Theory of design parameters for quasi-phase-matched waveguides and application to frequency doubling in polymer waveguides

A theory of dispersion in single-mode symmetric waveguides is presented for phase-matching second harmonic generation (SHG) of the fundamental modes, based on the approximate analytical waveguide theory of Botez. The theory is used to derive new equations for the maximum phase-matching distance allowed when there are random fluctuations in waveguide thicknesses, under critical and noncritical phase-matching conditions. The theory is also used to calculate the overlap integral as a function of the waveguide parameters V^ω and V^2ω. A new expression is derived for the efficiency of SHG in waveguides in terms of waveguide parameters that can be used to optimize SHG. Theoretical results are presented for typical LiNbO₃ and polymer waveguides. Quasi-phase-matched (QPM) waveguides are fabricated from nonlinear optical (NLO) polymers using the techniques of periodic poling and bleaching, and channel waveguides are printed by the bleaching of the NLO polymers. The NLO polymers are characterized for their refractive indexes, optical loss, NLO coefficients, and bleaching characteristics. Phase-matched SHG results are presented for the different fabrication methods over a distance of 0.5 cm, and an assessment is given of the relative strengths and weaknesses of the different fabrication approaches