Abstract

When beams at frequencies ω₀ and 2ω₀ are mixed in a medium with third-order nonlinearity χ⁽³⁾ a pattern of dc polarization fringes P_dc⁽³⁾ results whose grating vector is K = k_so − 2k_po, where k_po(r) and k_so(r) are the wave vectors at ω₀ and ω₀. In germanosilicate optical fibers, P_dc⁽³⁾ breaks the centrosymmetry of the amorphous core material (possibly by color-center alignment), creating a periodically modulated χ⁽²⁾ = χ_m⁽²⁾cos(K · r). This χ⁽²⁾ structure automatically phase matches the fundamental light to its second harmonic (SH).^1,2 Because the wave fronts of the participating beams do not have to be planar, the phenomenon may be labeled nonlinear holography.³ In a germanosilicate film waveguide, for example, a SH image beam at 2ω can be reconstructed, potentially with high efficiency, from a reference pump beam at ω ≈ ω₀. Phase-matched degenerate parametric amplification of a complex signal wave front at ω is also possible, and in a ring cavity parametric oscillation would permit high-efficiency re-creation of a complex beam at ω.

© 1990 Optical Society of America