Two-photon absorption under few-photon irradiation for optical nanoprinting

doi:10.21203/rs.3.rs-5059003/v1

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Two-photon absorption under few-photon irradiation for optical nanoprinting

https://doi.org/10.21203/rs.3.rs-5059003/v1

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Two-photon absorption (TPA) has been widely applied for 3D imaging and nanoprinting; however, the efficiency of TPA imaging and nanoprinting using laser scanning techniques is extremely low due to the trade-off shackle between resolution and efficiency. In this work, we unveil a novel concept, few-photon irradiated TPA (fpTPA), supported by a spatiotemporal model that describes the precise time-dependent mechanism of TPA under ultralow photon irradiance with a tightly focused femtosecond laser pulse. We demonstrate that a feature size of 26 nm (1/20 λ) and a pattern period of 0.41 λ with a laser wavelength of 517 nm can be achieved by performing two-photon digital optical projection nanolithography (TPDOPL) under few-photon irradiation using the in-situ digital multiple exposure (iDME) technique, improving printing efficiency by 5 orders of magnitude. Our work offers deeper insights into the TPA mechanism and encourages the exploration of new potential applications for TPA in nanoprinting and nanoimaging.

Physical sciences/Optics and photonics/Optical techniques/Lithography

Physical sciences/Physics/Optical physics/Nonlinear optics

Few-photon irradiated TPA achieves nanoprinting with unprecedented efficiency and resolution.

The two-photon absorption (TPA) process, which involves two quantum transitions originally studied by Maria Göppert-Mayer¹ based on Dirac’s dispersion theory², has found widespread application in various fields, including nonlinear spectroscopy³, fluorescence microscopy⁴, optical memory⁵, lithography^6-8. In general, the TPA rate of photoactive materials irradiated by a focused laser beam is proportional to the squared light intensity I². It is typically assumed that the two photons are simultaneously absorbed via a virtual state⁹. Since the absorption cross-section of TPA is extremely low, a tightly focused femtosecond laser beam is generally used in TPA fluorescence microscopy and lithography.

As a well-established nanoprinting technique, two-photon lithography (TPL) utilizing a femtosecond laser direct writing (LDW) can fabricate arbitrary two-dimensional (2D) and three-dimensional (3D) structures with feature sizes ranging from nanometers to micrometers.^10-12. Leveraging the quadratic nonlinearity of TPA and precise control over processing parameters¹³, TPL finds wide-ranging applications in microelectronics¹⁴, optics^15,16, mechanical electric microsystems¹⁷, biomedicine^18-20. However, with diffraction-limited focusing, the laser peak intensities can reach values as high as I = 10¹² W cm^–2,^21-22 accompanied by corresponding photon irradiance of 3 × 10³¹ s^–1 cm^–2 that is sufficient to enable appreciably effective TPA. Such high photon irradiance can easily trigger high-order nonlinear optical processes, leading to photobleaching, micro-explosions and a narrowed process window²³. Furthermore, TPA only occurs in the tiny area of the focused laser spot, resulting in extremely low throughput. Although multi-focus techniques^24-26 can partially enhance fabrication efficiency, the serial point-by-point writing protocol of LDW remains inadequate for efficiently fabricating structures with multiscale components, ranging from nanoscale to macroscale.

To improve the manufacturing efficiency of TPL, two-photon digital optical projection nanolithography (TPDOPL) technology has been developed²⁷. This method utilizes a digital micromirror device (DMD) as a digital mask²⁸ which can be easily changed by replacing the data of the digital mask with millions of pixels. The throughput of TPDOPL significantly exceeds that of LDW by several orders of magnitude^27,29. Meanwhile, a resolution of 32 nm, equivalent to 1/12 of the laser wavelength, was achieved by inducing TPA under irradiation with a laser peak intensity of only 1.40 × 10⁵ W/cm². This corresponds to a photon irradiance of 2.8 × 10²³ s⁻¹ cm⁻²,³⁰ which is almost 8 orders of magnitude lower than that required for LDW. Notably, the number of irradiated photons per pulse per pixel (N_spp) for a single DMD pixel was as low as 5, demonstrating that TPA can be effectively triggered under conditions of ultralow-photon irradiance, which we define here as few-photon irradiation.

