Conical Harmonic Generation in Isotropic Materials

A novel class of nonlinear optical processes is described in which radiation at the nth harmonic is generated through the use of a $(2n+1)$-order nonlinearity. Utilizing an odd-order nonlinearity, this process allows for the generation and amplification of both odd- and even-order harmonics in isotropic materials. Additionally, this process can always be phase matched in normal-dispersion materials without the use of birefringence. Experimental results are presented in which conical third-harmonic emission is generated from a sapphire sample.