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Abstract
We present the design, fabrication, and characterization of a compound infrared microlens array having an ultrashort focal length and a hyperbolic profile that comprises a PDMS microlens array and a GRIN lens. A concave microlens mold was first fabricated on a fused silica substrate using femtosecond laser irradiation followed by a wet etching process, and a standard replication process was employed to fabricate a PDMS convex lens array. To shorten the focal length further and cut off the visible spectrum of light, a graded DLC/silicon coating, which functioned as a GRIN lens and a visible light cut-off filter, was additionally deposited using dual-beam pulsed laser deposition. The lenslet diameter was 6 µm and the graded coating reduced the focal length from 4.5 to 2.9 µm.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microlenses are basic elements of miniaturized optical setups and devices [1] and have found a wide range of applications, such as in 3D imaging systems, sensing systems, fiber optic communication, and optical medical systems [2]. As the performance of the optical sensing and imaging systems improves, there has been an increasing demand for ultrasmall microlenses [3] (with a lenslet diameter less than 10 µm), which have shorter focal lengths, larger numerical apertures, less spherical aberrations, and better light collection efficiency, particularly in the infrared/near-infrared (near-IR) wavelength range. Microlens arrays play an important role in enhancing the imaging quality of charge-coupled devices and complementary metal-oxide-semiconductors as well as the light extraction efficiency of light-emitting diodes and organic light-emitting diodes. They are essential elements for visible-light-range optical applications, as well as for IR applications.
In recent years, a great deal of effort has been focused on microlens fabrication research. Dai et al. [3] demonstrated a liquid-crystal-based reconfigurable microlens that comprised vertically aligned carbon nanofibers (CNFs) grown on a Si substrate. The focal length was reported to be in the range of 6 to 12 µm depending on the applied voltage. However, there was no physically formed lens, and the microlens was created owing to a refractive index profile, which was generated via the electrical field from the CNFs under an applied voltage. Casse et al. [4] demonstrated a 2D photonic crystal microlens with a focal length of ∼12 µm fabricated using negative refractive materials. However, both the aforementioned methods are complicated and are not suitable for mass fabrication. Liu et al. [5] fabricated a low-cost IR polymer convex microlens array using a nano-imprinting technique. They demonstrated their microlens array having a 150-µm diameter and a focal length of 380 µm, and the numerical aperture value of the microlenslet was calculated as 0.4 with the working band covering a region of 780 nm to 2.2 µm. Kumaresan et al. [6] presented large-area microlens arrays of chalcogenide glass photoresists using grayscale maskless lithography, with a lenslet diameter of 150 µm and a large focal length of 9.33 mm for IR applications.
Recently, the laser fabrication method has drawn much attention because it is relatively simple and is suitable for mass production. Mihailov and Lazare [7] fabricated microlens arrays using excimer laser ablation of amorphous Teflon combined with subsequent annealing and melting of the produced polymer islands. Lenses with diameters of 50 to 385 µm, focal length of 480 µm, and numerical apertures between 0.2 and 0.3 were successfully fabricated. Sohn et al. [8] fabricated a spherical microlens array with a lenslet diameter of 50 µm and a square microlens array with a microlens size of 100 × 100 µm on fused silica via femtosecond laser writing and CO2 laser reshaping. The focal length of the microlenses was reported to be approximately 35 µm. Bian et al. [9] fabricated bioinspired compound eyes using femtosecond laser writing and chemical etching. The fabricated lens array had a lenslet diameter of 95 µm with a large focal length of approximately 607 µm. Tong et al. [10] reported on the fabrication of a large-scale microlens arrays via the femtosecond laser wet etching and replication process. Lenses with a unit size of 20 × 20 µm and a focal length of approximately 96.8 µm were reported.
