Light Wave Interactions in Active Nonlinear Crystals with Quadratic Nonlinearity

Recent results in the field of three-frequency wave interaction in homogeneous and inhomogeneous (periodically poled) active nonlinear crystals with quadratic nonlinearity are reviewed. The quasi-phase-matched processes of self-frequency doubling, self-frequency halving, and frequency mixing of the pump and laser radiations are studied. The consecutive quasi-phase-matched processes of the third-harmonic generation and parametric amplification with low-frequency pumping in periodically poled active nonlinear crystals are also investigated. The analysis is carried out for the case of a periodically poled Nd:Mg:LiNbO₃ crystal. Perspectives of using periodically poled active nonlinear crystals in laser devices with self-frequency conversion are discussed.     

Consecutive Q-switched self-frequency conversion in periodically poled active nonlinear crystals

The results of theoretical studies of consecutive processes of self-frequency conversion in a Q-switched regime are presented. A scheme consisting of a periodically poled active nonlinear crystal and modulator located in the cavity is analyzed. The time dynamics and energy characteristics of radiation at consecutive processes of self-frequency tripling and parametric self-frequency conversion are calculated using numerical methods. Parameters of cavity, pump, and Q switching corresponding to maximum powers of radiation are found.     

Time and Energy Characteristics of Radiation at <Emphasis Type="Italic">Q</Emphasis>-switched Self-Frequency Conversion

The results of a theoretical study of quasi-phase matched processes at self-frequency conversion in the Q-switched regime are presented. A scheme containing a periodically poled active nonlinear crystal and an acousto-optical modulator inserted inside the cavity is considered. Solutions of the set of equations describing such scheme are obtained by numerical methods. The time dynamics of the self-frequency doubling, self-frequency summing, and self-parametric frequency conversion processes are studied in detail. The energy characteristics of the radiation are also calculated and compared with those in the stationary regime.     

Optimization of self-frequency doubling in periodically and quasi-periodically poled nonlinear crystals

The theory of self-frequency doubling in a periodically poled nonlinear crystal is generalized to the case of varied domain thickness (quasi-periodically poled crystals). A particular statistical model of quasi-periodicity is considered. The effect of quasi-periodicity on the output emission intensity is calculated. The degree of quasi-periodicity allowable for practical applications is estimated, and the advantages of quasi-periodically poled crystals are discussed. The problem of maximization of the output emission intensity for periodically and quasi-periodically poled crystals is considered. The dependence of the output emission intensity on the crystal length is investigated, and an upper estimate for the maximum intensity is obtained. A formula for the optimal reflection coefficient of the output mirror as a function of the crystal length is derived.     

Efficient femtosecond optical parametric oscillators based on aperiodically poled nonlinear crystals

We discuss the use of aperiodically poled nonlinear crystals to improve conversion efficiency in a synchronously pumped ultrafast optical parametric oscillator. We show theoretically that with these crystals the conversion efficiency can be considerably higher than that obtained when a periodically poled crystal with the same length is used. Moreover, we show that pump threshold can be simultaneously improved by use of longer crystals.     

Mode conversion in quadratic nonlinear crystals

We propose a novel all-optical, nonlinear mode-conversion scheme based on cascaded three-wave-mixing phase-matched interactions in quadratic nonlinear crystals. We demonstrate the method experimentally by performing all-optical mode conversion of an input 1636 nm Hermite-Gaussian mode from the zeroth order to the first order using two periodically poled LiNbO(3) crystals. Nonlinear mode conversion of an input beam into a higher order, orthogonally polarized output beam can be realized using only one quasiperiodic nonlinear structure. Moreover, it can be enhanced for conversion of complex modes, e.g., Laguerre-Gaussian or Bessel modes.     

Phase-matched nonlinear diffraction

We report on a new (to our knowledge) configuration incorporating both birefringence and quasi-phase-matching, enabling efficient phase-matched nonlinear diffraction in one-dimensional periodically poled nonlinear crystals. We demonstrate the method experimentally, showing an efficient nonlinear diffraction to the first few orders in two types of crystals, MgO doped congruent lithium niobate and congruent lithium niobate, and characterize its efficiency dependence on the fundamental power, the propagation angle, and the crystal temperature. This configuration can increase efficiencies observed in nonlinear diffraction experiments, enables ferroelectric domain characterization by nonlinear microscopy, and can be used to determine the duty cycles of periodically poled nonlinear crystals.     

