Phase-matching Loci Research Articles

Spatiospectral transformation of noncollimated light beams diffracted by ultrasound in birefringent crystals

Spatiospectral structure of wave phase matching in birefringent crystals has a strong dependence on the geometry of the acousto-optic interaction and incident light spectrum. This dependence defines details of light beam profile transformation. It is especially important for imaging applications related to a large angular aperture and a wide spectral bandwidth of the incident light. In this paper, we demonstrate accurate three-dimensional plotting of a light transmission pattern without small birefringence approximation. The rather complicated shape of the phase-matching locus in the spatiospectral domain inevitably leads to residual spatially nonuniform chromatic aberrations in the spectral image. Theoretical consideration and computational modeling are confirmed by the experiments on Bragg diffraction in paratellurite crystal. The results are especially important for the development of acousto-optical imaging devices and laser beam shaping technologies.

Phase-matching loci and angular acceptance of non-collinear optical parametric amplification

A general study of phase-matching loci and associated angular acceptances is performed in the case of non-collinear parametric amplification. Numerical and analytical calculations, as well as measurements, are described for the uniaxial BBO crystal and the biaxial LBO crystal.

Collinear phase-matching loci of LBO crystal in three-wave interactions

By choice of a reliable dispersion relation of LBO crystal, the loci of LBO crystal in second harmonic generation and sum-, difference-frequency generation (three wave interactions) are presented over its entire transparency region for the first time, on the basis of a new topological classification of phase-matching direction loci in biaxial acentric crystals. The result shows that there are totally 7 loci and 9 transitions for second harmonic generation, 12 loci and 15 transitions for three wave interactions at the room temperature 20 °C. The temperature dependence of LBO yields that the noncritical phase-matching loci of second harmonic generation varies slowly in the range of 20–300 °C, while the phase-matching loci in three wave interactions demonstrate varying locus distribution in the spectral region with temperature.

Effective second-order nonlinearity in acentric optical crystals with low symmetry

We derive explicit expressions in the frame of the optical indicatrix for the second-order effective nonlinearity in biaxial crystals with point groups 2, m, and 1, governing the conversion efficiency in three-wave nonlinear optical interactions. The tabulated expressions for the monoclinic symmetry classes 2 and m are valid for all possible orientations of the optical indicatrix relative to the crystallographic frame and for propagation along an arbitrary direction outside the principal planes. They can be used for direct estimation of the effective nonlinearity in the same frame where the phase-matching loci are calculated. The relevant properties and conventions used for the newly emerging acentric monoclinic crystals belonging to the borate family are summarized and tabulated. The derivations are expected to help establish adherence to uniform nomenclature and conventions for these novel inorganic nonlinear crystals, and to eliminate ambiguity and increasing confusion in the literature and in the industrial specifications. The general expressions for the effective nonlinearity are reduced for triclinic crystals of point group 1 to simplified forms in the principal planes.

Optical properties of L-threonine crystals

Abstract Second- and third-order optical nonlinearities of L-threonine amino acid crystals grown from aqueous solution are investigated in this work. The absorption spectra indicate a good transparency between 250 and 1500 nm. Refractive indices were measured as a function of temperature and wavelength, allowing the determination of the thermo-optic and Sellmeier equation coefficients. Phase-matching curves for second harmonic generation from radiation at 1.064 μm were obtained. The conversion efficiency was measured along the entire phase-matching loci and its maximum value was found to be comparable to that of KDP. The nonlinear refractive index n 2 , measured through the Z-scan technique with femtosecond pulses, is of the order of 10 −20 m 2 /W.

Solution Growth and Characterisation of L-alanine Single Crystals

Single crystals of L-alanine have been grown from buffered aqueous solutions and characterised as to their optical quality via wavefront distortion analysis, electrooptical response and harmonic generation efficiency. Refraction indices as well as phase matching loci were found in satisfactory agreement with previously published data for crystals grown in non buffered solution. Estimates for the electro-optical response are reported for the first time. The experimentally observed crystal habit is discussed in terms of morphological importance (M.I.), which was found to be in disagreement with the predictions of crystallographic criteria based on the interplanar distance d hkl , on the periodic bond chains (PBC) and the attachment energy E att . This disagreement is tentatively attributed to the presence of impurities and non-appropriate supersaturation conditions.

Refractive-index measurements and Sellmeier coefficients for zinc germanium phosphide from 2 to 9 µm with implications for phase matching in optical frequency-conversion devices

Recent experiments in mid-IR frequency conversion reveal that older Sellmeier models for zinc germanium phosphide are inadequate for predicting phase-matching loci in zinc germanium phosphide optical frequency-conversion devices. This results in compromised device performance. We conduct a complete study of the refractive indices of zinc germanium phosphide from 2 to 9 µm and calculate new Sellmeier coefficients. The phase-matching calculations based on our new refractive-index data predict much more closely the results of several different mid-IR frequency-conversion experiments.

