Generation of Aspherical Optical Lenses via Arrested Spreading and

May 20, 2016 - Aspherical optical lenses with spatially varying curvature are desired for capturing high quality, aberration free images in numerous o...
6 downloads 7 Views 6MB Size
Download PDF
Article pubs.acs.org/Langmuir

Generation of Aspherical Optical Lenses via Arrested Spreading and Pinching of a Cross-Linkable Liquid Abhijit Chandra Roy,†,‡ Mridul Yadav,† Edward Peter Arul,†,⊥ Anubhav Khanna,¶ and Animangsu Ghatak*,†,‡,§ †

Department of Chemical Engineering, and ‡Center for Environmental Science and Engineering, Indian Institute of Technology, Kanpur,208016, India § INM-Leibniz Institute for New Materials and Saarland University, Campus D 2 2, 66123 Saarbrucken, Germany ⊥ Central Electrochemical Research Institute, CECRI (CSIR), Karaikudi, Sivaganga-630006, Tamil Nadu India ¶ Department of Chemical Engineering, Manipal Institute of Technology, Manipal, 576104, Karnataka India S Supporting Information *

ABSTRACT: Aspherical optical lenses with spatially varying curvature are desired for capturing high quality, aberration free images in numerous optical applications. Conventionally such lenses are prepared by multistep top-down processes which are expensive, time-consuming, and prone to high failure rate. In this context, an alternate method is presented here based on arrested spreading of a sessile drop of a transparent, cross-linkable polymeric liquid on a solid substrate heated to an elevated temperature. Whereas surface tension driven flow tends to render it spherical, rapid cross-linking arrests such flow so that nonequilibrium aspherical shapes are attained. It is possible to tune also the initial state of the drop via delayed pinching of a liquid cylinder which precedes its release on the substrate. This method has led to the generation of a wide variety of optical lenses, ranging from spherical plano convex to superspherical solid immersion to exotic lenses not achieved via conventional methods.

■

INTRODUCTION

simple fabrication methods for making aspherical lenses and compact optical systems. Several attempts have been made for preparing lenses via bottom-up approaches driven by one or more surfaces or body forces. For example, a UV curable polymeric liquid drop has been subjected to a large electrostatic field which distorts it to one with parabolic to even conic shape,8 resulting in lenses with very high curvature, that is, high magnification but small aberration. This method has been adapted also for preparing an array of microlenses (MLA) by combining the idea of microchannel-assisted generation of droplets of UV curable material9 and distortion of these droplets under electric field.10 However, these lenses are not suitable for applications requiring very high numerical aperture. MLA has been generated also by spatially varying electric field-induced dewetting of a UV curable thin polymeric film deposited on a substrate;11 a structured electrode works as a template here for generating lenses of different size, but the lenses nevertheless remain spherical. Recently cylindrical microfluidic channels were subjected to elastocapillary forces for designing optofluidic lenses with adjustable focus.12 These lenses were aspherical, but their cylindrical geometry limited their use in many microscopy applications. Lenses were prepared also by cross-linking a

In general, for spherical optical lenses, parallel rays of light which are closer to the optical axis converge at a point further away from where the rays occur at the periphery of the lens, that is, marginal rays converge. This phenomenon which causes the image to be blurred is known as spherical aberration. Conventionally, such aberration is eliminated by simultaneously using several lenses and optical components, thereby rendering an optical instrument complex, bulky, and difficult to handle. In contrast, optical lenses with spatially varying curvature, commonly known as aspherical lenses, can significantly reduce such optical defects. In fact, a single aspherical lens can replace a large system of several optical components yet maintain large numerical aperture, thus facilitating compact design and ease of operation. Naturally, there exists a huge demand for such lenses in a large variety of applications such as optical metrology,1 beam shaping,2 spectroscopy,3 acousto-optics,4 optical microscopy,5 laser physics6 and so on. Conventionally, fabrication of aspherical lenses with complex surface profiles involve multistep top-down processes such as molding, grinding, and polishing of hard materials. These processes require use of high precision machines, sophisticated control algorithms, precise control of temperature, humidity, and importantly highly skilled workmanship.7 All these factors render these processes time-consuming, complex, prone to high rate of rejection, and expensive. Hence there is a need for novel yet © XXXX American Chemical Society

