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Abstract
We developed a novel method for fabricating microlenses and microlens arrays by controlling numerical aperture (NA) through temporally shaped femtosecond laser on fused silica. The modification area was controlled through the pulse delay of temporally shaped femtosecond laser. The final radius and sag height were obtained through subsequent hydrofluoric acid etching. Electron density was controlled by the temporally shaped femtosecond laser, and the maximum NA value (0.65) of a microlens was obtained in the relevant studies with femtosecond laser fabrication. Furthermore, the NA can be continuously adjusted from 0.1 to 0.65 by this method. Compared with the traditional methods, this method exhibited high flexibility and yielded microlenses with various NAs and microlens arrays to meet the different demands for microlens applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microlenses (MLs) and microlens arrays (MLAs) are irreplaceable in micro-optical systems because of their light weight, small size, high integration, and excellent optical performance. MLs and MLAs are widely used in artificial compound eyes [1–3], optofluidic microchips [4,5], automotive light-emitting diode (LED) lighting [6], and light extraction enhancement of organic LEDs [7,8]. Depending on the application, requirements for the numerical aperture (NA) of MLs vary. For instance, a high NA can improve imaging resolution, whereas a low NA can achieve a larger view field. In the past, many methods, such as ultra-precision machining [9] of multi-axis machine tools, LIGA [10], ink-jet printing [11], nanoprinting [12], self-assembly [13], and the reflow technique [14,15], have been proposed for ML fabrication. These methods each have unique limitations. Ultra-precision machining exhibits low processing efficiency and is difficult to use to process glass. LIGA requires expensive masks, and the other methods can only be used to fabricate soft materials such as polymers.
Femtosecond (fs) lasers exhibit unique advantages, such as high accuracy fabricating and micro/nano structural fabricating [16–18]. Almost any material can be fabricated using a femtosecond laser. In the past few years, fs laser direct writing has become crucial for the fabrication of high-precision MLs. Fs-laser-induced two-photon polymerization can be used to fabricate three-dimensional (3D) microstructures by employing polymers with nanometer- scale precision [19,20]. This method can be used to fabricate highly accurate MLs, but it can only be used to fabricate polymers and is time consuming. Recently, with the improvement in processing efficiency and the requirements of high fill factor MLs, fs laser- assisted etching has become a popular method for ML fabrication. Fs laser-assisted dry etching can be used to process MLs out of hard and brittle materials, such as silica glass and sapphire [21,22]. An MLA with a large area and low surface roughness and without gap can be fabricated through fs laser-assisted dry etching, but this fabrication method is expensive. Fs laser-assisted chemical etching used to fabricate MLs was cost-effective and realized large-area, low-cost, high-efficiency, gapless 3D ML fabrication [23,24]; however, fabricating MLs with a continuously changing NA is difficult. Spatially shaped fs laser-assisted chemical etching can be employed to control the ML NA; however, achieving high-NA ML fabrication is difficult. Fabricating low-cost, high-efficiency, gapless, continuously variable NA MLAs remains a challenge.
Herein, we propose a novel method for such fabrication, which entails using temporally shaped fs laser-assisted chemical etching for ML fabrication. This method can be used to fabricate MLs with a continuously variable NA, which can reach up to 0.65. The temporally shaped fs laser exhibits two sub pulses to control electron distribution. The depth and radius of a modified area can be adjusted flexibly by controlling the energy and pulse delay. Here, the “modified area” means the change of structure of Si-O bonds, which makes the modified area easier to be removed by HF than the unmodified area. Hydrofluoric (HF) etching was used for changing the surface topography and to achieve high-quality ML processing. The proposed large-area, low-cost, high-efficiency method is simple and can be used for the fabrication of MLs with a variable NA from 0.1 to 0.65 on fused silica.
