Because of the requirements of miniaturization tech-nology, there is a continuing need for microelements.Micro-optical devices are applied in fields such asoptical fiber communications, optical data storage,and optical testing with wave-front sensors. Most ofthe microelements made so far have a surface or avolume modulation that is permanent. For someapplications1 it is desirable that the microelementshave a modulation that is dynamic. Efforts havebeen made to fabricate active membrane micromir-rors2 whose shape can be changed by means of one orseveral electrostatic actuators. These mirror mem-branes can be used to correct defocus, to focus laserbeams, or to compensate for the aberrations causedby an optical system or by atmospheric turbulence.3Another approach is to modify light beams with ac-tuators that apply forces to a thin glass mirror.4 Inaddition to these techniques, there are others thatuse materials such as oil and mercury to make dy-namic optical elements such as holograms5 and mir-rors.6
In this paper we propose the use of a gel to formdynamic diffraction gratings and negative micro-lenses. Instead of controlling the shape of the ele-ment by means of actuators, gel surface shaping ismade with light. Section 2 deals with a method offormulating the dyed gel and a means of measuringits refractive index. In Section 3 we determine thebest ratio of chemical constituents of the gel for the
The authors are with Centro de Investigaciones en Optica, Apar-tado Postal 1-948, 37000 Leon, Gto. Mexico. S. Calixto’s e-mailaddress is [email protected].
Received 15 November 1999; revised manuscript received 6April 2000.
3948 APPLIED OPTICS y Vol. 39, No. 22 y 1 August 2000
optimum surface-shape modulation of the irradiatedgel. In Section 4 the characteristics of the gel arestudied as interference patterns with low spatial fre-quencies were recorded. In Section 5 we describethe recording of the microlenses and the measure-ment of their focal distances. Some images thatthey produced are shown.
2. Polyacrylamide Gel Fabrication
The chemical properties of polyacrylamide gels havemade them the object of studies.7 These gels are ina phase intermediate between solids and liquids witha structure consisting of a network of long cross-linked polyacrylamide molecules that contain water.Nondyed gels can be made by mixing the compoundslisted in Table 1. These have good transmittance invisible light and a consistency that is neither hardnor soft.
For microelements to be fabricated, the gel shouldhave a flat surface. To do this, we molded the gelonto three pieces of glass plate ~5.7 cm 3 5.7 cm!, onef which had a circular hole through its center ofpproximately 4 cm diameter. This plate waslaced on top of a second plate, thus forming a moldnto which the chemical mixture was poured. Ahird plate covered this mixture to form a flat-toppedurface. After a few minutes the mixture becomes ael. Several gel thicknesses were obtained by use ofeveral different thicknesses for the glass plate withhe hole. It is noted here that thin gel layers dryaster than thick ones when the top glass plate isemoved and the gel exposed to air.
Another requirement for the recording of microele-ents was the addition of a dye to the gel. The
election of the dye depends on the recording wave-ength of the light source. Because our source wasn argon-ion laser that emitted green light ~l 5 514m!, we used Congo red dye because of its high ab-orption at that wavelength. To formulate these
ird
Table 1. Standard Acrylamide Gel Formulation
dyed gels, eight different solutions of the dye wereprepared in distilled water with the proportions of 1,2, 4, 8, 16, 24, 32, and 64 parts of Congo red ~one parts equal to 5 mg! in 125 ml of water. These will beeferred to as solutions 1–8. We prepared layers ofyed gel ~thickness of 5.8 mm! by replacing the dis-
tilled water mentioned in Table 1 by 25 ml of each ofthese solutions. It was noted that by use of 25 ml ofsolution 7 or 8, gel formation was inhibited in thefabrication process. In this case, only 18 ml wereused in those solutions in order to get a useful gel.
A spectrophotometer was used to find the trans-mittance of the dyed gels. Graphs in Fig. 1 showtransmittance as a function of wavelength. Notethat as the amount of dye increases, transmittance ofthe recording light ~l 5 514 nm! decreases until al-most no light gets through. Also note that for redlight ~l 5 633 nm! a 75% transmittance for gelformed with solution #8 can be obtained. Thus read-ing of the recorded information can be done with lightat this wavelength.
To measure the refractive index of the gel, an Abberefractometer was used. A value of 1.3505 was ob-tained.
