Fourier synthesis for fabricating blazed gratings usingreal-time recording effects in a positive photoresist
Lucila Cescato, Geraldo F. Mendes, and Jaime Frejlich
A method is described which allows the relative phase-shift adjustment of two successively recorded holo-graphic gratings. The residual real-time recording effect in a positive resist was used as a reference hologramfor operating an actively stabilized holographic setup and for adjusting both the spatial frequency and thecorresponding phase shift of the successively recorded Fourier components to produce a predeterminedperiodic profile structure in the film. Synthesis of a blazed holographic grating is reported here as anillustration of the possibilities of the process. The method may find use in optical and electrooptical devicefabrication requiring accurate spatial frequency and phase adjustment.
1. Introduction
The Fourier synthesis of periodic relief structures isof obvious relevance for producing blazed holographicgratings. The usefulness of such gratings is due to thefact that most of the advantages of holographic grat-ings1 may thus be combined with the high efficiencycharacteristics of ruled blazed gratings.
Fourier synthesis exhibits two main experimentaldifficulties besides those characteristic of holographicrecording itself: the necessity for accurate adjustmentof both the spatial frequency and the phase shift forthe successively recorded Fourier components.2 3 Theinterest of Fourier synthesis however is not limited toblazed gratings; the methods being developed for satis-fying these two critical adjustments may also be usedin the manufacture of some optical and electroopticaldevices not related to spectroscopy. Among these weshould mention waveguiding structures exhibitingstrong directional characteristics4 of potential interestin integrated optics, and the X/4-shifted successivegrating recording for single-mode frequency operationin a distributed feedback laser. 5 6
The recording of a blazed holographic grating byFourier synthesis is described here to illustrate thevarious steps in the process. Consequently no special
The authors are with State University of Campinas, Physics Insti-tute, Optics Laboratory, 13081 Campinas SP, Brazil.
care was taken to optimize either the grating profile orits efficiency.
II. Stabilized Spatial Harmonic Superimposition
An actively stabilized holographic setup was recent-ly analyzed7 and shown to operate efficiently for fixingthe interference pattern of light to a reference holo-gram. The phase shift f between them may be fixed at±t7r/2, 0, and 7r at will, always in a null-detection mode.The possibiity of using the real-time recording effect ina positive photoresist film (predominantly phase mod-ulation occurs) as the reference hologram was alsodiscussed, and preliminary results are shown.7 8
In this paper we show that this actively stabilizedsetup may operate for any value of , thus allowing oneto accurately superimpose successive spatial harmon-ics to permit the Fourier synthesis of arbitrary-shapedprofiles.
The operation of the setup is based on two-wavemixing of the interfering beams at the reference phasehologram as shown in Fig. 1. The irradiance alongIR iswritten as
IR = 110 + I2771 - 2 1112 'lo77i sin, (1)
where Ilno represents the transmitted part of 41, and,1I2 is the diffracted part of I2 along that direction.Any change in phase shift it is transduced into a corre-sponding variation in IR which is used for operating ananalogic negative feedback electronic loop for keeping4' stable against external perturbations. The correc-tion in 4 is carried out by an adequately placed piezo-electric-supported mirror in the setup. As suggestedby MacQuigg9 a very weak dither of frequency isapplied to the phase , in the setup. Because of nonlin-earity between t and IR [Eq. (1)], the latter exhibitsfundamental (Q-frequency) and second harmonic (2Q-
Fig. 1. Two-wave mixing scheme: Zi, 2, and 24 represent theinterfering, transmitted, and diffracted waves, respectively.
frequency) terms among others, which may be mea-sured using a lock-in amplifier tuned either to Q or to2Q resulting in the corresponding electric signals:
V0 = (VI)M COS/' R/OII' (2)
V20 = (V2u)M sinP KIR/OA/,
I N
LASER /iBEAM 12
H (K I
IY III II + 12I 2
SECOND HARMONICSWAVE - MIXING
H
I IT! + Y2\ i11 +E
\ ,+ 2
FUNDAMENTALWAVE-MIXING
Fig. 2. Fundamental and first harmonic recording wave mixingscheme: X, 2;rand 7i represent zero, first and second-order diffrac-
tion, respectively, of wavefront 2:i.
the irradiance along the observed direction [Eqs. (2)and (3)] we now have
(3)
where (V0)M and (V20)M are described in Ref. 7 anddepend on the diffraction efficiency of the referencehologram, the irradiance of interfering beams, the de-tector and piezoelectric responses, and the amplitudeof the frequency Q dither. Either V or V2g aboveshould be used as an error signal for operating thefeedback loop in a null-detection mode so that thestabilization is operated either for 4' = i-/2 (VQ = 0) or
= O,7r (V2 = 0), respectively. A simple analysisshows7 that a stable equilibrium is reached either for 4= +7r/2 or 4 = -7r/2 depending on the sign of theamplified V0 signal in the feedback loop, and similarlyfor = 0 or = 7 relative to the sign of V2Q. Anyperturbation in the holographic setup resulting in values different from those above produces a non-nullamplifier output acting on the piezoelectric-supportedmirror in such a way as to restore to its stable equilib-rium value.
