Generation and Decoding Colored Beams Carrying Orbital Angular Momentum

By nanoscale 3D printing, we produced miniaturized optical components processing information in the color and orbital angular momentum of beamlets using only light from a lamp. These colored vortex beams from incoherent white light promise anticounterfeiting through pairwise optical authentication.

Advances in nanofabrication coupled with strategic designs of nanostructure geometry have demonstrated exciting new capabilities in manipulating light. In polarization, amplitude, phase, and directional beaming of light, the phase vortex of light was discovered to carry orbital angular momentum (OAM) since1992, thus introducing a new dimension for controlling light.

In this research, we extended the generation of OAM beams to broader ambient lighting conditions by increasing the spatio-temporal coherence of incident incoherent white light. Combined with modulations in wavelengths and spatial positions, a multidimensional complementary optical “lock” and “key” can be realized. Due to the multiple helical eigenstates of OAM, the pairwise coupling between optical “lock” and “key” can be further extended to form a one-to-many matching and validation scheme, providing huge convenience for optical anti-counterfeiting, an application space that relies heavily on incoherent light sources.

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Light carrying orbital angular momentum (OAM) is a form of structured light that finds applications, e.g., in stimulated emission depletion (STED) microscopy for imaging at resolutions beyond the diffraction limit, quantum information processing to increase the number of possible photon states beyond the typical horizontal-vertical polarization, and optical communications to increase the number of communication channels for a given frequency. However, spatio-temporally coherent light sources are essential to generate OAM beams. These are the kind of light that we can expect from lasers or supercontinuum sources. The more common sources of light employed daily tend to be incoherent and broadband, i.e., white light sources, such as incandescent lamps, light emitting diode (LED), and sunlight. When we wanted to bring OAM into a new application space such as optical anti-counterfeiting, we figured that making it work with incoherent light sources would be a crucial step. While most optical anti-counterfeiting labels such as holograms have been adapted to work under ambient lighting conditions, which is convenient and low-cost for authentication.

So what would happen if one tried to use incoherent light to generate OAM beams? On one hand, low spatial coherence will smear out the characteristic doughnut-shaped beam and remove the phase singularity (Advances in Optics and Photonics 3.2 (2011): 161-204.). On the other hand, low temporal coherence will result in a blurry and iridescent light field (Physical Review Letters 88.1 (2001): 013901, New Journal of Physics 4.1 (2002): 66.), as shown in Fig. 1. 

Figure 1. OAM and vortex beams with low spatial and temporal coherence. (a) Blurry OAM beam generated by spiral phase plate under extended quasi-monochromatic beam illumination. (b) OAM beams under polychromatic incident light. (a) and (b) are adapted from Advances in Optics and Photonics 3.2 (2011): 161-204. (c) Drastic change in spectral component near a phase singularity. Adapted from Physical Review Letters 88.1 (2001): 013901. (d) Drastic change in colors near a phase singularity. Adapted from New Journal of Physics 4.1 (2002): 66.

To get clear and colored OAM beams from blurry and iridescent OAM beams, we modulate the spatio-temporal coherence of the OAM beams. Taking advantages of two-photon polymerization (TPP) 3D printing, we combine 3 functions into a microscale single photonic device, namely, OAM beam generator (the spiral phase), focusing lens (the converging phase), and nanopillar color-filter (spectral modulation). As shown in Fig. 2, we name such colored vortex beam (CVB) generator and decoder as CVB units. The spatial coherence is enhanced by miniaturizing the spiral phase plate, while the temporal coherence is enhanced by adding nanopillar color-filter on top.

Figure 2. (a) Spatio-temporal coherence diagram of light sources. The coherent laser near the origin exhibits the highest spatio-temporal coherence, while the white light source indicated with the cross is an example of poor coherence. (b) Four potential structures for generating CVB with white light illumination. The spatial coherence of incident white light is enhanced by miniaturizing the spiral phase plate, while the temporal coherence of incident white light is enhanced by adding nanopillar-based color filters. Through enhancements both in spatial and temporal coherence, the blurry white focal spot is converted into the green doughnut shaped intensity profile (insets).

To expedite the fabrication speed of CVB unit, a method of two-density three-step nanoscale 3D printing was developed. The inner base, smoother surface, and nanopillar color-filter were fabricated sequentially with different laser powers and scanning speeds (Fig. 3). The fabrication of a single CVB unit can be implemented in around 1 minute, providing the capability for large-area multiple CVBs array fabrication. 

Figure 3. Tilted SEM images of the CVB unit at different stages of our two-density three-step fabrication process showing rough inner region (a), smooth top surface of the CVB unit (b) and printing of nanopillars. Inset of (c) shows the magnified image of nanopillars with nanoscale diameter and microscale height.

