We report on the fabrication of binary Fresnel lenses by femtosecond laser surface ablation of poly(methyl methacrylate) (PMMA) substrates. Tight focusing of the laser pulses produced a minimum ablated feature size of 600 nm, enabling the creation of lenses with numerical apertures as high as 0.5 and focal lengths ranging from 500 µm to 5 mm. A precise control of the ablation depth allowed the achievement of a 30% focusing efficiency, close to the maximum theoretical value for this kind of lenses.
©2011 Optical Society of America
The use of optics in fields like telecommunications, data storage, sensing technology and medicine is pushing the demand for the continued miniaturization of optical elements such as microlenses, microprisms, and filters while maintaining a high optical quality. Normally these elements must be integrated into systems already containing other optical, electrical and microfluidic elements, requiring the fabrication process to be flexible, minimally invasive and capable of accurate alignment of components. This integration is expected to provide devices with improved mechanical stability and higher operation density.
An important example of an integrated optical element is the Fresnel lens , which is compact and capable of giving high numerical apertures (NAs) and short focal lengths with high focusing efficiencies. In practice, a quantized Fresnel lens is used as an approximation of the perfect diffractive lens, and its efficiency ranges from 10% to almost 100% depending on the number of quantization levels . In particular, binary Fresnel lenses (BFLs) provide the best compromise for most applications requiring an integrated lens; in fact, they are simple to fabricate with the creation of only two layers, while capable of focusing efficiencies that can approach the theoretical limit of 40% [3,4].
Polymeric materials offer important advantages in terms of versatility and cost-effectiveness for the fabrication of microsystems such as microfluidic chips and optical MEMS . In particular, poly(methyl methacrylate) (PMMA) is one of the most widely used polymers for applications involving optical components. PMMA has high transmission in the visible and near-infrared regions and is often used for plastic optical fibers and planar waveguide devices. The most widely used technologies for production of polymeric devices at low cost and high volume are injection molding and hot embossing. However, rapid prototyping techniques are extremely useful during the development of a new device or for small-series production. Commonly employed techniques for prototyping are micromilling , UV polymerization through photomasks , and CO2  or nano- to picosecond  laser micromachining.
In recent years, microfabrication by focused femtosecond laser pulses in transparent materials has received much attention . Compared to longer pulse sources, ultrashort laser pulses offer advantages in terms of rapid energy deposition, fast material removal with a minimal heat affected zone and a lower ablation threshold [9,11–14]. Ultrashort laser pulses have sufficiently high peak intensity to drive nonlinear multiphoton absorption when focused on the surface of polymers, enabling laser processing at wavelengths at which the material is transparent. This is in contrast to longer pulse sources (>10 ps), for which the energy is deposited via linear absorption, thus restricting the laser processing wavelength to the UV range. The absence of a wavelength dependence in the ablation mechanism with ultrashort laser pulses means that any material can be machined with the same laser independently of its bandgap. Moreover, the high potential of femtosecond laser processing relies on the fact that their pulse duration is shorter than the heat diffusion time, and ablated features do not show heat affected zones nor burr formation, as with longer pulse sources. In the regime of low laser fluences, high precision processing is thus possible with negligible mechanical damage around the processed area. Femtosecond laser micromachining of polymers, both in the bulk or on the surface, has been applied to the fabrication of optical memories , microchannels [16,17], waveguides [18,19] and diffraction gratings [15,17,20].
Most studies on the fabrication of BFLs by femtosecond laser micromachining have concentrated on fused silica glasses; here we review the most relevant results (all the focal lengths are given at a wavelength of 632.8 nm). The first approach consisted in fabricating amplitude Fresnel lenses by embedding voids in silica glass . A rather low NA lens (0.06) with a focal length of 3 mm was fabricated, showing an efficiency of just ~2%. More successful was the inscription of the lenses by inducing a refractive index modification in the silica glass [22,23]. Initially two BFLs were fabricated, with 0.04 NA and 0.1 NA, and focal lengths of 1cm and 2.4 cm, respectively. However, these lenses had efficiencies of 17% and 26% at 640 nm, because of the limited depth extension of the modified-refractive-index region . To increase the efficiency, a stack of lenses was fabricated . A BFL composed of 4 stacked lenses provided 0.07 NA, 3 mm focal length and 37.6% efficiency; the fabrication time was 21 hours. Srisungsitthisunti et al. have developed “modified volume Fresnel zone plates” [24,25], consisting of several layers of Fresnel zone plates where each zone is replaced with a single central ring in the middle of the zone. They achieved high diffraction efficiency (71%) with an eight layers lens, but with low NA (0.02) and a focal length of 20 mm. In summary, we can conclude that all the BFLs created by ultrashort laser pulses showed limited NA since the minimum achieved feature width was not smaller than a few micrometers. A second limitation of the above results is that the refractive index contrast induced in the bulk, without damaging the material, is below 10−2, which is insufficient to create a single high-efficiency phase zone plate, thus requiring the stacking of multiple lenses.