In this study, we designed and fabricated a compound IR microlens array that consists of a polydimethylsioxane (PDMS) microlens array and a gradient-index (GRIN) lens fabricated using diamond-like carbon (DLC) and silicon. A wet etching process followed by 1028 nm femtosecond laser irradiation was employed to fabricate negative microlens array patterns on a fused silica substrate. The negative microlens array was then used as a molding template for duplicating a PDMS convex microlens array that had a lenslet diameter of 6 µm, sag height of 1.6 µm, and focal length of 4.5 µm. To deposit a DLC/silicon GRIN lens on the PDMS microlens array, a novel dual-beam pulsed laser deposition (PLD) process was employed. Each lenslet had a hyperbolic profile, which is the ideal positive lens profile, and an ultrashort focal length of 2.9 µm. Finite-difference time-domain (FDTD) simulations were also conducted to validate the focal length, and the imaging tests showed a good optical imaging performance.
2. Design and fabrication of a compound infrared microlens array
Figure 1 shows a design of the compound microlens array with an ultrashort focal length, where the dark blue region represents a PDMS lenslet after replication, and r and H are the PDMS lens radius and sag height, respectively. The graded region shows an additionally deposited GRIN lens fabricated using DLC (light blue) and silicon (red).
The fabrication process of a compound IR microlens array was divided into three main steps, as illustrated in Figs. 2(a)–2(c). Firstly, a femtosecond laser was employed to generate small lenslet patterns (pitch distance and hexagonal packed arrangement were controlled in this process.); the fabricated sample was then immersed in hydrogen fluoride (HF) solution for etching in order to obtain smooth concave microlenses (Fig. 2(a)). Secondly, the replication process was conducted for the production of convex lenses (Fig. 2(b)). Finally, dual beam PLD was performed to fabricate a GRIN lens on the surface of the fabricated PDMS lens (Fig. 2(c)).
Fig. 2. Fabrication procedure for a compound IR microlens array. (a) Femtosecond laser irradiation and HF etching for fabricating a mold for the microlens array on fused silica, (b) fabrication of a positive PDMS microlens array, and (c) dual beam PLD deposition of a DLC/silicon graded coating.
As the first step, a 1028-nm, 220-fs femtosecond laser (Pharos15-200-PP) was employed to produce small craters on the surface of a 0.5-mm thick fused silica substrate. The fused silica substrate was cleaned in an ultrasonic bath using an ethanol solution for 20 min to remove the grease and contaminations, and it was then dipped into deionized (DI) water using an ultrasonic bath for another 15 min to obtain a clean surface. After drying with nitrogen gas, the cleaned substrate was fixed on a 3D x–y–z linear stage. The femtosecond laser was initially focused at the upper surface of the fused silica substrate. The incident laser beam was irradiated on the surface in a direction normal to the substrate surface with a microscope objective lens (Mitutoyo Plan Apo NIR ×20, N.A = 0.4). Breakdown-induced craters on the fused silica substrate surface were obtained with a single laser pulse. In this study, the pulse energy used for the fabrication was 0.45 µJ, and the beam waist and the produced crater diameter were approximately 4 µm and 1.5 µm, respectively. The pitch distance of the lens array was 8 µm by design, and the lenses were hexagonally packed. The substrate was translated at a speed of 0.1 mm/s. After the femtosecond laser irradiation, the inner surfaces of the craters were not clean and smooth, and therefore, ultrasonic cleaning was performed again to remove the debris before performing chemical etching. For the wet etching process, 10% HF was used for 30 min, and it was also put in an ultrasonic bath for removing air bubbles and for obtaining uniform etching. The laser induced craters evolved and formed smooth, uniform concave shapes in the isotropic chemical etching process.
After the concave lens array was successfully fabricated, the convex lens array was fabricated using a standard replication process. The PDMS pre-polymer was prepared by mixing Dow Corning Sylgard 184 silicone elastomer and Sylgard 184 curing agent in the ratio of 10:1. After being thoroughly mixed, it was put in the vacuum chamber and degassed for 30 min to eliminate air bubbles. Once the degassing was completed, the liquid mixture was poured onto the top surface of the fused silica substrate (with the fabricated concave lenses), and the substrate was baked in an oven for 6 h at a temperature of 60 ℃. The liquid polymer solidified in the oven, and the cured PDMS was then carefully peeled off. After the de-molding, a convex lens array was successfully obtained. The replication process is shown in Fig. 2(b).
