The nonlinear refractive indices and nonlinear third-order susceptibilities of quadratic crystals

The third-order nonlinear susceptibilities and nonlinear refractive indices of KDP, BBO, and LiNbO₃ crystals at wavelengths of 1064 and 532 nm are measured using the Z-scan technique. The measurements are made for different energies of incident radiation and different focusing conditions and crystal lengths. It is found that, as the angle between the light beam and the principal optic axis of a KDP crystal increases, the nonlinearity drops, with its magnitude at a wavelength of 1064 nm being higher than at 532 nm. For a BBO crystal, the nonlinearity dispersion is normal. The mechanisms of nonlinear losses in KDP, BBO, and LiNbO₃ crystals are identified. The values of the nonlinear susceptibilities thus obtained are analyzed and compared with the results of calculations based on an empirical model and with the data of other authors.     

Self-trapping and stable localized modes in nonlinear photonic crystals.

We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystals.     

Propagations of Airy Beams and Nonlinear Accelerating Optical Beams in Photorefractive Crystals with Asymmetric Nonlocality

The impact of the asymmetric nonlocal diffusion nonlinearity of Airy beams and nonlinear accelerating beams supported by photorefractive crystals is addressed. It is revealed how the asymmetric nonlocal response alters the evolution of these optical beams. It is found that the evolution of these beams presents a bending action under the influence of the diffusion nonlinearity. It is also shown that nonlinear accelerating beams can exist in photorefractive crystals with asymmetric nonlocality. These accelerating solutions have the same Airy‐like tail, and accelerate along parabolic trajectories. Soliton states are formed in the interaction of both in‐phase and out‐of‐phase Airy beams and nonlinear accelerating beams and also present a bending action because of the action of diffusion nonlinearity.     

Calculation of nonlinear optical polarization and phase matching in biaxial crystals

We present a general, analytical formula for the calculation of the unit vectors of the direction of vibration of the electric field strength in biaxial crystals. By means of this formula it is possible to calculate the effective nonlinearity for second-order nonlinear optical frequency conversion processes in biaxial crystals. For two highly efficient nonlinear optical crystals we have calculated the effective nonlinear susceptibility and walk-off angles. The results have been compared with numerical as well as experimental data of previous papers.     

Nonlinear focusing of picosecond baseband pulses in paraelectric crystals

The nonlinear baseband electromagnetic pulses of a wide spectrum that lies in terahertz (THz) range are investigated theoretically in the paraelectric crystals like SrTiO₃ at the temperatures ~ 77 K. The frequency dispersion is important in THz range there. The dominating nonlinearity of the crystal is cubic. The frequency dispersion and nonlinearity correspond to existence of envelope solitons and the modulation instability of long input envelope pulses, whereas in the transverse direction the modulation instability is absent. When the nonlinear wave is uniform in the transverse direction, the existence of soliton-like baseband pulses without a carrier frequency has been demonstrated. There exists a possibility to generate the regular sequences of short baseband pulses due to the nonlinearity in the paraelectric crystals. The nonlinear focusing of input long baseband pulses by the exciting antenna results in the formation of extremely short baseband pulses localized both in the longitudinal and transverse directions.     

Coupled multiwave interactions in aperiodically poled nonlinear optical crystals

A new type of coupled nonlinear optical interactions that can be implemented in crystals with an aperiodic modulation of the nonlinear susceptibility is studied. The quasi-phase matching condition is satisfied simultaneously for several conventional three-frequency processes involved in the interaction due to the aperiodic variation of the nonlinearity in space. A simple method for designing aperiodically poled nonlinear optical crystals is proposed and analyzed. The method is based on the superposition of nonlinearity modulations produced by several periodic functions simultaneously so that each of these functions individually corresponds to its own quasi-phase-matched nonlinear process. The dynamics of energy exchange during interaction of five waves with different frequencies that involves three coupled three-frequency parametric interaction processes is investigated thoroughly. The ratio between the effective nonlinear wave coupling coefficients and the amplitudes of pump waves is determined for the case in which the initial stage of the interaction is characterized by the parametric instability. It is demonstrated that the secondary simplification of the coupled differential equations with spatially modulated nonlinear coefficients, which leads to the system of equations with constant nonlinear coefficients, correctly describes the dynamics of interaction of the waves at distances of the order of 50 characteristic nonlinear lengths.     

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.     