For spatial harmonic superimposition the funda-mental grating is first recorded in a stabilized mode for4 = 0 profiting from real-time effects in positive re-sists.8 After that the holographic setup is adjusted2"10to have exactly the second spatial harmonic projectedonto the photoresist film. Such adjustment is madeusing the fundamental grating as the reference, inwhich case either the photoresist is partially developedto produce a low modulated relief fundamental grat-ing, or the nondeveloped real-time effect grating isused. As seen in Fig. 2, three directions are now avail-able at this stage for two-wave mixing detection foroperating the stabilization loop. The A-dependentterm in the irradiance expressions are all proportionalto cos4 as may be easily deduced for a phase grating.Assuming that the terms in Q and 2 are, respectively,proportional to the first and second phase derivative of
V. sing',
V2Q cos4',
(4)
(5)
with the asterisk referring to the second harmonicsetup. The second spatial harmonic recording maynow proceed in a stabilized mode by just choosing V*2or V2 to operate the feedback loop in which case thesuperimposition will be performed for a peak-to-peakphase shift of either 0, 7r, or ±7r/2, respectively.
Note that the whole superimposition process may becarried out profiting from the real-time effect operatedstabilization reported above, without any intermedi-ate development step.
Ill. Fourier Synthesis of Blazed Gratings
For the Fourier synthesis of blazed gratings, howev-er, the second spatial harmonic term needs to be super-imposed by a 7r/4 phase shift from the fundamentalgrating for optimum diffraction efficiency,10 asidefrom amplitude considerations that are easy to fulfill.
For adjusting such phase-shift conditions we firststabilized the setup for = 7r/2 for a short time (usingthe V,* term for operating the feedback loop) to allowthe (Vg)M to be measured using a simultaneously Q-tuned amplifier:
V*,(,r/2) = (V*,)M. (6)
A constant electric bias is then summed to the 2 termat the output of the amplifier in the stabilization loopnow measuring
Vl(1r/4) = (V*Q)M sin7r/4 = (V*,)MF2T2, (7)
where (V*Q)M is known from Eq. (6). We now have theinterference pattern of light (in the second harmonicsetup of Fig. 2) 7r/4 phase shifted (peak-to-peak) fromthe already recorded fundamental grating. The sec-
ond harmonic grating recording should now proceed ina stabilized operation mode because equilibrium isnow reached precisely for = 7r/4 leading to a nullamplifier output-plus-bias signal in the feedback loop.After that, the photoresist film sample is adequatelydeveloped for producing a surface relief grating. Ithas been experimentally shown'0 and also deducedfrom theory" that the fundamental and second spatialharmonic terms are the determinant ones concerningefficient performance at least for shallow gratings.This means that we may expect a good performingblazed grating by superimposing just the above report-ed two terms.
IV. Experimental Results
The holographic setup using the 458-nm Ar+ laserline in this work was described in Ref. 7. The ditherwas Q = 1750 Hz in frequency and 8° amplitude interms of phase shift at the interference pattern. Forrecording we used an -6-,4m thick AZ-1350J Shipleypositive photoresist film spin-coated on a high-resolu-tion photographic plate glass substrate 1.5 mm thick.The superimposition of a fundamental pattern 1.7,4m in period (peak-to-trough exposure of 300 mJ/cm 2 )and its second harmonic (peak-to-trough expsure of200 mJ/cm 2 ) was performed as described above exceptfor the fact that partial development (AZ-303 develop-er from Shipley, one part in seven of water, for 30 s) wasactually carried out after the fundamental recording.The sample was then washed in de-ionized water, driedin N2 flux, returned to the setup for second harmonicrecording, and finally developed in the same mixtureas above, for 60 s. The response curve for the photo-resist and developer used is strongly nonlinear for thelow level exposure energy density used here, includinga threshold at 200 mJ/cm 2 . A scanning electronicmicroscope (SEM) photograph of the resultant asym-metric grating is shown in Fig. 3. The diffractionefficiency measured by transmission for X = 6328 .tmwas I+/Io = 2.3 and I_/Io = 0.23. A ratio of I+/I_ = 10,well above the maximum 6.5 value predicted fromscalar theory,'0 was obtained.
