Gary R. Trott

Ball lens reflections by direct solution of Maxwell’s equations

We calculate ball lens reflections, using the exact solution of Maxwells equations for the scattering of a beam from a dielectric sphere. Our results are consistent to within 1 dB with measurements of backreflection to a single-mode fiber. We also calculate backreflection to an astigmatic spot laser diode.

Micro-size ball lenses for micro-optics: theory and experiment

Two modeling approaches for analyzing micro-size ball lenses will be described. Due to the low divergence angle of the light coming out of a single mode fiber (SMF), a Gaussian Optics analysis, integrated with ray tracing, is needed to design the optical subsystems such as fiber collimators. On the other hand, due to the large divergence angle of the light coming out of the laser diode (LD), an exact solution of Maxwells equation which can be obtained by spherical harmonic expansion, is needed in order to predict the coupling efficiency from a LD to a SMF accurately. These models were applied to the cases of forward coupling and back reflections with various arrangements of the optical elements. Excellent agreement was found between the predictions of these two models and the experimental results. These models are very important for assemblies using micro-machined micro-optical parts since they have little or no allowance for alignment adjustments.

Ball lens modeling for laser/fiber coupling. A direct solution of Maxwell's equations

We present optical designs for coupling between a commercial laser and a single mode fiber using one or two ball lenses. Our approach exploits the fact that the scattering of an arbitrary electromagnetic beam from a sphere is an exactly solvable problem. By solving Maxwells equations directly using spherical harmonic expansion of the input field, we can account for effects (spherical aberration, polarization, astigmatism) which are not easy to include by other approaches. We are able to implement this method to calculate reflection and transmission accurately with modest computational effort.

Optical applications of silicon micromachining technology

To implement optical submodules or systems of the future we have identified a few key components and technologies necessary to build optical products at Hewlett Packard. To be competitive these optical assemblies must be smaller, cheaper and more functional, then current optical products while maintaining or exceeding the existing performance level. To accomplish this task we introduce the idea of a silicon micro- optical bench (SMOB). The focus of the micro-optical bench has been laser submounts and collimators. However, while making advances in these platform technologies, the importance of micro parts which can be used to augment and expand the optical functions has become apparent. In this paper the role of silicon as a micro-optical bench substrate is described along with implementations of micro-optical benches. Silicon is an excellent choice as a base platform for SMOB technology because of its availability and excellent material properties and advanced processing technology. Structures to aid in batch assembly processes are easily constructed from silicon wafers. We show how to create structures which allow placement of ball lenses and other three dimensional structures to 1 micrometer accuracy. This can be accomplished in a batch process with the potential for reductions in cost of assembly. We have built generic laser submounts and collimators with various sizes of ball lenses. We show how the performance of these submounts agrees with the theoretical predictions. For fiber to ball coupling Gaussian methods work well. However, for laser to fiber coupling via ball lenses it is necessary to use a Maxwell equation solver in spherical coordinates to correctly predict the spherical aberration effects. The ball lenses can collect the laser light with great efficiency at a fraction of the cost for convectional GRIN or aspheric lenses. Furthermore, the small size allows the whole optical part to fit within standard hermetic packages.