Binary phase Fresnel lenses for generation of two-dimensional beam arrays

Binary phase Fresnel lenses for generation oftwo-dimensional beam arrays

Kasra Rastani, Abdellatif Marrakchi, Sarry F. Habiby, William M. Hubbard, Harold Gilchrist,and Robert E. Nahory

Two-dimensional arrays of mutually coherent optical beams are needed in holographic interconnections forboth recording and reading gratings. We analyze the use and limitations of binary phase Fresnel lenses togenerate beams for these applications. Two known techniques of ion beam milling and thin film depositionare compared to fabricate such lens arrays in SiO2 and Si3N4. Each lens in the 8 X 8 arrays has a 1.2-mmsquare aperture with a focal length of 20 mm. Diffraction of a single argon-ion beam into an 8 X 8 array ofhighly uniform coherent focused beams (with 12-Am spot size) was achieved by the lenses with an efficiency of-30% (41% theoretical limit). Key words: Binary phase Fresnel lens arrays, holographic interconnections.

1. IntroductionAvailability of 2-D source arrays is essential for opti-

cal interconnection and neural network architectures.Beams from these sources need to be coherent to re-cord gratings in storage media for holographic applica-tions. By diffracting from these gratings one or manysources (which may be mutually incoherent) in theinput plane can be routed to one or many elements of adetector array in the output plane.'- 3

We are currently investigating one such architectureknown as the photorefractive interconnect systemwith coherently erasable synapses (PISCES) (see Fig.1).3 In this configuration, the gratings are recorded ina photorefractive medium by two arrays of beams(shown to the left of the photorefractive medium) andthey are read out by another array (shown to the right).Use of the amplitude and phase spatial light modula-tors (SLMs) in the recording branches of PISCESallows for controlling the weight of each interconnec-tion.3 The output of the detectors can be fed back todrive the SLMs and hence adjust the weights for learn-ing neural network applications.

Various methods of generating 2-D beam arrays

The authors are with Bellcore NVC 3X-118,331 Newman SpringsRoad, Red Bank, New Jersey 07701-7040.

Received 4 August 1990.0003-6935/91/111347-08$05.00/0.© 1991 Optical Society of America.

from a single beam exists. One such method is to usebinary phase Dammann gratings.46 These gratingshave been used to generate beam arrays as large as 201X 201.5 The binary phase pattern of a Dammanngrating, however, is complicated because the positionof the transitions and the phase depth need to beoptimized for the desired beam configuration. 5 How-ever, once the design is completed the fabrication pro-cess is straightforward.

Both binary or blazed Fresnel microlenses have beenreported by others which are suitable for beam arraygeneration.7-'0 These diffractive lenses have the po-tential for mass production because of their simplicityof design and fabrication. Multilevel phase diffrac-tive microlens arrays have also been reported by Jahnsand Walker to achieve diffraction efficiencies as highas 91% with eight discrete phase levels."' The disad-vantage of this type of lens structure, however, is that itrequires multiple mask alignment, photolithographicpatterning, and deposition steps.

Here, we selected binary phase Fresnel lens arrays(BP-FLAs) because of their simplicity for use in opti-cal holographic interconnects. We will present thelimitations of such lenses in this context. In addition,two practical techniques of fabrication in SiO2 throughion beam milling and in Si3N4 through thin film depo-sition are compared. Results of diffracting a singleargon ion beam into arrays of mutually coherent beamsby these lenses are presented.

Although the theory of Fresnel lenses has beenknown for many years,'2 we will next present a briefanalysis of the binary phase types in the context ofholographic grating recording.

10 April 1991 / Vol. 30, No. 11 / APPLIED OPTICS 1347

CSA = COHERENT SOURCE ARRAY (NXN)ASLM = AMPLITUDE SPATIAL LIGHT MODULATORPSLM = PHASE SPATIAL LIGHT MODULATOR

CSA

ASLM

ASLM

PHOTOREFRACTIVEMEDIUM

CSAFig. 1. Schematic diagram of PISCES.

II. Theory of Binary Phase Fresnel LensesA typical binary amplitude Fresnel lens is shown in

Fig. 2(a), which consists of alternating opaque andtransparent zones. All zones of a binary phase Fresnellens (BP-FL), on the other hand, are transparent withan induced 7r phase shift between neighboring ones.Because of its transparency, the throughput efficiencyof a BP-FL is approximately four times better than abinary amplitude type. This makes BP-FLs moreattractive for use in interconnection applications.Next we analyze the diffractive properties of a binaryphase Fresnel lens.