Once the PDMS microlens array was fabricated, a 600 nm-thick functionally graded coating fabricated using DLC and silicon, which acted as a GRIN lens and a visible light cut-off filter, was deposited on the surface using the dual-beam PLD. The fabrication of functionally graded coatings by dual-beam PLD has been reported by Deng and Ki with their recent work on graded coatings for optical applications [11] and thermal applications [12]. The basic idea of this was to fabricate graded coatings by depositing two different materials along the coating growth (thickness) direction with good control of the material flux for each constituent. Before the deposition, a predesigned index profile should be determined, and in this study, we adopted the linear profile for simplicity.
In order to design an index gradient profile, the refractive index of the material mixture was calculated as a function of the mixture composition. Several mixture rules for refractive indices were available in the literature [13], and here, the volume fraction method was applied, which can be written as
where n1, n2, and nmix are the refractive indices of constituent 1, constituent 2, and the mixture, respectively; ${\phi _1}$ and ${\phi _2}$ are the volume fractions of constituents 1 and 2.In this study, DLC (carbon) and silicon were chosen as the two optical materials for the GRIN lens (graded coating) fabrication because of their low transmission in the visible light region and higher transmission in the near-IR region, making them desirable for near IR applications and devices. The refractive indices of two materials at 1000 nm wavelength (nDLC = 1.88 and nSi = 3.57) were used for the profile design. A 600-nm-thick graded coating was planned to be applied to the top surface of the fabricated PDMS microlens array. Its intended composition varied from 100% of pure DLC at the microlens surface to 100% of pure silicon at the lens–air interface smoothly and gradually. The linear profile is mathematically expressed as
where $x$ is the coordinate measured from the PDMS lens surface to the given location inside the graded coating, and $0 \le x \le 600$ nm.The volumetric content profiles of both the materials are presented in Fig. 3. The blue line represents the intended content profile of DLC while the red line is for silicon. As can be observed in Fig. 3, the composition of DLC decreases linearly from the PDMS lens interface to the coating–air interface, while that of silicon increases. Therefore, we can expect the index of the graded coating to change gradually and based on the volume fraction mixture rule.
To deposit the DLC-silicon GRIN lens with a linear profile using the dual-beam PLD, a 355-nm, 6-W picosecond laser (Coherent Talisker 355-4) was employed, which has a pulse width of 10–15 ps and a repetition rate of 200 kHz. A single laser beam was split into two beams using a 50/50 reflection/transmission beam splitter, and each split beam was controlled using a motorized attenuator. Both the attenuators were connected to a computer via an attenuator controller, and the action of the attenuators was governed by an inhouse LabVIEW program. Note that each attenuator worked as a beam shutter to control the effective laser irradiation time on the target material, and in this way, the amount of ablated (also deposited) material was controlled without changing the laser power. One of the split beams was focused on the carbon target inside the deposition vacuum chamber, and the other beam was focused on the silicon target. When the beams hit the target materials, silicon and carbon plasmas were induced. The generated plasma plumes were mixed together uniformly in space inside the vacuum chamber and were then deposited on the prepared PDMS lens array sample. In this manner, a mixture of two materials were deposited on one single sample. By controlling the deposition time of both the materials, a graded optical coating with a pre-designed content profile (Fig. 3) was fabricated. In this study, high-purity graphite (99.999%) and silicon (99.999%) were used as the targets, and prefabricated PDMS microlens array was used as the substrate. The PLD process was performed at room temperature (∼20 °C) in a vacuum chamber, and the pressure was maintained at ∼10−5 Torr using two turbomolecular pumps.
For depositing a graded coating with a designed linear content profile, the deposition rate of each material must first be known. Figures 4(a) and 4(b) show the deposition data curves for graphite (obtained with a laser power of 2.1 W) and silicon (obtained with a laser power of 1.7 W). Owing to the low deposition (ablation) rate of graphite, the data was gathered for up to 40 min in 10-min intervals. Silicon has a much higher deposition rate, and a total deposition time of 10 min was sufficient to build a 600-nm thick graded coating as only silicon and graphite of 300-nm thickness each were required. The deposition data for silicon were gathered at 2-min intervals.