In this work we demonstrate for the first time the fabrication of BFLs by femtosecond laser surface ablation on PMMA substrates. Micromachining parameters are investigated to optimize the fabrication times and the efficiency of the lenses. Several BFLs are produced with excellent control on the focal lengths, which range from hundreds of micrometers to some millimeters, yielding very good transparency and focusing efficiencies close to the theoretically expected value. We chose to produce phase Fresnel lenses on the surface and not in the bulk of the substrate for three reasons: i) the refractive index change with respect to air after ablation is much higher than that possibly induced in the bulk, thus enabling one to achieve the theoretical efficiency using a single lens; ii) the single laser scan width, provided by surface ablation with tight focusing objectives and exploiting nonlinear absorption, is extremely small (submicron), thus increasing the maximum NA of the lens; iii) structures on the surface can be easily replicated by soft-lithography, thus complementing the high precision and rapid prototyping of femtosecond laser micromachining with cost-effective and parallel mass-production techniques. Our results demonstrate that femtosecond lasers can be used as a fabrication tool to produce Fresnel lenses on the surface of PMMA; applications can be envisaged, for example, in the implementation of integrated optical detection in microfluidic lab-on-a-chips .
2. BFL principles
A two-level Fresnel lens, or a BFL, consists of a series of concentric ring zones whose outer radius, in the paraxial approximation, satisfies the equation :
As the minimum spatial period ΔR = RM - RM -1 occurs for the outermost zone where m = M, the minimum feature size that can be generated by the available technology equals half of the minimum period ΔR, and limits the total number of periods M that can be fabricated; as a consequence, the maximum numerical aperture of the lens NA = RM/f ≈λ/ΔR  can be increased by reducing the size of the minimum achievable feature.
A phase BFL has maximum diffraction efficiency when the phase shift between the two levels is equal to π. When this phase shift is achieved by surface grooves, the depth of the modulation must be equal to :
3. Femtosecond laser microfabrication of BFLs in PMMA substrates
Figure 1 shows a diagram of the setup used for the fabrication of Fresnel lenses on the surface of PMMA by femtosecond laser ablation. The laser source is a mode-locked Yb:KYW laser producing 350-fs pulses at 1030 nm, with energy up to 1 µJ . To improve the microstructuring resolution we used the second harmonic of the laser, generated by a temperature-tuned lithium triborate crystal with 50% conversion efficiency . The repetition rate was set to 10 kHz, to further reduce any thermal accumulation effects . The 515 nm laser beam was focused on the substrate surface by a 0.95-NA microscope objective (Olympus, 100 × ), the highest NA available from a dry focusing lens. The pulse energy was set to 25 nJ/pulse.
A PMMA substrate, commercially available from Vista Optics (Vistracryl CQTM non UV), was used, with a refractive index n = 1.489 at 633 nm. The sample was translated by a three-axis air-bearing stage (Aerotech FiberGlide 3D), with a precision of 100 nm. Under these conditions, ablation from a single scan resulted in a surface V-shaped trench. Atomic force microscopy provided a 600-nm width at half depth, which is significantly lower than the minimum feature sizes previously reported for BFLs fabricated by femtosecond lasers [21–25]. To ablate the regions that produce the lower level Fresnel zones, the sample was translated in concentric circles of ever-increasing radius (with a 600 nm step, which was the maximum spacing providing a sufficient overlap and a reasonably smooth floor of the ablated region) at a constant speed of 0.2 mm/s. With this resolution, the minimum spatial period ΔR that can be produced is 1.2 μm, and thus the maximum numerical aperture of the fabricated lenses is equal to NA = 0.5 for λ = 633 nm.
We fabricated lenses with different focal lengths at λ = 633 nm, to demonstrate the capability of femtosecond laser micromachining to produce custom lenses. Figure 2 shows three different BFLs consisting of 32 zones, corresponding to outer diameters of 250 µm, 500 µm, and 1 mm and designed to have focal lengths of 0.5 mm, 1.5 mm and 5 mm, respectively. As a consequence, these lenses have an NA of 0.25, 0.17 and 0.1, respectively. As can be appreciated from the figure, the ablated regions are quite transparent and homogeneous, which helps to minimize the transmission losses of the lenses.
3.1 Inhomogeneous depth compensation
Characterization of the produced BFLs with a contact profilometer (Alpha-Step IQ, KLA Tencor) showed that, when laser ablation is performed with the beam waist focused right at the surface, the depth of the ablated area is not constant in the different zones (see Fig. 3(a) ). The inner zones are deeper than the outer ones since they are created with a higher number of ring scans. This non-uniformity in depth profile, and thus in the phase shift provided by the alternating zones, decreases the lens efficiency.
