Scattering superlens

The resolution limit of optical microscopy is a significant hindrance to many fields of research. This is a critical limitation that cannot be easily surpassed simply by using shorter wavelengths. Besides the limited optical components and techniques for shorter wavelengths at the UV or x-ray range, photons at these energy levels are usually either harmful or have negligible light-matter interaction, which discourages their use as optical probes. This is especially pronounced in the field of bioimaging, where probing at the subcellular regime is critical for understanding life and disease.

To overcome these limitations, powerful ideas have been developed that allow sub-diffraction-limited imaging of biological specimens using visible light,¹ such as stimulated emission microscopy,² stochastic optical reconstruction microscopy,³ and photoactivated localization microscopy.⁴ However, these methods either rely on numerical post-processing to achieve super-resolution or use de-excitation of fluorescence surrounding the targeted area. As such, these methods do not directly control the near-fields and have severe limitations in directly delivering light to sub-wavelength volumes. The recent development of metamaterials has shown the strongest potential for direct control of the near-fields, through the construction of novel structures with unique refractive indices that are not ordinarily seen in nature.^{5, 6} These structures have demonstrated that the evanescent near-fields can be either enhanced or transformed to propagating far-fields to allow sub-wavelength imaging and light delivery. However, these techniques require stringent fabrication conditions and procedures, which complicates actual use.

In our recent work,⁷ we showed that multiple scattering^8–10 can be exploited to obtain a sub-wavelength focus at an arbitrary position (see Figure 1). Through the concept of time reversal, it was previously demonstrated in the microwave regime that the near-fields—which have been elastically scattered into propagating far-fields—can be effectively controlled by time-reversing only the propagating far-field components.¹¹ Here, we extend the same concept into the optics regime by using scatterers with sub-wavelength sizes. Using spatial light modulators that can control the phase of the impinging far-fields, we demonstrate that the phase of the resulting scattered near-fields can be controlled as well. There are no restrictions on the physical position of the focus due to the highly inhomogeneous structure and the high degree of freedom of the media. Through this demonstration we also propose that multiple scattering in biological tissue, which had been assumed to be unfavorable for imaging or light treatment, can—on the contrary—be used to steer and focus sub-wavelength light spots within its inhomogeneous tissue structure.

Figure 1. Near-field control using multiple scattering. (a) Conventional optics can only control propagating far-fields and generate a diffraction-limited focus with a width of ∼λ/2. (b) When a plane wave is incident on random media, the wave is multiply scattered and converted into multiple wave vectors that contain both propagating and evanescent terms. (c) By shaping the impinging wavefront, the resulting wave vectors can be phase-matched to construct a sub-wavelength focus at a target position. (d) Measured light foci using a scattering superlens. λ: Wavelength.

The success in transferring the impinging far-fields into near-fields through multiple scattering also means that 2D sub-wavelength near-field images can be measured at the far-fields using the transmission matrix (TM). The TM describes the linear relation between the input and output fields propagating through scattering media.^12,13 The TM containing near-field information is measured directly using a spatial light modulator for the generation of each focus, rather than modulating the input fields iteratively. This approach has the advantage that the relation between all the sub-wavelength input modes and the output far-field speckles can be used in parallel. Currently, using this approach, we are developing a dynamic super-resolution imaging technique for studying cell pathophysiology.

In summary, we have employed multiple scattering to control the phase of the near-fields, which was originally impossible using conventional optics. By phase matching the near-fields at target positions, sub-diffraction-limited optical foci could be obtained. We then used the same idea in the time-reversed manner where the relation between the impinging near-fields and the generated far-fields was investigated and used for wide-field sub-wavelength imaging. Both methods are based on multiple scattering, which can be used for all wavelengths, and the ‘scattering superlens’ turbid medium can be fabricated easily. In addition, control over the near-fields in terms of wavelength¹⁴ and polarization¹⁵ would also be possible due to the high degree of freedom in multiple light scattering. Furthermore, the concept of the delivery of near-field information to the far-fields via multiple scattering can also be employed with digital optical phase conjugation^16,17 or optical coherence tomography.^18,19 We anticipate that the technique can be further extended for real-time 2D imaging of biological samples, while sub-diffraction-limited optical light delivery can be used in various other areas, such as photolithography.