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.

Photolithography in the vacuum ultraviolet (172 nm) with sub-400 nm resolution: photoablative patterning of nanostructures and optical components in bulk polymers and thin films on semiconductors.

Precision photoablation of bulk polymers or films with incoherent vacuum ultraviolet (VUV) radiation from flat, microplasma array-powered lamps has led to the realization of a photolithographic process in which an acrylic, polycarbonate, or other polymer serves as a dry photoresist. Patterning of the surface of commercial-grade, bulk polymers (or films spun onto Si substrates) such as poly-methyl methacrylate (PMMA) and acrylonitrile butadiene styrene (ABS) with 172 nm lamp intensities as low as ∼10 mW cm-2 and a fused silica contact mask yields trenches, as well as arbitrarily-complex 3D structures, with depths reproducible to ∼10 nm. For 172 nm intensities of 10 mW cm-2 at the substrate, linearized PMMA photoablation rates of ∼4 nm s-1 are measured for exposure times t≤ 70 s but a gradual decline is observed thereafter. Beyond t∼ 300 s, the polymer removal rate gradually saturates at ∼0.2 nm s-1. Intricate patterns are readily produced in bulk acrylics or 40-200 nm thick acrylic films on Si with two or more exposures and overall process times of typically 10-300 s. The photoablation process is sufficiently precise that the smallest lateral feature size fabricated reproducibly to date, ∼350 nm, appears to be limited primarily by the photomask itself. Examples of the versatility and precision of this photolithographic process include the fabrication of arrays of aluminum nanomirrors, each atop a 350 nm or 1 µm-diameter Si post, as well as optical components such as transmission gratings or Fresnel lenses photoablated into PMMA.

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.