Received: December 18, 2015 Revised: May 7, 2016

A

DOI: 10.1021/acs.langmuir.5b04631 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir

Figure 1. (a) Schematic of experiment in which small quantity of the cross-linkable oligomer is released on a substrate maintained at an elevated temperature. (b) Top view of a lens captured using 3D optical profiler. (c−f) Side views of lenses of mass 5.3 mg fabricated at 80−200 °C on OTScoated silicon wafer. The curvature of these lenses is 0.19, 0.42, 0.74, and 0.76 mm−1, respectively. (g,h) Lenses of mass 5.3 mg fabricated on FCcoated silicon wafer. (i) Convex−concave lens prepared using convex surface of another lens as substrate. (j) Biconvex lens prepared using convex surface of another lens as substrate. (k) Lens-filter prepared by mixing oil soluble dye Sudan 2 with the cross-linkable liquid. Scale bar for figures a−k represents 1 mm. (l−o) Typical images of variety of microscopic objects captured using above lenses as in experiment of Figure S5. Micrograph (l) represents red blood cells (RBCs) from a healthy person which was magnified using a lens as in Figure 1e. Micrograph (m) represents RBCs affected by malaria pathogen Plasmodium falciparum; this image was captured using a lens fabricated by dispensing ml = 3.3 mg of liquid on an OTS-coated substrate maintained at 150 °C. Micrograph (n) represents neuron cell, captured by a lens (ml = 2.9 mg; substrate, OTS-coated plate at 200 °C). Micrograph (o) representing E. coli bacteria was captured with lens (ml = 0.6 mg; substrate, OTS coated silicon wafer at 150 °C). The conic constant for lenses used in images 1(l−o) are k = 0.25, 0.19, 0.12, and −0.2, respectively. The scale bar in each of (l−o) represents 10 μm.

■

RESULTS AND DISCUSSION Generation and Characterization of Lenses. In essence, our method involves dispensing a small volume of an optically transparent prepolymer liquid, for example, Sylgard 184 elastomer (mixed with the cross-linking agent in 10:1 w/w) on a preheated substrate, for example, silicon wafer coated with self-assembled monolayer (SAM) of octadecyltrichlorosilane (OTS) or 1H1H2H2H-perfluorooctyltrichlorosilane (FC) and heated uniformly to a desired temperature. The liquid was released using a digitally controlled motorized dispenser placed at an optimized vertical height from the substrate. For height >7 mm, air bubbles appeared within the lens, because of entrapment of air film sandwiched between the liquid puddle and the substrate (Supporting Information, Figure S1); for very small height 0 represent respectively a hyperboloid, paraboloid, prolate spheroid, spheroid, and oblate spheroid surface (details presented in Figure S7). Nonlinear regression with Levenberg−Marquardt algorithm29 was used to obtain κ and k. Since inclusion of higher order terms, r4, r6, ..., increased the fit accuracy insignificantly, these terms were not used for fitting the data. Figure 3a and Supporting Figure S8 show the phase diagram of conic constant k and curvature κ of lenses as a function of lens mass ml and substrate temperature TS. For constant TS, k decreases with decrease in ml, but κ increases. Similarly, for constant ml, the same effect on κ and k was observed when TS was increased. Beyond TS = 150 °C, no further alteration in κ and k were observed because limitation in heat transfer no longer allows the effect of TS to be felt away from the substrate. An estimate of curvature of a spherical cap can be made for a given mass of liquid ml and contact angle θ, κ = (πρ/3ml)1/3((1 − cos θ)(2 + cos θ))2/3, in which ρ is the density of the liquid. Noting that in most of our experiments θ remains somewhat larger than π/2 so that cos θ ≪ 2, and as obtained earlier, (1 − cos θ) ≈ TS3 (TS in °C), the curvature can be expected to scale as κ ∼ TS2/ml1/3. Thus, this relation captures the experimental observation that lens geometry depends strongly on TS and ml, both. In Figure 3b,c we show the exact dependence of curvature κ and conic constant k on these parameters as deduced from the analysis of several sets of experimental data. The conic constant k from different experiments scales as k ≈ ml/TS5, whereas curvature κ is found to scale as κ ≈ TS5/2(°C)/ml1/2 (or κ−2 ≈ ml/TS5), somewhat different from that predicted above, because the lenses in our experiments do not remain exactly spherical, so here κ represents curvature in the vicinity of their vertex. Second, for a larger mass of liquid, the flattening effect of gravity too influences κ and k which is not incorporated into the analysis. In fact, the relative effect of surface tension and gravity on a liquid drop can be understood in terms of capillary length defined as, lC = γ /ρg , where γ is the surface tension of the liquid, ρ is its density, and g is acceleration due to gravity. For PDMS, γ = 21.5 mN/m and ρ = 1026.9 kg/m3, the capillary length is estimated as lC = 1.46 mm, implying that, liquid drops with diameter larger than this value are expected to be affected by gravity. In other words, when the mass of liquid used for making the lenses exceeds mC = ρ × VC = ρ × lC3 ≈ 3.2 mg,

