Bernstein modes in density-modulated two-dimensional electron systems and quantum dots

We have prepared two-dimensional electron systems (2DES) in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}\mathrm{}$ heterostructures with laterally structured gate electrodes which allow us to tune the system from a density-modulated 2DES into a periodic array of isolated quantum dots. At small modulation amplitudes, with far-infrared transmission spectroscopy in a magnetic field, we observe the expected interaction of the magnetoplasmon with the Bernstein modes at harmonics $n{\omega }_c$ of the cyclotron frequency ${\omega }_c$ $(n=2,3\mathrm{}\dots ).\mathrm{}$ For large modulation, we find modes which occur below these resonances, e.g., in the regime ${\omega }_c$ to 2 ${\omega }_c.$