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

Handbook of optics

CRYSTALLINE MATERIALS Introduction Physical Properties Optical Properties Mechanical Properties Thermal Properties Magnetooptic Properties Electrooptic Properties Elastooptic Properties Nonlinear Optical Properties GLASSES Introduction Commercial Optical Glasses Specialty Optical Glasses Fused Silica Fluoride Glasses Chalcogenide Glasses Magnetooptic Properties Electrooptic Properties Elastooptic Properties Nonlinear Optical Properties Special Glasses POLYMERIC MATERIALS Optical Plastics Index of Refraction Nonlinear Optical Properties Thermal Properties Engineering Data METALS Physical Properties of Selected Metals Optical Properties Mechanical Properties Thermal Properties Mirror Substrate Materials LIQUIDS Introduction Water Physical Properties of Selected Liquids Index of Refraction Nonlinear Optical Properties Magnetooptic Properties Commercial Optical Liquids GASES Introduction Physical Properties of Selected Gases Index of Refraction Nonlinear Optical Properties Magnetooptic Properties Atomic Resonance Filters APPENDICES Safe Handling of Optical Materials Abbreviations, Acronyms, and Mineralogical or Common Names for Optical Materials Abbreviations for Methods of Preparing Optical Materials and Thin Films Fundamental Physical Constants Units and Conversion Factors

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Handbook of Optical Materials

Nonlinear Optical Crystals: A Complete Survey

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. >

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

Measurements of the absorption coefficient for KTP, LiIO/sub 3/, and LiNbO/sub 3/ are discussed. The variation of the refractive index with temperature has been measured for KTP and LiIO/sub 3/. It is necessary to know both the absorption coefficient beta and the variation in the indexes of refraction with temperature change dn/dT to determine the average power limit of a nonlinear interaction. With the dn/dT information, it is also possible to estimate the temperature half width of any nonlinear interaction by calculating the variation of the phase-matching condition with temperature. >

Some optical properties of KTP, LiIO/sub 3/, and LiNbO/sub 3/

A systematic evaluation of the spectral bandwidth and two acceptance angles of parametric generation processes is presented. The spectral bandwidth and acceptance angles are determined by expanding the wave vector mismatch in a Taylor series and retaining terms through second order. This allows a determination of these parameters even when the first order term vanishes. Conditions where the first order term vanishes are presented and compared with similar cases where the first order term does not vanish.

Parametric generation processes: spectral bandwidth and acceptance angles

A temperature-dependent Sellmeier equation is calculated for Ge. The accuracy of this temperature-dependent Sellmeier equation is compared with the internal consistency of the data. The phase-matching condition is discussed for four-wave mixing when two of the wave vectors are equal. The average power limit for four-wave mixing in a material like Ge is derived both for the case where one wave vector is fixed and for the case where two wave vectors are fixed. Using the derived Sellmeier equation, the average power limit for the four-wave mixing is calulated.

Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium

The temperature variations of the refractive indices of LiYF4, YLF, have been measured in the visible region of the spectrum. The temperature variation at 0.546 μm are −0.67×10−6/°C and −2.30×10−6/°C for the ordinary and extraordinary refractive indices, respectively. A Sellmeier equation was fit to more extensive room-temperature refractive-index data measured elsewhere.

Temperature variation of the refractive indices of yttrium lithium fluoride

The variation of refractive index with temperature is measured as a function of wavelength, temperature, and polarization for KDP and eight of its isomorphs. These data are used to predict the tuning rate for second-harmonic generation as a function of temperature. The predicted tuning rate compares well with the measured tuning rate. Reasonable agreement is found in most cases, the principal exceptions being those cases in which the data must be extrapolated significantly beyond the range of the measured values.

Norman P. Barnes

Papers

Some optical properties of KTP, LiIO/sub 3/, and LiNbO/sub 3/

Parametric generation processes: spectral bandwidth and acceptance angles

Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium

Temperature variation of the refractive indices of yttrium lithium fluoride

Variation of the refractive index with temperature and the tuning rate for KDP isomorphs