Here, we introduce a novel concept, few-photon irradiated TPA (fpTPA), offering a new perspective on the TPA process and its probability distribution under ultralow photon irradiance with a tightly focused femtosecond laser pulse. We developed a spatiotemporal model based on the wave-particle duality of light and photon distribution to describe the precise time-dependent mechanism of TPA. Through simulations using this model, we determined the probability and distribution of effective TPA (eTPA) as a function of varying photon irradiance. To validate the fpTPA concept and spatiotemporal model, we conducted TPDOPL experiments, which achieved a feature size of 26 nm, equivalent to 1/20 of the wavelength (λ), and improved patterning efficiency by 5 orders of magnitude, effectively breaking the trade-off shackle between resolution and efficiency in TPL. Additionally, we proposed and developed the in-situ digital multiple exposures (iDME) method, enabling extremely fine, dense, and complex patterning with TPDOPL. We describe the underlying physics of the fpTPA and demonstrate TPDOPL as a versatile and powerful tool for fabricating devices with high resolution, efficiency and accuracy in the fields of microelectronic integrated circuits, optical waveguides, and biological microfluidics.

TPA is widely recognized as the simultaneous absorption of two photons via a virtual state¹. From the perspective of quantum electrodynamics³¹, the process begins with the absorption of a photon, transitioning the system from the initial state (g) to an intermediate state (i). The absorption occurring at the intermediate stage without energy conservation is referred to as virtual absorption, and the intermediate state is known as the virtual state. Subsequently, a second photon is absorbed, completing the transition to the final excited state (e). The total energy is conserved, resulting in $\:{E}_{TPA}\approx\:2\hslash\:\nu\:$. To illustrate this, we use a simplified photon diagram, where photons with energy $\:\hslash\:\nu\:$ and polarization k are depicted as point-like particles. The interaction between the photon (with energy $\:\hslash\:\nu\:$) and the molecule can be represented by the time-ordered graph for TPA, as shown in the inset of Fig. 1A. (detail shown in S1)

The virtual state does exist; however, it does not remain populated long enough for the second photon to interact with the molecule before the virtual state “decays”. Therefore, the molecule can absorb two photons arriving at different times simultaneously when the time interval t₀ between the arrival of the two photons is less than the virtual state lifetime, $\:{\tau\:}_{i}$, as illustrated in Fig. 1A. An estimation of the intrinsic lifetime of the virtual state, $\:{\tau\:}_{i}$, can be obtained using Heisenberg’s uncertainty principle and the single intermediate state approximation³²,

$$\:{\tau\:}_{i}=h{\left(4\pi\:{\Delta\:}{\stackrel{\sim}{\nu\:}}_{ie}\right)}^{-1}$$

where h is Planck’s constant and $\:{\Delta\:}{\stackrel{\sim}{\nu\:}}_{ie}$ is the energy difference between the photon energy of $\:\hslash\:\nu\:$ and the stationary energy of the lowest excited state of the molecule (E₁). The values of $\:{\tau\:}_{i}$, calculated using Eq. (1) with the absorption cut-off wavelength of the photoresist AR-N-7520 utilized in this study, were confirmed to be 0.8 fs and 0.3 fs for incident laser wavelengths of 400 nm and 517 nm, respectively, as depicted in Fig. 1B. The relationship between $\:{\tau\:}_{i}$ and $\:{\Delta\:}{\stackrel{\sim}{\nu\:}}_{ie}$ is illustrated in Fig. 1C, clearly demonstrating that the values of $\:{\tau\:}_{i}$ are significantly dependent on $\:{\Delta\:}{\stackrel{\sim}{\nu\:}}_{ie}$.

