Nanobarcodes with multidimensional optical information beyond diffraction limit

Precise design and fabrication of heterogeneous nanostructures will enable nanoscale devices to integrate multiple desirable functionalities. But due to the diffraction limit (~200 nm), the optical uniformity and diversity within the heterogeneous functional nanostructures are hardly controlled and characterized. Here we report a set of nanobarcodes, each optically active section has its unique nonlinear responses to donut illumination patterns, so that one can discern each unit with super resolution. To achieve this, we rst realized an approach of highly controlled epitaxial growth and produced a range of one-dimensional heterogeneous structures. Each section along the nanorod structure display tunable upconversion emissions, in four optically orthogonal dimensions, including colour, lifetime, excitation wavelength, and power dependency. Moreover, we demonstrated a 210 nm single nanorod as the smallest polychromatic light source for the on-demand generation of RGB photonic emissions. Remarkably, within a space of 50 nm, only 1/20th of the excitation wavelength, multiple codes can be successfully coded and decoded in 4 optical dimensions. This precision control enables the fabrication of super capacity geometrical barcodes with theoretical coding capacity up to (24-1)4. This work benchmarks our new ability towards the full control of sub-diffraction-limit optical diversities of single heterogeneous nanoparticles.


Introduction
The frontier in nanomaterials engineering is to realize their composition control with atomic scale precision, so as to fabricate nanoscale structures with desirable morphological, interfacial and physical properties 1,2 . The control in uniformity and tuning the diversities of single luminescent nanoparticles, dot to dot, has already enabled many quantitative measurements and high-performance nanophotonic devices 3,4 . The next level of challenges and opportunities should be the controlled growth, manipulation and characterization of the hybrid and heterogeneous nanostructures that can incorporate multiple functionalities. But the nanoscale optical properties of such nanostructures are hardly accessible, due to the Abbe diffraction limit that con nes the best axial and lateral resolutions of far eld optical microscopy worse than 200 nm and 500 nm, respectively 5 .
Here we realize the artful control in the single-axis epitaxial growth of uniform one-dimensional lanthanide-doped nanoscale barcodes with high-dimensional optical signatures. Each section along the nanobarcode structure can be controlled to display tunable emissions and decoded by the superresolution microscopy, in four optically orthogonal dimensions. Within a space of 50 nm, multiple codes are successfully coded and decoded in four optical dimensions. This precision control has enabled the fabrication of super capacity geometrical barcodes with theoretical coding capacity up to (2 4 -1) 4 .

Results
Single-axis growth of heterogeneous nanobarcodes Fig. 1a summarizes the key procedure and critical conditions that lead to the desirable integration of photonics functionalities. The principle that directs the controlled epitaxial growth is based on the fact that the surfactants -oleic acid molecules (OAH) prefer to attach on the (001) facet while the oleic acid anions (OA -) bind more rmly onto the (100)/(010) facets of a β-NaYF 4 nanocrystal 30 . Here we nd that at a high OA -/OAH ratio (1:2) and slightly increased reaction temperature (310 o C), the crystal growth rate on the (001) facet can be a lot faster than that on the (100)/(010) facets and heterogeneous nanorods can be formed. For controlled one-axis nanocrystals formation, the amount of the precursor should be kept su ciently low for the directional growth process. For instance, when the concentration of the NaYF 4 shell precursor is kept at relatively high level (0.732 mmol/mL), the growth rates of 1.68 atomic layers per min on the (001) facet versus 0.26 atomic layer per min on the (100)/(010) facets were observed (Supplementary Text). If the supply of precursors is less than the demands in the epitaxial growth from the two (001) facets of the core nanocrystals (0.235 mmol/mL), desirable single-axis growth could be achieved ( Fig. S1 -S3). Notably, in the heterogeneous epitaxial growth process of nanorods, high OAconcentration is critical to avoid the formation of the dumbbell and core@shell structures of NaNdF 4 and NaLnF 4 (Ln = Yb, Er, Tm), respectively ( Fig. S4 and S5).