2. Experimental setup
2.1 ML fabrication
Figure 1(a) illustrates the experimental setup for temporally shaped fs laser fabrication. In this study, the fs laser Gaussian beam used was generated from a regenerative amplified Ti:sapphire fs laser system (Spitfire Ace-35F, Spectra-Physics, USA) with a pulse width, wavelength, and maximum repetition of 35 fs, 800 nm, and 1000 Hz, respectively. An attenuator was used to control the laser energy, and a mechanical shutter was used to control the pulse number delivered to the sample. A Mach–Zehnder interferometer with two ultrafast mirrors and a beam splitter (energy ratio 1:1) was used to realize the temporally shaped laser beam [25], where a Gaussian beam was split into two and two sub pulses were combined into a time-delayed pulse train. The pulse delay adjustment of double-pulse was achieved with a mirror translation of a Michelson interferometer, which was fixed on a one-dimensional high-precision translation stage. The temporally shaped beam was reflected through a mirror and focused on the sample surface by using a 20× microscope objective (NA = 0.45), and each point was irradiated with a pulse for sample modification. A six-dimensional translation stage (M-840.5DG, PI, Inc.) was employed to control the sample movement with movement accuracy of 1 µm for X and Y and 0.5 µm for Z, and a charge-coupled device was used to monitor fabrication in real time. Double-sided polished fused silica (10 mm × 10 mm × 1 mm), purchased from Hefei Kejing Materials Technology Co., Ltd., was used to fabricate MLs.
Fig. 1. (a) Schematic of temporally shaped fs laser fabrication (A: attenuator, S: shutter, BS: beam splitter, M: mirror, DM: dichroic mirror, MO: microscope objective, WS: white-light source). (b) Schematic of wet etching, and morphology changes obtained before and after HF etching.
Before laser fabrication, the samples were cleaned using an ultrasonic bath for 10 min. The different industrial HF based etchants provide different selectivity for silica [26,27]. In this paper, after laser irradiation, the samples were etched with 10% HF solution through ultrasonic assistance [Fig. 1(b)]. After etching, we ultrasonically cleaned the samples with alcohol and water for 10 min to ensure the complete removal of HF residue and a clean sample surface.
2.2 ML characteristics
The surface morphology and size of MLs were characterized using an optical microscope (OTM; BX 51, Olympus Inc.) and a scanning electron microscope (SEM; EM-30N, COXEM Inc). The 3D contour and depth dimension were characterized using a confocal laser scanning microscope (CLSM; OLS4100, Olympus Inc.).
3 Results and discussion
3.1 Unshaped fs laser fabricated ML results
An unshaped fs laser is often applied to fabricate MLs with single-pulse or multiple-pulse modification-assisted chemical etching. Figure 2 illustrates that single-pulse modification- assisted chemical etching was used to fabricate MLs with different morphologies by changing the pulse energy. By changing the energy from 1.4 to 3 µJ, we achieved different modification areas [Fig. 2(a)], and then the modified sample was etched using 10% HF solution for 2 h. The ML depth and radius were measured using the CLSM and OTM, respectively. We performed a statistical analysis on the radius and depth [Fig. 2(b)]. The ML radius and depth increased with an increase in the energy. The radius of curvature (R) and focal length ($|f |$) of the ML were calculated theoretically. Furthermore, the ML NA was calculated with the following formulas:
where h is the sag height of the ML, r is the ML radius, n0 is the refractive index of the air (n0 = 1), n is the refractive index of the material (fused silica n = 1.46), and θ is the half central angle of the concave (Fig. 3). Per the formulas, the NA reached the maximum value when the depth was equal to the radius for the same material (n = constant). Figure 2(c) presents the ML parameter curve as a function of energy. With an increase in energy, the ML focal length changed slightly and the NA increased gradually from 0.1 to 0.2.Fig. 2. (a) The first row presents the change in laser fabrication morphology with increasing energy from 1.4 to 3 µJ before etching, and the second row presents the change in ML morphology of the first row after 10% HF etching for 2 h. (b) Changes in ML radius and sag height obtained by increasing the energy. (c) Focal length (f), radius of curvature (R), and NA changes in the ML obtained by increasing the energy.
Many methods to control the ML NA are available. Figure 4 displays how the modification height can be controlled using the pulse number. The MLs were fabricated with an energy of 218 µW (NA = 0.45) and were etched for 5 h with 20% HF. When the pulse number reached 100, modification basically reached saturation [Fig. 4(a)], and the NA can only be controlled on a small scale [Fig. 4(b)]. The etching time can vary the NA. A single pulse was used to fabricate MLs with an energy of 110 µW (NA = 0.15), and they were etched with 20% HF. When the etching time was long, all modified areas were etched. When only the unmodified area was etched, the depth did not change and the diameter gradually increased [Fig. 5(a)]. Because the surface of the sample is etched at the same rate as the bottom of the ML. Figure 5(b) indicates that although the etching time can change NA, it is difficult to process multiple NA ML on one sample.
Fig. 4. (a) Changes in the ML radius and sag height obtained with an increase in the pulse number. (b) Focal length, radius of curvature, and NA changes in the ML obtained with an increase in the pulse number.