Biphotonic effect of azo-dye-doped liquid crystals using the sequential Z-scan technique

This study investigates the biphotonic effect of azo-dye-doped liquid crystals (ADDLCs) using the sequential Z-scan technique. A spot on the sample is illuminated by a green light for 6 s, and then the same spot is illuminated simultaneously with a red light and a green light for 6 s. Measurements are made by scanning the sample near the beam waist of the green laser. The results show that the biphotonic effect is important to the nonlinear coefficient of the sample. The variations of the optical Kerr constant with intensity of red light are measured. Measurement results demonstrate that the molecular reorientation of liquid crystals induced by the photoisomerization of the azo dyes dominates at low red-light intensity, but the thermal effect compensates for the molecular reorientational nonlinearity of the sample at high red-light intensity.     

Nonlinear refraction of undoped and Fe-doped KTiOAsO4 crystals in the femtosecond regime

The third-order optical nonlinearities in undoped and Fe-doped KTA crystals have been measured using the Z-scan technique with femtosecond pulses at 780-nm wavelength. The nonlinear refractive index is determined to be 1.7×10⁻¹⁵ cm²/W and 0,9×10⁻¹⁵ cm²/W for undoped and Fe-doped KTA, respectively. No two-photon absorption occurs in these crystals. It is shown that doping with Fe₂O₃ could weaken refractive nonlinearity of KTA, suggesting that Fe:KTA will improve the performance of KTA in high-intensity femtosecond laser applications. In addition, the measured nonlinear index of refraction in KTA crystals is about five times lower than that predicted by the two-band theory. One of the reasons for the discrepancy is given as the applicable limit of the simple theory in which a two-parabolic band model has been assumed in the analysis. Received: 3 June 1999 / Published online: 20 October 1999     

Dispersion and frequency dependent nonlinearity parameters in a graphite-epoxy composite

Longitudinal phase velocity and nonlinearity parameter have been measured as a function of frequency in the low megaHertz range in a laminate graphite-fiber-epoxy-resin composite. Amplitudes of both the fundamental and generated second harmonics were measured absolutely with a capacitive receiver. Phase velocity and nonlinearity parameter vary with frequency. The extent of the variance depends on the orientation of the fiber layers. Comparison is made between the nonlinear differential equation appropriate for crystals and a new equation that accounts for frequency dependence of phase velocity and nonlinearity parameter. The newer equation describes the data more accurately than the crystalline model does, but appears to require additional terms.     

Ultrafast optical switching in Kerr nonlinear photonic crystals

Nonlinear photonic crystals made from polystyrene materials that have Kerr nonlinearity can exhibit ultrafast optical switching when the samples are pumped by ultrashort optical pulses with high intensity due to the change of the refractive index of polystyrene and subsequent shift of the band gap edge or defect state resonant frequency. Polystyrene has a large Kerr nonlinear susceptibility and almost instantaneous response to pump light, making it suitable for the realization of ultrafast optical switching with a response time as short as a few femtoseconds. In this paper, we review our experimental progress on the continual improvement of all-optical switching speed in two-dimensional and three-dimensional polystyrene nonlinear photonic crystals in the past years. Several relevant issues are discussed and analyzed, including different mechanisms for all-optical switching, preparation of nonlinear photonic crystal samples by means of microfabrication and self-assembly techniques, characterization of optical switching performance by means of femtosecond pump-probe technique, and different ways to lower the pump power of optical switching to facilitate practical applications in optical information processing. Finally, a brief summary and a perspective of future work are provided.     

Ultrafast optical switching in Kerr nonlinear photonic crystals

Nonlinear photonic crystals made from polystyrene materials that have Kerr nonlinearity can exhibit ultrafast optical switching when the samples are pumped by ultrashort optical pulses with high intensity due to the change of the refractive index of polystyrene and subsequent shift of the band gap edge or defect state resonant frequency. Polystyrene has a large Kerr nonlinear susceptibility and almost instantaneous response to pump light, making it suitable for the realization of ultrafast optical switching with a response time as short as a few femtoseconds. In this paper, we review our experimental progress on the continual improvement of all-optical switching speed in two-dimensional and three-dimensional polystyrene nonlinear photonic crystals in the past years. Several relevant issues are discussed and analyzed, including different mechanisms for all-optical switching, preparation of nonlinear photonic crystal samples by means of microfabrication and self-assembly techniques, characterization of optical switching performance by means of femtosecond pump-probe technique, and different ways to lower the pump power of optical switching to facilitate practical applications in optical information processing. Finally, a brief summary and a perspective of future work are provided.     