3. Surface-Shape Modulation
For an optical microelement the refractive index, thesurface shape, or both can be spatially modulated.To investigate modulation induced by the recordingof green light in gels, we first placed a gel betweentwo glass plates and illuminated it with an interfer-ence pattern of 4 linesymm while a He–Ne laser illu-
Fig. 1. Transmittance as a function of wavelength for polyacryl-amide gels with a thicknesses of 5.8 mm. Parameter is theamount of dye for each gel.
Distilled water 25 mlAcrylamide 1.2 gMethylene-bis-acrylamide 0.033 gTetramethyl-ethylenediamine 0.6 mlAmmonium peroxodisulfate 0.010 g
minated the recording area. No diffracted orderswere found, indicating that no volume modulationhad been induced in the gel. Then the glass coverplate was removed, and the interference pattern wasagain recorded to show whether there was any sur-face modulation. This time some diffraction orderswere seen, showing that a surface modulation waspresent. This surface modulation will be referred toas a relief from here on.
To determine the chemical mixture that would pro-duce the highest relief, when green light patternswere recorded on the gel, we prepared a batch of eightindividual gel layers with each of the eight solutionsdescribed above. A ribbon-shaped argon laser beam~0.4 mm 3 2.0 mm, 35 mWycm2! was recorded oneach gel. The corresponding relief was observed andmeasured with an interference microscope. The re-lief formed on the gel evolves with time so the micro-scope image was recorded on videotape for furtheranalysis. Immediately after exposure, the gel beganto recover slowly; some time later it had recoveredcompletely, all traces of the recorded signal havingvanished. The extent of the deformation on eachsurface was measured with the interference patternsproduced by the interference microscope, before andafter exposure. The first one is used as a measure-ment reference pattern. The separation betweenconsecutive straight fringes is ly2, where l is thewavelength of the light used to form the interferencepattern. The pattern after exposure, or the de-formed pattern, is superposed to the first. One ob-tains the relief depth of the deformed fringe bycounting the number of reference fringes over whichit superposes times the mentioned half-wavelength.8Figure 2 shows the behavior of the relief depth as afunction of the exposure time.
In the first attempts to record the ribbon-shapedbeam, harder layers seemed to reach modulationdepths deeper than those with soft consistency. Tofabricate harder gels, we doubled the amount of bis-acrylamide, resulting in deeper modulation depths,except for gels made with solutions 7 and 8. Fromthe results of these experiments, two possible opti-mum mixtures were chosen: solution 5 by doubling
Fig. 2. Gels’ relief depth as a function of exposure time for fourdifferent solutions.
1 August 2000 y Vol. 39, No. 22 y APPLIED OPTICS 3949
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the amount of bis-acrylamide and solution 8. Figure3 shows two video frames from the interference mi-croscope. The curved interference fringes show thelight-induced relief on a gel layer made with solution8 after 25 s of exposure time.
This relief formation of the dyed gel, when illumi-nated, can be explained by the dynamic phenomenonof laser-induced thermocapillarity9 that occurs whenthe surface tension of a liquid is modified by localvariations in the surface temperature. If the tem-perature increases in some region of the surface, theliquid is displaced from this higher temperature re-gion to the lower ones so that the gel layer losesheight where the temperature is high and gains itwhere the temperature is low. This gel consistsmainly of water and a small amount of solid matter.The temperature variation in the gel surface causedby its exposure to green light was measured with asharp thermocouple probe inserted into the gel. A
Fig. 3. Video frames showing the relief of a gel layer ~solution 8!:a! before recording illumination and ~b! after 25 s illuminationith a ribbon-shaped argon-ion laser light.
950 APPLIED OPTICS y Vol. 39, No. 22 y 1 August 2000
change of a few tenths of a degree was measured.Thus thermocapillarity is a possible explanation ofthe relief formed when the gel is illuminated.
4. Dynamic Diffraction Gratings
The characteristics of the photosensitive materialsused in holography are usually determined by theefficiency of the diffraction grating. This grating ef-ficiency can be a function of several parameters suchas the ratio of the intensity of the two beams, spatialfrequency of the interference pattern, intensity of thewriting beams, and others. For some materials thiscan be done in real time; for others, only after pro-cessing. In Section 3 it was shown that the absorp-tion of light by the gel results in the formation of arelief. Also, it has been seen that its temporal re-sponse to the writing light is in the order of seconds.These characteristics gave us the unique opportunityto study, in real time, the evolution of diffractionefficiency in terms of the relief growth and relaxationof the gratings. To do this, we simultaneously usedtwo optical setups. Writing and reading of the grat-ings was done with a basic two-beam interferencesetup. The relief was studied with an interferencemicroscope ~l 5 589 nm! as before.
