PORTLAND, Ore. - Engineers at Purdue University claim to have conjured a mathematical model for metamaterials that designers can use to improve the resolution of lenses below the wavelength of light. Subwavelength focusing, for instance, could enable semiconductor lithography to plumb the nanoscale without having to use ultrashort-wavelength extreme-ultraviolet or X-rays. Others have already demonstrated metamaterials with subwavelength focusing for microwaves and acoustic waves.
Now, engineers at Purdue and elsewhere are working toward photonic metamaterials that provide subwavelength focusing for visible light. "We found you can partially compensate for field decay in a normal right-handed material with a central slab of left-handed [material], but only to a degree that is a function of the lens' material and geometry," said doctoral candidate Ming-Chuan Yang, an EE who performed the work with professor Kevin Webb, also an EE at Purdue. Also contributing to the work was MIT professor Keith Nelson, assisted by MIT doctoral candidate David Ward.
Metamaterials put macroscopic objects sized for a desired subwavelength into a giant-sized crystalline lattice, which interacts in the opposite way from natural materials.
By interceding a central, planar, left-handed material with a negative index of refraction inside a normal lens, the evanescent waves can be partially reclaimed, thereby compensating for field decay in right-handed lenses and extending their resolution into subwavelengths. Unfortunately, according to the Purdue research team, losses in real materials are inevitable, making "perfect" lenses with infinite resolution a practical impossibility.
While the fabled "perfect" lens may be illusory, the Purdue EEs maintain that a careful choice of metamaterial and geometry can achieve an application-specific degree of subwavelength resolution improvement. In the Purdue model, left-handed materials have simultaneous resonances in both their electric- and magnetic-field dipole moments, which implies that there must be concomitant absorptive losses that prevent "perfection."
All natural materials follow the "right-hand rule." Since left-handed materials have a negative index of refraction-bending light inward, instead of outward-a flat lens can nevertheless focus electromagnetic waves.
Webb's group at Purdue used for their simulation an ideal electric current source centrally located within a slab of left-handed material. The field solution, which would otherwise have been a purely evanescent field, showed that with uniform amplitude and uniform power excitation, field growth and power dissipation would limit field growth with inevitable losses. The real and imaginary components of the magnetization and polarization indicated that a dispersive solution must always incorporate some loss into the field solution, even when the team completely surrounded the left-handed material by right-handed material.
The Purdue EEs concluded that field decay in right-handed materials could be partially compensated for by a centrally located left-handed material, and showed how the amount of compensation could be quantified in terms of the material used and its geometric configuration.
The improvement possible with particular materials and geometries, according to Webb and Yang, can be predicted by solving its specific power- and field-growth equations.
"Webb's group's research quantifies negative refraction, so that others can evaluate its usefulness," said Fil Bartoli, a program director in the Electrical and Communications Systems Division within the National Science Foundation. "This is just the kind of step that may enable the construction of the first materials with negative refractive indices that improve optical wavelength-imaging systems."