KDP晶体三倍频实验和分析

报道了ＫＤＰ晶体中的三倍频产生的实验研究，计算了比较了直接三倍频过程和级联过程对ＫＤＰ晶体三阶有效非线性系数的贡献，并探讨了ＫＤＰ作为非线性晶体材料三阶非线性系数测量基准的可行性。     

Observation of the second harmonic generation pumped by microscopic to extraterrestrial incoherent light sources

I report on the experimental demonstration of the second harmonic generation in bulk nonlinear crystals excited by light emitting diode, halogen lamp and the Sun. Practical application for measurement of autocorrelation functions of incoherent non-laser driven sources via second order nonlinearity is demonstrated for the first time.     

Spatially Periodic Inhomogeneous States in a Nonlinear Crystal with a Nonlinear Defect

Spatially periodic inhomogeneous stationary states are shown to exist near a thin defect layer with nonlinear properties separating nonlinear Kerr-type crystals. The contacts of nonlinear self-focusing and defocusing crystals have been analyzed. The spatial field distribution obeys a time-independent nonlinear Schrödinger equation with a nonlinear (relative to the field) potential modeling the thin defect layer with nonlinear properties. Both symmetric and asymmetric states relative to the defect plane are shown to exist. It has been established that new states emerge in a self-focusing crystal, whose existence is attributable to the defect nonlinearity and which do not emerge in the case of a linear defect. The dispersion relations defining the energy of spatially periodic inhomogeneous stationary states have been derived. The expressions for the energies of such states have been derived in an explicit analytical form in special cases. The conditions for the existence of periodic states and their localization, depending on the defect and medium characteristics, have been determined.     

Peculiarities of Localization of Excitations near the Interlayer between Nonlinear Focusing Media under Conditions of Nonlinear Interactions with Layer Interfaces

Physics of the Solid State - Localized states exist in a three-layer structure comprised of the two nonlinear crystals with p-ositive nonlinearity, between which a linear plate with a finite...     

Simultaneous process of embossing and poling at elevated temperatures: a simple technique for nonlinear grating formation in polymer films

A simple technique for fabrication of nonlinear gratings in polymer films, based on simultaneous embossing and poling, is proposed and demonstrated. A master grating consisting of a metal electrode with a dielectric die was fabricated and used for repeated embossing of the grating structures into nonlinear optical polymers at elevated temperatures. At the same time, we applied high voltage to the polymer films to induce second-order nonlinearity. The grating profile and the nonlinearity were estimated, as well as the mass productivity of nonlinear gratings.     

Optical backpropagation for fiber-optic communications using highly nonlinear fibers

A technique to realize an effective negative Kerr nonlinear coefficient using two highly nonlinear fibers is presented. This technique is used compensate the fiber nonlinearity in optical backpropagation.     

Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity

This research presents a new technique for nonlinear Rayleigh surface wave measurements that uses a non-contact, air-coupled ultrasonic transducer; this receiver is less dependent on surface conditions than laser-based detection, and is much more accurate and efficient than detection with a contact wedge transducer. A viable experimental setup is presented that enables the robust, non-contact measurement of nonlinear Rayleigh surface waves over a range of propagation distances. The relative nonlinearity parameter is obtained as the slope of the normalized second harmonic amplitudes plotted versus propagation distance. This experimental setup is then used to assess the relative nonlinearity parameters of two aluminum alloy specimens (Al 2024-T351 and Al 7075-T651). These results demonstrate the effectiveness of the proposed technique – the average standard deviation of the normalized second harmonic amplitudes, measured at locations along the propagation path, is below 2%. Experimental validation is provided by a comparison of the ratio of the measured nonlinearity parameters of these specimens with ratios from the absolute nonlinearity parameters for the same materials measured by capacitive detection of nonlinear longitudinal waves.     

Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics

A dual frequency mixing technique has been developed for measuring velocity changes caused by material nonlinearity. The technique is based on the parametric interaction between two surface acoustic waves (SAWs): The low frequency pump SAW generated by a transducer and the high frequency probe SAW generated and detected using laser ultrasonics. The pump SAW stresses the material under the probe SAW. The stress (typically <5 MPa) is controlled by varying the timing between the pump and probe waves. The nonlinear interaction is measured as a phase modulation of the probe SAW and equated to a velocity change. The velocity-stress relationship is used as a measure of material nonlinearity. Experiments were conducted to observe the pump-probe interaction by changing the pump frequency and compare the nonlinear response of aluminum and fused silica. Experiments showed these two materials had opposite nonlinear responses, consistent with previously published data. The technique could be applied to life-time predictions of engineered components by measuring changes in nonlinear response caused by fatigue.