Fig. 5. (a) Changes in the ML radius and sag height obtained with an increase in the etching time. (b) Focal length, the radius of curvature, and NA changes in the ML obtained with an increase in the etching time.
Thus, the difficulty of fabricating MLs with a high NA by using these traditional methods were demonstrated.
3.2 Results of temporally shaped fs laser fabricated ML
We developed a novel method to fabricate MLs with a high NA and vary the NA continuously. By changing the pulse delay between double subpulses, we can continuously vary ML morphology. Therefore, MLs with a continuously changing NA (up to 0.65), which is slightly less than the theoretical maximum NA (0.66) of fused silica MLs, can be fabricated using our method. First, the modified point of fused silica was fabricated by changing the pulse delay from 0 to 500 fs with a subpulse energy of 1.5 µJ (energy ratio = 1:1) [the first row of Fig. 6(a)]. The change in surface topography is not clearly before etching, because of modification rather than ablation. Morphological differences caused by different pulse delays can be observed after etching 2 h (10% HF) [the second row of Fig. 6(a)]. Figure 6(b) presents the sag height profile, which indicates that the MLs exhibited a smooth depth profile. Figure 6(c) illustrates the SEM images of the morphology of the MLs fabricated with pulse delays of 250, 300, 350, and 400 fs. The MLs fabricated through double-pulse fs-laser-assisted HF etching exhibited high quality [Fig. 6(c)], and the radius of MLs remained almost constant with these various pulse delays.
Fig. 6. (a) The first row presents the laser fabrication morphology obtained with the pulse delay from 0 to 500 fs (energy ratio = 1.5:1.5 µJ) before etching, and the second row presents the ML morphology of the first row after etching 2 h (10%HF). (b) Profile of the MLs corresponding to the second row of (a). etching with 10% HF. (b) Sag height profile for the second row of (a). (c) SEM images of the morphology of the MLs fabricated with the pulse delays of 250, 300, 350, and 400 fs. Two dotted boxes represent different characterizations of the same results.
Our proposed method for controlling ML morphology can be used to control the ML radius and depth effectively. We performed statistical analysis on the ML radius and depth [Fig. 7(a)]. When the pulse delay changed from 0 to 150 fs, the ML radius and depth increased simultaneously. When the pulse delay changed from 150 to 450 fs, the ML radius remained almost unchanged but the ML depth gradually increased. Subsequently, the depth decreased with the continued increase in the pulse delay. When the pulse delay was 450 fs, the depth reached the maximum, which was close to the radius. The formula indicated that the NA reaches the maximum when the radius and the depth are the same. The inset of Fig. 7(a) presents a pseudo-color image and 3D image of the ML obtained from the CLSM at the pulse delay of 450 fs. The three MLs exhibited the same profile and size under the same fabrication conditions, which demonstrated fabrication consistency. The radius of curvature, focal length, and NA of the ML can be calculated using formulae (1), (2), and (3), respectively. With an increase in the pulse delay from 0 to 450 fs, NA can be continuously varied from 0.25 to 0.65 [Fig. 7(b)]. When the pulse delay was 450 fs, the maximum NA of 0.65 was attained. Combined with the traditional methods fabrication results, NA can be continuously controlled from 0.1 to 0.65. The radius, height, and NA of the ML fabricated using our method were compared with those of MLs fabricated by changing the energy, pulse number, and number of shaped shots, as described in other relevant studies (Table 1). Our method further improved the capability of ML fabrication. An ML with a customized NA can be realized using our new method, and an ML with a high NA can be fabricated, which can satisfy the demands of various applications for MLs.
Fig. 7. (a) Changes in the ML radius and sag height obtained with an increase in the pulse delay of the temporally shaped fs laser; the inset presents a pseudo-color image and 3D image of an ML acquired from the CLSM at the pulse delay of 450 fs. Scale bar is 20 µm. (b) Focal length, radius of curvature, and NA changes in the ML obtained with an increase in the pulse delay of the temporally shaped fs laser.
Table 1. NA for the ML fabricated using our method and corresponding ML reported in other relevant papers.
