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Highly corrected close-packed microlensarrays and moth-eye structuring on curved surfaces

Kenneth M. Baker

The fabrication of near-micrometer-sized close-packed coherent microlens arrays on spheric or asphericsurfaces has been accomplished by use of a compact holographic projector system that was developed forproducing multimicrometer down to submicrometer grid patterning on curved surfaces. The microlensarrays, which can be utilized as moth-eye relief structures, are formed in a photoimageable bisbenzocy-clobutene polymeric resin by a photolytic process involving standing-wave interference patterns from theholographic projector system. Because of absorption, each integral microlenslet of the finished arrayspossesses a near-paraboloid contour. The trajectories of the meridional rays from each microlenslet canbe optimized to intersect at either a single point or a locus of points. © 1999 Optical Society of America

OCIS codes: 350.3950, 110.3960, 040.1240, 220.4610.

1. Introduction

A. Background

Microlens arrays have many applications, rangingfrom digital optical processing to displays to retrore-flecting screens.1 They are used in integral photog-raphy in which images are recorded from a range ofviewpoints, so, when the recording is illuminated, theimages are reconstructed with full parallax, reveal-ing a three-dimensional effect.2–4 In photocopierand facsimile machines microlens arrays form short-focal-path erect images over large scanning areas.5,6

Microlens arrays are used to enhance the efficiency ofdetector arrays by focusing all the incident light ontothe active ~pixel! areas7 and for Hartmann–Shackwave-front sensors in which different sections of awave front are focused into a series of spots and thedistortion of the wave front is measured by compar-ison of the position of these spots to those of spotsproduced by a reference beam.8–10 Arrays of micro-lenses are used for focusing clock pulses and biasbeams onto optical switch arrays in optical logic cir-cuits11 and are a convenient means of coupling be-ween bundles of single-mode telecommunicationsbers.12 They are also used as collimators for the

The author is with Optimerix Company ~818-782-8718!, 13659ictory Boulevard, Van Nuys, California 91401-1735.Received 18 May 1998; revised manuscript received 9 September

998.0003-6935y99y020352-05$15.00y0© 1999 Optical Society of America

352 APPLIED OPTICS y Vol. 38, No. 2 y 10 January 1999

coherent addition of beams from laser-diode arrays inwhich diffractive coupling from an external-cavityfeedback mirror is introduced,13 as optical couplersfor laser-diode arrays to pump rod and fiber laserslongitudinally,14 and as grouped collimators for thesteering of a single laser beam.15

When the center-to-center periodicity betweeneach integral microlenslet is shorter than the wave-length of the illuminating light, the microlens arrayscan be implemented as antireflection-structured~ARS! surfaces. This antireflection ~AR! structuringeffectively duplicates the surface-relief structuringfound on the corneas of certain night-flying moths toreduce surface reflections that would otherwise be-tray the moth to its predators.16

B. Moth-Eye Surface-Relief Structures

Electron microscope images of these moths’ corneasreveal a surface covered with conical protuberancesapproximately 200 nm in height and located in ahexagonal array with a center-to-center grid spacingalso of approximately 200 nm.16 It was theorizedthat these surface structures represent the opticalspectrum analog to the radar-reflection-suppressingstructures lining anechoic test chambers, acting in away similar to graded-index materials because thematerial density and thus the effective index mono-tonically varies as a function of depth.17 Becausethe change in density between the incident mediaand the bulk material is gradual rather than abrupt,electromagnetic radiation is accepted into the bulkmaterial with little reflection.

Windows and lenses fabricated with moth-eye sur-

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face structures exhibit low reflectance at thematerial–air interface and combine high transmit-tance over a broad wavelength band with a wide an-gular acceptance. Moth-eye surfacing might bepreferable to conventional thin-film AR coatings ei-ther for use with incident wavelengths for whichideal coating materials may not be available or forsevere environmental applications in which adhesionand thermal-expansion mismatches would render ARcoatings unreliable.

Generally, for effecting the maximum transmit-tance with the minimum diffraction and scatterlosses, the following rules need be applied18–21:

~1! The protuberances must have a height equal toat least 40% of the value of the longest operationalwavelength:

h 5 0.4l2. (1)

~2! For operation at normal incidence the center-to-center structural spacing must be less than thevalue of the shortest operational wavelength dividedby the index of the material:

L , l1yn. (2)

~3! For operation at oblique incidence or for wideangular acceptance the center-to-center structuralspacing must be less than half the value of the short-est operational wavelength divided by the index ofthe material:

L , l1y2n. (3)

~4! When using a higher-bulk-index substrate ma-terial the sides of pyramidal protuberances must ex-hibit an increasingly nonlinear taper.

