Recent advances in the field of nonlinear optical phenomena are reviewed with particular empphasis placed on such topics as parametric oscillation self-focusing and trapping of laser beams, and stimulated Raman, Rayleigh, and Brillouin scattering. The optical frequency radiation is treated classically in terms of the amplitudes and phases of the electromagnetic fields. The interactions of light waves in a mterial are then formulated in terms of Maxwell's equations and the electric dipole approximation. In this method, non-linear susceptibility tensors are introdueed which relate the induced dipole moment to a power series expansion in field strengths. The tensor nature and the frequency dependence of the nonlinearity coefficients are considered. The various experimental, observations are described and interpreted in terms of this formalism.

https://ieeexplore.ieee.org/iel5/5/31089/01447053.pdf

Nonlinear optics

The theory of quasi-phase-matched second-harmonic generation is presented in both the space domain and the wave vector mismatch domain. Departures from ideal quasi-phase matching in periodicity, wavelength, angle of propagation, and temperature are examined to determine the tuning properties and acceptance bandwidths for second-harmonic generation in periodic structures. Numerical examples are tabulated for periodically poled lithium niobate. Various types of errors in the periodicity of these structures are then analyzed to find their effects on the conversion efficiency and on the shape of the tuning curve. This analysis is useful for establishing fabrication tolerances for practical quasi-phase-matched devices. A method of designing structures having desired phase-matching tuning curve shapes is also described. The method makes use of varying domain lengths to establish a varying effective nonlinear coefficient along the interaction length. >

/pdf/quasi-phase-matched-second-harmonic-generation-tuning-and-20kentxvs1.pdf

Quasi-phase-matched second harmonic generation: tuning and tolerances

A theoretical study is presented on the optimization of second harmonic generation (SHG) and parametric generation (PG) by a laser beam in a uniaxial nonlinear crystal. Numerically computed curves show the dependence of the SHG power, and the reciprocal of the PG threshold power, on the parameter l/b, where l is the optical path length in the crystal and b is the confocal parameter (determined by the focal length of the focusing lens and the minimum radius of the laser beam, assumed to be in the TEM00 mode of an optical resonator). The calculations take full account of diffraction and double refraction. In the absence of double refraction, the optimum focusing condition is found to be l/b=2.84. For PG the optimization of the crystal length l is also discussed, and curves are given showing the dependence of the threshold on l for the case in which signal and idler have the same losses. It is shown that the computed functions are also relevant to the mixing of two Gaussian beams and to parametric amplificat...

Parametric Interaction of Focused Gaussian Light Beams

The boron–oxygen compound LiB3O5 is recognized as a new nonlinear-optical crystal. This follows theoretical calculations of the second-harmonic generation (SHG) coefficients using the anionic group theory and the complete neglect of differential overlap approximation to obtain the localized wave functions of component groups. An optically perfect single crystal with space group Pna21, grown at the Fujian Institute of Research on the Structure of Matter by the high-temperature flux method, is found to be transparent from 160 nm to 2.6 μm. It has a SHG coefficient comparable with that of β-BaB2O4 as well as two other outstanding advantages: a high damage threshold of 25 GW/cm2 (at 1.064 μm, 0.1 nsec) and a wide acceptance angle of 25 mrad for θ ≠ 90° and 95 mrad for θ = 90° with a 6-mm-long crystal.

New nonlinear-optical crystal: LiB 3 O 5

High-harmonic generation (HHG) traditionally combines ~100 near-infrared laser photons to generate bright, phase-matched, extreme ultraviolet beams when the emission from many atoms adds constructively. Here, we show that by guiding a mid-infrared femtosecond laser in a high-pressure gas, ultrahigh harmonics can be generated, up to orders greater than 5000, that emerge as a bright supercontinuum that spans the entire electromagnetic spectrum from the ultraviolet to more than 1.6 kilo-electron volts, allowing, in principle, the generation of pulses as short as 2.5 attoseconds. The multiatmosphere gas pressures required for bright, phase-matched emission also support laser beam self-confinement, further enhancing the x-ray yield. Finally, the x-ray beam exhibits high spatial coherence, even though at high gas density the recolliding electrons responsible for HHG encounter other atoms during the emission process.

/pdf/bright-coherent-ultrahigh-harmonics-in-the-kev-x-ray-regime-1zfs4wmtus.pdf

Bright Coherent Ultrahigh Harmonics in the keV X-ray Regime from Mid-Infrared Femtosecond Lasers

The induced nonlinear electric dipole and higher moments in an atomic system, irradiated simultaneously by two or three light waves, are calculated by quantum-mechanical perturbation theory. Terms quadratic and cubic in the field amplitudes are included. An important permutation symmetry relation for the nonlinear polarizability is derived and its frequency dependence is discussed. The nonlinear microscopic properties are related to an effective macroscopic nonlinear polarization, which may be incorporated into Maxwell's equations for an infinite, homogeneous, anisotropic, nonlinear, dielectric medium. Energy and power relationships are derived for the nonlinear dielectric which correspond to the Manley-Rowe relations in the theory of parametric amplifiers. Explicit solutions are obtained for the coupled amplitude equations, which describe the interaction between a plane light wave and its second harmonic or the interaction between three plane electromagnetic waves, which satisfy the energy relationship ${\ensuremath{\omega}}_{3}={\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$, and the approximate momentum relationship ${\mathrm{k}}_{3}={\mathrm{k}}_{1}+{\mathrm{k}}_{2}+\ensuremath{\Delta}\mathrm{k}$. Third-harmonic generation and interaction between more waves is mentioned. Applications of the theory to the dc and microwave Kerr effect, light modulation, harmonic generation, and parametric conversion are discussed.

Interactions between light waves in a nonlinear dielectric

/pdf/interactions-between-light-waves-in-a-nonlinear-dielectric-2m21ug6r84.pdf

Interactions between Light Waves in a Nonlinear Dielectric

Ibispaperexaminesindetniltheeffectsofhighandlowewrgy electron, X-ray, and ultraviolet radiation 00 oxidized silicon surfaces and planar devices. Two permanent effects of Mnizimg radiation on oxidized silicon surfaces are d' I* ~ 'dmi: 1) Tbe buildup of a positive space charge within the oxide, and 2) 'Ihe creation of fast dace states at the oxide- silicon interface respltiug in increased surface recombtion velocity. llre dependence of these effects on dose and dose rate, on bias amed daring irradiation, and 011 strpetarnl parameters is disarpsed and a theory is pre- sented which arromts for the observed feature of the spaaxbarge buildup. This theory involves trppping of holes which are generated within tbe oxide by tbe radiation. It is sbown that all dew of tbe experimental observations can be accounted for by asnming a high ddty of hole trap near the oxide- silia~~ interface whicb desays rapidly with distnnce into the oxide. Radiation-induced cbanges in the characteristics of MOS and junction field-effect tramistors, pn juodm diodes, and pn-p and n-pn trnnsistors

J. A. Armstrong

Papers

Interactions between light waves in a nonlinear dielectric

Interactions between Light Waves in a Nonlinear Dielectric

Effects of Ionizing Radiation on Oxidized Silicon Surfaces and Planar Devices