+ A1r 4 + A 2 r 6 + ... (1)

where z is the height from the vertex of the curved surface, r is the radial coordinate, κ defines the curvature in the vicinity of D

DOI: 10.1021/acs.langmuir.5b04631 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir

Figure 4. (a−e) Sequence of images depicts the process of forming lenses via a combined effect of arrested spreading and liquid cylinder pinching. A needle (diameter D = 1.6−2.5 mm) with a hanging blob of liquid was brought within a vertical height of l = 0.4−0.8 mm from the substrate so that the liquid blob comes in contact with it; the syringe needle was then retracted vertically up at different speeds, vw = 0.2−1.5 mm/sec. (f−h) High frame rate camera was used to capture the evolution of the liquid cylinder leading to pinching and thereafter attainment of the equilibrium shape. The series of plots 1−6 in each case represent the corresponding profiles of the liquid cylinder captured at different time τ. The set of plots f−h represent the needle retraction speed vw = 0.2, 0.312, and 1.5 μm/sec, respectively.

become a sphere. The ratio of these two time scales leads to a dimensionless number NK = τS/τQ = μK/γρCpd which suggests that an aspheroid is expected for larger values of NK, that is, for a liquid with large viscosity and thermal conductivity but smaller surface tension and specific heat. However, for these material properties remaining unaltered, NK can be increased by decreasing d, that is, by using diminishing quantity of liquid for forming the lens and by delaying the effect of surface tension driven flow. Delayed Pinching of a Liquid Cylinder. The above possibility was explored by modifying the one-step process described in Figure 1a. Here, the needle was first brought within 0.4−0.8 mm vertical height of the preheated substrate with a blob of desired size of the cross-linkable liquid hanging at its tip (Figure 4a). The liquid contacted the substrate, but was not allowed to detach from the needle tip; instead, soon after the liquid began to spread on the substrate, it was retracted by moving the syringe up (Figure 4b−d) at a desired speed, vw = 0.2−4.0 mm/sec. A liquid bridge was formed which first got stretched, eventually pinching off at a critical pull-off distance (Figure 4e). Followed by pinching, the liquid cylinder tended to assume the spherical shape before it got cross-linked. However, for a small quantity of dispensed liquid, the lens assumed aspherical profiles with negative k. The dynamic evolution of the dispensed liquid leading to pinching of the liquid cylinder and then attainment of the final shape of the lens is captured in sequence of optical micrographs in Figure 4f−h. Here a needle of diameter D = 1.6 mm was first brought within 0.8 mm of a substrate maintained at TS = 150 °C and was then withdrawn at vw = 0.2, 0.312, and 1.5 mm/sec, respectively. The series of plots in Figure 4f−h shows that, after pinching of the cylinder, the shape of the liquid drop does not change everywhere, but only beyond certain height hcross from the substrate, as depicted by the dashed lines. The cross-linking front propagates from the substrate to this height before pinching occurs. For needle retraction velocity, vw = 0.2, 0.312, and 1.5 mm/sec, this height was found to be 0.63, 0.4, 0.2 mm which were attained within time, τ < 5, 3, and 1 s, respectively. With the representative numbers of thermal conductivity K = 0.15 W/mK, specific heat Cp = 1.46 kJ/kgK, and density ρ =