The probability of TPA is critically influenced by the spatial and temporal distribution of incident photons from a tightly focused femtosecond laser pulse. Each photon can be treated as a discrete event, with its position adhering to a Poisson distribution within the focal spot. Figure 2A illustrates a model depicting the interaction between a tightly focused photon stream, characterized by a repetition frequency R, pulse width $\:\tau\:$, and photosensitive molecules within the photoresist. Considering the time-dependent mechanism of TPA, we hypothesize that two photons, each with energy ℏν where $\:\hslash\:\nu\:$ < E₁ ≤ $\:2\hslash\:\nu\:$, continuously interact with the same molecule within the time interval $\:{\tau\:}_{i}$ (Fig. 1A). This interaction facilitates the effective TPA (eTPA) of the molecule. The time-averaged number of eTPA at position r and time t is given by

$$\:⟨{n}_{TPA}(r,t)⟩={\left(\frac{\lambda\:}{hc}\right)}^{2}{\delta\:}_{i,j}{\delta\:}_{j,k}⟨I(r,t)\bullet\:I(r,t-{t}_{0})⟩$$

where $\:{\delta\:}_{i,j}$ and $\:{\delta\:}_{j,k}$ are the single-photon absorption coefficients from i to j states and j to k states, respectively. $\:I(r,t)$ and $\:I(r,t-{t}_{0})$ represent the energy flow density separated by time t₀ at position r. $\:I(r,t)/(hc/\lambda\:)=n(r,t)$ is defined as the photon flow density. The precise spatial position of a photon as an individual particle colliding on the focal plane is uncertain. However, the distribution of incident photons can be represented by the light intensity distribution of a tightly focused laser spot, as calculated by the point spread function (PSF) (for details on the light intensity distribution, see Supplementary Information S2 and figure S1). Similarly, the exact timing of an individual photon reaching the focal plane within the pulse duration 𝛤 is also uncertain, though the hyperbolic secant function (HSF) can describe the temporal profile of the femtosecond laser pulse. Consequently, the potential distribution of eTPA under few-photon irradiation with a femtosecond laser pulse must incorporate both spatial and temporal uncertainties associated with the photons in the pulse.

We employ the Monte Carlo method to simulate the spatial and temporal stochastic processes of photons within a femtosecond pulse, coupled to a focusing system with a numerical aperture (NA) of 1.49 (for detailed quantum model, see Supplementary Information S3 and figure S2). Each focused photon beam originates from a pixel in the graphics generator, such as DMD, and the sampling area on the focal plane is defined as 3 nm × 3 nm in the simulation. Subsequently, the number of eTPA (N_eTPA) is calculated by integrating the spatial and temporal methods as described above.

The triggerable N_eTPA increases quadratically with the N_spp at wavelengths of 400 nm and 517 nm (Fig. 2B), consistent with the I² relationship. The shorter pulse width of the femtosecond laser enhances N_eTPA (Fig. 2C) by temporally increasing the probability of effective second photon absorption. Our simulations indicate that achieving reliable eTPA a single pulse requires approximately 1000 and 1800 photons (N_spp) at wavelengths of 400 nm and 517 nm, respectively, with a pulse width of 238 fs. When the pulse width narrows to 100 fs, the required N_spp decreases to 400 and 1000, aligning with the temporal distribution of photons in an ultrashort pulse laser. The N_eTPA at wavelengths of 400 nm is nearly seven times greater than at that of 517 nm when using the same pulse width (refer to fig. S3 and Table S2). Reducing the pulse width from 238 fs to 100 fs results in a 2.4-fold increase in N_eTPA. This suggests that shorter pulse widths significantly enhance the probability of triggering eTPA. The efficiency of photon conversion to N_eTPA depends on $\:{\tau\:}_{i}$; longer $\:{\tau\:}_{i}$ values yield higher N_eTPA. This correlation with $\:{\Delta\:}{\stackrel{\sim}{\nu\:}}_{ie}$ (Fig. 1C) implies that incident photon energy closer to E_lowest likely increases N_eTPA due to extended $\:{\tau\:}_{i}$.