Morphology uniformity of heterogeneous nanobarcodes
By achieving such a strict control, the HAADF-STEM micrographs (Fig. 1b) show the fabrication of a series of heterogeneous rod structures with each segment of tunable length (e.g. 5 nm and 10 nm) by adjusting the time for precursor injection. Also, the number of the segments can be well controlled (e.g. 10 and 18 segments) by controlling the composition of precursors. Figure 1c shows a large area HAADF-STEM image of highly uniform 18-segment nanorod structures with a consistent length of 5 nm for each segment. The invariant 42 nm of the diameter for the heterogeneous rods with different segments con rms the absolute control in the single-axis growth (Fig. S6). Remarkably, the statistical results shown in Fig. 1d further con rm that these nanorods are exceptionally uniform even in the thickness of each segment. By calculating the precursor injection speed and the thickness of each segment, it is shown that the growth rates of both NaYF 4 and NaErF 4 on the (001) facet are one atomic layer per min. The use of the inert segments of NaYF 4 in the one-dimensional heterogeneous nanorods can minimize the diffusions of optically active ions and therefore allow arbitrary integration of multiple and orthogonal optical responses to form nanobarcodes.

Super resolving nanobarcodes' optical segments
To super resolve the optical information of different segments of single nanobarcodes, we employ an annular excitation pro le (donut-shape illumination beam) in a typical confocal microscopy setup. As illustrated in Fig. 2a, the size of the donut beam is large with a full-width at half-maximum (FWHM) around 300 nm, set by the diffraction limit of the excitation point spread function (PSF). By taking advantage of both the non-linear optical responses of upconversion luminescence and its low saturation intensity levels, the emission PSF can produce a much smaller dark area, with the FWHM down to around 29 nm (Fig. S7b-c), allowing the emission saturation mode to be used for super-resolution imaging. 31 Note that instead of the stimulated emission depletion (STED) super-resolution microscopy con guration [12][13][14]32 that only works for depleting the emissions from UCNPs doped with Tm 3+ ions, our current method is a lot simpler and broadly compatible with different emitters, doping concentrations, and emission bands. 31 The use of a single beam donut illumination design avoids the sophisticated system alignment and temporal synchronization of both Gaussian excitation and donut depletion beams required by STED.
We rst decode a set of sub-diffraction-limit nanobarcodes with a pair of the identical active segments grown on both ends. As shown in Fig. 2b, by a donut-shaped excitation beam scan across heterogeneous nanorods, a negative contrast will be generated when any one of the optically active units is positioned within the donut beam, so that the nal image of a single nanobarcode will be presented as two negativecontrast spots (1 and 3), as shown in Fig. 2c. As the spatial resolution of our emission saturation mode microscopy is 29 nm (Fig. S7 b-c), the limit in decoding the two active segments is at the distance of 50 nm (see our simulation results in Fig. S7d-f). To experimentally verify the optical resolving power, we further fabricate ve batches of distance-tuneable nanobarcodes (Fig. S8). As the centroids of the dark spots in each negative super-resolution image ( Fig. 2d and Fig. S9) can be used to localize the active segments in the nanobarcodes, the super-resolution images of the ve types of representative nanobarcodes shows the central distance increasing from 76 to 141 nm, which is highly consistent with the TEM results (Fig. 2e). As the length of the active segments is around 20 nm, the separation distance between active units (the length of the inert section) is 55 to 120 nm (Fig. S8). These results con rm the spatial decoding power of our single-beam super resolution approach as around 55 nm, which is comparable to the reported super-resolution techniques used for barcode decoding. [33][34][35][36] Notably, due to the nonlinear power dependence property of the emission PSF, choosing an appropriate excitation power is critical in optimizing the localization accuracy (Fig. S10).
Moreover, as shown in Fig. 2f and Fig. S11a, the single-donut-beam approach can be used to resolve the high-density nanobarcodes. By taking advantage of the pair of identical segments on each single nanorod, the sample distance of as close as 69.8 nm, signi cantly below the diffraction limit, can be super resolved. Furthermore, as shown Fig. 2g and Fig. S11b, the super-resolution approach can successfully resolve two populations of nanobarcodes with active segmental distances of 90 nm and 120 nm, respectively. The distance between two types of nanobarcodes as close as 59.2 nm has been resolved. These results highlight the advantage of our geometrical barcode with structural rigidity compared to other soft barcodes. 34,37 Selective activation of nanobarcodes' segments The optically active units doped by lanthanide ions, typically with characteristic 'ladder-like' multiple excited states, can generate near infrared (NIR), visible, and ultraviolet luminescence with sharp spectrum, large (anti-)Stokes shift, and inherent long lifetime. 11,38−40 As the emission saturation super resolution mode is not limited by the types of lanthanide emitters, we can code and decode the nanorods by using a diverse choice of lanthanide co-dopants. First, it is rather a straight-forward strategy by collecting the emission information from different wavelength windows, i.e., NIR and red emissions from Tm 3+ and Er 3+ emitters (Fig. S12), respectively. Then, we also evaluate the new capability using different concentrations of emitters in each segment. The power-dependent property 38,41 (Fig. 3a) allows the selective activating the segments of nanobarcodes beyond the diffraction limit. Selective activation of two sections doped by the relatively lower concentration of emitters (4% Tm 3+ ) and higher concentration of emitters (10% Tm 3+ ) can be achieved by using low and high power density of 980 nm excitation, respectively (Fig. 3b). The distances of different active pairwise are consistent with that from the TEM characterization (Fig. 3c-d  and Fig. S13). Notably, the emission difference from the two segments can be further decoded by the time-resolved mode, as the highly doped sections display a much shorter lifetime (Fig. S14).

