Methods and apparatus are disclosed for the nonlinear generation of sum and difference frequencies of electromagnetic radiation propagating in a nonlinear material. A waveguide having a waveguide cavity contains the nonlinear material. Phase matching of the nonlinear generation is obtained by adjusting a waveguide propagation constant, the refractive index of the nonlinear material, or the waveguide mode in which the radiation propagates. Phase matching can be achieved even in isotropic nonlinear materials. A short-wavelength radiation source uses phase-matched nonlinear generation in a waveguide to produce high harmonics of a pulsed laser.
This invention was made with U.S. government support under contracts PHY8920108 and ECS9616079, awarded by the National Science Foundation, and contract DEFG0296ER12196, awarded by the Department of Energy. The government has certain rights in the invention.