effect of gravity becomes dominant in shaping the droplet profile: the drop turns oblate with conic constant k estimated to be positive. The data presented in Supporting Information, Figure S8 and those in Figure 3 show that curvature as high as 2 mm−1 and conic constant as low as 0.1 are attained. While, with increase in κ, the ability of the lenses to magnify an object increases, with a decrease in k the spherical aberration of the lenses diminishes and both the conditions are simultaneously satisfied. Nevertheless, k continues to remain ≥0, even for the combined effect of very small ml and large TS, although, prolate spheroids with negative k are preferred for many applications. To understand the range of parameters which can lead to negative k, the competing effect, importantly the characteristic time scales of transient transfer of heat through a progressively cross-linking liquid and concomitant surface tension induced flow in the vicinity of the vertex of the lens is considered. Since the crosslinking reaction occurs almost instantaneously in the vicinity of the substrate, particularly for those at elevated temperature, the reaction time scale is expected to be small. In contrast, transfer of heat and material through the drop are expected to occur at comparatively slower rate. Within the liquid drop, the heat flows from the substrate−liquid interface toward its vertex via conduction (remaining symmetric in the meridian plane), along with it the cross-linking front also propagates upward. Conduction remains the primary mode of heat transfer, as at elevated temperature cross-linking leads to increase in viscosity which minimizes the effect of convection. The time scale for heat transfer τQ can be shown (Supporting Information, Figure S9) to scale with density ρ, specific heat Cp, and thermal conductivity K of the liquid as τQ ≈ ρCpd2/K; here height d of the drop is the characteristic distance through which the heat conduction occurs. In the absence of gravity (drop diameter < capillary length26), surface tension driven flow allows the drop to attain the stable spherical shape in the vicinity of the vertex, the characteristic time for which can be shown to depend on viscosity μ and surface tension γ of liquid: τS ≈ μd/γ. The relative magnitude of these two time scales determines the specific shape of the final lens: for τQ < τS, the lens is expected to turn aspheroid, whereas for the reverse case, it is expected to E

DOI: 10.1021/acs.langmuir.5b04631 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir

Figure 5. Lenses prepared as in Figure 4 were used for capturing magnified images of microscopic objects, for example, a TEM copper grid. (a−h) Optical micrographs correspond to two sets of lenses prepared at two different retraction speeds of the syringe needle: vw = 0.312 (a−d) and 0.5 (e− h) mm/sec. Insets show lenses prepared with liquid blobs of different sizes hanging from the needle. Magnified image of a TEM copper grid of size 21 μm × 21 μm was captured using the above lenses in combination with a 10× microscope objective as in Figure S11. The magnification M and conic constant k of lens system for micrographs (a−d) were calculated to be (M, k) (a) 600×, 0.28; (b) 800×, 0.15; (c) 1660×, − 0.2; and (d) 1970×, − 0.63. Those for micrographs (e−h) were calculated to be (M, k) (e) 700×, 0.006; (f) 900×, − 0.11; (g)1250×, − 0.3; and (h) 1800×, − 0.86. The scale bar, in all images, represents 1 mm. (i, j) Profiles depict trace of lenses corresponding to Figure 3a−d (vw = 0.312 mm/sec) and Figure 3e−h (vw = 0.5 mm/sec). The solid and dashed lines represent actual and scaled profiles, respectively. The scaled profiles are obtained such that the base radius of scaled traces 2′−4′ match with that of lens 1. For both sets of plots, traces 1−4 correspond to lenses in Figure 3a−d and Figure 3e−h, respectively. (k) A typical profile of normalized intensity, I/I0 as obtained along the dashed line on image (a) is plotted with respect to distance n. The slope of this plot at the locations of sharp change in intensity are obtained as a measure of the optical resolution of the lenses. (l) The bar chart shows the resolution for lenses as in images a−h. The error bars represent the standard deviation of data from several measurements.

