Deep learning beats the optical diffraction limit

In our digital age, we generate an ever-increasing amount of data (terabytes per day), making its storage and long-term access increasingly challenging. Hard disk drives have become very popular because of mass production and relatively low cost, but their storage capacity no longer satisfies our needs for information storage. Moreover, their lifespan is just a few years¹. Optical data storage offers an attractive alternative for ‘big data’, allowing an increase in both capacity and longevity. For example, it has been proposed that optical data memory could last for centuries, with a capacity of over 10 terabytes².

Optical data storage systems have evolved from CDs and DVDs to Blu-ray disks. But the recording capacity of such disks is limited by the diffraction limit of the laser used to write to the disk, which can store just one bit of information per area to reach 200 GB per disk at most³. Clearly, this is not enough to satisfy the ongoing information expansion, and new methods and techniques are urgently needed. Now, writing in Nature Nanotechnology, Wiecha et al. report a method that can beat the diffraction limit by using a deep learning approach with the potential to increase the storage capacity up to nine bits per diffraction-limited area⁴.

To achieve this, the authors propose to use subwavelength dielectric nanostructures to encode multiple bits of information per diffraction-limited area. Instead of encoding a single bit with a nanoparticle, they analyse the full spectrum of a finite square array of silicon nanoparticles by using a deep learning approach and show that each combination can be uniquely resolved. The success of this method is based on two key aspects — the use of high-refractive-index dielectric nanoparticles with a characteristic scattering profile, and the post-processing of the data by deep learning methods.

Silicon, the material of choice in microelectronics, has also become indispensable in modern nanotechnology. It was recently demonstrated that subwavelength silicon nanoparticles have rich optical properties, including electric and magnetic resonances, strong nonlinear response and harmonic generation. These properties have led to the emergence of a new field of all-dielectric metasurfaces that could be used for advanced communication, sensing, imaging and holographic application⁵. And now, by using the artificial neural network approach, silicon nanoparticles can prove competitive for applications in optical data storage.

In their current approach, Wiecha et al. use a 300 × 300 nm² square that is subdivided into smaller blocks, enabling the encoding of information bits. Depending on the number of blocks and their arrangement within the square, various bits can be written. The basic principle can be illustrated by using a four-bit array, with four blocks inside the square (Fig. 1). Each block, with a size of 120 × 120 nm², can be empty or filled with a 90-nm-thick silicon nanoparticle. Empty blocks can be thought of as ‘zeros’ and filled blocks as ‘ones’, rendering the total capacity of the square four bits (or a ‘nibble’) with 16 possible configurations. To distinguish two different polarizations, the researchers also introduced a 60-nm-wide L-shaped border made of silicon. Such patterns can be viewed as QR codes for a particular bit of information. Moreover, owing to current nanofabrication facilities, the structures can be fabricated with high precision.

A subwavelength silicon nanoparticle can support optical resonant modes in the visible frequency range owing to its high refractive index⁵. By arranging the particles in a diffraction-limited area, Wiecha et al. were able to encode multiple bits of information⁴. A diffraction-limited square area is divided into smaller blocks forming an array, and each block in the array is either filled or not with a silicon nanoparticle, representing a 1 or 0 unit of information. For example, in the case of a four-bit array, there are 16 possible configurations (which is enough to represent a hexadecimal unit), four of which are depicted here. In other words, a four-bit array can be used to encode four bits (a ‘nibble’ or half-byte) of information. Wiecha et al. collected the optical spectra of various configurations with a dark-field microscope and postprocessed them with an artificial neural network. Some configurations can produce similar responses for different polarizations. To resolve them uniquely by polarized optical spectroscopy, an L-shaped border was introduced. Such a robust readout mechanism allows various possible configurations to be distinguished in a diffraction-limited area. The technique is not limited to four-bit arrays and has also been demonstrated for nine-bit arrays⁴.

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As the next step, the dark-field spectra of all possible combinations for two incident polarizations can be collected and fed to an artificial neural network trained for robust readout. Based on various samples, the authors were able to take into account both the network loss and error rates, to achieve fast and accurate readout. Importantly, in this approach one does not need the full spectra but can accurately retrieve the information from reduced spectra at selected wavelengths such as red (R), green (G) and blue lines (B). This enables parallel readout using RGB colours directly from microscope images.

Wiecha et al. push the limits of the optical data storage even further with nine-bit arrays, in which each square is subdivided into a 3 × 3 matrix with 512 possible configurations, allowing them to encode nine bits (or one byte + one bit) of information in the diffraction-limited area. This beats the capacity of Blu-ray disks in gigabytes per square inch.

The current platform still has some limitations. Smaller block sizes might yield similar far-field spectra for different patterns, owing to the lack of strong resonant response, leading to an error in the information retrieval. Also, because of increased material losses, shorter wavelengths cannot be used to encode information. But these limitations might be overcome by using other semiconductor materials with higher refractive index and lower dissipative losses, such as AlAs or GaP (ref. ⁶).

This newly developed approach, in general, does not have any technical constraints; it should be suitable for fully automated set-ups and fast readout of very large datasets. It provides a robust solution for ‘smart’ ultrahigh-density optical data storage using planar nanostructures, going beyond the data density of the Blu-ray disk. Other key advantages of using silicon nanostructures include scalability, low cost and durability of long-term optical memory. Besides this, similar to QR-code scanners, one may expect the implementation of fast information readout of large data sets by means of handheld smartphone-based microscopy⁷.