The spatial and temporal stochasticity of photons at the focal spot determines the potential distribution of N_eTPA. Under few-photon irradiation, the randomness in the distribution of eTPA decreases as N_spp increases, as illustrated in fig. S4. A lower N_spp results in a higher variance coefficient for the probability of eTPA occurrence (Table S1), attributable to quantum random noise (fig. S4). Nonetheless, while pulse accumulation increases N_eTPA, it does not affect the efficiency of triggerable eTPA (fig. S5). Next, we focus on the spatial distribution of eTPA. Typical examples with an N_spp of 6000 and an irradiated pulse number (N_pluse) of 700 are shown in Figs. 2D and 2E (and fig. S6) for wavelengths of 400 nm and 517 nm, respectively. The statistical densities of N_eTPA (d_eTPA) are presented in Fig. 2F. We calculated the N_eTPA within a circular belt of 4 nm width and divided it by the area of the belt. The d_eTPA sharply decreases from the center of the focal spot, reaching approximately half its value at a radius of 8 nm, independent of wavelength (Figs. 2F-G). This result indicates that the resolution of TPA under few-photon irradiation can significantly can significantly surpass the diffraction limit of the employed wavelength.

To evaluate the effectiveness of our proposal concept and spatiotemporal model, we conducted TPDOPL using a femtosecond pulse laser and a DMD (Fig. 3A, fig. S7). The DMD, with a megapixel-resolution projection layout of arbitrary features, is irradiated by a flat-top beam and focused onto a photoresist film on a cover glass using an oil-immersion objective lens (Nikon, 100×, NA 1.49). We chose a commercially available non-chemically amplified (non-CA) negative photoresist (AR-N 7520) because its degree of polymerization, driven by the stepwise photopolymerization mechanism, is easily controllable and quantifiable for N_eTPA under few-photon irradiation. This resist has an absorption peak at 323 nm and an absorption cut-off wavelength of 353 nm (fig. S8), ensuring that only TPA occurs when using femtosecond pulse lasers at both 400 nm and 517 nm wavelengths. Utilizing this system, a uniform exposure of 80 × 100 µm² can be achieved in a single exposure field, as demonstrated in fig. S9. Note that the number of excitable molecules in the photoresist by TPA should be less than the calculated N_eTPA from the proposed model. The calculated N_eTPA predicts the possible opportunity and distribution of eTPA under photon irradiation from the viewpoint of incident photons, but it ignores the molecular concentration, distribution, and quantum yield of TPA in the photoresist. Furthermore, the conversion efficiency from excited molecules by TPA to the practically initiated coupling reaction between molecules should be considered. The number of reaction sites of the photosensitive molecules is ultimately limited by the final absorbed N_eTPA and their quantum yield to initiate the reaction.

We utilized incident light with an average power of 1 mW after passing through the objective lens as an illustrative example, specifically with parameters N_spp = 1250 (0.48 fJ/pulse pixel) and N_pulse = 1 × 10⁷. The distribution of N_eTPA for a line composed of one pixel demonstrates a notable 24% reduction in full width at half maximum (FWHM) compared to the photon distribution (Fig. 3A). According to photopolymerization theory^33,34, the relationship between the concentration of photosensitive molecules (M) excited by TPA and the photon distribution is nonlinear. As the reaction step is repeated, the molecular weight at the center of the exposure field increases exponentially due to the chemical cross-linking reaction. The concentration distribution of photosensitive molecules involved in the reaction is illustrated in Fig. 3B (Supplementary Information S3 for more details). The exponential increase in molecular weight leads to faster gelation at the exposure field's center, forming insoluble polymer networks more quickly than in the surroundings. Consequently, the superposition and coordination of optical and chemical nonlinearity can effectively reduce the feature size in TPDOPL under few-photon irradiation.

To investigate the effectiveness of the proposed spatiotemporal model for TPDOPL under few-photon irradiation, we fabricated separate lines using our TPDOPL system with a femtosecond laser wavelength (λ) of 517 nm and pulse width of 238 fs. Using a single-pixel DMD layout, a line with an average width of 41 nm and a minimum feature size of 28 nm (Fig. 3C) was achieved under the irradiation of a total incident photon number per pixel of 4.37 × 10¹¹ (0.167 µJ) with accumulation N_pulse of 8.5 × 10⁷ pulses containing N_spp of 5.14 × 10³ (1.97 fJ/pulse pixel). Correspondingly, we calculated the eTPA distribution using the same photon flux as the experimental result in Fig. 3C but only performed 8.5 × 10³ pulses in simulation. The simulation result shown in Fig. 3D indicates that the eTPA distribution is concentrated in a central area of about 30 nm. This validates the effectiveness of our spatiotemporal model for predicting the feature size of TPDOPL under few-photon irradiation.

