Fresnel diffraction and fractal patterns from polygonal apertures

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 (>104 cm-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 2nd-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.

Computational Imaging Prediction of Starburst-Effect Diffraction Spikes

When imaging bright light sources, rays of light emanating from their centres are commonly observed; this ubiquitous phenomenon is known as the starburst effect. The prediction and characterization of starburst patterns formed by extended sources have been neglected to date. In the present study, we propose a novel trichromatic computational framework to calculate the image of a scene viewed through an imaging system with arbitrary focus and aperture geometry. Diffractive light transport, imaging sensor behaviour, and implicit image adjustments typical in modern imaging equipment are modelled. Characterization methods for key optical parameters of imaging systems are also examined. Extensive comparisons between theoretical and experimental results reveal excellent prediction quality for both focused and defocused systems.

Fractal modes and multi-beam generation from hybrid microlaser resonators

Fractals are ubiquitous in nature, and prominent examples include snowflakes and neurons. Although it has long been known that intricate optical fractal patterns can be realized with components such as gratings and reflecting spheres, generating fractal transverse modes from a laser has proven to be elusive. By introducing a 2D network of microspheres into a Fabry-Pérot cavity bounding a gain medium, we demonstrate a hybrid optical resonator in which the spheres enable the simultaneous generation of arrays of conventional (Gaussian) and fractal laser modes. Within the interstices of the microsphere crystal, several distinct fractal modes are observed, two of which resemble the Sierpinski Triangle. Coupling between adjacent fractal modes is evident, and fractal modes may be synthesized through design of the microsphere network. Owing to a unique synergy between the gain medium and the resonator, this optical platform is able to emit hundreds of microlaser beams and probe live motile cells.

Although fractal optical patterns have been realized previously, the direct generation of fractal modes from a laser has proven challenging. Here, Rivera et al. modify an optical cavity with a microsphere array to produce fractal laser modes and probe live cells, which serve as a component of the resonator.

Devil's lenses

In this paper we present a new kind of kinoform lenses in which the phase distribution is characterized by the "devil's staircase" function. The focusing properties of these fractal DOEs coined devil's lenses (DLs) are analytically studied and compared with conventional Fresnel kinoform lenses. It is shown that under monochromatic illumination a DL give rise a single fractal focus that axially replicates the self-similarity of the lens. Under broadband illumination the superposition of the different monochromatic foci produces an increase in the depth of focus and also a strong reduction in the chromaticity variation along the optical axis.