Second harmonic generation phase-matching locus for 7.5 mol% Nb:KTP crystals at near-infrared wavelengths

Both the type-II second harmonic generation (SHG) phase-matching locus in the three principal planes of 7.5 mol% Nb:KTiOPO/sub 4/ (KTP) crystals for wavelengths less than 1.8 /spl mu/m and the type-II SHG phase-matching locus for 7.5 mol% Nb:KTP crystals for wavelengths of 970, 980, 1064.2, and 1311.4 nm are calculated on the basis of the Sellmeier equations. When compared with those in KTP crystals, the shapes of these curves are almost the same in the two crystals. These imply that Nb doping does not significantly change the phase-matching properties of KTP crystals, even though it does largely change the phase-matching parameter of KTP crystals. These make Nb:KTP crystals more attractive in direct SHG of semiconductor laser radiation to produce blue coherent light.

Determination of the refractive indices by variable azimuth reflectometry from a single sample face

We have investigated a method for the evaluation of the indices of refraction of crystalline materials of any symmetry based on the measurement of the reflectance from one single face of the sample for several azimuthal orientations. After a consistency test performed on fused silica and crystalline quartz we have applied the method to as-grown crystals of monomethylurea, a biaxial nonlinear optical material recently synthesized. The phase matching loci calculated from the refractive indices determined in this way are in good agreement with the experimental ones, thus demonstrating the viability of the procedure also for biaxial systems. The limits and the advantages of the method are briefly discussed.

Linear and nonlinear optical properties of organic crystals: MBANP and its derivatives

In addition to possessing strong optical nonlinearity, the (−)-2-(α-methylbenzylamino)-5-nitropyridine (MBANP) crystal has been shown to have unusual linear optical properties. Two methyl derivatives of MBANP have now been synthesized and grown as large single crystals; their refractive indices have been measured as a function of frequency and second-harmonic generation, including the determination of the phase matching loci has been investigated. Data is also available on the racemic form of crystalline MBANP. The properties of this family of crystals have been reviewed and an attempt is made to relate the experimental responses of the crystals to their molecular structure and the calculated properties of the molecules.

Refractive Indices of the Optically Nonlinear Organic Crystal (S)-3-Methyl-5-nitro-N-(1-phenylethyl)-2-pyridinamine

The refractive indices of structurally well-characterized crystals of the new optically nonlinear organic crystal (S)-3-methyl-5-nitro-N-(1-phenylethyl)-2-pyridinamine have been measured from 480 to 660 nm and fitted to four-parameter Sellmeier equations with an accuracy of ±3 × 10-3 to ±5 × 10-3. The value of ny was accurately verified by the measurement of the external angle of incidence required, at the (101) plane, to observe type I phase matching with a fundamental wavelength of 1064 nm. The phase matching locus has been established and is of Hobden class eight. The values of the nx, ny, and nz refractive indices at 532 nm were found from the Sellmeier equations to be 1.690, 1.901, and 1.725, respectively, and their relative magnitudes are correlated with the molecular arrangement in the crystal lattice. This material is a member of a series of pyridinamines that can exhibit the phenomenon of frequency-dependent orientation of their dielectric axes. Since this compound crystallizes in an orthorhombic structure, rotation of the dielectric axes is precluded for symmetry reasons.

Second-harmonic generation in biaxial crystals for a focused fundamental Gaussian laser beam: application to ()2-α-(methylbenzylamino)- 5-nitropyridine single crystals

The second-harmonic nonlinear optical susceptibility tensor of (-)2-α-(methylbenzylamino)-5-nitropyridine single crystals has been calculated from electric-field-induced second-harmonic generation (SHG) data and the oriented-gas model. From this tensor the calculated value of the maximum effective nonlinear optical susceptibility deff for phase-matched SHG was found to be 6.5 pm V-1. Calculations along the whole of the phase-matching locus show that the highest value of deff is in the region of the lowest values of the second-harmonic wave beam walk-off angle. The walk-off angle of the fundamental is approximately five times smaller. A theory necessary for the optimization of SHG efficiency in biaxial crystals is developed and it is shown that, for the range of crystal lengths and beam walk-off angles available, the criteria for the selection of the parameters w0,z0, and Δk for optimization of the second-harmonic signal are the same in biaxial and uniaxial crystals. The optimal configuration for the highest second-harmonic efficiency on the phase-matching locus has been determined. The maximum SHG figure of merit, P2ω(l)/Pω2(0), is found to be 3.7×10-3 W-1 for a 50-mm-long crystal.