965 kg/m3 of PDMS, the characteristic time for heat transfer to a height d = 0.63 mm is estimated as τQ ≈ 3.7 s which matches rather closely with ∼5 s as observed in experiments. Two different limits of the needle retraction velocity can be considered: for a very small value of vw < 0.2 mm/sec, the cross-linking front reaches almost the tip of the needle resulting in a defective lens (Figure S10). For a large value of vw > 0.5 mm/sec, the cross-linking front remains far away from the lens vertex, so flow driven by surface tension gets sufficient time leading to an equilibrium spherical profile of the lens. Therefore, an intermediate speed of retraction, for example, vw = 0.312 mm/sec was found to be optimum for generating the prolate spheroids. In fact a wide range of lenses from SILs to prolate spheroids could be generated as shown in insets of images in Figure 5a−d which were prepared on OTS-coated silicon wafer at TS = 150 °C using a needle of diameter D = 1.6 mm and retraction velocity vw = 0.312 mm/sec. In the vicinity of the lens vertex, the lens profile was found to vary from oblate (positive k) to prolate (negative k) spheroid as the quantity of

dispensed liquid was diminished: for the lens in Figure 5a, k = 0.28, but with a decrease in ml, it decreased to −0.63 (lens in Figure 5d). To have a measure of magnification of these lenses, magnified images of a TEM grid (Figure 5a−h) were captured by the experiment described in Figure S11, which shows that magnification as high as ∼2000 times could be achieved. A similar set of lenses (insets of images in Figure 5e−h) with somewhat larger k resulted when vw was increased to 0.5 mm/ sec. Faster pinching allows the pinched cylinder to equilibrate over longer time, before getting cross-linked, thereby resulting in nearly self-similar spherical caps. Self-similarity of shapes is examined in Figure 5i,j where solid lines represent the traces of lenses in images 5a−d and images 5e−h, respectively. The abscissa and ordinate of these traces were multiplied with a scaling factor defined as the ratio of base radius of lens 1 to that of that particular lens and plotted as the dashed lines. For example, for traces 2 and 3 in Figure 5j (vw = 0.5 mm/sec) the scaling factors were calculated as 1.29 and 1.78, respectively. The resultant scaled profiles represented by dashed lines 2′ and F

DOI: 10.1021/acs.langmuir.5b04631 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir

Figure 6. Lenses were prepared as in Figure 4 but by retracting the needle vertically up in multiple steps. In all cases an OTS-coated silicon wafer was used as the substrate. (a) The lens at the inset was fabricated using a needle of diameter D = 1.6 mm and retracted vertically up continuously at vw = 1.5 mm/sec. A TEM grid of size 21 μm × 21 μm was magnified using this lens in combination with a 10× microscope objective as in Figure S11. The magnification and conic constant of this lens were found to be M = 420× and k = 0.53. (b) The lens was prepared by retracting a needle of diameter D = 2.5 mm at vw = 1.25 mm/sec in two different steps with an intermediate resting step for 4 s at a vertical height of l = 2.0 mm from the substrate. The magnification and conic constant of this lens were M = 680× and k = −0.03. (c, d) Wing of a mosquito was captured at two different magnifications by using two different lenses. The lens for capturing image c was prepared by simultaneously retracting the needle and withdrawing the dispensed liquid from the substrate maintained at TS = 110 °C. (e, f) The lenses were fabricated on substrates maintained at TS = 200 °C using a needle of D = 1.6 mm, which was retracted at 1.25 mm/sec in two different steps with an intermediate resting step for 1 s at vertical height 1 mm and 1.5 mm, respectively. (g) The lens was fabricated by retracting the needle in equal steps of 0.5 mm but at different speed vw = 0.312, 1.5, 2.1, and 3.75 mm/sec. (h) The needle was retracted in multiple steps of different retraction speed and step sizes: (1.5 mm/sec, 0.4 mm), (0.625 mm/sec, 0.3 mm), (0.312 mm/sec, 0.2 mm), (0.156 mm/sec, 0.1 mm), and (312 μm/sec, until pinching off the cylinder). The scale bar, wherever not mentioned, represents 1 mm.

