity, for which I find a simple analytical expression. I discuss the effects of the higher order harmonics of the grating on solitary wave propagation.

Parametric solitons in two-dimensional lattices of purely nonlinear origin

We demonstrate spatial solitons via twin-beam second-harmonic generation in hexagonal lattices realized by poling lithium niobate planar waveguides. These simultons can be steered by acting on power, direction, and wavelength of the fundamental frequency input.

Spatial solitons in chi(2) planar photonic crystals

We analyze light self-confinement induced by multiple nonlinear resonances in a two-dimensional chi(2) photonic crystal. With reference to second-harmonic generation in a hexagonal lattice, we show that the system can not only support two-color (1+1)D solitary waves with enhanced confinement and steering capabilities but also enable novel features such as wavelength-dependent soliton routing.

Parametric light bullets supported by quasi-phase-matched quadratically nonlinear crystals

We present a comprehensive analysis of the dynamics of three-dimensional spatiotemporal nonspinning and spinning solitons in quasi-phased-matched (QPM) gratings. By employing an averaging approach based on perturbation theory, we show that the soliton's stability is strongly affected by the QPM-induced third-order nonlinearity (which is always of a mixed type, with opposite signs in front of the corresponding self-phase and cross-phase modulation terms). We study the dependence of the stability of the spatiotemporal soliton (STS) on its energy, spin, the wave-vector mismatch between the fundamental and second harmonics, and the relative strength of the intrinsic quadratic and QPM-induced cubic nonlinearities. In particular, all the spinning solitons are unstable against fragmentation, while zero-spin STS's have their stability regions on the system's parameter space.

Spatial solitons in type II quasiphase-matched slab waveguides

The existence and dynamics of one-dimensional spatial solitons formed upon propagation in quasiphase-matched gratings, through three-wave parametric interaction, is analyzed. We study the general case in which the grating exhibits a periodic modulation of both the refractive index and the second-order susceptibility. It is demonstrated that for negative effective wave vector mismatch the induced third-order nonlinearities increase the domain of soliton instability. Finally, the dependence of the efficiency of the second harmonic generation process in the soliton regime, on the parameters of the grating, is discussed.

Weak beam control of multiple quadratic soliton generation

Theoretical predictions and experimental observations show that a weak harmonic seed beam can control the process of generating multiple quadratic solitons in periodically poled KTiOPO4 by inputting only a fundamental beam. This all-optical switching does not depend on the relative phase of the input beams, an unusual property for such coherent solitons.

Two-dimensional solitons in quasi-phase-matched quadratic crystals

We study the existence and dynamics of two-dimensional spatial solitons in crystals that exhibit a periodic modulation of both the refractive index and the second-order susceptibility for achieving quasi-phase-matching. Far from resonances between the domain length of the periodic crystal and the diffraction length of the beams, it is demonstrated that the properties of the solitons in this quasi-phase-matched geometry are strongly influenced by the induced third-order nonlinearities. The stability properties of the two-dimensional solitons are analyzed as a function of the total power, the effective wave-vector mismatch between the first and second harmonics, and the relative strength between the induced third-order nonlinearity and the effective second-order nonlinearity. Finally, the formation of two-dimensional solitons from a Gaussian beam excitation is investigated numerically.

Spatial optical simultons in nonlinearly coupled planar waveguides

With second-harmonic generation in surface and buried planar waveguides achieved by direct and reverse proton exchange in lithium niobate, we demonstrate a novel kind of quadratic spatial simulton: The transverse-electric fundamental input and the transverse-magnetic second-harmonic waves nonlinearly couple two superimposed planar waveguides, permitting transverse localization of light at room temperature and at excitations as low as 340 nJ in 20-ps pulses.

Properties of quadratic multi-soliton generation near phase-match in periodically poled potassium titanyl phosphate

The properties of the multi-quadratic-soliton generation process have been investigated both theoretically and experimentally near and on phase-match in non-critically-phase-matched, periodically poled, potassium titanyl phosphate (PPKTP). It was found that multi-soliton generation occurs primarily due to asymmetry in the input beam and at phase-matching. The number of solitons generated depended on the input intensity in a non-trivial way.

Quadratic spatial solitons in periodically poled KTiOPO4

The evolution of fundamental beams into quadratic spatial solitons was investigated in a periodically poled bulk KTiOPO4 crystal near and at phase matching. Various soliton properties, such as trapping efficiency as a function of phase mismatch, poling-induced walk-off, and the effects of pulse width, beam width, and input beam quality, were measured. Effects attributed to the presence of cubic nonlinearities were also observed.

Two-dimensional type I quadratic spatial solitons in KNbO(3) near noncritical phase matching

Experiments on the properties of quadratic, two-dimensional spatial soliton properties in KNbO(3) near and at noncritical phase matching (NCPM) are reported. The NCPM geometry leads to unique features such as a large angular bandwidth for soliton generation, weak dependence of soliton composition on intensity and incidence angle, and unique multisoliton-generation properties.

Nonlinear dynamics of higher-order solitons near the oscillatory instability threshold

Nonlinear theory describing the dynamics of solitons in the vicinity of oscillatory instability threshold with a low frequency offset is developed. The theory is tested on the example of parametric degenerate four-wave mixing. All major predictions of our theory are in agreement with the results of direct numerical modeling. This includes the position of oscillatory instability threshold, instability rates, and various instability development scenarios.

Efficiency of quadratic soliton generation

We report what is believed to be the first experimental demonstration of soliton content as a function of the intensity of input light for multicolor quadratic solitons. Experiments were conducted with spatial solitons excited with Gaussian beams in a bulk crystal cut for second-harmonic generation. The effects introduced by the finite crystal length and by the scheme employed to elucidate the soliton energy are highlighted.

Experiments in quadratic spatial soliton generation and steering in a noncollinear geometry

Generation of spatial solitons with noncollinear excitation beams was experimentally investigated for type II second-harmonic generation in KTP. Spatial switching at a distance of 220microm and steering in a 330-microm range were demonstrated. Changes in soliton behavior induced by modification of the phase-matching condition (and) or by an imbalance of the inputs at the fundamental frequency have been characterized.

Engineerable generation of quadratic solitons in synthetic phase matching

We show that the efficiency and the mismatch bandwidth of quadratic soliton formation under conditions of second-harmonic generation can be enhanced in an important way in synthetic phase-matching profiles. Soliton excitation in smooth but arbitrary profiles is shown to be well described by a reduced variational approach. The potential of abrupt, nonadiabatic profiles for improved soliton formation is numerically revealed.