Controlling the disorder properties of quadratic nonlinear photonic crystals

We experimentally demonstrate a modulation scheme for disordered nonlinear crystals that combines periodic modulation and disordered sections. The crystal is divided into a set of identical periodically poled building blocks, whereby each block is followed by a short section of random length. We use this scheme to achieve broadband second harmonic generation in KTiOPO4 nonlinear crystals while independently controlling the bandwidth and the center of the converted wavelengths as well as the efficiency of conversion. The trade-off between bandwidth and efficiency is improved in comparison with periodically poled crystals.     

Noncollinear second-harmonic generation in periodically poled KTiOPO4 excited by the Bessel beam

Frequency doubling in periodically poled KTiOPO(4) excited by the Bessel-like distribution of the fundamental radiation has been investigated. Theoretical analysis and experiments show that the use of noncollinear geometry provides new possibilities for engineering nonlinear interactions in periodically poled crystals. We demonstrate conversion of the ring-shaped fundamental mode to the axial second-harmonic beam with 30% efficiency for 220-muJ Q -switched Nd:YAG pulses.     

Frequency doubling of phase-modulated femtosecond laser pulses in periodically poled and chirped nonlinear crystals

The second harmonic generation (SHG) at a wavelength of 0.8 μm by 50-and 10-fs pulses with and without phase modulation (PM) was systematically studied in LiNbO₃ crystals with regular domain structure and linearly varied domain thickness. The main results were obtained by numerical method, taking into account the difference between group velocities of interacting pulses and the group-velocity dispersion. In the approximation of the given field of the fundamental radiation, an analytical expression was derived for the spectral density of the second harmonic in the periodically poled nonlinear crystal (PPNC) under nonstationary excitation conditions. It was numerically found that the conversion efficiency of about 90% can be achieved by doubling the frequency of 50-fs laser pulses without PM in the LiNbO₃ PPNC. The maximum conversion efficiency for the SHG by PM pulses is achieved at a certain optimum chirp step in the crystal domain length, which depends on both the value and sign of frequency modulation.     

New approaches for the fabrication of photonic structures of nonlinear optical materials

We revisited two different strategies to fabricate 1D photonic crystals of nonlinear optical dielectric materials based on ultrafast laser ablation of the surface of an RbTiOPO₄ crystal, and selective etching of ferroelectric domains of the surface of a periodically poled LiNbO₄ crystal. We evaluated their behaviour as Bragg diffraction gratings. We also presented the recent advances we developed in a new procedure of fabrication of 2D and 3D photonic crystals of KTiOPO₄ (KTP) grown on the surface of a KTP substrate by liquid phase epitaxial means within the pores of a silicon macroporous template. Optical, structural, morphological, and compositional characterization for the photonic crystals produced through this technique are presented.     

Direct third harmonic generation due to quadratic cascaded processes in periodically poled crystals

We report the first, according to our knowledge, experiment for direct third harmonic (TH) generation in periodically poled quadratic crystals. TH radiation of a diode array pumped and acousto-optically Q-switched Nd:YVO₄ laser is generated in a 25 mm long periodically poled lithium niobate (PPLN) crystal of period 7.0 μm. A theoretical model is developed that explains the experimental results. It predicts that the efficient phase-matched direct TH generation in periodically poled structures with duty factor 0.5 requires even order quasi-phase matching. In contrast to the similar experiments in bulk birefringence crystals, where direct phase matched TH signal is the sum of the contribution of both intrinsic and cascaded cubic nonlinearities, in periodically poled quadratic crystals only cascaded cubic nonlinearity contributes to the direct phase-matched TH signal.     

Mapping of periodically poled crystals via spontaneous parametric down-conversion

A new method for characterization of periodically poled crystals is developed based on spontaneous parametric down-conversion. The method is demonstrated on crystals of Y:LiNbO₃, Mg:Y:LiNbO₃ with non-uniform periodically poled structures, obtained directly under the Czochralski growth procedure and designed for application of 1.064 μmpumped OPO in the mid-infrared range. Infrared dispersion of refractive index, effective working periods and wavelengths of OPO were determined by special treatment of frequency-angular spectra of spontaneous parametric down-conversion in the visible range. Two-dimensional mapping via spontaneous parametric down-conversion is proposed for characterizing spatial distribution of bulk quasi-phase matching efficiency across the input window of a periodically poled sample.     

