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. >

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

We review progress in quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3. Using the electric-field poling process, we can reliably fabricate 0.5-mm-thick crystals with uniform domain structures over a 15-mm length. Periodically poled material retains the low-loss and bulk power handling properties of single-domain LiNbO3, and quasi phase matching permits noncritical phase matching with d33, the highest-valued nonlinear coefficient. Optical parametric oscillators pumped by 1.064-μm pulsed Nd:YAG lasers have been operated over the wavelength range 1.4–4 μm with tuning by temperature or by quasi-phase-matched period. We have shown an oscillation threshold as low as 0.012 mJ with a Q-switched pump laser and pumping at greater than ten times threshold without damage. We have also demonstrated a cw doubly resonant oscillator near 1.96 μm pumped directly with a commercial cw diode laser at 978 nm.

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Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO 3

Sources and systems for far-infrared or terahertz (1 THz = 10(12) Hz) radiation have received extensive attention in recent years, with applications in sensing, imaging and spectroscopy. Terahertz radiation bridges the gap between the microwave and optical regimes, and offers significant scientific and technological potential in many fields. However, waveguiding in this intermediate spectral region still remains a challenge. Neither conventional metal waveguides for microwave radiation, nor dielectric fibres for visible and near-infrared radiation can be used to guide terahertz waves over a long distance, owing to the high loss from the finite conductivity of metals or the high absorption coefficient of dielectric materials in this spectral range. Furthermore, the extensive use of broadband pulses in the terahertz regime imposes an additional constraint of low dispersion, which is necessary for compatibility with spectroscopic applications. Here we show how a simple waveguide, namely a bare metal wire, can be used to transport terahertz pulses with virtually no dispersion, low attenuation, and with remarkable structural simplicity. As an example of this new waveguiding structure, we demonstrate an endoscope for terahertz pulses.

Metal wires for terahertz wave guiding

Domains in ferroelectrics were considered to be well understood by the middle of the last century: They were generally rectilinear, and their walls were Ising-like. Their simplicity stood in stark contrast to the more complex Bloch walls or N\'eel walls in magnets. Only within the past decade and with the introduction of atomic-resolution studies via transmission electron microscopy, electron holography, and atomic force microscopy with polarization sensitivity has their real complexity been revealed. Additional phenomena appear in recent studies, especially of magnetoelectric materials, where functional properties inside domain walls are being directly measured. In this paper these studies are reviewed, focusing attention on ferroelectrics and multiferroics but making comparisons where possible with magnetic domains and domain walls. An important part of this review will concern device applications, with the spotlight on a new paradigm of ferroic devices where the domain walls, rather than the domains, are the active element. Here magnetic wall microelectronics is already in full swing, owing largely to the work of Cowburn and of Parkin and their colleagues. These devices exploit the high domain wall mobilities in magnets and their resulting high velocities, which can be supersonic, as shown by Kreines' and co-workers 30 years ago. By comparison, nanoelectronic devices employing ferroelectric domain walls often have slower domain wall speeds, but may exploit their smaller size as well as their different functional properties. These include domain wall conductivity (metallic or even superconducting in bulk insulating or semiconducting oxides) and the fact that domain walls can be ferromagnetic while the surrounding domains are not.

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Domain wall nanoelectronics

This article reviews acoustic microfiuidics: the use of acoustic fields, principally ultrasonics, for application in microfiuidics. Although acoustics is a classical field, its promising, and indeed perplexing, capabilities in powerfully manipulating both fluids and particles within those fluids on the microscale to nanoscale has revived interest in it. The bewildering state of the literature and ample jargon from decades of research is reorganized and presented in the context of models derived from first principles. This hopefully will make the area accessible for researchers with experience in materials science, fluid mechanics, or dynamics. The abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques common in microfluidics, along with the many applications in microfluidics and nanofluidics that appear through the literature.

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Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics

A Sellmeier equation for the extraordinary index of congruent lithium niobate is derived. The source data for the fit contain previously published data [Opt. Commun.17, 322 (1996); erratum20, 188 (1997); J. Appl. Phys.45, 3688 (1974)] and new measured tuning data for an optical parametric oscillator using periodically poled lithium niobate. Phase-matching predictions are accurate for temperatures between room temperature and 250 °C and wavelengths ranging from 0.4 to 5  µm.

Temperature-dependent Sellmeier equation for the index of refraction, n e , in congruent lithium niobate

The growth in the uses of lithium niobate for infrared applications has created a need for knowledge of its optical characteristics in the infrared spectral region for the purpose of designing phase-matched or quasi-phase-matched devices. We report measurements of the refractive indices of congruently grown lithium niobate and lithium niobate doped with 5 mol. % magnesium oxide. We use these results to predict the tuning curve of a room-temperature multigrating optical parametric oscillator in each material.

Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol. % magnesium oxide–doped lithium niobate

Vapor transport equilibration was used to prepare lithium niobate crystals of a variety of controlled off‐congruent compositions. Crystals were characterized through measurement of the ferroelectric Curie temperature Tc and measurement of the temperature for noncritical phase matching TPM of second‐harmonic generation from both 1.064‐ and 1.32‐μm laser sources. Across the majority of the single‐phase region, both Tc and TPM were observed to vary nearly linearly with Li/Nb ratio. The variation in TPM with Li/Nb ratio was observed to change direction within the single‐phase region at some small but finite compositional interval away from the Li‐rich phase boundary. Crystals equilibrated to the Li‐rich phase boundary had excellent optical homogeneity. Preparation of Li‐poor crystals was hampered by extremely slow lithium diffusivity and problems with second‐phase precipitation.

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Preparation and characterization of off-congruent lithium niobate crystals

A simple experimental method for determining optical second-order polarizabilities of organic molecules for second harmonic generation (SHG) is developed by using a two-level quantum mechanical model. Required values of excited-state dipole moments are obtained from a solvatochromic method based on the theoretical treatment of McRae. Second-order polarizabilities obtained by this method for a series of compounds compare well with those obtained by the conventional EFISH technique. The solvatochromic method has the important advantage that measurements can be made rapidly with simple equipment available in most chemistry laboratories.

Dieter H. Jundt

Papers

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

Temperature-dependent Sellmeier equation for the index of refraction, n e , in congruent lithium niobate

Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol. % magnesium oxide–doped lithium niobate

Preparation and characterization of off-congruent lithium niobate crystals

A solvatochromic method for determining second-order polarizabilities of organic molecules