Res. Chem. Intermed.
, Vol. 34, No. 2–3, pp. 217–228 (2008)
Koninklijke Brill NV, Leiden, 2008.
Also available online - www.brill.nl/rci
State of the art of the sphere method, a unique
characterization technique for non-linear crystals
, BENOIT BOULANGER
and JULIEN ZACCARO
Institut Néel, Centre National de la Recherche Scientiﬁque & Université Joseph Fonrier, BP 166,
38402 Grenoble Cedex 9, France
Laboratoire de Cristallographie, Centre National de la Recherche Scientiﬁque,
25 Avenue des Martyrs, BP 166, 38042 Grenoble Cedex 09, France
Received 12 November 2006; accepted 20 January 2007
Abstract—We report the sphere method as a unique characterization technique for the complete study
of non-linear optical properties for frequency conversion in new materials belonging to the uniaxial or
biaxial optical class. It relies on the use of a single crystal with millimetre dimensions cut as a sphere,
combined with a tuneable laser source. With the sphere method we perform direct measurements
of phase-matching angles and associated conversion efﬁciencies for second harmonic, sum- and
difference-frequency generation. Furthermore, we follow the orientation of the dielectric frame as
a function of the wavelength for monoclinic and triclinic crystals. It also allows the determination of
the magnitude of the principal refractive indices in biaxial crystals based on the study of the double
refraction affect at the exit of a sphere. By combining the analysis of all these data simultaneously,
we determine Sellmeier equations reliable over the whole transparency domain and we are able to get
the non-zero elements of the second-order susceptibility tensor of uniaxial or biaxial crystals. Finally,
the sphere method is completely self-sufﬁcient for the study of biaxial crystals.
Keywords: Metrology; non-linear optical properties; frequency conversion; birefringent crystals.
When dealing with non-linear crystals, the knowledge of the dispersion equations
of the magnitudes of the principal indices, in the whole transparency range of the
studied material, is of prime importance. Indeed, the phase-matching directions
for sum- or difference-frequency conversion depend on the ratios between the
principal refractive indices . Crystals belonging to the uniaxial and biaxial
optical classes are concerned. For example, biaxial crystals have three principal
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