Described herein are electromagnetic traps or tweezers. Desired results are achieved by combining two recently developed techniques, 3D negative refraction flat lenses (3DNRFLs) and optical tweezers. The very unique advantages of using 3DNRFLs for electromagnetic traps have been demonstrated. Super-resolution and short focal distance of the flat lens result in a highly focused and strongly convergent beam, which is a key requirement for a stable and accurate electromagnetic trap. The translation symmetry of 3DNRFL provides translation-invariance for imaging, which allows an electromagnetic trap to be translated without moving the lens, and permits a trap array by using multiple sources with a single lens.