The radius of the mth zone (Ri) in a Fresnel lens isgiven by

R'= mR2, (1)

where R, is the radius of the inner zone. The ampli-tude transmittance t(R2) is thus periodic in R2 withperiod 2R2. By analyzing the diffraction of this peri-odic function, we will show that at discrete points alongthe axis of the lens the optical field is maximum. Wealso show that the additional condition of a -r phaseshift between neighboring zones (see Fig. 2) eliminatessome of these points.

One can represent t(R2) as a Fourier series expan-sion:

t(R 2) = Eanexp R2 )n=- I

(2)

where an, the amplitude of the nth Fourier component,is

a,= - J t(R2) exp(-irn )d(R2). (3)

For an incident plane wave with wavelength X, the fielddistribution U(x',y',z) at a point behind a BP-FL isdetermined from the Fresnel diffraction equation:

R 2 2R 2 3R2 MR 2

(b)Fig. 2. (a) Schematic diagram of a binary amplitude/phase Fresnellens. In the amplitude lens every other zone is opaque, while in thephase lens they are all transparent with an induced 7r phase shiftbetween the neighboring zones. (b) The phase shift induced by abinary phase Fresnel lens as a function of R2. The period of thisfunction is 2R 2. The amplitude of the transmittance function is

Unity.

1348 APPLIED OPTICS / Vol. 30, No. 11 / 10 April 1991

(a)

A

it

PhaseShift

*

i

U(x',y',z) = J J t(R2) exp(+ [(x - x')2 + (y - y,)2])dxdy, (4)

where the integration is over the aperture of the lens.In Eq. (4), we have omitted an unimportant phase termoutside of the integral. Substituting Eq. (2) in Eq. (4)and using the relationship R2 = x2 + y2 , the field will be

U(x',y',z) a, exp ( 7 (x'2 + Y'2)) Jexpi7r(x2 + y2)

X n + 1 )]exp[ 2ir (xx' + YY')]dxdy. (5)

This distribution [Eq. (5)] is maximized when the ex-ponent involving (x2 + y2 ) is equal to zero.13 Themaxima occur at

2RIzn = , A n =041423 (6)

The field distribution at the plane z = Zn is, therefore,

U(XY, z) = a exp ( 2 + 12)) i(ejzx , + E b

(7)

In the above equation, the sinc function is the result ofintegrating over a rectangular aperture with dimen-sions Lx and Ly. In addition, the second summation inEq. (7) accounts for the contributions from fields thatfocus at other planes along the axis. It is evident fromEq. (7) that the field maximum at plane Zn is equal to an(magnitude of the nth Fourier component).

Now, we introduce the additional condition of theperiodic 7r phase shift. The amplitude transmittancefor this case is shown in Fig. 2(b), which can be repre-sented by

t(R2) = [exp(i) rec R - 2R R 1

+ rect(R2- 2mRI - 3R2/2)]

In the above equation, Mrepresents the number of thezones (we assumed it to be even), and 0 is the inducedphase shift, which is equal to xr. The first rect functionaccounts for the phase shifted zones and the second forthe zones with no phase shift. To simplify the analy-sis, we normalize the period 2R2 to 1. Doing so andreplacing Eq. (8) in Eq. (3) yield

1 /-ilrn\,,a = 2expi 2 [-1 + exp(-irn)] sinc -. (9)

\2 2J 2'

Note that the integration was conducted over a period(i.e., m = 0). The bracket in Eq. (9) is either zero or -2according to

[-I+ xp(ir) [-2 n (2j + 1) j =0,1,2,. (0[-1 + exp(-i7rn)] { j, otherwise. (10)

Therefore, the maximum field amplitude is nonzeroonly for n = +1,+3,+5,. . ., and it is equal to sinc(n/2).This result coupled with Eq. (6) yields the well-known

result that such lenses act as both converging anddiverging with foci located at

R2i = A n =A,3+,..(1

nX'

Squaring the maximum field amplitude gives us themaximum intensity

n'r 2sin-\~

In = sinc2 2 = 2 n = ,35 ...... . .(12)2 n2

2~~~~~~~~~~~(2

Diffraction efficiency into the primary focus (n = -1)is determined from Eq. (12) to be 41%. For secondaryfoci, the efficiencies reduce as 1/n2 .