For increased durability diamond films can begrown conformally on window and lens materialsthat are fabricated with moth-eye surfaces.22–24 Theconical or pyramidal proturberances promote agreater density of nucleation sites while increasingthe surface area. Diamond films coat materials veryuniformly, with high adhesion, and do not sacrificeoptical performance.

Another application for continuous-relief micro-structuring that is similar to moth-eye structuring isthat of emitter tips for field-emission displays.25–27

Most field-emission displays use arrays of microtipstructuring composed of conical electron-emittingcathodes that face a light-emitting phosphor-coatedanode screen. These emitters, usually of submi-crometer size, are fabricated in silicon or, more com-monly, in molybdenum films. Thousands of themare used for each pixel of the display.

In these and many other applications the fabrica-tion of microlens arrays on design-specified curvedsurfaces would be very desirable. Like other micro-structures, most microlens arrays are fabricated onflat surfaces because they are derived from tech-

niques starting from flat e-beam or laser-writtenlithographic plates. For curved-surface fabricationholographic methods provide an ideal approach. Aholographic process involving the exposure of positivephotoresist followed by replication and embossingtechniques has resulted in close-packed microlens ar-rays, and the method is applicable to curvedsurfaces.28–30

In a past collaboration that included the author, aholographic method resulting in direct fabrication ofa close-packed microlens array was demonstrated.31

This was achieved by the exposure through its base ofa substrate coated with a thin film of a photoimage-able bisbenzocyclobutene ~BCB! polymeric resin, fol-lowed by a development process. Here the BCBmaterial acts as negative photoresist. However, inneither this nor the aforementioned holographic pro-cess was an attempt made to correct for the stretch-ing of the holographic pattern field when it wasapplied to a curved photosensitive surface. In thiscase the patterning becomes elongated in the direc-tion of curvature.

Now, by using the compact holographic projectorsystem that was described in the preceding compan-ion paper32 to this one regarding the fabrication ofsubmicrometer grid patterning on curved surfaces,the author was able to develop a new curved-surfacemicrolens-array fabrication technique. The resultsare highly corrected ~evenly sized! close-packed co-

erent microlens arrays with each integral microlens-et possessing a near-paraboloid contour arising fromither a hexagonal or a square-shaped base.

2. Pattern Characterizations

The two types of microlens arrays were fabricated.Figures 1~a! and 1~b! illustrate the curved-field equi-angular three-beam and four-beam standing-wavepatterns as they are created within a thin film of thephotoimageable polymeric resin coated onto a curvedsurface. The complexed sinusoidal modulations arerecorded within the photoimageable material and re-vealed by the development process.

Figures 2~a! and 2~b! are three-beam and four-eam, respectively, integral sinusoidal microlenslets,s profiled with the laser-analysis program GLAD ~Ap-lied Optics Research!. As described in the preced-ng paper32 and according to scalar theory, in which

polarization effects are ignored, the three-beam in-terference exposure pattern has a maximum inten-sity of IMAX 5 9 at the center of each periodic spot. Itan be shown by calculation that, at I 5 1, the contours an exact hexagon, as is shown in Fig. 2~a! at the topf the skirted area near the base of the microlenslet.imilarly, the four-beam pattern, which has a maxi-um intensity of IMAX 5 16 at the center of each

periodic spot, can be shown by calculation to have thecontour at I 5 0 of an exact square, as shown at thease of the microlenslet of Fig. 2~b!.For the three-beam pattern, IMAX is calculated as

10 January 1999 y Vol. 38, No. 2 y APPLIED OPTICS 353

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the square of the vector sum of the three interferingfields:

IMAX 5 uE1 1 E2 1 E3u2, (4)

where the E fields are assumed to be plane waves, asdefined by28

En 5 An exp i~kn 1 rn 2 vt! j, (5)

here v is the frequency; t is the time; and, for theth wave, An is the amplitude, kn is the wave vector,

rn is the direction of propagation, and j is a unitvector expressing the transverse nature of the fields.