In spite of the possibility of performing harmonicsuperimposition without development it was not donefor the experiment illustrated by Fig. 3, in order tohave a high diffraction efficiency developed funda-mental grating for operating the second harmonic re-cording in a stabilized mode. By that time we wereafraid that doing otherwise the real-time grating aris-ing during second harmonic recording would interferein the stabilization process. Later theoretical devel-opment discussed in Sec. V and subsequent experi-ments, however, showed that there is no such interfer-ence. Consequently and from that moment on, har-monic superimposition was always carried out withoutintermediate development, profiting from the real-time effects in positive photoresists.
V. Real-Time Effects for Fourier Synthesis
Experimental results showed that real-time effectsarising from second harmonic recording do not inter-
Fig. 3. SEM photograph of the cross section of a 1.7-/im periodFourier synthesized blazed grating in a positive photoresist.
fere at all with the fundamental real-time modulatedgrating being used as the reference for the stabilizingsystem. This means that intermediate partial devel-opment before second harmonic superimposition isnot at all necessary for stabilized Fourier synthesis.All experiments following that described in Fig. 3 weresuccessfully carried out without partial development.Assuming that fo(x) and f,(x) represent the real-timephase modulations for the fundamental and secondharmonic grating, respectively, along the x axis, thecomplex transmittance grating is expressed as
expi&Wf0 (x) + f1(x)]I 1 + ifo(x) + if1 (x)](8)
for fo(x) andf1 (x) << 1.J
In such a case we have both sinusoidal gratingssummed and their diffraction effects consequently be-ing added too (from Fourier transform linearity theo-rem and scalar diffraction theory).12 The second har-monic real-time grating being necessarily in-phase (4= 0 or 1r) with the interference recording pattern oflight, its 2Q term is formulated as in Eq. (3) and conse-quently zero-valued. Consequently no interferencearises from it as long as the 2Q tuned amplifier is in thestabilization feedback loop.
VI. Conclusions
The high performance stabilization setup we usedtogether with the real-time recording effect arising in apositive resist film and the possibility of simultaneous-ly measuring the Q- and 2Q-frequency terms in thetwo-wave mixed irradiance across the reference holo-gram allows adjusting any value at will for the phaseshift between superimposed gratings. For otherthan 0, r, or ±17r/2, however, the stabilization does notoperate in the null-detection mode so that a poorerperformance is expected. In fact for null-detectionoperation, the equilibrium is reached for VQ = 0 or V2Q
= 0, and the corresponding value for 4 is consequentlynot affected by changes in other parameters (especial-ly the laser intensity fluctuation and changes in thediffraction efficiency of the reference hologram) in-cluded in VQ or V2Q. In the present case, however, it isnot VQ or V2Q but its addition to the electric bias that is
zero at equilibrium. Consequently the correspondingvalue for 4 depends on the above-mentioned changes.
A fact was already reported in this paper whichenables Fourier synthesis to be carried out withoutpartial intermediate development: the fundamentalreal-time effect grating-operated stabilization systemis not disturbed by real-time effects from progressiverecording of second harmonics as long as the 2 fre-quency tuned lock-in amplifier is in the stabilizationloop. Carrying out Fourier synthesis without partialdevelopment simplifies the whole process and im-proves reliability because photoresist behavior is con-siderably modified once it has been in contact with thedeveloper. Moreover, some changes occur in photore-sist film after development which prevent good match-ing of the recorded grating with the interference pat-tern from which it was recorded, except for a relativelysmall central area, correspondingly reducing the usefularea for Fourier synthesis. Avoiding partial develop-ment substantially increases such a useful area al-though no comparison has yet been attempted.
This paper reports preliminary results on the sub-ject, showing its potentialities. No systematic evalua-tion of its performance has yet been undertaken.
This work was supported by FINEP, CNPq, andFAPESP. We acknowledge H. C. Carvalho for theSEM photograph.
References1. M. C. Hutley, "Interference (Holographic) Diffraction Gra-
tings," J. Phys. E 9, 513 (1976).2. M. Breidne, S. Johansson, L. E. Nilson, and H. Ahlen, "Blazed
Holographic Gratings," Opt. Acta 26, 1427 (1979).3. E. G. Loewen and L. Bartle, "Triangular and Sinusoidal Grooves
in Holographic Gratings-Manufacture and Test Results,"Proc. Soc. Photo-Opt. Instrum. Eng. 240, 27 (1980).