A. Gratings Diffraction Efficiency
Gel layers 2 mm thick ~solution 8! were used to recordnterference patterns. The writing beams from anrgon-ion laser interfered over a small gel region;6-mm diameter!. Spatial frequency of the inter-erence patterns ranged between 4 and 50 linesymm.o that the recording grating would be undisturbed,e used an attenuated beam from a He–Ne laser withdiameter of approximately 5 mm for reading.Figure 4 shows the diffraction efficiency of a gel-
ecorded grating with 4 linesymm. Five power den-ities are shown. Each curve in Fig. 4 showsaturation after a sufficient exposure time. Maxi-um diffraction efficiency for each curve is a function
f the power density of the writing beams. Figure 5hows gel response to different spatial frequencies ofhe interference pattern. Power density of the writ-ng beams was 71 mWycm2. Note that when the
Fig. 4. Diffraction efficiency as a function of exposure time duringrecording of an interference pattern of 4 linesymm by gel. Fivepower densities are shown.
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spatial frequency increases, the maximum attaineddiffraction efficiency decreases. The maximum spa-tial frequency response shown in Fig. 5 is for 10 linesymm. Experiments were also made for spatialfrequencies of as many as 50 linesymm, showing thatdiffraction efficiency at these spatial frequencies waseven weaker.
B. Grating Relief
Intensity distribution when two coherent beams in-terfere at an angle is sinusoidal. When this distri-bution is recorded in a photosensitive medium, onewould guess that the produced modulation shouldresult in the same sinusoidal form. However, be-cause of nonlinearities10 the modulation is not trulysinusoidal. To investigate the grating relief, weagain used the interference microscope. Figure 6shows three photographs taken from a sequence ofthe relief growth for a grating with 4 linesymm. InFig. 6~a!, because no recording light was present, theringes from the interference microscope are straight,mplying that the gel surface was flat. Figure 6~b!hows the relief variation in the fringes, after a 5-sxposure time. Finally, Fig. 6~c! shows the varia-ion, after 15 s of exposure time. The shape of therating relief appears sinusoidal.Figure 7 shows the relief depth for a 4-lineymm
rating during growth and relaxation. Three differ-nt power densities are shown. During recording,n initial increase in the relief depth is followed byaturation at approximately 30 s. Shortly after theecording ends, grating relief relaxation begins, andhe recording quickly loses its relief depth.
During the recording of gratings, the direction ofhe reading beam was normal to the surface throughhe recording region. The observation of diffractedrders from this beam, in the far field, was a surendication that a grating was formed. When a grat-ng with 4 linesymm was recorded, the first diffractedrders appeared within the first second, their bright-ess increasing quickly. Soon, second and thenhird orders were also seen, the latter being the faint-st of all. For a 10-lineymm grating, the diffractedar field was formed by the zero and the first orders,
Fig. 5. Gel response to three different spatial frequencies of theinterference pattern. Power density of the writing beams was of71 mWycm2 in all cases.
s shown in Fig. 8. Faint second orders were ob-erved only with an increased intensity of the writingeams. At the end of the recording, when the gelegan to recover its initial surface flatness, these dif-racted orders gradually disappeared.
In the Section 5 it will be shown that by irradiationf the gel surface with a beam of a circular crossection, negative lenses can be formed. The inter-
Fig. 6. Gel relief growth at different times during illuminationwith an argon-ion laser interference pattern of 4 linesymm. ~a!Fringes from the interference microscope are straight, implyingthat the gel surface before illumination was flat. ~b! Sinusoidalvariation in the fringes after a 5-s exposure time. ~c! Variationafter 15 s of exposure time.
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ference patterns described above had a circular crosssection, resulting in negative lens formation in thegel as well as the sinusoidal pattern. This resultedin a negative lens modulated by a diffraction grating.When reading light irradiated the recorded area, itexperienced diffraction owing to the grating and re-fraction owing to the negative lens. The result ofthese effects was that a divergence of each beam foreach order was observed even when the angular po-sition of each order was maintained as determined bythe grating equation.
