Quadratic Nonlinear Media Research Articles

Stable One‐Dimensional Periodic Wave in Kerr‐Type and Quadratic Nonlinear Media

We present the propagation of optical beams and the properties of one‐dimensional (1D) spatial solitons (“bright” and “dark”) in saturated Kerr‐type and quadratic nonlinear media. Special attention is paid to the recent advances of the theory of soliton stability. We show that the stabilization of bright periodic waves occurs above a certain threshold power level and the dark periodic waves can be destabilized by the saturation of the nonlinear response, while the dark quadratic waves turn out to be metastable in the broad range of material parameters. The propagation of (1+1) a dimension‐optical field on saturated Kerr media using nonlinear Schrödinger equations is described. A model for the envelope one‐dimensional evolution equation is built up using the Laplace transform.

Modulation instability of ultrashort pulses in quadratic nonlinear media beyond the slowly varying envelope approximation

We report a modulational instability (MI) analysis of a mathematical model appropriate for ultrashort pulses in cascaded quadratic-cubic nonlinear media beyond the so-called slowly varying envelope approximation. Theoretically predicted MI properties are found to be in good agreement with numerical simulation. The study shows the possibility of controlling the generation of MI and formation of solitons in a cascaded quadratic-cubic media in the few cycle regimes. We also find that stable propagation of soliton-like few-cycle pulses in the medium is subject to the fulfilment of the modulation instability criteria.

Second- and third-harmonic parametric scattering in disordered quadratic media

We study frequency conversion via interaction of two fundamental beams in quadratic nonlinear media with random distribution of the ferroelectric domains. We demonstrate broadband second- and third-harmonic generation, analyse both spatial and polarization properties of the emitted harmonics and show that they closely follow the theoretical predictions.

Ultrabroadband Optical Phenomena in Quadratic Nonlinear Media

We present a comprehensive framework to study the nonlinear evolution of ultrabroadband optical pulses in quadratic nonlinear media. We employ a nonlinear envelope equation that goes beyond the traditional slowly varying approximation and allows treatment of all the harmonics by means of a single equation. We exploit this model to simulate recently observed supercontinuum phenomena such as ultrabroadband parametric downconversion and the generation of octave-spanning spectra from femtosecond pulses.

Two-color interface vortex solitons

We study the existence and properties of vortex solitons supported by an interface between two distinct optical lattices imprinted in nonlinear quadratic media. We analyze the impact of guiding parameters of lattices and phase mismatching conditions on the existence and stability of two-color interface vortex solitons. The salient point is that interface vortex solitons feature highly asymmetric profiles, and are stable throughout almost the entire existence domain.

Theoretical analysis of power swapping in quadratic nonlinear medium

Nonlinear optical effects in quadratic nonlinear mediums for the traditional frequency conversion generally involve two or three incident optical waves and transfer the power of the input signal wavelength to another new generated wavelength. The authors find that bidirectional power swapping can be carried out by proper waveguide length and power arrangement when two signals and two continuous-wave pumps simultaneously take part in the quadratic nonlinear interactions. Theoretical analyses referring to four incident optical waves are presented, taking into account the cascaded sum- and difference-frequency generation in a periodically poled lithium niobate waveguide. We apply such theory to ultrafast data information swapping and derive analytical solutions clearly indicating the swapping condition. An example of bidirectional ultrafast data information swapping is demonstrated.

Quantization of electromagnetic field in quadratic continuous nonlinear absorptive dielectrics

This paper reports that in the quantization of electromagnetic field in the dielectrics, the wave equation with regard to the Green function is analytically solved by a direct integral method for a quadratic continuous nonlinear absorptive dielectric medium. The quantization of the electromagnetic field in such a nonlinear absorptive dielectric is carried out for which the material dielectric function is assumed as a separable variable about the frequency and the space coordinate. The vacuum field fluctuations for different spatial continuous variations of dielectric function are numerically calculated, which shows that the present result is self-consistent.

Generation of correlated UV and visible rainbows

We demonstrate concurrent frequency up-conversion and down-conversion in a quadratic nonlinear medium for the generation of correlated ultraviolet and visible rainbows with one-to-one angular and spectral correspondence, facilitating generation of continuously tunable and photon-momentum-dependent multi-wavelength UV and visible twin photons.

Generation of narrow-band correlated photon pairs by spontaneous down conversion in a cavity

The problem of generating a narrow-band biphoton field during spontaneous parametric down conversion of light in a quadratic nonlinear medium in a cavity is discussed. It is shown that, in the case of double resonance (for signal and idle fields), the form of the single-photon wave packet is biexponential and has a half-width determined by the photon life time in the cavity. An experiment is carried out on the generation of narrow-band biphotons in a crystal of lithium iodine with I-type matching in a frequency degenerate collinear regime. The second-order correlation function of the cavity-enhanced biphotons is measured using the electric nanosecond time delay line.

Ultrashort spatiotemporal optical solitons in quadratic nonlinear media: Generation of line and lump solitons from few-cycle input pulses

By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given.

Third-harmonic generation via broadband cascading in disordered quadratic nonlinear media

We study parametric frequency conversion in quadratic nonlinear media with disordered ferroelectric domains. We demonstrate that disorder allows realizing broadband third-harmonic generation via cascading of two second-order quasi-phase matched nonlinear processes. We analyze both spatial and polarization properties of the emitted radiation and find the results in agreement with our theoretical predictions.

