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Fig. 1a shows a schematic of the SLM-based femtosecond laser two-photon lithography system. The laser source was a custom designed femtosecond amplification system that generated 90 fs transform-limited pulses with a repetition rate of 1 MHz. The second harmonic wave generated by the β-barium borate (BBO) crystal (centered at 525 nm) was expanded to a width of ~8 mm to illuminate the SLM (Holoeye PLUTO, 1920 × 1080 pixels), which matched the active area size of the screen. The spatial intensity distribution characteristics of the LDoF beams were determined using a dynamic phase mask loaded onto the SLM, as shown in Fig. 1b. The phase mask is a superposition of two parts: the phases of the LDoF beams and the blazed grating (BG). The BG is employed to diffract the reproduced image to the -1st order such that the zeroth-order diffracted light caused by the defect of the SLM pixelated structure can be filtered with an iris. A lens (L, f = 1m) and a microscope objective (MO, Olympus 20×, NA = 0.4) comprise the 4-f system, which scales and relays the modulated beam into the photoresist (MicroChem, SU-8 2002). A neutral-density (ND) filter controls the pulse energy used for exposure. As shown in Fig. 1c, the LDoF beam was reconstructed at the back focal plane of the MO; this initiates polymerization within the blue dashed box. By modulating the phase mask, we ensured that the LDoF beams penetrated the full thickness of the photoresist layer. The combination of the exposure of the LDoF beams with the movement of the high-precision X-Y displacement stage enables the parallel precise direct writing of complex microstructures.
Fig. 1 a Schematic of the spatial light modulator (SLM)-based two-photon polymerization (2PP) system. HWP, half-wave plate; BE, beam expander; M1 and M2, mirrors; SLM, spatial light modulator; ND, neutral density filter; L, lens; MO, microscope objective. b Illustration of the phase mask loaded on the SLM, comprising the phase of LDoF beams and a blazed grating. c Partial enlargement of the focal region, showing the relative position of the LDoF beams and the photoresist. The blue dashed box indicates the region where two-photon absorption occurs. d Scanning electron microscopy (SEM) image of the crisscross structure. Scale bar = 10 μm.
Before manufacturing the binary optical elements, we fabricated a series of crisscross structures using the SU-8 2002. Fig. 1d shows a scanning electron microscopy (SEM) image of the microstructure after development. Under a scan speed of 170 μm/s and a single pulse energy of 1.5 nJ, the line width is measured to be approximately 1.7 μm, which provides a quantitative indicator for the feature size of LDoF beams direct writing.
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Owing to the flexibility of the adaptive phase modulation of the SLM, the focusing characteristics of LDoF beams can be modified easily. By loading the axilens hologram onto the SLM, laser beams with different radii can be focused at different positions and a long focal depth can be generated. The phase distribution with a wavelength λ can be written as31
$$ \varphi (r) = \frac{{\pi {r^2}}}{{\lambda \left({f_0} + \dfrac{{\Delta z}}{{{R^2}}}{r^2}\right)}} $$ (1) where r is the radial coordinate, f0 is the focal distance, Δz is the focal length, and R is the radius of the diffraction plane. Here, aiming at improving the manufacturing throughput while maintaining the desired spatial resolution and feature definition, we select the hologram parameters as f0 = 2 m and Δz = 0.5 m. Scaled down by the 4-f system, the resulting numerical and experimental results of the intensity profile of LDoF beams are shown in Fig. 2, exhibiting high consistency. Fig. 2a, b show the longitudinal intensity distribution along the z axis; the interval between the two orange dashed lines indicates where the intensity exceeds the polymerization threshold. In this longitudinal range, near-uniform polymerization was initiated. However, we simulated the longitudinal intensity distribution of Gaussian beams focused by a low-NA objective (NA = 0.25), as shown in the inset of Fig. 2a. A comparison of the white solid and dashed lines in Fig. 2a indicate that the corresponding range of the Gaussian beams is notably shortened compared to the LDoF beams, resulting in a more rigorous requirement for the flatness and precise positioning of the sample. Notably, the radial dimension of the Gaussian beams is similar to that of the LDoF beams, whose full width at half maximum (FWHM) is 1.085 μm; the FWHM of LDoF beams is approximately 1.235 μm, ensuring a sufficiently fine feature size. Fig. 2c, d show the radial intensity distribution at the focal plane.
Fig. 2 Numerical and experimental intensity distribution of the LDoF beams. a, b Longitudinal intensity distribution of LDoF beams along the z-axis. The inset in a is the simulated longitudinal intensity distribution of the Gaussian beam focused by a microscope objective (NA = 0.25). The white solid and dashed lines represent the normalized intensity curves of LDoF and Gaussian beams at the center of the spots, respectively. c, d Radial intensity distribution at z = 190 μm.
