Silicone microlenses and interference gratings

Sergio Calixto

Interference gratings, plano–convex microlenses, and spherical microlenses have been made in silicone.Lenses were fabricated by the melting method. Two substrates have been tried: glass and Teflon.The latter substrate lets us fabricate low-f-number lenses. We made spherical microlenses by placingpieces of silicone near a thermal source and studied resolution of the lenses by investigating the imagesthey gave of a test chart. We made low-spatial-frequency gratings by recording interference patternsand studied parameters involved in the recording. A study of the profile of the gratings and lenses wasdone with a mechanical surface analyzer. © 2002 Optical Society of America

OCIS codes: 350.3950, 160.5470.

1. Introduction

Applications of micro-optical elements in photonic de-vices are manifold. Among these elements are lensesand gratings that are used to couple light into or outof fibers and to couple detectors and modulators toother devices.1–3 There are several fabrication meth-ods that produce good microlenses. However, thesemethods are time consuming,4 involve expensiveequipment, and could release toxic materials. Thusthese elements are expensive to fabricate. Whenthousands of microelements are needed in tools andcomponents for consumer electronics, for example, it isbetter to use cost-effective elements made with com-mon materials and simple methods. In this paper aredescribed, possibly for the first time, the results ofusing silicone to fabricate microlenses by the meltingprocess. In Section 2 the material is described. InSection 3 methods are presented to fabricate lenseswith plano–convex and spherical profiles as well as totest images produced by some microlenses. In Sec-tion 4 the results of recording low-spatial-frequencyinfrared interference patterns on flat silicone sub-strates and on microlenses are described.

2. Material

Silicone5 is any of a class of synthetic polymer com-pounds of the general form �R2SiO�x, where R is an

S. Calixto �scalixto@foton.cio.mx� is with the Centro de Investi-gaciones en Optica, Apartado Postal 1, 948 Leon, Gto. G.P. 37000,Mexico.

Received 29 August 2001; revised manuscript received 14 De-cember 2001.

0003-6935�02�163355-07$15.00�0© 2002 Optical Society of America

organic group. They contain ring or chains of alter-nating silicon and oxygen atoms with the organicgroups attached to silicon. They are used, for exam-ple, in lubricating oils, water repellents, and electri-cal insulators. Silicone rubbers are syntheticpolymers of dimethylsiloxane �CH3�2 SiO. They canvulcanize at high-temperature vulcanizing or room-temperature vulcanizing.

Material that we used in the experiments wastaken from a glue gun6 available commercially. Thematerial was shaped like a rod approximately 10 mmin diameter and 10 cm in length. To measure sili-cone transmittance, we made thin disks with differ-ent thicknesses by cutting from the rod a cylinderwith a thickness of approximately six times the de-sired disk thickness. Then this cylinder was placedbetween two flat glass plates. Metal spacers wereplaced between the glass plates to obtain the desireddisk thickness. The plates were then placed in anoven whose temperature was raised to approximately80 °C. After approximately 10 min at that temper-ature, the oven was turned off and allowed to cool.The thin silicone discs were obtained by separatingthe glass plates. Thicknesses from approximately100 �m to 1.5 mm were obtained with this technique.The light transmittance of the disks was measuredwith a spectrophotometer. Different disk thick-nesses were considered. Figures 1�a� and 1�b� showtransmittance in the UV–near-infrared region.Midinfrared transmission is seen in Fig. 1�c�. Ow-ing to the high absorption at some wavelengths of themidinfrared region, modification to the shape of thesilicone material can be done with these wavelengths.The moderate and good transmissions, shown by thinfilms, in the visible or near-infrared regions let usmodulate light with these wavelengths.

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3. Microlens Fabrication

A well-known method of making microlenses is themelting method.1 With this method it is possible tomake plano–convex lenses with different diametersand f-numbers �f-number is the effective focal length�clear aperture of a lens�.7 In this method, small cyl-

inders with a diameter close to the desired lensdiameter are formed, by lithography1 or by mechan-ical methods,8 over a glass substrate. The substrateand the cylinders are placed in an oven, and thetemperature is raised. At a given temperature, thecylinders melt, and, owing to surface tension, theliquid assumes a hemispherical shape. After cool-ing, a plano–convex lens is obtained. By using avariant of the melting process, we were able to makespherical lenses. In the following paragraphs we de-scribe the fabrication methods.