Similarly, for the four-beam pattern, IMAX is givenas the square of the vector sum of the four interferingfields:

IMAX 5 uE1 1 E2 1 E3 1 E4u2. (6)

3. Experiment

The microlens arrays were fabricated on severaltypes of optical substrates with varying curvatures.The substrates were spin coated at 2000–5000 rpm

Fig. 1. ~a! Three-beam curved microlens a

Fig. 2. ~a! Three-beam integral microlen

54 APPLIED OPTICS y Vol. 38, No. 2 y 10 January 1999

on their convex surface with either Cyclotene 4024-40or 4026-46 negative-acting photoimageable BCBpolymeric resin ~The Dow Chemical Company!. Af-er exposure, which was made through the base ofach substrate at a wavelength of 363.789 nm undermmersion conditions in the holographic projectorystem,32 the coated substrates were developed ~Ad-

vanced Development System, developer DS2100! andhermally cured according to the processing proce-ure.33 Cyclotene 4024-40 has a nominal coating

thickness of 5 mm ~variation is 3.5–8.0 mm! and Cy-lotene 4026-46 has a nominal coating thickness of 10m ~variation is 7.0–15.0 mm!. Cyclotene 4024-40r 4026-46 has been formulated to have a high pho-osensitivity at 365 nm. After full processing it hasrefractive index of 1.562 at 589 nm and has been

sed for the fabrication of optical channel waveguidesnd interconnects.34

Figure 3~a! shows a scanning electron microscope~SEM! photomicrograph of a microlens array pre-pared by exposure of a substrate coated with Cyclo-tene 4024-40 to the three-beam interference patternfollowed by processing. The center-to-center period-

and ~b! four-beam curved microlens array.

and ~b! four-beam integral microlenslet.

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icity here is approximately 2 mm. Figure 3~b! showsSEM photomicrograph of a microlens array pre-

ared by exposure of a substrate also coated withyclotene 4024-40 to the four-beam interference pat-

ern followed by processing. The periodicity here ispproximately 2.5 mm. Note the similarities be-ween Figs. 3~a! and 1~a! and between Figs. 3~b! and

1~b!.Fused-silica microlens arrays can be fabricated

from BCB polymeric-resin microlens arrays on fused-silica substrates by use of a reactive-ion-etching pro-cess that has been used on melted-photoresistmicrolens arrays.35 The pattern is transferred ontothe fused-silica substrate by careful control of theetch ratio of the BCB material to SiO2 by use of acombination of oxygen and fluorocarbon-containinggases. The gas mixture is balanced to result in a 1:1etch ratio so that the materials both etch at the samerate. After the BCB material is etched away com-pletely, the microlens pattern in SiO2 is left. Theprocess works quite well on shallow curved surfacesin which the direction of etching remains relatively

Fig. 3. SEM photomicrographs of ~a! a three-beam microlens ar-ay and ~b! a four-beam microlens array.

normal to the surface. For highly curved substratesthe substrate must be rotated so that the direction ofetching always remains relatively normal to the partof the surface undergoing etching.

Continuous-relief microstructuring with an ap-pearance similar to that shown in Fig. 3~b! and di-ectly etched onto fused silica by a process derivedrom crossed-fringe-patterning exposures in photore-ist has recently been made commercially availables an ARS material.36 In this instance, with a fea-

ture depth of 0.5 mm and a periodicity of 0.3 mm, theRS material’s typical residual reflectivity at the Nd:AG wavelength of 1.064 mm is less than 0.25%.he process involves exposing a photoresist-coatedubstrate to a two-beam laser interference patternonsisting of parallel fringes and then rotating theubstrate by 90° for a second exposure.26,27,37 The

main difference between the two-beam double-exposed interference pattern and the four-beam si-multaneously exposed interference pattern is thatthe four-beam pattern is close packed and the double-exposed two-beam pattern is not. However, in thecommercial product described, the etching processused has created a partial close-packing effect, al-though with some imperfections.

4. Conclusions

A holographic projector system has been used to pro-vide an accurate and a practical method for the fab-rication of microlens arrays and moth-eye structuringon curved surfaces. The aspect ratio, which involvesheight versus the base area of each integral micro-lenslet ~which determines the focal length!, can beontrolled by manipulation of the exposure, the pat-ern size, and the thickness and the absorptance ofhe photoimageable material. Variations in optimi-ation of the holographic projector system’s internalens design allow for highly corrected ~evenly sized!

microlenslets on either spheric or aspheric surfaces,with the trajectories of the meridional rays from eachmicrolenslet intersecting at either a single point or alocus of points along an optical axis centralized to aspecified whole microlens array.

The author thanks Rick Foster, formerly the Mar-keting Manager, Advanced Electronics Materials,The Dow Chemical Company, Midland, Michigan, forhis generous contribution of Cyclotene photoimage-able BCB resins and developer. He is now theGlobal Marketing Director of the MicroelectronicsMaterial Division, Cabot Corporation, Aurora, Illi-nois.

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