Simplified superoscillatory lenses for super-resolution imaging.

In recent years, superoscillations have become a new method for creating super-resolution imaging systems. The design of superoscillatory wavefronts and their corresponding lenses can, however, be a complicated process. In this study, we extend a recently developed method for designing complex superoscillatory filters to the creation of phase- and amplitude-only filters and compare their performance. These three types of filters can generate nearly identical superoscillatory fields at the image plane.

Semi-analytic simulation of optical wave propagation through turbulence.

Split-step wave-optical simulations are useful for studying optical propagation through random media like atmospheric turbulence. The standard method involves alternating steps of paraxial vacuum propagation and turbulent phase accumulation. We present a semianalytic approach to evaluating the Fresnel diffraction integral with one phase screen between the source and observation planes and another screen in the observation plane. Specifically, we express the first phase screen's transmittance as a Fourier series, which allows us to bring phase screen effects outside of the Fresnel diffraction integral, thereby reducing the numerical computations. This particular setup is useful for simulating astronomical imaging geometries and two-screen laboratory experiments that emulate real turbulence with phase wheels, spatial light modulators, etc. Further, this is a key building block in more general semianalytic split-step simulations that have an arbitrary number of screens. Compared with the standard angular-spectrum approach using the fast Fourier transform, the semianalytic method provides relaxed sampling constraints and an arbitrary computational grid. Also, when a limited number of observation-plane points is evaluated or when many time steps or random draws are used, the semianalytic method can compute faster than the angular-spectrum method.

Construction of arbitrary vortex and superoscillatory fields.

Superoscillations, oscillations of a bandlimited signal at frequencies greater than its band limit, have been verified both theoretically and experimentally. The design of such superoscillatory waves, however, has typically relied on complicated mathematics. We introduce a simple Fourier method to construct superoscillations in the transverse plane of an optical field in the form of optical vortices.

Changing image of correlation optics: introduction.

This feature issue of Applied Optics contains a series of selected papers reflecting recent progress of correlation optics and illustrating current trends in vector singular optics, internal energy flows at light fields, optical science of materials, and new biomedical applications of lasers.

Correlation optics in progress: introduction to the feature issue.

This feature issue of Applied Optics contains a series of selected papers reflecting recent progress of correlation optics and showing, in part, the trend from micro-optics to nano-optics.

Emerging correlation optics.

This feature issue of Applied Optics contains a series of selected papers reflecting the state-of-the-art of correlation optics and showing synergetics between the theoretical background and experimental techniques.

Diffraction of evanescent waves and nanomechanical displacement detection.

Sensitive displacement detection has emerged as a significant technological challenge in mechanical resonators with nanometer-scale dimensions. A novel nanomechanical displacement detection scheme based upon the scattering of focused evanescent fields is proposed. The sensitivity of the proposed approach is studied using diffraction theory of evanescent waves. Diffraction theory results are compared with numerical simulations.

Simulating fields of arbitrary spatial and temporal coherence.

Optical coherence theory typically deals with the average properties of randomly fluctuating fields. However, in some circumstances the averaging process can mask important physical aspects of the field propagation. We derive a new method of simulating partially coherent fields of nearly arbitrary spatial and temporal coherence. These simulations produce the expected coherence properties when averaged over sufficently long time intervals. Examples of numerous fields are given, and an analytic formula for the intensity fluctuations of the field is given. The method is applied to the propagation of partially coherent fields through random phase screens.