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Summary: VOLUME 88, NUMBER 2 P H Y S I C A L R E V I E W L E T T E R S 14 JANUARY 2002
Multiple Nonlinear Optical Interactions with Arbitrary Wave Vector Differences
Keren Fradkin-Kashi,* Ady Arie, Pavel Urenski, and Gil Rosenman
Department of Electrical EngineeringPhysical Electronics, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel
(Received 12 June 2001; published 26 December 2001)
We present a novel method for simultaneously phase matching several nonlinear optical interactions
within a single crystal. Quasiperiodic modulation of the nonlinear coefficient enables one to achieve
high frequency mixing efficiencies for interactions with arbitrary wave vector differences. Doubling
of two different frequencies as well as direct frequency tripling is experimentally demonstrated. The
temperature- and wavelength-dependent properties of these interactions are explored. We discover that
periodic approximation to the quasiperiodic structure shifts the phase-matched wavelengths.
DOI: 10.1103/PhysRevLett.88.023903 PACS numbers: 42.70.Mp, 42.79.Nv
Phase matching between interacting waves in a non-
linear optical interaction is an essential condition for
achieving high frequency conversion efficiency. Although
naturally a wave vector difference, Dk, is caused by the
dispersion of the nonlinear material, it can be compensated
by several methods (see Table I). Traditionally, this was
achieved using the birefringence properties of the nonlin-
ear material [1,2]. In 1962, Armstrong et al. [3] proposed
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