plane, albeit remaining symmetric in the azimuthal plane. The usefulness of these lenses was demonstrated by capturing the magnified image of a TEM copper grid as in Figure S12 and also microscopic objects such as scales on the wings of a mosquito. Figure S12 show that an object can be focused at multiple locations along the optical axis because of their specific shape. Thus, these experiments open up the possibility of tuning the optical characteristics of the lens via several parameters which are to be dynamically controlled and optimized for attaining specific optical performance. Reproducibility of Lenses. To examine the reproducibility of lenses prepared via methods presented in Figure 1 and Figure 4, a large number of lenses, fabricated at identical conditions, were analyzed. For example, a needle of diameter 1.6 mm was used to dispense a liquid drop of @7.8 mg on an OTS-coated silicon wafer maintained at TS = 110 °C as in Figure 1a. The side view of 45 such lenses was analyzed for obtaining the distribution p(κ) of maximum curvature κ in the vicinity of their vertex. Since 45 is a statistically significant number, it accurately captures the lens variability. In Figure 7a we plot p(κ) as a function of κ for substrate temperature varying from TS = 110−180 °C. p(κ) was calculated by obtaining the number fraction of lenses that had curvature within a given range. The distribution gets somewhat narrower for higher temperature (TS ≈ 180 °C) of the substrate, implying that rapid cross-linking, or rapid increase in viscosity has a dampening effect on perturbations as expected. For each case, the distribution results in an average value and a standard deviation, which are plotted in Figure 7b. Here we have presented also the data for similar lenses prepared on FC-

3′ superimpose on solid line 1, signifying that lenses in images 5e−g were nearly self-similar. However, self-similarity broke down for trace 4 where rapid cross-linking of a small quantity of liquid did not allow surface tension driven equilibrium to be attained. In contrast, the traces in Figure 5i, (corresponding to vw = 0.312 mm/sec) were neither self-similar nor spherical signifying a diminished effect of surface tension at smaller vw. In Figure 5 we present also a measure of optical resolution of lenses which was obtained from the intensity profile of images captured by them. For example, in Figure 5k we show a typical intensity profile measured along the dashed line n on Figure 5a. The slope of such a profile at the locations of rapid change in intensity was obtained as such locations represent transition from masked, that is, dark to unmasked, that is, bright portion of the image. A large value of the slope signifies high resolution. The bar chart in Figure 5l represents the resolution of lenses as in Figure 5a−h. Needle Retracted in Steps at Variable Speed. While in a previous experiment the needle was retracted vertically up from the substrate at uniform speed, we will now show that several exotic lens shapes result when the needle retraction speed is suitably programmed. In Figure 6 we present these results in which the needle was retracted in multiple equal or different steps of identical or different retraction velocity. Similarly lenses were prepared also via simultaneous retraction of the needle following dispensing the liquid on the substrate and then withdrawal of the same. These sequence of multiple steps result in large variety of lenses, for example, ones with a large negative conic constant, lenses having side steps, and the ones the curvature of which vary drastically in the meridian G

DOI: 10.1021/acs.langmuir.5b04631 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir

linking reaction of the liquid to achieve different aspherical shapes. This particular feature of our method contrasts to others including those in which spherical lenses are generated by simply dispensing a cross-linkable liquid onto a substrate.30 Importantly, large curvature, that is, high magnification of lenses, and negative conic constant, that is, minimal aberration, are simultaneously attained in a single-step process which makes it amenable to easy scaleup. We have introduced also a dimensionless quantity to account for the competing effect of the cross-linking reaction and surface tension driven flow which finally determine the optical characteristics of the lens. The generality of the fabrication method is demonstrated by preparing lenses of various sizes and shapes including exotic shapes not achieved by any conventional methods. We have demonstrated also the use of these lenses by capturing magnified images of several microscopic objects. Importantly we have shown that images captured using these lenses compare well with those captured by conventional microscope objectives (Figure S14).

■

EXPERIMENTAL SECTION

■

ASSOCIATED CONTENT

Polydimethylsiloxane (PDMS) (Sylgard 184, procured from Dow Corning, USA) was used for preparing the lenses. Silicon wafers procured from Nanoshel (USA) were used as substrates. Silane molecules, octadecyltrichlorosilane (OTS), 1H1H2H2H-perfluorooctyltrichlorosilane (FC) molecules purchased from Sigma-Aldrich (USA) were used for surface chemical modification of the substrate by forming self-assembled monolayers (SAM). A digitally controlled motorized dispenser procured from Holmarc, India, was used to release droplets of PDMS from the syringe needles. A digitally controlled hot plate procured from CAT, Germany, was used to uniformly heat the substrate.