Since the beam at the primary focus has the maxi-mum intensity, it is suitable for both recording andreading holographic gratings. The beams from thesecondary foci, however, can cause erasure of the pri-mary gratings or record undesirable secondary grat-ings. In systems sensitive to this problem, multilevelphase Fresnel lenses which have de-emphasized higherorder foci can be used. In the next section, we considermore issues in designing BP-FLAs. In addition, fabri-cation procedures in two substrates SiO2 (glass) andSi3N4 (silicon nitride), and their comparison will bepresented.

111. Design and Fabrication

In designing BP-FLAs, an important parameter isthe focal length of each element. A suitable value foruse in our interconnection application is 20 mm (for X=0.514 Am). This value yields a 101-,m radius for thefirst zone as determined using Eq. (11). Equation (1)yields thirty-five zones parallel to the sides for a 1.2-mm square aperture.

Now let us consider the implications associated withthe number of elements in the array. For example, an8 X 8 array aperture will have a 9.6-mm square, usingthe above lens design, which is quite practical to fabri-cate and use in a system. A 32 X 32 array, on the otherhand, having a 38.4-mm square aperture is cumber-some. Hence, there will be design trade-offs to consid-er.

Given a fixed wavelength, the two parameters, aper-ture size (number of zones) and focal length, can bemanipulated to make BP-FLs suitable for large arrays.Reducing the first parameter (number of zones) has adisadvantage that increases the focal spot size. Wewill also be limited by the size of the center zone andthe fact that a few zones are needed to make the lensfunction.

Reducing the second parameter (focal length) allowsfor larger packing density by reducing the radii of thezones. Reducing the focal length, however, constrictsthe incorporation of other components of the holo-graphic system such as SLMs.

Our design has an 8 X 8 array consisting of 1.2-mmaperture lenses with a 20-mm primary focal length.An optical micrograph of the mask used in patterningthe BP-FLAs is shown in Fig. 3. This mask was gener-


iv~~~~ 9, # 00;;S

Xte~ ~ ~ a \s e~v

X: :a a

*s t::0 a.7 '. "a a: atg0

Lit<~~~a

PHOTORESISTCOATING

PHOTORESIST

SUBSTRATE(SiO2 )

PHOTOLITH.PATTERNING

1.2 mmFig. 3. Electron-beam generated mask used for patterning BP-FLAs on both SiO2 and Si3N4. The array consists of 8 X 8 square

aperture elements, each 1.2 mm wide.

ated by the electron-beam writing technique whichsimulated circles with polygons having 0.5-,gm sides.

It was mentioned before that every other zone in aBP-FL induces a ir phase shift on the incident field.This is accomplished by generating steps with height dthat satisfies

d =-. (13)2An

where An is the change in refractive index between theneighboring zones. We fabricated BP-FLAs with ap-propriate step heights in a SiO2 substrate and in aplasma chemical vapor deposited (CVD) Si3N4 thinfilm. The details of fabrication are given in the follow-ing sections.

A. Fabrication in SiO2

In this section, we present the details of fabricating aBP-FLA in an optical quality SiO2 (glass) (n = 1.5)substrate by the selective ion-beam milling technique.Although we have used iO2 as our substrate, thistechnique can just as easily be used to fabricate Fresnelmicrolenses in other materials, such as GaAs orLiNbO3. For the case of SiO2 , the desired step heightis 0.51 ,um, as determined from Eq. (13) using An = 0.5between glass and air, and X = 0.514 ,gm. The fabrica-tion sequence is shown in Fig. 4.

In this technique, photoresist is used as the blockingmask for the ion beam milling process. We first coatedthe substrate with AZ1512, an AZ photoresist product(1.2 ,Mm thick), exposed it through the patterning mask(see Fig. 3), and then developed it. To harden thephotoresist to withstand the high energy argon-ion-beam milling, we flood-exposed the photoresist pat-tern for 5 min, and then hard baked it at 1400C for 1 h.

Exposed to an argon-ion beam (0.25-mA/cm 2 cur-rent density, and a voltage of 500 V), SiO2 mills at anominal rate of 0.01 /Lm/min. This process was con-ducted for a duration of 51 min. Following removal of

rmm//A X77777

PHOTORESISTREMOVAL

V

U

HARD BAKE1400C, 1 HR.

