Methods and limitations of subwavelength imaging

The field of subwavelength imaging is in the enviable position of having already proven itself in a number of practical applications; in the future, it seems reasonable to suppose that even more widespread adoption of subwavelength techniques will occur. A sound theoretical underpinning, however, is helpful if such progress is to be rapid. Surveying advances across the varieties of subwavelength imaging, the following general rules appear to apply: Subwavelength techniques are either true, or functional; the former are agnostic to the details of the matter to be imaged, but the latter require (often ingenious) experimental constraints to obtain a subwavelength image. Even true subwavelength techniques cannot produce images if the matter to be imaged is spread over three dimensions; a restriction to two dimensions is necessary. Similar to the diffraction limit for wavelength imaging, for true subwavelength imaging the limit on resolution is given by Eq. (15) or some similar relation. In general, it will be inversely proportional to the distance to the sensor and proportional to the logarithm of a value that quantifies the quality of the sensor. This is the signal-to-noise ratio in the case of computational image reconstruction; it is the lossy part of the permittivity or permeability in a Pendry superlens. In particular, the proposed resolution limit on subwavelength imaging is buttressed by the fact that three unique approaches to predicting resolution limits in subwavelength systems yielded identical results. Equations (22), (9), and (15) were derived in entirely different contexts but are virtually identical in form. It remains to be seen whether the scientifically and economically important forms of subwavelength imaging will be predominantly true or functional. If they are functional; the limitations described in this paper are of little practical use. However, if they are true, hopefully these rules will help guide future designs. Specifically, they suggest that the key to high-resolution subwavelength imaging is high-Q, low-noise detection systems, as well as minimizing the distance to the sensor and isolation of one particular imaging plane. One limitation of the above analysis is that the resolution limit was always taken in the limit of very low frequency and large image wavevector, to ensure that there were no confounding effects with wavelength imaging. Interference effects were ignored. It is unclear if the limits on resolution expressed above apply in an intermediate regime between wavelength and subwavelength imaging. One possibility in this intermediate regime would be to repeat the analysis that led to Eqs. (21) and (22), but to jettison the assumption that the frequency of the radiation was very small and the image wave vector very large [that is, to use Eq. (23)]. Nevertheless, this does not change the fundamental logarithmic relationship among noise, distance, and resolution. Additionally, since no practical devices have been developed for intermediate-wavelength imaging, it seems that the low-frequency limit is likely the most useful expression.