Figure 7. Figure depicts the reproducibility of lenses presented as in Figure 1a. (a) The bar chart depicts the probability distribution p(κ) of maximum curvature of lenses (in the vicinity of the vertex) prepared under a set of identical conditions, for example quantity of crosslinkable liquid ml = 7.6 ± 0.2 mg dispensed using a needle of diameter D = 1.6 mm on a substrate which is an OTS-coated silicon wafer maintained at specific TS. (b) The bar chart represents the average curvature κ̅ extracted from the above data and plotted against TS for both OTS- and FC-coated substrates. (c) Average conic constant k̅ of the lenses corresponding to plot a are plotted against TS for both OTSand FC-coated substrates. The right most bar in panels b and c correspond to lenses prepared by the method presented in Figure 4: an OTS-coated silicon wafer heated to 150 °C temperature was used as the substrate and the needle (diameter 1.6 mm) retraction speed was maintained at 0.321 mm/sec. The error bars in all cases represent the standard deviation of the data.

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b04631. Optimal height for releasing liquid drop for making lenses; AFM imaging of the surface of the lenses; characterization of azimuthal symmetry; fabrication of convex-concave and biconvex lens; Figures and other experimental details as described in the text (PDF)

coated substrate at identical conditions. In all cases the standard deviation is found to be within 5% of the average value, and the reproducibility of lenses are similar for these two different surfaces. In Figure 7c, we plot the average conic constant k̅ of these lenses as a function of TS. Here too, the standard deviation diminishes with increase in TS, that is, for lenses with decreasing conic constant. To test the reproducibility of lenses prepared by the method presented in Figure 4, a large set of lenses were prepared by maintaining identical conditions. The right most bar in the bar charts in Figure 7b,c and the data presented in Figure S13 show that for these lenses too the error remains with 5% of the average value.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS A.G. acknowledges financial assistance from Department of Science and Technology, Government of India, through Grant DST/TM/SERI/2k11/80(G).

■

SUMMARY We have presented a novel route for producing high quality aspherical optical lenses by using the coupled effect of arrested spreading and pinching of a dispensed liquid drop along with rapid crosslinking to produce wide ranging lenses: solid immersion lenses with large numerical aperture to prolate spheroids with negative conic constant to compact optical devices such as lens-filters. In particular we make use of competing dynamics of spreading of a drop of cross-linkable liquid on a substrate and the unidirectionally progressing cross-

■

REFERENCES

(1) Born, M.; Wolf, E. Principles of Optics, 7th ed.; Cambridge Univ. Press: 1999, Vol. 211. (2) Hoffnagle, J. A.; Jefferson, C. M. Beam shaping with a planoaspheric lens pair. Opt. Eng. 2003, 42, 3090. (3) Shalyapin, V. N.; Goicoechea, L. J. Deep optical imaging and spectroscopy of the lens system SDSS J1339 + 1310. Astron. Astrophys. 2014, 568, 1−11. H