77//A 7777/

�J1rLr-

Fig. 4. Sequence for patterning and selective ion beam millingtechnique for fabricating BP-FLAs on SiO2 .

the photoresist, the step height was determined using astylus type surface profiler to be -0.53 ,um (4% morethan the calculated 0.51 ,m). (The effect of the devi-ation from the optimal step height is to reduce the lensdiffraction efficiency.) A section of the fabricatedarray is shown in Fig. 5. A micrograph with largermagnification, shown in Fig. 6, reveals a structure thathas uniform surfaces and sidewalls needed to minimize

1350 APPLIED OPTICS / Vol. 30, No. 11 / 10April 1991

U

_ _

U/111/l/l/1111IT17,777177777M

(PLASMA CVD)

Si3 N4

SUBSTRATE(SiO2 )

PHOTORESISTCOATING

PHOTORES

PHOTOLITH.PATTERNING

IST

Fig. 5. Scanning electron micrograph (55X) of a BP-FLA fabricat-ed on SiO2 as described in the text. The array consists of 8 X 8elements, each with a 1.2-mm square aperture. The graininess is an

artifact of the microscope.

PLASMA ETCH Si3 N4CF4 /2 5W ETCH RATE(0.28 Torr) v , 20/i

/////A_?2 A////1 1/min ///

PHOTORESISTREMOVAL

Fig.6. Scanning electron micrograph(286X) of a BP-FL fabricatedon SiO2 shows highly uniform surfaces. The graininess is an artifact

of the microscope.

unwanted scattering. The graininess in both Figs. 5and 6 is an artifact of the microscope.

B. Fabrication in Si3N4

In this section, details of fabricating a BP-FLA in athin film of plasma chemical vapor deposited (CVD)Si 3N4 by the selective plasma etching process are pre-sented. Figure 7 shows the sequence for this fabrica-tion.

A film of Si3N4 (0.26 Am thick) was first deposited ona glass substrate. Since the refractive index of plasmaCVD Si3N4 depends on the deposition conditions, itwas precisely determined to be 2.05, using an ellipso-metric technique. The required step height, using Eq.(13), is 0.25,im.

UFig. 7. Sequence for the patterning and plasma etching technique

for fabricating BP-FLAs on plasma-CVD Si3N4.

Photoresist was again used as the blocking mask forthe plasma etching process. Its coating and pattern-ing procedures were identical to those of the SiO2 casedescribed in the previous section. In the case of Si3N4,however, we did not harden the photoresist pattern byflood-exposing and hard-baking. The reason is thatthe plasma etch process used reacts minimally withphotoresist.

Exposed to CF 4/0 2 plasma (0.28-Torr pressure and


I ........ ' '.............. .

. .................... ........... .. . o.. .. ...,,{.O..... .

V

*:R:-:: : :.l '.-..:. e 111.. 7a 11an- .17I .7 .7 .

1- 1.2 mm O 1 1Fig. 8. Optical micrograph (56X) of a BP-FLA fabricated on Si3N4. 1 .2mmThe array consists of 8 X 8 elements, each with a 1.2-mm square Fig. 10. An 8 X 8 array of beams focused at 20 mm when the beam

aperture. from an argon-ion laser was diffracted from the BP-FLA fabricatedon SiO2 .

Fig. 9. Scanning electron micrograph (2800X) of a section of theSi3N4 BP-FL. The only visible nonuniformity results from a 0.5-jpm

step size used for patterning the original mask.

50-W power), Si3N4 etches at a nominal rate of 0.087,Mm/min. This process was conducted for a 3-min.duration, yielding a 0.26-/im fabricated step height(-4% more than the desired height of 0.25 gim). Anoptical micrograph of the resulting BP-FLA is shownin Fig. 8. Figure 9 is a scanning electron micrograph ofa section of the fabricated BP-FLA. The only nonuni-formities visible on the sidewalls are caused by the 0.5-/im sides of the polygon in the original mask.

Let us compare the fabrication steps of the twotechniques. Ion beam milling does not require theadditional steps of deposition of thin film and thecalibration of its refractive index (plasma CVD Si3Ni

IntensityScan

}Fig. 11. Scan of the intensity across four generated spots revealing

uniformity. The maximum intensity variation is -6%.

in our case). In addition, absorption in the thin filmand Fresnel reflections at multiple boundaries (be-tween the substrate and the film) can reduce the dif-fraction efficiency of this type of BP-FLA.

IV. Performance AnalysisHere we discuss the results of diffracting a single

collimated argon ion beam from either of the SiO2 andSi3N4 BP-FLAs to generate an 8 X 8 array of mutuallycoherent beams. (The collimated beam was wideenough to have a nominally uniform intensity over the


(a)

(b)

12 pm

Intensity* Scan

I IntensityScale

Intensity-4-- Scan

Intensity__________________________ Scale

12 pmFig. 12. Diffraction pattern at the focal plane of a single BP-FL:(a) SiO2 , (b) Si3N4 . The patterns are characteristic of the diffrac-

tion from square apertures and are identical for both lens types.

full array.) The diffraction pattern and efficiency atthe primary focus (20 mm) are analyzed and comparedfor the two lens types.