3. Results and discussion
Figure 5(a) shows the scanning electron microscope (FE-SEM, Quanta 2000, FEI) image of the fabricated PDMS microlens array before a GRIN lens was deposited. As shown in the SEM image, the lenslets were in a hexagonal arrangement and were uniformly packed. The diameter of each lens was measured to be approximately 6 µm, and the height of the sag was measured to be approximately 1.6 µm. The 3D surface morphology was also investigated using a laser scanning confocal microscope (LSCM, Olympus LEXT OLS3100), and the obtained result is shown in Fig. 5(b). The cross-section lenslet profile was measured using the confocal microscope, and the measured profile is presented in Fig. 5(c) along with a hyperbola because the hyperbola is the ideal profile for a perfect refractive lens. As we can see, the fabricated lens profile agreed well with the hyperbolic fitting line. Based on the measurement result and the hyperbolic fitting curve, the focal length $f$ of the lenslets was calculated as [14]
where $n\; $ is the refractive index of PDMS (n = 1.406), and R is the radius of curvature at the vertex, where K is the aspherical constant, H is the sag height, and r is the lens radius, respectively. For a hyperbola, K = - e2 < -1, and e = 2.202 (for our PDMS lens based on the lens profile) is the eccentricity of the fitted hyperbolic equation. The calculated focal length of the microlenses was 4.5 µm.Fig. 5. (a) SEM image (45° tilted) and (b) confocal microscope image of the fabricated PDMS convex microlens array. (c) Measured lens profile and a hyperbolic fitting line.
To investigate the focusing performance of the PDMS lens, the intensity distribution of the focused light was measured using a laser scanning confocal microscope (FV1000, Olympus), and the obtained results are presented in Fig. 6. Figures 6(a) and 6(b) present an image of the microlens array and the corresponding intensity distribution created when the microlens array was illuminated by a normally incident 488-nm laser beam. Each red dot in Fig. 6(b) presents a focusing point of the lens. In Fig. 6(c), the intensity distribution along the blue dashed line in Fig. 6(a) (that passes through the centers of the three microlenses) is presented, and the focusing points are shown in the white box in Fig. 6(b). From the results, it can be observed that each lenslet forms a sharp focusing point (Fig. 6(b)) and possesses a good focusing capability.
Fig. 6. Focusing performance of the PDMS microlens array. (a) Confocal microscopic image of the microlens array. (b) The corresponding intensity distribution created when the microlens array was illuminated by a normally incident 488-nm laser beam. (c) The intensity distribution along the blue dashed line in (a).
Figure 7 shows the imaging test result conducted using a total internal reflection microscope (Olympus motorized Inverted Microscope IX81). In this test, a halogen lamp was used as a light source, and the alphabet “S” was used as the imaging object. As shown in the Fig. 7, a clear image of “S” was obtained for every lenslet, which demonstrates that the fabricated PDMS microlens array exhibits a good optical imaging performance.
Fig. 7. Imaging test result of the PDMS microlens array obtained with a halogen lamp as the light source and a letter “S” as the imaging object.
After the quality and performance of the PDMS microlens array were verified, a compound IR microlens array was fabricated by depositing a 600 nm-thick DLC/silicon graded coating on the pure PDMS microlens array discussed above. Figures 8(a) and 8(b) present an SEM image of the microlens array (FE-SEM, Quanta 2000, FEI) and a confocal measurement of the lenslet cross-section profile (LSCM, Olympus LEXT OLS3100), respectively. With the additional DLC/silicon coating, as shown in Fig. 8(a), the lens surface was not as smooth as that of the pure PDMS lenses (Fig. 5(a)) because the plasma plume produced by the picosecond laser ablation can contain relatively large particles. Figure 8(b) shows that the lenslet has a hyperbolic profile even with an additional coating.
Fig. 8. (a) SEM image (45° tilted) of the compound IR microlens array. (b) Measured lenslet profile shown with a hyperbolic fitting line.
