Lensless focusing with subwavelength resolution by direct synthesis of the angular spectrum

We consider the coherent superposition of unfocused wave fronts for lensless focusing of electromagnetic waves with subwavelength resolution. Near the focal point, intensity distributions generated using the approach approximate those generated using lenses. Far from the focal point, discretization of spatial frequencies results in a trade-off between the number of wave fronts and the accuracy of the approximation. We experimentally demonstrate the feasibility of the approach by generating an approximation of an azimuthally polarized Bessel beam with a focal spot diameter full width at half maximum intensity of 0.37 . © 2006 American Institute of Physics. DOI: 10.1063/1.2213912 O F CO PY The ability to focus electromagnetic waves with subwavelength resolution is essential to a wide range of applications including microscopy, semiconductor lithography, and optical trapping. Focusing is most commonly accomplished using refractive lenses, and lenses with resolutions limited only by diffraction are ubiquitous. However, there are instances where focusing with lenses is difficult or not feasible. For example, focusing with subwavelength resolution is technically challenging in the x-ray, ultraviolet, and infrared regions of the spectrum, due largely to the lack of suitable refractive materials. Alternate approaches employed in these regions of the spectrum have included reflective lenses and diffractive Fresnel zone plates, and more recent approaches include capillary optics, compound refractive lenses, and photon sieves. An intriguing approach to focusing electromagnetic waves is the coherent superposition of unfocused wave fronts. This approach has been proposed in several contexts including optical phased-array beam steering, phaselocked laser arrays, and coherent combination of singlemode optical fibers. In the context of focusing with subwavelength resolution, the approach offers numerous important advantages. In particular, the approach can be implemented entirely using flat mirrors i.e., refractive materials are not required . Also, resolution is not affected by lens aberrations. Further, since the phase of each wave front is independently modulated, subwavelength accuracy is not required in the construction of the apparatus. In this letter we consider the coherent superposition of unfocused wave fronts for focusing electromagnetic waves with subwavelength resolution. The approach can be understood using the “angular spectrum of plane waves” concept. The angular spectrum of plane waves concept asserts that any propagating monochromatic field can be represented as a superposition of homogeneous and inhomogeneous i.e., evanescent plane waves. In the scalar approximation of electromagnetic wave theory, the directions, amplitudes, and phases of the plane waves are related to the field by a Fourier