As a PhD student, I like reading fantasy novels and watching animations in my leisure time. One of my favorite webcomics and anime series is called Under One Person (Hitori no Shita: The Outcast). Inheriting from traditional Taoism, the characters in Under One Person are gifted and have magic powers. One of the magic powers is to sketch out luminous tallies floating in air (Fig. 4(a)), which can be used to dispel evil attacks and protect the good. It just so happened that one day, I was thinking is it possible to create a tally with luminous photons to shield from counterfeiting and enhance optical security? Motivated by such a fantasy idea, I commenced literature investigation and finally selected three dimensions to encode optical information, i.e., color, spatial degree of freedom, and orbital angular momentum of light. The multidimensional validation is in accord with the origin meaning of a Chinese character “符”, which means “accordance” and “tallies with complementary features”. One example is the tiger tally, a 2,300-year-old tiger-shaped tally, was used to authenticate military orders. One piece was held by the military general, and the other complementary piece held by the monarch. When brought together, the two pieces would precisely match like pieces of a puzzle, as their outer shapes, inner morphology, and surface characters are complementary (Fig. 4(b)).

Figure 4. (a) Luminous tallies from traditional Taoism. (b) Photograph of a tiger tally pair from ancient China, used as security tokens due to the three-dimensional complementary nature of outer shape, inner morphology, and surface characters.

Inspired by such luminous tallies, we designed and fabricated photonic tallies, which consists of CVB array encoding color, spatial position, and OAM information. As shown in Fig. 5, it shows colored rings with different radius on the focal plane of the first Photonic Tally A, where the radius depends on the topological charge of CVB. When overlaid and aligned with different pieces of photonic tally “key”, namely, Photonic Tally B1, B2, and B3, it shows different patterns of colored rings on the combined focal plane. The hidden information can be machine readable and thus can be validated against a database.

Figure 5. Schematic of photonic tally pair. With white light illumination, the photonic tally forms an array of colored doughnuts at the focal plane, encoding color and OAM information. Combined with different photonic tallies B, distinct output patterns form at the combined focal plane, e.g., colored dots array, colored doughnuts with specific topological charges (e.g., increasing outwardly), and eliminated color channels. Inset with white outline: schematic of colored vortex beam (CVB) unit.

The detection method is also simple and convenient, only requires an ordinary optical microscope and reducing the aperture of the light source in the transmitted illumination mode. The CVB unit is difficult to distinguish under the electron microscope and optical microscope, but when the microscope is focused on its focal plane, it will show a colored doughnut shaped intensity distribution with different diameters. The color depends on the height of the nanopillars, and the diameter of the ring depends on the topological charge of the vortex light. Using the three degrees of freedom of the beam's color, spatial position, and orbital angular momentum, the photonic tally can encrypt information such as numbers and graphics, as shown in Fig. 6.

Figure 6. Single photonic tally piece and corresponding encrypted information. Photonic tally pieces showing “SUTD” letters in color and 100 first digits of “π” in topological charges (a), predesigned spatial pattern “□” (b). (c) Colored tetris with arbitrary spatial coordinates and random topological charges. All scale bars are 50 μm. The column with red outlines is SEM images. Column with orange outlines shows optical micrographs of the fabricated photonic tally pieces. Column with purple outlines shows optical micrographs taken at the focal plane of photonic tally pieces and illuminated with collimated broadband white light. The last column with blue outlines is the corresponding hidden topological charge information.

With only a 10-by-10 CVB unit array as a demonstration, considering three color channels and 11 eigenstates with topological charges ranging from -5 to 5, a single photonic tally piece can achieve 33100 possible combinations. It is more secure than the traditional optical verification methods. When the photonic tallies that encrypt different information are superimposed, the CVBs are superimposed or annihilated, thus the pre-designed content is presented on the observation plane. Therefore, different content can be decrypted with different photonic tallies. As shown in Fig. 7, when the encrypted "π photonic tally" is superimposed on the calculated and designed "π photonic tally", "A photonic tally" and "B photonic tally", the "⸬ photonic tally ", "□ photonic tally" and "֎ photonic tally" can be obtained. Such kind of mutual and cross optical verification method provides great convenience for optical pairing verification anti-counterfeiting.

Figure 7. Cross-validation mode for photonic tallies. (a)- (b) When the photonic tally encrypted digital or graphic information is superimposed with the photonic tally with conjugate topological charge, a photonic tally of color dot matrix with a topological charge of 0 is formed. (a), (c) and (d) "π photonic tally" and three other photonic tallies are superimposed to obtain different pre-designed contents, the "⸬ photonic tally ", "□ photonic tally" and "֎ photonic tally". The numbers represent topological charges and can be read out using a machine.

Conclusion and Outlook

Using two-photon polymerization 3D printing, we designed and fabricated CVB units, which can generate CVBs under incoherent white light illumination. Based on the CVB, we designed and fabricated photonic tally. Multi-dimensional optical encryption and decryption are performed in color, spatial position, and orbital angular momentum, providing an optical anti-counterfeiting mode with cross-pair verification function. We pointed out in the article that although the focal length of the currently used CVB unit is fixed, by introducing additional degrees of freedom such as focal length and polarization, higher-dimensional light field manipulation and optical anti-counterfeiting can be further realized. Using small light sources such as LED light sources or new physical mechanisms such as continuum bound states can further enhance the spatiotemporal coherence of CVB, providing possibilities for high-dimensional optical anti-counterfeiting, high-dimensional optical quantum computing, and optical quantum storage.

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