准相位匹配倍频系统的带宽性质研究

根据准相位匹配倍频原理,讨论了实现宽带二次谐波转换需要满足的条件.以周期性极化铌酸锂晶体和掺杂氧化镁（7mol%）周期性极化铌酸锂（7mol%MgO-PPLN）晶体为例,分别比较了0型（e+e→e）和Ⅰ型（o+o→e）两种准相位匹配情况下宽带高效二次谐波转换的特性.研究表明,对于7mol%MgO-PPLN晶体,同时满足准相位匹配条件和群速度匹配条件的中心波长和带宽向短波方向移动,且0型（e+e→e）准相位匹配情况下可以获得更大的带宽.     

Quasi-phase matching in LiNbO3 using nonlinear coefficients in the XY plane

We report quasi-phase-matched second-harmonic generation in periodically poled lithium niobate (PPLN), where both fundamental and second-harmonic waves are ordinary waves. It provides a lower-limit value for d₂₂ of 1.1 pm/V. The measured temperature and wavelength bandwidth of the second-harmonic signal are in good agreement with the theoretical predictions. Since the d₂₂=d_YYY nonlinear coefficient of LiNbO₃ changes its sign as a result of electric field periodic poling along the Z direction, we deduce that all tensor components of the second-order susceptibility χ⁽²⁾ of trigonal 3m crystals are reversed, thereby expanding the quasi-phase-matching possibilities in these crystals. Furthermore, it enables the realization of all-optical processes based on the nonlinear coefficients in the XY plane, such as all-optical polarization rotation in PPLN, as well as multipartite entanglement experiments based on simultaneous phase matching using different elements of χ⁽²⁾ in a single LiNbO₃ crystal. PACS 42.65.-k; 42.65.Ky; 42.65.Lm     

Lateral patterning of nonlinear frequency conversion with transversely varying quasi-phase-matching gratings

We demonstrate control of the nonlinear conversion across a beam profile by using periodically poled lithium niobate with a laterally nonuniform quasi-phase-matching grating. As a representative experiment, generation of a flat-top second-harmonic beam is demonstrated.     

Surface second-harmonic generation based on periodically poled LiNbO3 nonlinear optical crystal

We have generated a second-harmonic generation(SHG) of a Q-switched microchip Nd:YAG laser on the surface of a periodically poled LiNbO3(PPLN) nonlinear crystal near the grazing incidence angle.Three individual SHG waves as transmitted homogeneous,inhomogeneous and reflected radiations have been generated and their intensities are measured and characterized within a desirable range of about 10 different incidence angles of the Nd:YAG laser as pump source on the PPLN surface.The basic of surface nonlinear radiation is also investigated and similar results are calculated and extracted from the theory.Comparison between calculated and measured data shows that they are in good agreement with each other.     

A compact and high efficiency diode pumped green laser based on MgO doped PPLN

In this work, an efficient intra-cavity second harmonic generation of green laser in a periodically poled MgO doped LiNbO₃ (MgO:PPLN) bulk crystal using a compact Nd:YVO₄ laser as a fundamental laser source is reported. Different length, different working temperature MgO:PPLN crystals are tested and investigated in the SHG experiments. The maximum output power at 532 nm is 6.2 W at the absorbed pump power at 808 nm of 14 W, the optical to optical conversion efficiencies from 808 to 532 nm and 1064 to 532 nm are 43 and 77%, respectively, the instability in 2 hours is less than 5%.     

Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch

We consider an index-guiding silica photonic crystal fiber with a triangular hole pattern and a periodically poled quadratic nonlinearity. By tuning the pitch and the relative hole size, second-harmonic generation with zero group-velocity mismatch is found for any fundamental wavelength above 780 nm. The nonlinear strength is optimized when the fundamental has maximum confinement in the core. The conversion bandwidth allows for femtosecond-pulse conversion, and 4%-180%W(-1)cm(-2) relative efficiencies were found.     

Parametric oscillation at 2.1 μm in periodically poled RbTiOAsO4

An Nd:YAG laser-pumped periodically poled RbTiOAsO₄ (PPRTA) optical parametric oscillator (OPO) near degeneracy is reported. At a pump power of 3.7 W, a net conversion efficiency of 43% was obtained. These crystals were found to be phase-matchable for the higher order quasi-phase-matched second-harmonic generation (SHG) in the visible range. Detailed analyses of the phase-matching properties for these processes were made by using the published Sellmeier and thermo-optic dispersion formulas.