Refractive Index Measurements of Barium Titanate From .4 to 5.0 Microns and Implications for Periodically Poled Frequency Conversion Devices

AbstractBarium titanate has recently been suggested as a possible candidate for use in periodically poled optical frequency conversion devices. We report refractive index measurements which are critical to periodically poled device designers and present quasi phase matching loci which can be used to design an optical parametric oscillator in periodically poled barium titanate

Optical properties of L-alanine Organic Crystals

This work reports on the optical properties of L-alanine crystals grown from aqueous solution using the well-known slow evaporation method. Linear properties including absorption spectra and refractive indices are determined, as well as nonlinear properties of second harmonic generation (SHG), such as the phase-matching loci and efficiency. Although the SHG efficiency is smaller than those of other known materials, the study of L-alanine crystals is very important since it is part of more complex aminoacids including L-arginine and asparagine, with much higher SHG efficiency. Some mechanical properties are also presented, namely hardness and thermal expansion coefficients.

Theoretical analysis of the spatial phase-matching loci for second-harmonic generation and multiwave-mixing interactions

We report a theoretical analysis on spatial noncolinear phase matching of multiwave mixing and its application to a second-harmonic-generation (SHG) experiment. From the numeric calculations, the noncolinear phase-matching properties in general situations were determined. The theory gives the applicability for all noncolinear phase matching. Fine coincidences between theoretical calculations and observed spatial loci on noncollinear phase-matching SHG were confirmed. Relations that allow the calculation of the noncollinear phase-matching angle for any case of SHG are established. As an example, the noncolinear phase-matched SHG pattern on a screen is calculated numerically in the case of SHG of 1064 nm from a Nd:YAG laser under the phase-matched condition for two organic nonlinear crystals: 1-(2-thienyl)-3-(4-methyphenyl) propene-1 (TC-28), which is biaxial, and (2-furyl) methacrylic anhydride (FMA), which is uniaxial. Experimental results compared quite favorably with the theoretical analysis. Noncolinear phase matching may be of great practical interest in optical multiwave-mixing processes, such as optical parametric oscillation and optical parametric amplification. This technique also can be used for the measurement of crystal optical constants.

Phase-matching considerations of four-wave interaction processes in biaxial crystals

In light of the principle of phase matching (PM) in biaxial crystals, PM types for four-wave interaction processes are discussed. The relationships among the refractive indices of the four interacting waves are analyzed to classify PM topologies. A computer program is developed to characterize and obtain PM directions and their loci. As examples, PM loci for direct third-harmonic generation in four biaxial crystals are presented.

L-Histidine tetrafluoroborate: a solution-grown semiorganic crystal for nonlinear frequency conversion

The crystal structure, refractive indices, and phase-matching conditions for a new nonlinear optical material, L-histidine tetrafluoroborate (HFB), are reported. HFB grows readily, displays favorable mechanical characteristics, and has adequate birefringence to permit phase-matched parametric processes over much of its transparency range (250 nm to 1300 nm). The phase-matching loci and angular sensitivity for second-harmonic generation of 1064-nm light in single crystals of HFB were measured. The effective nonlinearity for HFB is comparable with that of beta-barium borate (~2 pm/V), and its angular sensitivity [delta(Deltak)/deltatheta] is somewhat smaller.

Harmonic generation in ferroelectric liquid crystals: Phase matching loci

Ferroelectric liquid crystals (FLCs), a new class of organic nonlinear materials have a variety of interesting properties and potential applications. Using commercial FLCs and an FLC mixture specifically formulated for enhanced nonlinear optical properties, we studied the room-temperature global phase-matching properties for type I and type II frequency doubling of 1.06-μm radiation. Although the second-harmonic coefficients of the different FLC mixtures differ by as much as two orders of magnitude, the phase-matching loci are remarkably similar.

Temperature insensitive SHG at 0.5321 mu m in KTP

KTP has been found to have the special phase-matching loci where the temperature-induced phase mismatch becomes zero for type-1 and type-2 SHG of the Nd:YAG laser frequency at 1.0642 mu m. This was demonstrated for type-1 phase matching. In addition, the temperature derivatives of the refractive indexes and the absolute value of d/sub 33/ are reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions

Standards which eliminate ambiguity in reporting nonlinear phenomena, especially in the increasingly complex realm of biaxial crystals, are proposed. In order to restore uniformity to the designation of crystallographic axes and crystal tensor properties, adoption of IEEE/ANSI Std. 176, with a small but much needed modification for crystal class mm2, is recommended. For the reporting of nonlinear interaction characteristics, other frames are proposed which result in simpler rules than heretofore given for categorizing phase-matching loci, and for characterizing eigenmode polarizations, double refraction, effective nonlinear coupling, and first- and second-order acceptance bandwidths (angular, spectral, thermal) along these loci. Similarities as well as differences between biaxial and uniaxial crystals are emphasized. >