Upholding the diffraction limit in the focusing of light and sound

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.

Realization of an ultrathin acoustic lens for subwavelength focusing in the megasonic range

“…Thus, the transmission efficiency of an acoustic lens with a narrower FWHM is generally more decreased. The physical basis for this phenomenon can be more reliably supported from 4 . Consequently, the focusing performance and the transmission efficiency have a trade-off relationship to each other.…”

“…Finally 4 clarified more reasonable criteria about overcoming the diffraction limit in the focusing application as the following two: (1) The smallest period of the spatial Fourier components in the image plane is less than λ/2, (2) More than approximately 50% of the incident acoustic power is focused in the main focusing area. Indeed, our study has focused on the first criterion.…”

“…Unfortunately, current systems have a focusing limit which relates approximately to the wavelength of the wave used. Formally, the focusing limit, d , is limited by the wavelength of the wave used, λ, and the Numerical Aperture (NA) of the imaging system as d = 0.61λ/NA (i.e., the Rayleigh diffraction limit ) 3 , 4 . Meanwhile, to overcome this diffraction limit and realize acoustic imaging and therapy systems with subwavelength focusing performance, acoustic lenses can be considered as a viable solution.…”

The Possibility of Focusing the Acoustic Radiation Into a Region Less Than the Diffraction Limit

“…Как в оптике, так и в акустике критерий Рэлея [2] устанавливает предел поперечного разрешения в дальнем поле равного λ/2. Преодолеть этом предел возможно с помощью специальных линз из метаматериалов [3][4][5][6][7]. Экспериментально было показано, что можно достичь разрешение равное λ/2 [8][9][10].…”

Synthesis of discrete phase-coherent optical spectra from nonlinear ultrasound

“…Acoustic power of up to ∼ 1 kW is readily achievable with medical high-intensity focused ultrasound (HIFU) transducers that have a ∼ 50% electrical-to-acoustic conversion efficiency [36]. Moreover, it has been shown that the focal area of the transducer may be reduced by using acoustic metamaterials, which allows focusing ultrasound into deep-subwavelength, 1/40 of the incident wavelength spots [37]. Thus, the required acoustic power may be decreased to ∼ 20 mW.…”