Visualizing interfacial energy transfer within nanobarcode
We can further decode the information encoded through interfacial energy transfer and migration in heterogeneous upconversion system. Here, by designing the Yb 3+ /Er 3+ co-doped upconversion segment closely packed with Yb 3+ /Nd 3+ co-doped sensitization segments (Fig. 3e), we show the selective activation and decoding of these neighbouring segments. This is achieved by either exciting the upconversion segment using the 980 nm donut illumination or the nearby sensitization segments by the 808 nm donut illumination, where the energy migration from Nd 3+ → Yb 3+ → Yb 3+ → Er 3+ occur across the interface. Because the 808 nm donut excitation only examines where the material absorbs, we can localize the photon-sensitization segments with Nd 3+ as dopants (Fig. S15). Following the same principle, the 980 nm donut excitation is responsible for diagnosing the location of Yb 3+ ions by reading the Er 3+ emissions. The super-resolution images (Fig. 3f) clearly reveals both the Nd 3+ and Yb 3+ sensitization segments with the centre-to-centre distance around 7.2 nm, which is further veri ed by the TEM characterization (Fig. 3g, 3 h and Fig. S15). For the rst time, we precisely localize the position of closely packed sensitizer sections and visualize the energy transfer effect at nanoscale. The developed method have the potential to precisely study the interfacial energy transfer across two neighbouring segments, which will further open the door for ne tuning of the emission 11 and excitation 42 wavelengths, emission intensity 43 and lifetimes 17 .

Sub-diffraction-limit RGB-switchable pixel
The ability of selective activations of high-dimensional emission diversities from a single nanorod can further create a sub-diffraction-limit RGB-switchable pixel, on demand and in response to the speci c excitation wavelength and illumination pattern, as illustrated in Fig. 4. This experiment takes advantage that the tunable donut and Gaussian excitation pro les at 980 nm and 808 nm can be commensurate to the bilateral symmetry of the barcode strati cation. When a relatively large 980 nm donut excitation is used, only the pair of Red units (NaYF 4 :30%Yb 3+ ,2%Er 3+ ) on the end of the rod can be selectively illuminated. The smaller size of 980 nm donut excitation only activates the pair of Blue units (NaYF 4 :40%Yb 3+ ,4%Tm 3+ ) in the middle of the nanorods. And the 808 nm confocal spot of excitation is responsible for illumining the central Green emission unit (NaYF 4 :15%Er 3+ ), since neither of the Red unit or the Blue unit has the effective absorbance at 808 nm. White emission can be generated through the combined use of the 808 nm confocal and 980 donut excitations. These results show our ability to selectively activate different optical units in heterogeneous nanostructures, which opens the door to build more sophisticated nanophotonic devices that can on-demand display a set of high-dimensional digitized photonic emissions with super-capacity optical information storage.