Generation and control of phase-locked conical wave packets in type-I seeded optical parametric amplification

We demonstrate a technique for broadband conical pulse generation based on a continuum seeded parametric amplification process in quadratic nonlinear media. We show that by using an appropriately focused broadband weak seed we are able to selectively generate and amplify a single phase-locked conical wave packet. We present experimental spatiotemporal spectra obtained with two different crystals in type I phase-matching configurations, showing the generation and amplification of single X-type and O-type wave packets, respectively, and we compare the results with the stationary wave modes that can be supported in the parametric amplification process. On the basis of numerical calculations, we also show that the broadband $\text{signal}+\text{idler}$ phase-matched field generated by the amplifier may be characterized by a well-defined phase velocity, whose control is guaranteed by the tunability of the amplifier spectral gain curves.

Pulse measurements by randomly quasi phase matched second harmonic generation in the regime of total internal reflection

We demonstrate experimentally the frequency doubling in disordered quadratic nonlinear media in the regime of total internal reflection of the fundamental beam. We show how the transversely emitted second harmonic can be employed for an efficient characterization of short laser pulses.

Synthesis of picosecond pulses by spectral compression and shaping of femtosecond pulses in engineered quadratic nonlinear media

Narrow-bandwidth picosecond pulses of predetermined spectral and temporal shapes are generated with high efficiency by frequency conversion of femtosecond pulses in lithium tantalate crystals with engineered quasi-phase-matching structures. We give examples of the synthesis of Gaussian and super-Gaussian picosecond pulses and also of a pair of synchronized phase-coherent picosecond pulses with a predetermined carrier-frequency difference.

Two-color surface lattice solitons

We study the properties of surface solitons generated at the edge of a semi-infinite photonic lattice in nonlinear quadratic media, namely two-color surface lattice solitons. We analyze the impact of phase mismatch on the existence and stability of nonlinear surface modes and find novel classes of two-color twisted surface solitons, which are stable in a large domain of their existence.

Stability of temporal solitons in uniform and “managed” quadratic nonlinear media with opposite group-velocity dispersions at fundamental and second harmonics

The problem of the stability of solitons in second-harmonic-generating media with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field, which is generic to available χ (2) materials, is revisited. Using an iterative numerical scheme to construct stationary soliton solutions, and direct simulations to test their stability, we identify a full soliton-stability range in the space of the system’s parameters, including the coefficient of the group-velocity-mismatch (GVM). The soliton stability is limited by an abrupt onset of growth of tails in the SH component, the relevant stability region being defined as that in which the energy loss to the tail generation is negligible under experimentally relevant conditions. We demonstrate that the stability domain can be readily expanded with the help of two “management” techniques (spatially periodic compensation of destabilizing effects) – the dispersion management (DM) and GVM management. In comparison with their counterparts in optical fibers, DM solitons in the χ (2) medium feature very weak intrinsic oscillations.

Observation of spectral drift in engineered quadratic nonlinear media

Spectral blueshifts of femtosecond pulses induced by quadratic cascaded nonlinearities are experimentally studied in an engineered aperiodically poled stoichiometric lithium tantalate crystal with optimized nonlinear pattern and chirp of the input pump pulses. Starting from nearly Gaussian input pulses centered at 1420nm with 70nm spectral width, spectral shifts as high as 40nm were obtained in combination with an almost unaltered spectral shape and a transform-limited pulse duration.

Half-cycle optical soliton in quadratic nonlinear media

We show that a few-cycle pulse launched in a quadratic medium may result in a half-cycle soliton in the form of a single hump, with no oscillating tail. The analysis involves the derivation of a Korteweg-de Vries (KdV) equation from both a classical and a quantum mechanical simple model of matter-radiation interaction. The sign of the electric field in the half-cycle KdV soliton is fully determined by the properties of the material, which definitely breaks the phase invariance.

Three-Wave Trapponic Solitons for Tunable High-Repetition Rate Pulse Train Generation

We demonstrate that the parametric mixing of an ultrashort Zakharov-Manakov (ZM) soliton pulse with a quasi-continuous-wave (CW) signal in a weakly quadratic nonlinear and dispersive medium may lead to the generation of a three-wave soliton with variable speed, or trappon. We show that trappons may provide a novel mechanism of cavityless ultrashort pulse train generation. The timewidth, the amplitude and the repetition rate of the generated pulse trains may be controlled in a stable manner by adjusting the intensity level of the CW signal and/or the ZM short soliton pulse.

Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities

We present a detailed study of soliton compression of ultrashort pulses based on phase-mismatched second-harmonic generation (SHG) (i.e., the cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The single-cycle propagation equations in the temporal domain including higher-order nonlinear terms are presented. The balance between the quadratic (SHG) and the cubic (Kerr) nonlinearity plays a crucial role; we define an effective soliton number—related to the difference between the SHG and the Kerr soliton numbers—and show that it has to be larger than unity for successful pulse compression to take place. This requires that the phase mismatch be below a critical level, which is high in a material where the quadratic nonlinearity dominates over the cubic Kerr nonlinearity. Through extensive numerical simulations we find dimensionless scaling laws, expressed through the effective soliton number, that control the behavior of the compressed pulses. These laws hold in the stationary regime, in which group-velocity mismatch effects are small, and they are similar to the ones observed for fiber soliton compressors. The numerical simulations indicate that clean compressed pulses below two optical cycles can be achieved in a β-barium borate crystal at appropriate wavelengths, even for picosecond input pulses.