Abstract: The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space. Described herein is a multiwavelet-based neural operator learning scheme that compresses the associated operator's kernel using fine-grained wavelets. The system embeds the inverse multiwavelet filters to learn the projection of the kernel onto fixed multiwavelet polynomial bases. The projected kernel is trained at multiple scales derived from using repeated computation of multiwavelet transform. This allows learning the complex dependencies at various scales and results in a resolution-independent scheme. These techniques exploit the fundamental properties of the operator's kernel, which enables numerically efficient representation. These techniques show significantly higher accuracy in a large range of datasets.

Abstract: A DBR laser, such as a semiconductor DBR laser is disclosed having improved frequency modulation performance. The laser includes a split gain electrode and a tuning electrode. A modulating current encoding a data signal is injected into a first section of the gain electrode whereas a substantially DC bias voltage is imposed on a second section of the gain electrode positioned between the first gain electrode and the tuning electrode. The first and second gain electrodes are electrically isolated from each other and the tuning electrode by a large isolation resistance. In some embodiments, the isolation resistance is generated by forming the electrodes on a P+ layer and removing portions of the P+ layer between adjacent electrodes. Capacitors may couple to one or both of the second gain electrode and the tuning electrode.

Abstract: A DBR laser, such as a semiconductor DBR laser is disclosed having improved frequency modulation performance. The laser includes a split gain electrode and a tuning electrode. A modulating current encoding a data signal is injected into a first section of the gain electrode whereas a substantially DC bias voltage is imposed on a second section of the gain electrode positioned between the first gain electrode and the tuning electrode. The first and second gain electrodes are electrically isolated from each other and the tuning electrode by a large isolation resistance. In some embodiments, the isolation resistance is generated by forming the electrodes on a P+ layer and removing portions of the P+ layer between adjacent electrodes. Capacitors may couple to one or both of the second gain electrode and the tuning electrode.