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Conventional axicons are refractive optical elements that convert an incident beam into a Bessel beam (Fig. 3a-1). They have rotational symmetry about the z-axis; their refractive properties are characterized by the base angle, α, and refractive index, n. Regarding the incident light as a class of rays parallel to the z-axis, they refract at the conical surface and cross the z-axis at the same angle θa. Considering Snell’s law and small angle approximation, θa is calculated to be
Fig. 3 Design of the binary diffractive axicon. a Illustration of the generation of quasi-Bessel beams by a-1 an axicon and a-2 a BOE. b Schematic of the transformation from a refractive axicon to a binary diffractive axicon.
$$ {\theta _a} = (n - 1)\alpha $$ (2) The non-diffracting propagation distance of the generated Bessel beam is related to the dimensions of the incident beam, which is expressed as
$$ {z_{\max }} = \frac{\rho }{{\tan {\theta _a}}} $$ (3) where ρ is the radius of the incident beam. Meanwhile, scalar diffraction theory views optical elements as infinitely thin surfaces; therefore, the transmission function of the axicons is calculated as
$$ T(R) = \exp \left[ {i{\varphi _m}\left( {1 - \frac{R}{{{r_a}}}} \right)} \right] $$ (4) where R is the radial coordinate and ra is the radius of the axicon aperture. φm represents the maximum phase shift that can be introduced:
$$ {\varphi _m} = (n - 1){r_a}\tan \alpha \cdot k $$ (5) where $k = 2\pi /\lambda $is the wave vector and λ is the wavelength. In response to the demand for miniaturization of optical systems, the principle of using a binary diffractive axicon to approximate a refractive axicon is shown in Fig. 3b. To significantly decrease the thickness, the optical path delay introduced by the refractive axicon was compressed to 0–λ. The resulting diffractive lens, also known as a kinoform lens, correspondingly introduces a phase shift varying continuously between 0 and 2π to the incident light. The transmission function is denoted by
$$ {T_{DOE}}(R) = \exp \left\{ {i \cdot \text{mod} \left[ {{\varphi _m}\left( {1 - \frac{R}{{{r_a}}}} \right),2\pi } \right]} \right\} $$ (6) For a kinoform lens, the maximum phase shift difference introduced by the material is 2π or integer multiples of it. At the pre-designed wavelength λ0, the thickness of the kinoform lens is defined by
$$ h = N \cdot \frac{{{\lambda _0}}}{{n - 1}} $$ (7) where N is a positive integer and n represents the refractive index of the photoresist.
However, the fabrication of continuous surface profiles remains challenging. To date, the manufacturing of kinoform lenses relies heavily on approximation32. Hence, it is necessary to use stepped phase profiles to approximate continuous relief structures, that is, BOEs proposed by Veldkamp et al.33. Assuming one phase step, the binarized phase profile of the diffractive axicon is shown in Fig. 3b, composed of a central disk and several concentric rings of the same height, h/2. Fig. 3a-2 shows a schematic of quasi-Bessel beams modulated by the BOE. The kth-order diffraction angle formed by the diffractive axicon can be expressed as34
$$ \sin {\theta _k} = k\frac{\lambda }{{2\Lambda }} $$ (8) where k = 1, 2, 3, … is the diffraction order and Λ is the pitch of concentric rings. Substituting θa in Eq. 2 with θk, the position where the kth-order diffracted beams intersect with the z-axis can be obtained as follows
$$ {z_k} = \frac{\rho }{{\tan {\theta _k}}} \approx \frac{{2\Lambda \rho }}{{k\lambda }} $$ (9) After the phase distribution of the axicons is binarized, the output consists of a superposition of several quasi-Bessel beams of different orders35. Higher orders correspond to smaller main-lobe sizes and shorter propagation distances. Therefore, interference among higher-order beams is inevitable, and has been demonstrated to cause intensity oscillations along the optical axis36. In regions where multiple beams coexist, tiny but intense spots or donut-shaped patterns appear owing to constructive or destructive interference between two Bessel-function electromagnetic fields, respectively.
High throughput direct writing of a mesoscale binary optical element by femtosecond long focal depth beams
- Light: Advanced Manufacturing 4, Article number: (2023)
- Received: 19 June 2023
- Revised: 27 November 2023
- Accepted: 29 November 2023 Published online: 17 December 2023
doi: https://doi.org/10.37188/lam.2023.042
Abstract: Bessel beams have multiple applications owing to their propagation-invariant properties, including particle trapping, optical coherence tomography, and material processing. However, traditional Bessel-beam shaping techniques require bulky components, which limits the development of miniaturized optical systems for integration with other devices. Here, we report a novel femtosecond laser direct writing strategy for fabricating mesoscale (from submicrometer to subcentimeter) binary optical elements with microscale resolution. This strategy utilizes femtosecond beams with a long focal depth to increase throughput while reducing the constraints on critical sample positioning. As a demonstration, we manufactured and characterized a 2.2 mm diameter binary axicon. The experimentally measured quasi-Bessel beam intensity distribution and the numerical results were remarkably consistent, demonstrating a suitable tradeoff between the overall size, efficiency, and structural fidelity. Furthermore, a compact Bessel lens containing binary axicons was constructed and successfully used for femtosecond laser mask-less ablation of periodic grating-type surface plasmon polariton excitation units. The demonstrated approach shows significant potential for fabricating customizable integrated optical components.
Research Summary
High-throughput direct writing of a mesoscale binary optical element
Traditional Bessel-beam shaping techniques require bulky components, which limits the development of miniaturized optical systems for integration with other devices. Femtosecond laser direct writing is a mask-less lithography technology with high precision, but is limited by the tradeoff between overall size, throughput, and resolution. Professor Ming-lie Hu's team from Tianjin University proposed a femtosecond laser direct writing strategy based on beams with long depth of focus, which allows fabricating mesoscale high-quality binary diffractive axicons with only single-layer scanning. The team demonstrated that the three-dimensional morphology and optical properties of the prepared binary axicon were highly consistent with their design, and this technique was expected to significantly improve the manufacturing efficiency of various types of functional diffractive optical elements without sacrificing the precision.
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