In this study, the x-ray photoelectron spectroscopy (XPS) depth profiling method (K-alpha spectrometer, Thermo Fisher) was adopted to measure the content profiles of DLC and silicon. The XPS depth profiling etching was conducted using 1-keV Argon ion energy. The etching area was 2 × 4 mm. Silicon and graphite were the major constituents of the graded coating, and the sputter etching rate ratio was assumed to be $\textrm{Si}:\textrm{C} \approx 1:1$ for the sake of simplicity. The K-alpha spectrometer had aluminum Kα with a pass energy of 50 eV, a measuring spot size of 0.2 mm, and an energy step size of 0.1 eV. Figures 9(a) and 9(b) present the measured XPS peak variation results for both C1s (that of carbon) and Si2p (that of silicon), respectively. As shown, starting from the coating surface (air–coating interface) to the coating-PDMS interface, the Si2p peak decreases while the C1s peak increases, thus indicating that the coating is graded as planned.
Fig. 9. (a) XPS measured C1s peak variation along the coating thickness direction for DLC content; (b) XPS measured Si2p peak variation along the coating thickness direction for silicon content; (c) An C1s XPS peak fitting example for the location indicated by a dashed blue arrow in (a) and (d); (d) Calculated DLC volume percentage at each location inside the graded coating.
The atomic ratio of Si2p and C1s at a measurement location was calculated using the area ratio of each peak measured from XPS, and all the peaks were fitted using the XPSPEAK software after the background was appropriately subtracted. The atomic ratio was defined as
where ${I_C}$, ${I_{Si}},$ ${S_C}$, and ${S_{Si}}$ are the calculated total peak area of graphite, total peak area of silicon, sensitivity factor of C1s, and sensitivity factor of Si2p, respectively, ${S_C} = 0.25,\; $ and ${S_{Si}}$ = 0.27. Figure 9(c) shows an example of the XPS peak analysis conducted at one location inside the coating (the location indicated by a dashed blue arrow shown in Fig. 9(a)). All the possible valence states C1s peaks were added and fitted using XPSPEAK software, but no content of C–O was observed, and only C–C and C–Si bonds were found in the results. In Fig. 9(c), the total area of the two peaks (C–C and C–Si) was calculated as 35915. While for the same location, the total peak area for silicon was 15290. Based on the atomic ratio formula, the atomic ratio of carbon and Si was calculated as C:Si $\approx $ 2.53:1. The molar volume of carbon was 5.29 cm3 and that of Si was 12.17 cm3, and the volume ratio per atom was calculated as vC:vSi = 5.29:12.17 = 1:2.3. Therefore, the volume ratio of carbon and silicon at this plane was VC:VSi = 1×2.53:2.3×1 = 2.53:2.3. Finally, the volumetric content of carbon was calculated as 2.53/(2.53 + 2.3) $\approx $ 52.4%. The volumetric content of each plane (seven planes in total, as shown in Fig. 9(a) and 9(b)) was calculated and the results were drawn in Fig. 9(d). Figure 9(d) shows that the measured results agree with the intended linear profile reasonably well, which validates that the refractive index profile of the coating was graded based on the aforementioned mixture rule.FDTD simulations were also conducted for the focal length validation. An inhouse FDTD program with a domain of 15 × 15 × 20 µm with convolutional perfectly matched layer (CPML) [15] conditions on each boundary was adopted at the wavelength of 1000 nm. The refractive indices used for the simulation were nPDMS = 1.406, nDLC = 1.88, and nSi = 3.57, respectively. Figure 10 shows the electric field at the middle symmetric plane of the domain for both pure PDMS lens and a PDMS lens with a DLC/silicon graded coating. As shown in Fig. 10, a 1000-nm Gaussian light was incident on the lens from the top of the domain. Figure 10(a) presents the near-IR beam interaction with the pure PDMS lens, while Fig. 10(b) shows the beam interaction with the GRIN lens, respectively. A clear focal length reduction was observed. The focal length for pure PDMS lens was calculated to be 4.12 µm, which is very close to the theoretically calculated result of 4.5 µm, and the focal length of the GRIN lens (after deposition) was only 2.90 µm. The focal length reduction from the graded coating was calculated to be approximately 29.6%, which met our requirement of an ultrashort focal length.
