Higher-order fractal transverse modes observed in microlasers

Two classes of higher-order, fractal spatial eigenmodes have been predicted computationally and observed experimentally in microlasers. The equatorial plane of a close-packed array of microspheres, lying on one mirror within a Fabry-Pérot resonator and immersed in the laser gain medium, acts as a refractive slit array in a plane transverse to the optical axis. Edge diffraction from the slit array generates the high spatial frequencies (>10⁴cm^-1) required for the formation of high-order laser fractal modes, and fractal transverse modes are generated, amplified, and evolve within the active medium. With a quasi-rectangular (4-microsphere) aperture, the fundamental mode and several higher-order eigenmodes (m = 2,4,5) are observed in experiments, whereas only the m = 1,2 modes are observed experimentally for the higher-loss resonators defined by triangular (3-microsphere) apertures. The fundamental and 2^nd-order modes (m = 1,2) for the 4-sphere aperture are calculated to have qualitatively similar intensity profiles and nearly degenerate resonant frequencies that differ by less than <0.1% of the free-spectral range (375 GHz) but exhibit even and odd parity, respectively. For all of the observed fractal modes, the fractal dimension (D) rises rapidly beyond the intracavity aperture array as a result of the high spatial frequencies introduced into the mode profile. Elsewhere, D varies gradually along the resonator axis and 2.2 < D < 2.5. Generating fractal laser modes in an equivalent optical waveguide is expected to allow the realization of new optical devices and imaging protocols based on the spatial frequencies and variable D values available.