Nonlocal dark solitons under competing cubic-quintic nonlinearities.

We investigate properties of dark solitons under competing nonlocal cubic-local quintic nonlinearities. Analytical results, based on a variational approach and confirmed by direct numerical simulations, reveal the existence of a unique dark soliton solutions with their width being independent of the degree of nonlocality, due to the competing cubic-quintic nonlinearities.

Monitoring and dynamic control of distance and tilt angle measurements in micro-alignment instrument using an imaging approach.

An accurate and simple optical triangulation method is proposed for determining the distance and the tilt angle between the window and the SQUID sensor in a scanning SQUID microscope (SSM) system. The surface of window near the sensor plane is roughened with Alumina powder so that the incident and reflected traces of the laser beam passing the window surface become visible and can be measured precisely with a normal optical microscope. Using the proposed approach, the distance between the sensor and the sample can be reproducibly adjusted to 30 microm or less. This method can also be applied to photolithography apparatus to detect the relative positions of the mask and the wafer.