Photon irradiance density and the accumulated pulse numbers critically influence the line width of TPDOPL. By decreasing N_spp from 1.12×10⁴ (4.30 fJ/pulse pixel) to 6.52 × 10³ (2.51 fJ/pulse pixel), the average line width of the polymer line was reduced from 164 nm to 43 nm under the accumulation of 6 × 10⁷ pulses, achieving a minimum feature size of 26 nm (1/20 λ), as shown in Fig. 3E. The N_eTPA under different N_spp irradiations can be observed in fig. S10. The relationship between the polymer line width and photon irradiance density is depicted in Fig. 3F, indicating that the feature size can be reduced by decreasing the photon irradiance density. However, lower photon irradiance density may increase line roughness due to quantum noise, which can increase edge roughness for extremely fine lines (fig. S11). On the other hand, increasing the accumulation of pulses with a fixed photon flux density leads to a widening of the line width, as shown in Fig. 3G.

Another significant aspect pertains to periodic lines in photolithography, which determine the potential feature density achievable in device applications. Generally, the minimum distinguishable period between adjacent lines is dependent on the wavelength and determined by the equation HP (half pitch) = 0.5 λ/NA, following the Sparrow criterion³⁵. When the design pattern period is less than the minimum resolvable distance between two lines, double patterning lithography (DPL) can overcome this problem³⁶. For instance, at λ = 517 nm and NA = 1.45, this criterion yields an approximate value of 217 nm. We designed a line array using the DMD pixel period of 7.56 µm combined with 2 pixels on and 1 pixel off periodically (fig. S12A), corresponding to a period of 226.8 nm. Using irradiation conditions with N_pulse = 6 × 10⁷ and N_spp = 1.52 × 10⁴ (5.84 fJ/pulse pixel), the lines were indistinguishable (fig. S12C). We efficiently utilized the flexibility of TPDOPL by using a DMD as a digital mask, enabling in-situ digital multiple exposures (iDME) to print dense features without being constrained by the diffraction limit. Exploiting DMD characteristics, two split layouts with a period of 2‘p’ are sequentially loaded in situ for double exposure, achieving an exposure result with a period of ‘p’, as depicted in Fig. 4A. Under twice alternating exposure of N_pulse = 6 × 10⁷ and N_spp = 8.53 × 10³ (3.28 fJ/pulse pixel), we successfully achieved a dense line array with a period of 210 nm (HP ~ 0.3 λ/NA), a linewidth of 150 nm, and a gap spacing of 60 nm, as shown in Fig. 4B, surpassing the diffraction limit.

Taking advantage of TPDOPL-iDME, we can achieve distinguishable dense structure patterning. When the pitch is less than 5 pixels, a single exposure cannot meet the resolution consistent with the design pattern (fig. S13). Figure 4C shows a typical circuit layout selected from a commercial chip, including isolated and dense lines with a width of 3 or 7 pixels and intervals of 1 and 2 pixels between lines (fig. S14). We employ algorithms³⁷ to strategically distribute polygons with interspacing distances below 2 pixels across distinct sub-masks, optimizing their arrangement for TPDOPL-iDME. SEM images show that direct single exposure causes indistinguishable results in dense line areas (Fig. 4D). By splitting this layout into two (Fig. 4E) and performing our TPDOPL-iDME approach, we successfully achieved the expected circuit patterning (Fig. 4F). The dense lines are clearly distinguished, and the periods agree well with the design. Furthermore, by optimizing exposure parameters and layout design for TPDOPL-iDME, line width, period, and gap distance can be controlled for finer and denser feature patterning.

Optical devices with curved and circular microstructures have been fabricated using TPDOPL, such as patterns including arrayed waveguide gratings and micro-ring resonators³⁸. The radius of the ring affects the value of the free spectral range, and the gap or spacing between the guide and the ring affects the coupling ratio between the waveguide and the ring³⁹. Through layout design and the TPDOPL-iDME method, we can fabricate micro-ring filters with varied radius pitches. The widths of the circular rings can be adjusted from 220 nm to 346 nm by increasing N_pulse under the irradiation of N_spp = 8.53×10³ (3.28 fJ/pulse pixel) (fig. S15 A). We patterned the line waveguides first, then fabricated circular rings with different diameters (Fig. 5A), leveraging TPDOPL-iDME. The gap distances between the line and circular rings can be finely adjusted from 66 nm to 480 nm (fig. S15B), optimizing the structures and improving the properties of photonic resonance devices.