DOI: 10.1021/acs.langmuir.5b04631 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir (4) Kaplan, A.; Friedman, N.; Davidson, N. Acousto-optic lens with very fast focus scanning. Opt. Lett. 2001, 26, 1078. (5) Gambin, Y.; Legrand, O.; Quake, S. R. Microfabricated rubber microscope using soft solid immersion lenses. Appl. Phys. Lett. 2006, 88, 174102. (6) Cao, Z.; Wang, K.; Wu, Q. Aspherical anamorphic lens for shaping laser diode beam. Opt. Commun. 2013, 305, 53. (7) Kim, H. S.; Kim, E. J.; Song, B. S. Diamond turning of large offaxis aspheric mirrors using a fast tool servo with on-machine measurement. J. Mater. Process. Technol. 2004, 146, 349. (8) Zhan, Z.; Wang, K.; Yao, H.; Cao, Z. Fabrication and characterization of aspherical lens manipulated by electrostatic field. Appl. Opt. 2009, 48 (22), 4375. (9) Zhu, X.; Zhu, L.; Chen, H.; Yang, M.; Zhang, W. Fabrication of multi-scale micro-lens arrays on hydrophobic surfaces using a drop-ondemand droplet generator. Opt. Laser Technol. 2015, 66, 156. (10) O’Neill, F. T.; Owen, G.; Sheridan, J. T. Alteration of the profile of ink-jet-deposited UV-cured lenses using applied electric fields. Optik 2005, 116, 158. (11) Li, X.; Tian, H.; Ding, Y.; Shao, J.; Wei, Y. Electrically templated dewetting of a UV-curable prepolymer film for the fabrication of a concave microlens array with well-defined curvature. ACS Appl. Mater. Interfaces 2013, 5, 9975−9982. (12) Roy, A. C.; Ghatak, A. Design of an adaptable optofluidic aspherical lens by using the elastocapillary effect. Adv. Opt. Mater. 2014, 2, 874. (13) Lee, W. M.; Upadhya, A.; Reece, P. J.; Phan, T. G. Fabricating low cost and high performance elastomer lenses using hanging droplets. Biomed. Opt. Express 2014, 5, 1626. (14) McCloskey, D.; Donegan, J. F. Planar elliptical solid immersion lens based on a cartesian oval. Appl. Phys. Lett. 2013, 103, 091101. (15) Mansfield, S. M.; Kino, G. S. Spectrometric determination of the refractive index of optical wave guiding materials used in Lab-On-aChip applications. Appl. Phys. Lett. 1990, 57 (24), 2615. (16) Mansfield, S. M.; Studenmund, W. R.; Kino, G. S.; Osato, K. High-numerical-aperture lens system for optical storage. Opt. Lett. 1993, 18 (4), 305. (17) Chaudhury, M. K.; Whitesides, G. M. Direct Measurement of interfacial interactions between semispherical lenses and flat sheets of poly(dimethylsiloxane) and their chemical derivatives. Langmuir 1991, 7, 1013. (18) Cardenas-Valencia, A. M.; Dlutowski, J.; Fries, D.; Langebrake, L. Spectrometric determination of the refractive index of optical wave guiding materials used in Lab-On-a-chip applications. Appl. Spectrosc. 2006, 60, 322. (19) Chaudhury, M. K.; Whitesides, G. M. Direct measurement of interfacial interactions between semispherical lenses and flat sheets of poly(dimethylsiloxane) and their chemical derivatives. Langmuir 1991, 7, 1013−1025. (20) Terris, B. D.; Mamin, H. J.; Rugar, D. Near-field optical data storage. Appl. Phys. Lett. 1996, 68 (2), 141. (21) Gennes, P. G. De. Wetting: statics and dynamics. Rev. Mod. Phys. 1985, 57 (3), 827. (22) Marmur, A. Adv. Colloid Interface Sci. 1983, 19, 75. (23) Milchev, A.; Binder, K. Droplet spreading: A Monte Carlo test of Tanner’s law. J. Chem. Phys. 2002, 116, 7691−7694. (24) Biance, A.-L.; Clanet, C.; Quéré, D. First Steps in the spreading of a liquid droplet. Phys. Rev. E 2004, 69, 016301. (25) Eddi, A.; Winkels, K. G.; Snoeijer, J. H. Short time dynamics of a viscous drop spreading. Phys. Fluids 2013, 25, 013102. (26) Blokhuis, E.; Shilkrot, M.; Widom, B. Young‘s Law with Gravity. Mol. Phys. 1995, 86 (4), 891. (27) Kweon, G.; Kim, C. H. Aspherical Lens Design by Using a Numerical Analysis. J. Korean Phys. Soc. 2007, 51, 93. (28) Hecht, E. Optics, 4th ed.; Addison-Wesley: 2002. (29) Levenberg, K. A method for the solution of certain non-linear problems in least squares. Quart. Appl. Math. 1944, 2, 164.

(30) Sokuler, M.; Gheber, A. L. Nano fountain pen manufacture of polymer lenses for nano-biochip applications. Nano Lett. 2006, 6 (4), 848−853.

I

DOI: 10.1021/acs.langmuir.5b04631 Langmuir XXXX, XXX, XXX−XXX