Super-capacity optically orthogonal nanobarcodes
Using the controlled single-axis epitaxial growth approach and the donut-shaped illumination, we develop a four-dimensional (4D) optical barcoding technique within the diffraction limit. The four orthogonal dimensions include excitation wavelength, power density, emission wavelength and emission lifetime (Fig. 5a). The combination allows us to arbitrarily assemble the many multiple functional segments with the diverse optical properties within a heterogeneous nanorod. Figure 5b shows one batch of such a highly uniform nanoscale barcode structure with six distinct segments, separated by a ∼2.5 nm inert NaYF 4 layer. Donut-shaped illumination leads to the super-resolution decoding of the sophisticated optical signatures in the four channels of optical dimensions (Fig. S17-18). Figure 5c shows a typical super-resolution image of the optical barcodes in 4D, which is in stark contrast with the conventional confocal images. Notably, the pairwise design of the segments allows false alarm rate-free decoding for the multi-dimensional super-capacity optical barcodes. Within a space of 50 nm, only 1/20th of the excitation wavelength, we demonstrate the precision control in coding and decoding of four codes (Fig. 5c), which has higher coding density than any geometrical barcodes reported in literatures 34,36,44,45 . Through freely adjusting the distance and the order of different codes, this precision control has enabled the fabrication of super capacity geometrical barcodes that can potentially produce up to (2 4 -1) 4 digits of optical nanobarcodes. As a demonstration, we summarize additional part of this barcode library in the supporting information Figure S19. To our knowledge, this represents the smallest geometrical barcode with super-capacity optical multiplexing capability to encode large amounts of information 33,34,36 .

Discussion
We demonstrated here an important advance in coding and decoding of optical information at the nanoscale and many potentials in utilising the sub-diffraction-limit optical characterization and selective activation of doping units with a set of high-dimensional digitized and differentiable photonic emissions. Both the artful growth of a library of heterogeneous nanostructures with exceptionally high uniformity and precise discerning of diverse non-linear responses at super-resolution are the key technology enablers. We anticipate that such barcode structures would attract broad interests in a range of applications as information nanocarriers for bio-nanotechnology, life sciences, data safety and storage, once they are incoporated into a variety of matrixes. 35,36,46 The inorganic nanobarcode structures are rigid and it is easy to control the distance accuracy of different codes for the geometrical encoding, in stark contrast with soft geometric barcode counterparts such as dye-tagged DNA barcodes. 34,37 Moreover, they are chemically and optically stable, which enables them as idea information-coded nanocarriers for drug delivery and long time tracking, once the surface of the barcode structures is further modi ed and functionalized with probe molecules and cargos. 7,29 The developed geometrical nanobarcodes could be simultaneously used for tagging different cellular species and identi ed by the super-resolution nanoscopy, bypassing the need for the stepwise addition of dyes for multiplexed imaging of intracellular structures. 47,48 The speed of this super-resolution technique remains low, but this disadvantage can also be circumvented by employing parallelized scanning with beam arrays in the future. 49 These nanobarcodes are also readily applicable for high-security anticounterfeiting when different batches of them are blended with inks and can be readily printed on high-value products for authenti cation. 35 Not limiting to technological applications, the geometrically distinct nanostructures provides a unique model for photophysics study, including the dynamics of one-dimensional energy transfer and have the potential to open the door for optical study of heterogeneous nanomaterials.

Methods
Details and any associated references are provided in the Supplementary Information.

Data availability
All the relevant data are available from the correspondence authors upon reasonable request.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. SI1July.docx