5. Dynamic Microlenses
As indicated in the Section 4 it is possible to recordnegative lenses. By irradiating with an argon-ionlaser beam of 3-mm diameter, we could produce dy-namic microlenses with diameters from 0.25 to 2 mm.To do this, we used metallic sheets with circular holeshaving diameters of 250 mm, 500 mm, 1.1 mm, and 2
m to cover the gel. At recording time, each sheetas placed as close as possible to the surface of the gel
o avoid the recording of diffraction effects. The re-ording beam then illuminated the hole for a fixedxposure time. A gel layer thickness of approxi-ately 1 mm with solution 8 was used.During exposure, the writing beam energy was ab-
orbed by the gel, producing a concave lens. Imme-iately after exposure, the gel surface began to
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952 APPLIED OPTICS y Vol. 39, No. 22 y 1 August 2000
ecover slowly until it reached its initial flatness.he shortest focal distance for each lens was observedt the end of the exposure time.We measured dynamic focal distances of the re-
orded lenses by looking ~with an ordinary micro-cope! at the evolving images produced by theenses.11 The object consisted of an asterisk formed
of strips of black tape stuck on a ground glass plateand placed approximately 75 cm away from each ofthe lenses. The asterisk was illuminated by a white-light source. The following steps were used in theexperiment to measure the focal distances: An ex-posure of 8 min was given with the laser beam irra-diating the gel, thus forming a negative microlens.The image produced by the microlens was observedwith the microscope, and its linear position wasmarked. This process was repeated every 4 min.Knowing the position where the microlens surfacewas focused and the position of its images made itpossible to calculate the value of the focal distance.Graphs in Fig. 9 show the behavior of the focal dis-tance as a function of relaxation time for three dif-ferent lens diameters. In the graphs, a blurredimage could be seen even outside the range of thevertical bars. The smaller the lens, the steeper theslope of these curves as is shown in Fig. 9.
This slope change can be explained as follows:When a lens with a given diameter is recorded, acircular region is warmed by the laser light. Afterexposure this area cools faster for small lenses.Thus the relaxation time for a large lens is longerthan that for a small lens.
Examples of some images given by a microlens inthe relaxation step can be seen in Figs. 10~a!–10~c!.
ote the changes in contrast and magnification of themages due to the changes of lens curvature.
The quality of the lens surface was determinedith the interference microscope mentioned in Sec-
ion 4. With its help it was possible to follow theeformation of the surface from the beginning of thexposure time. Before the lenses were formed, theat surface of the gel was indicated by the straight-ess of the interference fringes. Then when the
enses were formed, the interference fringes becameurved and finally became circular. Figure 11 dis-
Fig. 9. Behavior of focal distance as a function of relaxation timewhen three lenses with different diameters were investigated.
Fig. 7. Relief depth for a 4-lineymm grating during growth andrelaxation. Three different power densities are shown.
Fig. 8. First diffracted orders besides the masked zero order for a10-lineymm grating. Power density of the writing beams was 36mWycm2.
plays one of these patterns taken after 40 s of expo-sure time. At the end of 8 min, many circularinterference fringes were present, showing that theconcavity had a large sagitta. Because of the largenumber of interference fringes, it was impossible tocount them and thus measure the sagitta.
In an attempt to form better microlenses givingsharper images, we made gels with different amountsof dye. Solutions 3 and 5 were tried in addition tosolution 8. We found that the latter formed the bestimages.
In the Introduction, it was mentioned that thereare membrane micromirrors and thin glass mirrorsthat can change their surface profile by means ofactuators. Microlenses made in gels could present adesired relief if continuous-tone masks were used in-stead of the metallic sheets with a hole. Thesemasks could have a given spatial transmittance ~e.g.,parabolic!.11 Microlenses and other optical ele-ments with improved surface profiles could be made.
6. Conclusions
It has been shown that dyed polyacrylamide gels canform dynamic relief optical elements by means of therecording of spatial distributions of light. With aninterference microscope the relief growth and relax-ation of low spatial frequency gratings and microlenseswere studied. For the former elements, it was seenthat its shape was close to a sinusoidal. For micro-lenses, focal distances were determined with their dy-namic images. Examples of images are shown.
We thank D. J. Lougnot for discussions on thechemical behavior of the dyed polyacrylamide gel.We also thank O. Stavroudis for help with the gram-mar. This research was supported in part by a Con-sejo Nacional de Ciencia y Tecnologı́a grant 28467-U.
Fig. 11. Interference pattern of a microlens, given by an interfer-ence microscope. It was taken after 40 s of exposure time.
Fig. 10. Images observed in the relaxation step of a microlenswith a 2-mm diameter. ~a! Microlens had a focal distance f 5 219mm, 30 s after the end of illumination. ~b! Focal distance f 5 227mm, after 4 min. ~c! Focal distance f 5 241 mm, after 12 min.Note the changes in contrast and magnification among the images.
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5. J. Lewandowski, B. Mongenau, M. Cormier, and J. Lapierre,
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