Transition from Ince-Gaussian beams to nondiffractive Mathieu beams

We show that under the appropriate conditions, the Ince-Gaussian modes (IGBs) of stable resonators display a behavior very similar to that of the Mathieu beams (MBs), exhibiting nondiffracting propagation and self-healing properties. We show that the high-order IGB propagates in a quasi-nondiffractive manner within the same conical region as any nondiffractive beam, even when their profiles do not match exactly. Our results indicate new, to our knowledge, methods to generate a quasi-nondiffractive MB from spherical resonators and provide more efficient ways to generate them in the Fourier space. These high-order IGBs are an excellent option for applications where a quasi-nondiffractive, but not exact, behavior is required.