3.3 Explanation of temporally shaped fs laser controlled ML morphology
The fs laser can be used to modify the structure of fused silica [Fig. 8(e)]. When the fs laser interacts with fused silica, the most and most-stable six-membered ring structure with Si–O bonds in the fused silica was transformed into a three-membered or four-membered ring structure; the angle of the Si–O–Si bond was reduced compared with the average angle of Si–O–Si in unirradiated fused silica. The decrease in the bond angle caused the deformation of the structure of valence electrons outside O, and the deformed valence electrons led to an increase in the reactive activation of O. When sample participated in the reaction, the three- membered and four-membered ring structures were more easily destroyed by HF [27,36]. The ponderomotive action of laser and resonant absorption also have been reported to explain the modification mechanism of silicon dioxide caused by laser irradiation [37]. In this study, the change of electron density is used to explain the modification mechanism. In the case of the same energy density, pulse irradiation caused a sharp increase in the electron density on the sample surface layer, and forms a plasma on the surface, resulting in a large amount of reflection of the photon energy in a pulse tail [38]. The reflectivity of the pulse center part even exceeds 0.8, which prevented the deposition of the photon energy along the depth [39]. Double pulses can be used to vary the reflection of the photon energy. The first pulse excited the electron [Fig. 8(a)]. When the pulse delay was short, the surface electron excited using the first pulse reflected the photon of the second pulse [Fig. 8(b)]. The decay time of the electron density is around one hundred femtoseconds due to the nature of the fused silica itself. Therefore, the modification of fused silica by double pulses with a delay within one hundred femtoseconds is basically the same as that by single pulse. With the increase in the pulse delay, the electron density of the surface became relatively lower and lasted for a long time, which led to a decrease in the reflectivity of the skin layer. The amount of photon energy deposited on the irradiated sample increased. When the pulse delay was suitable, all the electrons excited through the second pulse were absorbed [Fig. 8(c)]. Moreover, MLs with the maximum NA were fabricated. When the pulse delay was long, the second pulse was used to re-excite the electrons after those excited through the first pulse healing [Fig. 8(d)] [40–42].
Fig. 8. Fabrication by changing the pulse delay. (a) Electron excitation for the first pulse. (b)– (d) Electron excitation for the second pulse with an increase in the pulse delay. (e) Changes in the internal structure of fused silica after laser modification.
Temporally shaped fs lasers can be used to obtain larger diameter and depth of modified size [23]. Etching determined the final morphology. The etching efficiency of modified and unmodified regions is different. The modification depth of double pulse was different from that of single pulse [Fig. 1(b)]. After the HF etching process, two pits with different depths were obtained. By increasing the etching time, two different concave spheres were fitted through etching. Therefore, changing the pulse delay can vary the morphology of MLs; consequently, the NA is adjusted.
3.4 MLA fabrication
In our proposed ML fabrication method, each ML required only one pulse triggered using the laser system, which was temporally shaped into two sub pulses. Combined with the flying punch method, we achieved high-efficiency fabrication. In addition, we realized MLA fabrication with a large area; and different shapes MLs were fabricated. MLs were processed to obtain a square and hexagonal array structure by changing the ML arrangement (Fig. 9). Two MLAs were fabricated with a pulse delay of 450 fs and sub pulse energy of 1.5 µJ (energy ratio = 1:1). After 2 h etching treatment with 10% HF, the morphology of MLAs was characterized using the SEM. Figure 9(a) presents the fabrication result of a square MLA, and Fig. 9(c) presents an enlarged view of a part of Fig. 9(a). Figure 9(b) presents the fabrication result for a hexagonal MLA, and Fig. 9(d) presents an enlarged view of a part of Fig. 9(b). We achieved high-quality and high-efficiency MLA fabrication with different shapes and different NA values.
Fig. 9. SEM images of the morphology of an MLA. (a) Morphology of a square MLA. (b) Morphology of a hexagon MLA. (c) Enlarged view of a part of (a), and (d) enlarged view of part (b). Dotted boxes of the same color represent local magnification.
4 Conclusions
In conclusion, we proposed a novel method for controlling ML morphology through temporally shaped femtosecond laser. This method can be used to continuously adjust the ML NA from 0.1 to 0.65 through controlling the pulse delay. When the pulse delay was 450 fs, the maximum NA of 0.65 was attained. This method exhibits high flexibility and can be used to achieve large-area fabrication with high quality and efficiency. In this manner, fused silica modification depends on electron density, which can be controlled by the temporally shaped femtosecond laser. Therefore, we can obtain MLs with different NA values through temporally shaped femtosecond laser to meet the demands of various applications for MLs.
Funding
National Key Research and Development Program of China (2018YFB1107200); National Natural Science Foundation of China (51675049); Beijing Municipal Natural Science Foundation (JQ20015).
Disclosures
The authors declare no conflicts of interest.
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