Upholding the diffraction limit in the focusing of light and sound

TL;DR

This paper reviews the concept of the diffraction limit in light and sound focusing, arguing that recent claims of surpassing it do not hold when a reasonable definition is applied, and concludes that the limit remains unbroken.

Contribution

The paper provides a critical review of experimental claims of sub-diffraction focusing, clarifying that the diffraction limit still stands under a reasonable definition.

Findings

Experimental techniques claiming sub-diffraction focusing do not violate the diffraction limit.

The diffraction limit remains valid when defined by wave number bounds or focal spot size.

Various methods like super-resolution, metamaterials, and antennas do not break the diffraction limit.

Abstract

The concept of the diffraction limit put forth by Ernst Abbe and others has been an important guiding principle limiting our ability to tightly focus classical waves, such as light and sound, in the far field. In the past decade, numerous reports have described focusing or imaging with light and sound "below the diffraction limit". We argue that the diffraction limit defined in a reasonable way, for example in terms of the upper bound on the wave numbers corresponding to the spatial Fourier components of the intensity profile, or in terms of the spot size into which at least 50% of the incident power can be focused, still stands unbroken to this day. We review experimental observations of "subwavelength" or "sub-diffraction-limit" focusing, which can be principally broken down into three broad categories: (i) "super-resolution", i.e. the technique based on the modification of the pupil of the optical system to reduce the width of the central maximum in the intensity distribution at the expense of increasing side bands; (ii) solid immersion lenses, making use of metamaterials with a high effective index; (iii) concentration of intensity by a subwavelength structure such as an antenna. Even though a lot of interesting work has been done along these lines, none of the hitherto performed experiments violated the sensibly defined diffraction limit.