A. Plano–Convex Lenses

To make plano–convex lenses, we made several diskswith different thicknesses using the method outlinedin the above paragraph. Thicknesses were 110, 300,500, and 1500 �m. A hole punch with an inner di-ameter of approximately 950 �m was used to perfo-rate the disks and obtain several preforms with acircular shape. These preforms were laid over flatglass. After melting, lenses with different diame-ters and thicknesses were obtained. Profiles ofthese lenses were measured with a mechanical sur-face analyzer that uses a stylus �sharp needle�9; someprofiles are shown in Fig. 2. We can see in thisfigure that preforms with the largest thickness �1500�m� formed lenses with diameters of approximately1760 �m. These diameters are longer than that ofthe preform �approximately 950 �m�. Thin pre-forms �110 �m� gave lenses with almost the samediameter as that of the preform.

Fig. 1. Transmittance of silicone disks as a function of wave-length for the �a� and �b� UV–nearinfrared region and �c� for themidinfrared wavelength. The parameter shown is the thicknessof the layers.

Fig. 2. Profile of lenses taken with a mechanical surface analyzer.The parameter is the preform’s thickness before the melting step.The preform’s diameter was approximately 950 �m.

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The back focal length7 of the lenses was measuredwith the following method. An object was placedapproximately 1.5 m from the lens. The image of theobject given by the microlens was investigated with amicroscope. The image was at the focal plane. Thelocation of the microscope along the optical axis wasmarked. Then the microscope was focused on thesurface of the lens, and the microscope-traveled dis-tance was measured. This distance is the back focallength. Results can be seen in Fig. 3.

It was mentioned that the formation of the lensesby the melting method is due to surface tension.The actual shape of the lens depends on the criticalangle between the substrate and the melted materialat its edge. This angle in turn depends on the sur-face energy of the substrate and the surface tension ofthe liquid. The higher the surface energy, thesmaller the critical angle, indicating better surfacewettability. However, if the surface energy is poorand there is enough liquid in the volume of the pre-form, a nearly hemispherical lens will be formed.The large critical angle allows the fabrication oflenses with high numerical apertures.10,11 To formsilicone lenses with a smaller f-number, we used flatTeflon as a substrate instead of glass. Figure 4 pre-sents the spherical profiles of some silicone lensesmade on a Teflon substrate. To compare the profilesof the lenses made on glass and on Teflon, somecurves of Figs. 2 and 4 have been redrawn and shownin Fig. 5. It is possible to see that lenses with smalldiameters �approximately 900 �m� made on glassand on Teflon do not show a difference in either pro-file or diameter. However, there is a difference forlarger lenses. Lenses made on glass show a largerdiameter �1760 �m� and smaller height �409 �m�when compared with lenses made on Teflon �1450 �mdiameter, 566 �m high�. In both cases, the preformdiameter was approximately 950 �m.

Fig. 3. Back focal distance as a function of the preform’s thick-ness. The parameter is the preform’s diameter.

Fig. 4. Profile of lenses taken with a surface analyzer. Teflonwas the substrate during melting time. The parameter is thepreform’s thickness before melting.

Fig. 5. Profile of lenses made on glass ��a� and �b�� and Teflon ��c�and �d��.

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B. Spherical Lenses

Spherical lenses show shorter focal distances thanplano–convex ones. Silicone spherical lenses werefabricated by use of the following procedure. Smallpreform cylinders were cut with a hole punch, thenpierced �with a pin� and placed close to a hot plate.When a given temperature was reached, the siliconemelted and formed a sphere because of surface ten-sion. With this method it is possible to make sili-cone spherical lenses as small as a few hundredmicrometers or as large as a few millimeters. Someexamples are shown in Fig. 6�a�. These lenses wereused to form images; an example is shown in Fig. 6�b�.

Surfaces of small spherical lenses could not be mea-sured with the mechanical surface analyzer over theentire aperture because depths were too large andslopes too steep. Thus only the top of a given lenswas probed with the surface analyzer. It is interest-ing how close the profile of the microlens surface is tothe arc of the best-fitting circle. Figure 7�a� showstwo graphs, one given by the surface anlyzer and theother, the best-fitting circle. The error or differencebetween the circle and the measured values is shownin the lower part of Fig. 7�a�. An enlargement of thiscurve is shown in Fig. 7�b�. For a perfect fit of themeasured points with the circle, the error should bezero everywhere. Maximum deviation was approx-imately �2 �m.

To test the performance of an optical system, weused a test target.12 This target consists of a seriesof alternating light and dark bars of equal width.The system forms the image of several sets of pat-terns with different spacings. The finest set inwhich the line structure can be discerned is consid-

ered the limit of resolution of the system. To test theimage resolution of some spherical silicone micro-lenses, we used an U.S. Air Force 1951 test target.13

Lenses with a good spherical shape were able to re-solve the bars in group 5, element 2. The distancebetween bars of this group is approximately 27 �m.The photograph for Fig. 8 is the image given by themicrolens of the elements in group 5.