Fig. 10. FDTD simulation results with a 1000-nm light on the focal length reduction of the graded coating. (a) pure PDMS lens with a focal length of 4.12 µm. (b) PDMS lens + GRIN lens with a focal length of 2.90 µm.
To investigate the transmission spectra of the fabricated microlens arrays, the transmission curves of a pure DLC (600 nm), pure silicon (600 nm), pure PDMS (2 mm), and DLC/silicon graded coating (600 nm) (each was deposited on a 0.5-mm thick fused silica substrate) were obtained using an ultraviolet visible near-IR spectrophotometer (Agilent, Cary 5000), and the obtained results are shown in Fig. 11. In Fig. 11, the black solid line represents the transmission curve of the PDMS polymer, which is considerably transparent from 300 nm to 1600 nm. The red and green solid lines are the measured transmission values for the deposited DLC and silicon, respectively. As shown, silicon has a larger transmission in the near-IR region as compared with DLC. But for both materials, the transmission decreases as the wavelength decreases from near-IR, and becomes virtually zero at approximately 750 nm, which is approximately the upper bound of the visible spectrum of light. Therefore, both the deposited DLC and silicon coatings are practically opaque in the visible-light range, and they could be used as a filter to cut off visible light while performing well in the near-IR region. The DLC/silicon graded coating (blue line) also exhibits a similar characteristic, and thus, it can serve many near IR applications and devices.
Fig. 11. Transmission curves for deposited DLC (red line), deposited silicon (green line), graded DLC/silicon coating (blue line), and pure PDMS (black line) from 200 nm to 2000nm.
Figure 12 presents the imaging test results of the compound IR microlens array conducted using total internal reflection microscopy and a photoactivated localization super resolution microscopy (Carl Zeiss Axio Observer Z.1). The light source of the total internal reflection microscopy was a halogen lamp in the visible to near-IR range (although the majority of the visible light was blocked owing to the extremely low transmission of the graded coating). The same “S” letter (as the one used for the pure PDMS imaging test) was employed as the imaging object. As shown in Fig. 12(a), a very clear and crisp image of “S” appeared on every single lenslet. This demonstrates that the fabricated GRIN lenslets had good optical imaging properties under the halogen lamp light. The light source for photoactivated localization super resolution microscopy was a 1000-nm laser beam. A clear image of “S” was also formed on each lenslet, as shown in Fig. 12(b). Owing to the limitation of the equipment, 1000 nm was the largest laser wavelength we could use, but we believe the microlens array could perform similarly well for larger near-IR wavelengths as well, as the transmission values increase with the wavelength.
Fig. 12. Imaging test results for the compound IR microlens array obtained using (a) total internal reflection microscopy with a halogen lamp (visible to near IR) and (b) a photoactivated localization super resolution microscopy with a 1000-nm wavelength laser beam.
4. Conclusions
In this study, the successful design, fabrication, and characterization of an index-graded microlens array with an ultrashort focal length was reported. The major findings of this research are summarized as follows:
- 1) The fabricated positive PDMS microlens array had a lenslet diameter of 6 µm and a sag height of 1.6 µm and provided an ultrashort focal length of 4.5 µm, which is close to an FDTD simulation result of 4.12 µm.
- 2) The compound IR microlens array was fabricated by additionally depositing a DLC/silicon GRIN lens. With the GRIN lens, the focal length was reduced further to 2.9 µm.
- 3) Both the pure PDMS and compound IR microlens arrays had a hyperbolic lenslet profile. The imaging tests showed good optical imaging performance for both the microlens arrays.
- 4) As DLC and silicon exhibit extremely low transmission in the visible-light region but much higher transmission in the near-IR region, the compound microlens array can be used in many near IR applications.
Funding
National Research Foundation of Korea (NRF-2017R1A2B2009942).
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