An isolated quantum dot is modelled by a potential box with deltaprofiled, penetrable potential walls embedded in a large outer box with infinitely high potential walls which represent t h e work function with respect to a vacuum. W e calculate the energies E and t h e density of states of the electron gas in t h e quantum dot as functions of t h e strengths of the potential walls of the inner box. As t h e strengths of the opposite potential walls increase pairwise from small lo large values, t h e density of States shows smooth crossover from the three-dimensional E'I2form to the quasi-two-dimensional (02D) staircase and further down to t h e Q l D sawtooth and t h e delta-function peaks of the QOD electron gas.
We propose a simple nondestructive method to obtain refractive-index profiles of a graded-index (GRIN) light-focusing rod by means of a diffraction grating. In our proposed method, a laser beam is illuminated through a diffraction grating perpendicular to the axis of the GRIN lens and the separation between the zeroth and first-order diffraction peaks is measured and analyzed. The results demonstrate that the refractive-index profiles of commercially available GRIN lenses can be successfully reconstructed.
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