Fig. 6. �a� Spherical lenses. Diameter of the smallest lens isapproximately 700 �m. �b� Images of letter B formed by thelenses.

Fig. 7. �a� Comparison between the best-fitting circle and thecurve obtained with a surface analyzer of the top of a sphericallens. On the lower part is shown the difference �error� betweenboth curves. �b� Enlargement of the error.

Fig. 8. Image of a test target �U.S. Air Force 1951� given by aspherical lens. Group 5, element 2 can be seen.

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4. Interference Gratings and Hybrid-Lens Grating

For many years researchers have tried to find a suit-able medium to record interference patterns given byradiation coming from a CO2 laser �� � 10.6 �m�.Materials made of oils,14 wax,15 plastics,16 and othersubstances17 have been tried. Silicone shows a lowmelting temperature and high midinfrared absorp-tion �Fig. 1�c��. Thus an attempt was made to recordinterference gratings. Disks of approximately 3.5cm in diameter and approximately 200 �m in thick-ness were used as substrates to record interferencepatterns. Sinusoidal interference patterns wereformed by two plane coherent wave fronts that inter-sected at an angle. Parameters involved in the re-cording of these interference gratings are the powerdensity �P�area� of the recording beams, exposuretime �texp�, spatial frequency of the interference pat-tern, and energy density �E�area � P�area texp�.After the sinusoidal interference pattern was re-corded, a set of lines with shallow depth was found onthe silicone surface. The distance between twonearest lines is given by the formula � � 2d sin ,where 2 is the angle between the recording beamsand � the wavelength of light. Because surface mod-ulation is made by heat, spatial frequencies of therecorded gratings cannot be more than a few lines permillimeter. Recorded spatial frequencies were 3.5,5.3, 8.5, and 14 lines�mm. For each frequency a setof exposures was made, keeping the fixed power den-sity of the two beams at 7 W�cm2. Profiles of thegratings were measured with a mechanical surfaceanalyzer. An example of one set of exposures �3.5lines�mm� is shown in Fig. 9. To find the depth ofeach profile, the scale on the right side of the figurecan be used. In the first �top� curve �texp � 100 ms�,it is possible to see that there are flat surfaces be-tween shallow depths. Flat surfaces occurred be-cause there the intensity of the light was not enoughto heat �and then modify� the surface of the silicone.This phenomenon is also evident in the second andthird curves. However, in the fourth curve �texp �130 ms�, the profile presents a sinusoidal-like shapethat is due to the lateral heat conduction from warmto cold regions. In the last curve �texp � 150 ms�, thegrating presents a shallow modulation. Lateralheat conduction has softened the material too much,

and the relief formed at the beginning of the exposurewas destroyed at the end of the exposure time.

In holography the recording medium should fulfillcertain requirements, and one of those is the re-sponse �modulation� to different spatial frequencies.Ideally, this response should be the same for all fre-quencies. However, in real materials, the modula-tion diminishes when the spatial frequency increases.In Fig. 10 four gratings profiles are shown. Eachprofile has a different spatial frequency. Thesecurves were chosen from every set of exposures �likethe one shown in Fig. 9� because they looked like asine modulation. By plotting the maximum modu-lation for each spatial frequency, we get Fig. 11. Wecan see that modulation becomes smaller as spatialfrequency increases. This decreasing of modulation

Fig. 9. Grating profiles given by a mechanical surface analyzer.The parameter was exposure time.

Fig. 10. Profiles of various interference gratings. Recordingpower was kept constant at 7 W�cm2. Spatial frequency was theparameter.

Fig. 11. Depth modulation as a function of spatial frequency ofinterference gratings.

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is due to the short distance between thermal fringeswhen spatial frequency is high. Thus by lateral con-duction, heat can warm more easily the places be-tween thermal fringes, causing a low modulation.

The three fundamental parameters in the record-ing of interference patterns are time of exposure,beam power, and spatial frequency of the interfer-ence pattern. We study the phenomenon of variablepower, keeping spatial frequency and time of expo-sure �50 ms� fixed. Profiles of the gratings measuredwith a mechanical surface analyzer are shown in Fig.12. The depths of modulation can be found with thescale shown on the left side of the figure. With pow-ers of 20 and 24 W, no modulation was seen; only thewrinkle of the silicone disk surface is present in thecurves. For 28 and 32 W, a modulation consisting ofshallow depths is present. For 36 and 40W, sinelikecurves appear. Finally, for 44 W, modulation issmall.