4. S. T. Penq and T. Tamir, "Directional Blazing of Waves Guidedby Asymmetrical Dielectric Gratings," Opt. Commun. 11, 405(1974).
5. H. A. Haus and C. V. Shank, "Antisymmetric Taper of Distrib-uted Feedback Lasers," IEEE J. Quantum Electron. QE-12,532(1976).
6. L. D. Westbrook, "Properties of Quarter-Wave Shifted DFBLasers in the Presence of a Taper," Electron. Lett. 23, 518(1987).
7. J. Frejlich, L. Cescato, and G. F. Mendes, "Analysis of an ActiveStabilization System for a Holographic Setup," Appl. Opt. 27,0000 (1988), same issue.
8. L. Cescato, G. F. Mendes, and J. Frejlich, "Stabilized Holo-graphic Recording Using the Residual Real-Time Effect in aPositive Photoresift," Opt. Lett. 12, 982 (1987).
9. D. R. MacQuigg, "Hologram Fringe Stabilization Method,"Appl. Opt. 16, 291 (1976).
10. S. Johansson, L-E. Nilsson, K. Biedermann, and K. Kleveby"Holographic Diffraction Grating with Asymmetrical GrooveProfiles," Applications of Holography and Optical Data Pro-cessing, E. Marom, A. A. Friesem, and E. Wiener-Avnear, Eds.(Pergamon, New York, 1976), p. 521.
11. A. Roger and D. Maystre, "The Perfectly Conducting Gratingfrom the Point of View of Inverse Diffraction," Opt. Acta 26,447(1979).
12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill,New York, 1968).
Books continued from page 1966
Color Theory and Its Application in Art and Design, SecondEdition. By GEORGE A. AGOSTON. Springer-Verlag, NewYork, 1987. 286 pp. $59.50.
The book COLOR THEORYAND ITS APPLICATION TO ARTAND DESIGN is a lucid discussion of the major areas of colorscience as they relate to artistic use of color. Agoston states that hisaim is "to present a comprehensible discussion of certain technicaltopics and recent developments in color science that I believe are ofreal interest to artists and designers." As an artist and educatorwith training and experience in engineering, Agoston is able toprovide a valuable link between those working in color science andthose artists and designers using color for its aesthetics.
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For those readers who are unfamiliar with the first edition ofCOLOR THEORY AND ITS APPLICATION IN ART AND DE-SIGN, some description of Agoston's approach as well as the topicsselected and his coverage is appropriate. However, the readershould also refer to the review of the first edition appearing in Appl.Opt. 19, 2071 (1980). His approach is to present technical informa-tion so that a background in science or mathematics is not necessaryto follow the text. He avoids the use of equations but includesgraphs to illustrate his points.
All readers are brought to a common starting point by his initialdiscussions of the concept of color. After considering biological,psychological, and psychophysical approaches to color, he discussesperceived colors, light and color, and colored materials. Next, thetechnical specification of colors is introduced with the use of chro-maticity diagrams. The standard CIE specification is describedhere.
The seventh chapter marks the point at which the major revisionsof the first edition begin to occur. The techniques of specifyingcolor are elaborated and used in many different situations. Thischapter discusses the more traditional colored materials such aspaints, inks, and dyes, as well as other systems such as television andpointillism. Other items such as photography, four-color printing,and the irridescent colors of liquid crystals have been added. Newsections to the chapter include discussions of high contrast colors,metamers, metameric illumination, and color rendering. The wholequestion of metamerism and the effect of illumination on colors is ofvital interest to artists and designers. Thus this is an extremelyvaluable addition.
The next chapters deal with color systems and color naming.Chapter 8 includes the most common systems in use throughout theworld: the CIE Color Space; Munsell Color System; the OstwaldColor System; the German Standard Color Chart (DIN); the Nat-ural Color System and Swedish Color Atlas; and Chromo Cosmosand Chromo Cosmos and Chromaton from Japan. Chapter 9 isdevoted entirely to a discussion of the Optical Society of AmericaUniform Color Scales. This is an enlargement of a five-page sectionof Chap. 8 in the first edition. Although the new discussion in thischapter provides a greater appreciation for the OSA Uniform ColorScales and makes their use less formidable, this is the one sectionwhere the reader must refer closely to the diagrams to understandthe text completely. Without a physical model it may be difficultfor readers to visualize the full ramifications of the discussion. In
