An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces (Extended Abstract)

The notion of geometric continuity is extended to an arbitrary order for curves and surfaces, and an intuitive development of constraints equations is presented that are necessary for it. The constraints result from a direct application of the univariate chain rule for curves, and the bivariate chain rule for surfaces. The constraints provide for the introduction of quantities known as shape parameters. The approach taken is important for several reasons: First, it generalizes geometric continuity to arbitrary order for both curves and surfaces. Second, it shows the fundamental connection between geometric continuity of curves and geometric continuity of surfaces. Third, due to the chain rule derivation, constraints of any order can be determined more easily than derivations based exclusively on geometric measures

Shape change of Galileo probe models in free-flight tests

Scale models of the Galileo Probe made of polycarbonate, AXF5Q graphite, carbon-carbon composite, and carbon-phenolic were flown in a free flight range in an ambient gas of air, krypton, or xenon. Mach numbers varied between 14 and 24, Reynolds numbers between 300,000 and 1,000,000, stagnation pressures between 31 and 200 atm, and stagnation point heat transfer rates between 10 and 1,000 kW/sq cm. Shadowgraphs indicate gouging ablation of the aft portion of the frustum; the gouging was moderate in air and severe in the noble gases. The graphite models break in the same region. An explanation of the phenomena is offered in terms of the strong compression and shear caused by the reattachment of a turbulent separated flow. Conditions are calculated for similar tests appropriate for Von Karman Facility of the Arnold Engineering Development Center in which a larger model can be flown in argon

-1 V bias 56 Gbps germanium waveguide p-i-n photodetector with silicon contacts

We demonstrate a silicon-contact-only 56 Gbps germanium waveguide photodetector operating at -1 V. The dark current is below 4 nA and the responsivity is 0.74 A/W at 1550 nm and 0.93 A/W at 1310 nm

Vertically emitting annular Bragg lasers using polymer epitaxial transfer

Fabrication of a planar semiconductor microcavity, composed of cylindrical Bragg reflectors surrounding a radial defect, is demonstrated. A versatile polymer bonding process is used to transfer active InGaAsP resonators to a low-index transfer substrate. Vertical emission of in-plane modes lasing at telecom wavelengths is observed under pulsed optical excitation with a submilliwatt threshold

Continuous-wave operation of electrically pumped, single-mode, edge-emitting photonic crystal Bragg lasers

The authors demonstrate an electrically pumped, single-mode, large-area, edge-emitting InGaAsP/InP two dimensional photonic crystal Bragg laser operating in continuous-wave condition. The laser uses a weak index perturbed, polymer-planarized, surface photonic crystal structure to control the optical mode in the wafer plane. They find that the laser operates in single transverse and longitudinal modes. They compare the performance of the photonic crystal Bragg laser with a broad-area laser fabricated from the same wafer and the comparison shows that the performance penalty incurred by the photonic crystal is small

Room temperature continuous wave operation of single-mode, edge-emitting photonic crystal Bragg lasers

We report the first room temperature CW operation of two dimensional single-mode edge-emitting photonic crystal Bragg lasers. Single-mode lasing with single-lobed, diffraction limited far-fields is obtained for 100μm wide and 550μm long on-chip devices. We also demonstrate the tuning of the lasing wavelength by changing the transverse lattice constant of the photonic crystal. This enables a fine wavelength tuning sensitivity (change of the lasing wavelength/change of the lattice constant) of 0.072. This dependence proves that the lasing mode is selected by the photonic crystal lattice

Transmission and group delay of microring coupled-resonator optical waveguides

We measured the transmission and group delay of microring coupled-resonator optical waveguides (CROWs). The CROWs consisted of 12 weakly coupled, microring resonators fabricated in optical polymers (PMMA on Cytop). The intrinsic quality factor of the resonators was 18,000 and the interresonator coupling was 1%, resulting in a delay of 110-140 ps and a slowing factor of 23-29 over a 17 GHz bandwidth

Polymer Microring Coupled-Resonator Optical Waveguides

We present measurements of the transmission and dispersion properties of coupled-resonator optical waveguides (CROWs) consisting of weakly coupled polymer microring resonators. The fabrication and the measurement methods of the CROWs are discussed as well. The experimental results agree well with the theoretical loss, waveguide dispersion, group delay, group velocity, and group-velocity dispersion (GVD). The intrinsic quality factors of the microrings were about 1.5 times 10^4 to 1.8 times 10^4, and group delays greater than 100 ps were measured with a GVD between -70 and 100 ps/(nm x resonator). With clear and simple spectral responses and without a need for the tuning of the resonators, the polymer microring CROWs demonstrate the practicability of using a large number of microresonators to control the propagation of optical waves