In regard to photographic emulsions, the law ofreciprocity states that the result of a photochemicalreaction is determined by the total exposure. Thismeans that the density of the image is determined bythe exposure, which is equal to the intensity multi-plied by the time of exposure. Thus, regardless ofthe range of values assumed by either the intensity orthe exposure time, the density is a function of theproduct. However, most photographic materialsshow some loss in sensitivity at high or low intensi-ties; this is known as reciprocity law failure. In ourcase, the recording of interference gratings, depth ofmodulation is the result of making an exposure to thesilicone substrate.

To test the reciprocity effect of silicone films, thefollowing experiment was done. Keeping the record-ing energy density fixed �E�area � power�area texp � 1.03 J�cm2�, we made two recordings. In thefirst, texp � 160 ms and power density � 6.49 W�cm2.In the second, texp � 80 ms and power density � 12.99W�cm2. The resulting profiles can be seen in Fig.

13. This result suggests that to obtain a deep profileit is better to use high-power beams and short expo-sure times, which cause less lateral heat conduction.

The use of hybrid optical elements, refractive–diffractive, was reported by early researchers inholography.18 Later, more studies19 and applica-tions20,21 were done. With respect to micro-optics,refractive–diffractive microlens arrays have beenused, for example, in a microspectrometer array sys-tem.22 In the preceding paragraphs we have shownthat it is possible to fabricate silicone microlenses andinterference gratings. Now we report our studies onmicrolenses with an integrated grating in one of itssurfaces. Several plano–convex lenses were fabri-cated with diameters ranging from approximately 0.5to approximately 1.5 mm. We recorded a sinusoidalinfrared interference pattern �17 lines�mm� on onesurface of the lenses by placing them in the region ofthe infrared interference pattern. This optical ele-ment, lens plus grating, now modulates light by fo-cusing it, by means of the lens, and by diffracting it.Thus when light from a He–Ne laser was directed tothe hybrid elements, three spots of light were seen onthe focal plane, as shown in Fig. 14. The one in themiddle had the highest intensity �zero order�. Thisspot is not well defined, meaning the some geometri-cal aberrations are present in the lens. The focallength of that lens was approximately 3.5 mm.

5. Conclusion

Because the silicone was obtained from a commercialsupplier, it contained small dust particles that af-

Fig. 12. Profiles of different recorded interference gratings.Spatial frequency ��4 lines�mm� and time of exposure �50 ms�were kept constant. The parameter was the power of the writingbeams.

Fig. 13. Profiles of two recorded gratings. Energy was kept con-stant. Time of exposure and power were the parameters.

Fig. 14. Intensity spatial distribution in the focal plane of the lensthat had an interference grating recorded in one of its surfaces.

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fected the transmittance of light. For better results,the use of pure silicone is suggested.

We have presented two methods for the fabricationof silicone microlenses and the recording of interfer-ence gratings. The profiles of these elements weremeasured with a mechanical surface analyzer. Thisinstrument gives good results, but its stylus slightlyscratches the surfaces of the elements. A noncon-tact instrument would be preferable.

It was mentioned that to make spherical lenses thesilicone preform was punctured with a pin. Afterthe melting step a spherical lens was formed, andthese lenses had a pinhole left by the pin. Althoughthis hole does not interfere too much with image for-mation, it would be better to find another method tosustain the preform during melting time. We havetried unsuccessfully to melt silicone pieces while theyare flying on a flux of hot air.

In Section 1 we mentioned some references relatedto the fabrication of microelements by several meth-ods. In addition, a method that uses a multifunc-tional acrylic monomer coated on glass is described inRef. 23. Spatial polymerization is made by greenlight that passes through a mask. Then the wholefilm is cured with UV light. Croutxe-Barghon et al.succeeded in forming lenses with diameters of hun-dreds of micrometers and sagittas of approximately5–6 �m. Unfortunately, this method cannot formspherical lenses.

Finally, microelements made with silicone could beused in communication devices based on infrared-emitting diodes with a wavelength approximately800 nm. This infrared radiation has been consid-ered a prospective alternative to radio for indoorwireless communications.24 Also, thin diffractive–refractive elements can be used in telecommunica-tion systems in which wavelengths of 1.3 and 1.5 �mare used because silicone shows good transmission atthose wavelengths �Fig. 1�b��.

We thank Ricardo Vera-Graziano, AntonioMartinez-Richa, Reyna Duarte-Quiroga, ManuelOrnelas-Rodriguez, and O. Stavroudis for fruitfuldiscussions. Also, we thank I. Gradilla for micro-lens studies made with an electronic microscope.This research was supported in part by the MexicanNational Council of Science and Technology�CONACyT�.

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