The flexibility of TPDOPL-iDME allows us to create arbitrary patterns with various sizes, shapes, and densities, applicable not only in microelectronics and microphotonics but also in microfluidics^40,41. Microfluidics in microbiology offer an in vitro platform for interactions among diverse cell types, enabling real-time observation and assessment of reaction processes⁴². We designed a rectangular module to substitute the cell chamber and a circular module to replace the cell secretion chamber, with channels of varied sizes to facilitate the addition and observation of multiple cell types and their reactions⁴³. Figure 5B shows complex patterns of biological microfluidics fabricated by TPDOPL-iDME, where square cell incubators (3 × 3 µm²), rectangular cell chambers (2.8 × 6 µm²), and circular cell collectors with micrometer and sub-micrometer scales are connected by different channels with widths from 70 nm to 800 nm (Fig. 5B iii), effectively carrying and separating viruses of different sizes. Most biomolecular analytes are below microns in size⁴⁴, especially foreign objects such as viruses⁴⁵, which are usually 20–300 nm in size. Cross-scale biological microfluidics, from micrometer to nanometer, hold promise for providing research platforms for new diagnostic and therapeutic methods for viruses like the new coronavirus.

In this study, we introduced a novel concept, few-photon irradiated TPA (fpTPA), offering a new perspective on understanding the TPA process and its probability distribution under the few-photon irradiation from a tightly focused femtosecond laser pulse. The concept of fpTPA is based on the principles of wave-particle duality and the spatiotemporal uncertainty of photons inherent to such laser pulses. Furthermore, we have developed a spatiotemporal model to accurately describe the definite time-dependent mechanism of TPA. The simulated results using this model clearly indicate that the probability of TPA is strongly dependent on the lifetime of the molecule's virtual state under few-photon irradiation. Notably, the distribution of TPA under few-photon irradiation is significantly narrower compared to the diffraction limit of the tightly focused light spot. The results obtained from the TPA spatiotemporal model and simulations challenge existing understandings of TPA, offering a deeper insight into the TPA mechanism under few-photon irradiation and encouraging the exploration of new potential applications for TPA in such conditions.

As validation, the results of TPDOPL experiments show good agreement with the simulations. Notably, by optimizing N_spp and N_pulse in TPDOPL, we achieved a smaller feature size of 26 nm (1/20 λ) with a laser wavelength of 517 nm, compared to 32 nm (1/12 λ) with a laser wavelength of 400 nm. Furthermore, the structure period of 210 nm (0.41 λ) and a gap distance of 37 nm were significantly decreased by performing iDME. This technique has proven powerful for creating dense structures when we finely control the line width. Additionally, digital projection lithography with a DMD as the digital mask is equivalent to possessing millions of individual laser focus spots, improving the patterning efficiency for multiscale structures by approximately 5 orders of magnitude. Consequently, TPDOPL under few-photon irradiation effectively breaks through the trade-off shackle between resolution and efficiency.

The iDME technique in TPDOPL is suitable not only for nanoprinting but also for nanoimaging. Although TPA microscopy has been widely applied for 3D bioimaging, its resolution has not reached the nanoscale with femtosecond laser scanning. By employing the concept of fpTPA and iDME technique, it is possible to achieve rapid imaging with nanoscale resolution. The thousands of focused spots generated by the discrete multiple focuses with DMD pattern design can simultaneously trigger TPA in thousands of molecules with minimal photon irradiation. The positions of TPA fluorescence at each focus spot can be distinctly imaged. By rapidly changing the designed discrete multiple focuses with DMD, a TPA fluorescence image with nanoscale resolution can be obtained in a short time.