To tailor the ablation depth so that it remains constant in all the ablated zones, the focus of the fabrication laser beam was initially positioned above the sample surface to decrease the depth of the inner zones and then progressively moved towards the sample as the radius of the ablated zone increased. Figure 3(b) shows a surface profilometer scan along the radial direction of one lens fabricated with the depth tailoring technique; the different zones have a similar depth within 200 nm. The average depth is about 500 nm, which is slightly smaller than the optimal depth of 650 nm (see Eq. (2)) required for the 633 nm wavelength. From the profilometer scans we also obtained a quantification of the roughness at the bottom of the ablated regions, which is approximately 50 nm; this is an excellent result compared to those previously reported in the literature . This value could be further improved by decreasing the spacing between adjacent scans, but at the expense of a longer processing time, which at present is on the order of 20 minutes for a single lens.
4. Characterization of the BFLs
We next investigated the focusing properties of the fabricated BFLs. A monochromatic light beam incident on the lens converges at the focal spot on the optical axis. To measure focal length and focusing efficiency of the BFLs, we used a HeNe laser at a wavelength of 632.8 nm. The focal length is measured by focusing the collimated laser beam with the BFL and then imaging by a 20 × objective lens the focal spot on a CCD (Spiricon LBA-USB-SP620-1550), placed at a distant and fixed position; we then translate the 20 × objective closer to the BFL in order to image on the same CCD the surface of the BFL. The distance between the two objective positions provides the focal length of the BFL. Table 1 reports the measured and theoretical values for the three lenses presented in Fig. 2. The measured focal lengths are in good agreement with the expected ones if considering their very low value (it can be noted that the relative error become less significant as the focal length increases). The discrepancies between the experimental and the theoretical focal lengths reported in Table 1, can be completely attributed to an error of less than 1 µm in the radius of the fabricated Fresnel zones, which is due to the 600 nm minimum feature size previously discussed.
In Fig. 4(a) we present the image (magnified by the 20 × objective) of the focal spot generated by a lens with 500-µm focal length when it is illuminated by the He-Ne laser; the spot is symmetrical and has a Gaussian profile. In Fig. 4(b) we show the strong wavelength dependence of the BFL focal length by illuminating it with white light and imaging the focal spot in the red. This behavior, well known for Fresnel lenses, can be understood from Eq. (1): for a fixed RM and M, i.e. for a given lens, the focal length is inversely proportional to the wavelength λ of the incident light. This effect could be exploited in fluorescence detection where the fluorescence signal could be at focus on a diaphragmed power meter, while the excitation light background, being out of focus, would be reduced.
The efficiency of the 500-µm focal length BFL was estimated by first focusing the He-Ne beam with a 10 × microscope objective (0.25 NA) and then measuring at a large distance the power of the light recollimated by the BFL. The efficiency is then calculated as the ratio of the power measured at the image plane of the BFL with respect to the power transmitted through the PMMA substrate in a position without the lens. In this way we could demonstrate that the depth optimization shown in Fig. 3(b) increases the efficiency of the lenses from 10% to 30%; this value is quite high for femtosecond laser fabricated BFLs, and even more significant if one considers that these lenses have numerical apertures higher than 0.1 [21–25], as briefly discussed in the Introduction. Phase BFLs have a theoretical maximum efficiency of approximately 40%, assuming a phase variation of π and 100% transmission. On the other hand amplitude BFLs have a maximum efficiency of just 10%. Thus, the 30% efficiency that we measured for our optimized BFLs indicates that they are indeed behaving as phase lenses and that we are close to the maximum theoretical efficiency. Further optimization, in particular tailoring the ablation depth for the specific wavelength in use, is expected to close the gap with the theoretical value.
To demonstrate the imaging quality of a femtosecond laser fabricated BFL we show in Fig. 5 an image of a paperclip produced by the lens of Fig. 2(a). The paperclip was back-illuminated with white light, imaged by the BFL and then magnified by a 10 × microscope objective, which was positioned after the lens to re-focus the image on a CCD camera. It can be appreciated how the BFL is capable of producing faithful and undistorted images.
In summary, we have demonstrated that femtosecond laser ablation is an effective method for the fabrication of binary Fresnel lenses on the surface of polymers such as PMMA. With the optimized structuring parameters BFLs can be rapidly prototyped on PMMA substrates with high numerical apertures and short focal lengths. The properties of the lenses can be flexibly adjusted to meet the requirements of their final application, while achieving focusing efficiencies close to the theoretical value. Future work will explore the possibility of fabricating multilevel Fresnel lenses and will include BFLs in polymer lab-on-a-chip for integrated optical sensing.
This work was supported by the European Commission, FP7 Project Contract No. ICT-2007-2-224205 micro-Fabrication of polymeric Lab-on-a-chip by Ultrafast lasers with Integrated optical Detection (microFLUID) and by the Regione Lombardia, project ID-MAN-18-16559 MINILAB.
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