The 8 X 8 array of spots diffracted from the SiO2component is shown in Fig. 10. An intensity scanacross four of the focused spots in Fig. 11 shows a gooduniformity with a maximum intensity variation of-6%. Such uniformity across the array is crucial inminimizing the unwanted variations from one gratingto another during holographic recording and readout.

The diffraction efficiency of the SiO2 sample wasmeasured to be 29% at the primary focal plane. Todetermine this value, we first measured the back-ground intensity between foci in the transverse dimen-sion at this plane; the beam intensity was measuredagain with the sample removed and replaced with aplain glass substrate (to compensate for Fresnel reflec-tions). The ratio of the increase in the backgroundintensity (between the two cases) to that of the secondcase yielded the desired efficiency. Reasons for thereduced efficiency compared to the expected 41% aregiven at the end of this section.

The quality of the generated optical beams is alsoimportant in holographic interconnect applications.The existence of high spatial orders at foci, for exam-ple, can lead to recording and interconnection errors.Noisy gratings can reduce the signal-to-noise ratio(SNR) and the dynamic range available at the detectorarray.

The diffraction pattern of a single beam focused by aSiO2 BP-FL is shown in Fig. 12(a), revealing goodbeam quality. The sinc2 type intensity distribution ofthis beam is the result of the square aperture of thelens, as predicted by Eq. (7). According to this equa-tion, the width of main lobe S, (or the separation of thetwo zeros on either side of the main lobe) is

(14), 2Xz-

For the result of Fig. 12(a), zn is 20 mm (for n =-1) andLx is 1.2 mm, yielding a 17-,um separation. On thisbasis, the beam spot size was determined from Fig.12(a) (measured to the l/e2 point) to be -12 jim.

An array of 8 X 8 beams generated by the Si3N4 BP-FLA revealed uniformities similar to those of the SiO2case. The diffraction pattern of a single beam isshown in Fig. 12(b). This pattern also has sinc2 distri-bution and is identical to that of the SiO2 case shown inFig. 12(a). The measured diffraction efficiency andspot size for this lens were about 31% and 12 Aim,respectively. Within measurement errors, these val-ues are in close agreement with those of the SiO2 lens.

To investigate why the measured efficiencies forboth lens types were lower than the expected 41%, weimaged the higher-order foci to determine the locationand intensity for each type. In both cases, they wereobserved at distances ff/2,f13,f/4,f/5, showing that wehave unexpected foci at f/2,f/4. Their respective in-tensities were also larger than expected, and the varia-tions for the SiO2 lens were different than those in theSi3N4 type. The above results suggest the possibilityof statistical variations in step heights, which can causethe diffraction of beam into higher foci. The reduc-tion in efficiency can therefore be the result of thesevariations and scattering at the sidewalls.

V. SummaryArrays of mutually coherent beams are needed for

recording and reading holographic gratings in someoptical interconnect applications. Binary phase Fres-nel lenses offer a practical and simple means of gener-ating modest size arrays (i.e., 8 X 8), while maintainingreasonable focal lengths (i.e., 20 mm) to allow theincorporation of other components, such as spatiallight modulators. A disadvantage of this type of lensis its multiple focusing which can cause recording ofunwanted gratings or erasure of the desired ones. Wecompared two techniques for the fabrication of binaryphase Fresnel lenses. An 8 X 8 array of lenses (eachwith a 1.2-mm aperture and 20-mm focal length) wasfabricated in SiO2 with selective ion beam milling.(This technique can also be used in other substrates,such as GaAs or LiNbO3.) A similar lens array wasfabricated in Si3N4 through thin film deposition (plas-ma CVD) and CF4/0 2 plasma etching. The ion beammilling technique appeared to have fewer steps andparameters that are easier to control compared to thedescribed deposition method. Highly uniform arraysof coherent focused beams were generated when dif-fracting a single argon ion laser beam by both lens


types. The diffraction properties of both lenses werealmost identical at their primary focal planes. At thislocation, the diffraction efficiencies were -30% (com-pared with 41% theoretical) and beam spot sizes were-12 jum, for both cases.

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Binary phase Fresnel lenses for generation of two-dimensional beam arrays

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