Finally, it is noteworthy that the distribution of TPA induced by few-photon irradiation has been narrowed down to the nanometer scale, independent of the light wavelength. Theoretically, the linewidth fabricated by TPDOPL could be reduced to nearly 10 nm or less by selecting compatible photoresist molecules and optimizing processing parameters. Additionally, the minimal period would be limited only by the pixel size of the DMD with the iDME method. By combining TPA under few-photon irradiation with iDME, it is promising to achieve single-molecule imaging and nanoprinting at the sub-10 nanometer scale.

Experimental system and fabrication method

Using a fiber laser with a fundamental wavelength of 1035 nm, a femtosecond pulse at 517 nm was generated via a frequency-doubling crystal. The pulse repetition rate was 1 MHz, with each pulse lasting 238 fs. Single-color bitmap images of 1920$\:\times\:$1080 pixels were created using Photoshop to meet the loading requirements of the DLP6500 1080p DMD. The images were projected onto the photoresist sample using a Nikon oil-immersion objective with 100× magnification and a NA of 1.49 (see Supplementary S8 for details).

Printed photoresist samples were prepared on clean glass slides (size: 24 mm$\:\times\:$40 mm, thickness: 0.13–0.16 mm). HMDS was applied for adhesion enhancement, followed by spin-coating undiluted AR-N-7520 commercial resist at 7000 r.p.m. for 60 minutes to achieve a uniform thin film. Subsequently, soft-baking was performed on a hotplate at 85°C for 1 minute. After exposure, development was carried out using AR 300 − 47 developer for 1 minute at 22°C.

Computational simulation methods

To better explore the principles of two-photon absorption under few-photon and experimentally verify them, we utilized MATLAB to establish a vector optical field distribution model based on the theory of vector optics. Subsequently, we integrated Monte Carlo random distribution algorithms to statistically distribute photons within a single pulse randomly. The statistical distribution of the reaction quantity of two-photon absorption conforms to the square of the intensity, rendering the optical field distribution particle-like. The virtual state lifetime was obtained through the Heisenberg’s uncertainty principle. The number of photons per pixel within a single pulse was calculated based on the average power behind the objective lens, while the number of pulses was determined according to the exposure time (see Supplementary S1-S3 for details).

Acknowledgments: We thank the staff of the Electron Microscopy LAB of the Institute of Photonics Technology for providing morphology characterization services. We thank the staff of the Institute of New Energy Technology for providing UV-VIS absorbance measurement services. We thank Prof. Yayi Wei and Dr. Lisong Dong from Institute of Microelectronics of Chinese Academy of Sciences for providing the layout data of the M1 metal layer.

Fundings: We acknowledge funding support from the National Key Research and Development Program of China (2016YFA0200500); the Major Talent Program of Guangdong Province (2019CX01Z389); the Science and Technology Planning Project of Guangzhou (202007010002); the National Natural Science Foundation of China (62005097); the Basic and Applied Basic Research Foundation of Guangdong Province (2023A1515010652, 2023A1515011404, 2023A1515012820).

Author contributions: X.-M. D., M.-L. Z., Y.-Y. Z., and X.-Z. D. conceived of and designed the study. Z.-X. L., Y.-Y. Z., and X.-Z. D. set up the TPL systems, developed the control system and performed the TPL experiments. Z.-X. L., Y.-Y. Z., and J.-T. C. performed the simulations. F. J., and Z.-X. L. evaluated the photopolymer resists. Z.-X. L., and Y.-Y. Z. performed SEM imaging of nanopatterns. X.-M. D., Y.-Y. Z., M.-L. Z., Z.-X. L. and X.-Z. D. analyzed the results. X.-M. D., Z.-X. L., Y.-Y. Z. and M.-L. Z. prepared the manuscript with input from all coauthors, and all coauthors edited the manuscript.

Competing interests: A US patent application related to this work has been filed with X.-Z. D., M.-L. Z., and X.-M. D. as co-inventors. All authors declare that they have no other competing interests.

Data and materials availability: All data are available in the manuscript or the supplementary materials.

License information: Copyright © 2022 the authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original US government works. https://www.science.org/about/science-licenses-journal-article-reuse

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Two-photon absorption under few-photon irradiation for optical nanoprinting

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Few-photon irradiated two-photon absorption

Two-Photon Optical Projection Nanolithography

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