Microlenses and microlens arrays have applications in various fields, which is primarily due to their miniaturization and easy integration. The numerical aperture (NA) is an essential parameter that significantly affects imaging quality. In the field of micro-imaging, one approach to achieve higher imaging quality is manufacturing multiple lenses with different focal lengths within a single plane. Therefore, the efficient fabrication of microlenses and microlens arrays with controllable heights is crucial for enhancing the imaging effect.

In 2010, Chen et al. put forward a maskless method for rapidly fabricating microlens arrays on quartz surfaces using femtosecond laser single-spot exposure combined with wet etching. This technique allows for flexible control of size and arrangement by adjusting parameters such as laser pulse energy, etching time, and displacement platform. However, one limitation of this method is that it cannot achieve deep structure due to laser energy loss caused by surface damage. As a result, the aspect ratio of the laser-modified area is small, making it challenging to fabricate microlenses with high NA.

To solve this problem, the regular front-side processing method has been improved through multiple exposures in the Z-axis direction, which increases the numerical apertures, but it cannot reach its theoretical maximum. Furthermore, researchers have conducted extensive studies on optical field modulation which have successfully produced quartz microlenses with high numerical apertures that approach the theoretical limit of 0.46. However, it should be noted that these methods rely on precise optical devices and involve complex processes.

Microlenses and their arrays are prepared by hydrofluoric acid wet-etching assisted femtosecond laser processing method, and the preparation process is divided into two steps, first using femtosecond laser to modify the material on the bottom surface, and then using 20% hydrofluoric acid for wet etching under 25 ℃.

In the preparation of high aspect ratio modified regions of quartz substrates, we propose a self-modulating laser processing method based on aberrations. In this method, the femtosecond laser is focused on the lower surface of the quartz substrate, so that the closely focused laser propagates through the interface of two different materials, and the longitudinal spherical aberration caused by the mismatch of the refractive index increases the longitudinal size of the laser focusing spot. This spherical aberration phenomenon becomes more and more obvious with the increase of the numerical aperture of the objective lens and the depth of focus, which enables the longitudinal stretching of the laser focus, resulting in the processing of modified areas with high aspect ratios on the quartz substrate.

Microlenses and microlens arrays have been prepared by laser with a pulse width of about 300 fs and a wavelength of 1030 nm combined with a three-dimensional air flotation platform. Firstly, the influence of pulse energy on the morphology and numerical aperture of microlenses has been explored by the control variable method. On this basis, the defocus position has been regulated, which effectively increases the numerical aperture of the microlens, and a high numerical aperture quartz microlens that reached the theoretical limit has been successfully prepared.

First, the same parameters are used to compare the process of microlens formation during wet etching in regular front-side processing and self-modulating processing, which proves the advantages of self-modulating processing in the modified region with a high aspect ratio (Fig. 3).

Next, the morphological characteristics of microlenses processed under different laser single pulse energies using the self-modulating method are explored. With the increase of laser single pulse energy, the change of the radius of curvature is 1.46 μm, the change range of NA is 0.19-0.41, and the NA reaches 0.41 (Fig. 4) when the single pulse energy is 309 nJ. On this basis, the defocus position is changed, and the lens parameters processed by regular front-side processing and self-modulating method are compared. The depth and width of the microlenses prepared by the two processing methods increase approximately linearly with the increase of the defocus position, and the width of the microlenses processed by the self-modulating method is slightly larger than that of the microlenses prepared by the front-side processing method, and its depth is close to twice that of the front-side processed microlenses. The maximum value of the lens prepared by the front-side method is only 0.33, while the theoretical limit value of the lens (0.46) is reached by the self-modulating method at the defocus position of 11 μm (Fig. 5).

Finally, a large-area microlens array with NA=0.44 has been prepared on the back of the quartz substrate by laser self-modulating method. The microlenses are neatly arranged, uniformly sized, with rounded edges and good surface quality (Fig. 6). Furthermore, by changing the defocus position, a microlens array composed of 9 microlenses with different NA has been prepared, and the NA range is 0.28-0.45 (Fig. 7). These two structures prove the feasibility of laser self-modulating method in processing large-area microlens arrays with tunable NA.

We propose a novel method for fabricating microlens arrays on the back side of quartz by an aberration-based self-modulating laser processing technique, and this method allows for producing microlenses with adjustable numerical apertures to achieve the theoretical maximum value (NA_max=0.46). The essential advantage of this approach is its simplicity compared with other methods, as it does not require additional optical modulation devices. Experimental results demonstrate the successful fabrication of microlenses using this method. Furthermore, our study investigates the effects of pulse energy and defocus position on the shape and numerical aperture of the microlenses. By adjusting these parameters, the problem of a small aspect ratio in the modified region during regular front-side processing is effectively resolved.

Future research can focus on optimizing the processing parameters to enhance the uniformity and stability of the fabricated microlens arrays. Additionally, exploring the feasibility of fabricating microlens arrays through different materials and shapes would be a helpful direction for further investigation. Overall, we present an effective method for fabricating microlens arrays with various shapes. This technique has great potential for applications in zoom-free imaging systems, 3D imaging, and beam shaping.