May 1, 1992 / Vol. 17, No. 9 / OPTICS LETTERS 685

Kinoform with 64 phase levels for use as an array generator

Long Pin and Hsu DahsiungDepartment of Applied Physics, Beijing University of Posts and Telecommunications, Beijing 100088, China

Wu Minxian and Chin KuofanDepartment of Precise Instruments, Tsinghua University, Beijing 100084, China

Gao ShipingMicroelectronic Research Center, Chinese Academy of Sciences, Beijing, China

Received October 7, 1991

A transmissive kinoform with 64 phase levels is demonstrated that is used as a beam array generator. Thiskinoform converts a single beam to a 5 X 5 beam array. The measured diffraction efficiency is 75.56%, nearthe designed value of 79.68%. The measured intensity difference among the different diffraction orders ofthe 5 X 5 beam array is 21.56%, and the designed value is 10.99%. The total aperture of the kinoform is10 mm x 10 mm.

Array generators are optical systems that split asingle beam from a laser source into a one- or two-dimensional array of beams. Applications of such adevice include multiple imaging, star couplers, andoptical computing, which are used to produce arraysof optical or photoelectronic devices with illumina-tion beams.

One type of multilevel phase kinoform is a trans-mission or reflection grating with multiphase levelsin cells and with the same cell size in a period.1 Thephase levels of cells in a period of the grating aredetermined in an optimal design procedure to havean array of diffraction orders with desired diffrac-tion efficiency and intensity distribution. A mul-tiphase level kinoform has a higher diffractionefficiency and a lower reconstruction noise than aDammann grating with binary phase levels does. 4

Recently Walker and Jahns proposed a new type ofmultilevel phase kinoform with multiphase levels incells and with variable cell sizes in a period.5 Thiskinoform has better designed parameters than doesthe kinoform with multiphase levels in cells andwith the same cell size in a period.6' 7 In this Letterwe report the design and fabrication of a trans-missive kinoform with 64 phase levels and with thesame cell size in a period.

If a multilevel phase kinoform is placed in the in-put plane of a Fourier-transforming optical system,owing to the periodicity, a grid of equally spacedlight spots appears in the output plane. These spotscorrespond to the diffraction orders of the two-dimensional kinoform grating,

A(m,n) = if exp[i0(xy)]exp[-2wri(mx + ny)]

number of desired diffraction orders is (2M + 1) X(2N + 1), 4(x,y) is a periodic function 4(x +T.,y + Ty) = 4 (x,y), and T, and Ty are the periodsalong the x and y axes, respectively.

The phase relief is taken to be constant withineach rectangle (xi+, - xl,yp+l - yp),

4(x,y) = Ip,

xe[xz,x1+1], 1 = O,1,...,L - 1,

ye[yp, Yp+l], p =0,1,..P -1. (2)

The optical intensities associated with variousdiffraction orders characterized by integers (m, n)are given by'

P(m, n) = IA(m, n)12

= (LP)-2 sinc2(m/L)x sinc2(n/P)[C2(m, n) + S2(m, n)], (3)

where P(m, n) is the optical intensity of the (m, n)diffraction order, sinc(x) = sin(wx)/(irx), and

L-1 P-1C(m, n) = > > cos[4lp - 27r(ml/L + np/P)],

1=0 p=O

L-1 P-1S(m, n) = > > sin[4lp - 2r(iml/L + np/P)].

1=0 p=O

(4)

(5)

One of the most successful algorithms in the op-timization of a complex combinatorial system issimulated annealing.8 We have used a simulatedannealing algorithm for optimal design of this mul-tiphase level kinoform. The merit function Mf ofoptimization can be defined as

X dxdy, (1)

where A(m, n) is the optical amplitude associatedwith the various diffraction orders characterized byintegers (m, n), m= -M, ... , M, n = N,... , N, the

M NMf = I > [Pe- P(mn)]2,

m=-M n=-N(6)

where Pe is the designed intensity of the diffractionorders and we assume that every useful diffraction

0146-9592/92/090685-03$5.00/0 © 1992 Optical Society of America

(A1,E[0, 2irr],

686 OPTICS LETTERS / Vol. 17, No. 9 / May 1, 1992

Table 1. Light Intensity of the 5 x 5 Diffractional Beam Array

Designed Values Measured Values

0.0326 0.0316 0.0321 0.0289 0.0284 0.0362 0.0250 0.0357 0.0262 0.02930.0318 0.0321 0.0329 0.0324 0.0328 0.0321 0.0301 0.0310 0.0309 0.03370.0338 0.0345 0.0341 0.0325 0.0319 0.0355 0.0354 0.0253 0.0283 0.02550.0316 0.0317 0.0311 0.0327 0.0308 0.0293 0.0251 0.0279 0.0319 0.03190.0300 0.0315 0.0314 0.0321 0.0317 0.0273 0.0312 0.0323 0.0322 0.0262

order has the same optical intensity, and M and Nare the required diffraction orders along the x andy axes, respectively.

The merit function is minimized with respect tothe phase values 0p, I = 0,...,L- 1; p = 0,...,P - 1. The optimization process was first madewith continuous phase values, and then the continu-ous phase values were quantized into 64 discretevalues. With the structure of 10 X 10 cells in a pe-riod and a 5 x 5 output beam array, the designeddiffraction efficiency is 79.68%. For the conve-nience of reconstruction, a period of the kinoform is250 Am X 250 Am, and each cell has a size of25 ,m x 25 Am. This size of the cells can beachieved without difficulty with our facilities andequipment. In Table 1 the theoretical light intensi-ties of all 5 X 5 diffraction orders are listed.

A relatively simple fabrication process may beemployed that uses K steps for generation of a kino-form with 2K phase levels.9 To make a 64-phase-level kinoform we need six binary amplitude masksand to use the process of photolithography and ionetching six times. Fabrication of a multilevel phasekinoform consists of two steps: (i) binary ampli-tude mask production and (ii) photolithography andetching.

Each binary mask was calculated, and the patternof the kth mask represents a 2ir/(2k) phase shift,with k = 1, ... , K. To fabricate the 64-phase-levelkinoform we need six masks for phase shift etchingand another mask for aperture and alignment signs.The binary amplitude masks were made withthe pattern generator CGA 3600 and reduced withCGA 3696.

The substrate is a plate of quartz glass with bothsides polished. First the substrate was coated witha layer of Cr, then a layer of photoresist was spreadon the layer of Cr. A binary pattern of apertureand alignment signs is transferred to the layer ofphotoresist by using photolithography. After theaperture and alignment signs were etched, the pat-terns of the masks were implemented by photo-lithography and reactive ion etching in turn. Thephotoresist AZ1350 is used as a protective layerof reactive ion etching, as the multilevel phasekinoforms were made out of quartz glass by usingreactive ion etching. The precision of alignmentprocedure is 1 Am for the lithophotography machineMJB-3 used. The kth etching depth can be deter-mined as

5d = A/[2k(n - 1)],

If the reconstruction wavelength is 0.63 ,m, theminimum etching depth is approximately 0.02 ,Amfor six processes of lithophotography and ion etchingin our case.

Reactive ion etching is implemented in an FD-2reactive ion etching machine. The etching speed isapproximately 40 nm/min. When the etching depthis near the desired depth, an a step is used to mea-sure the etching depth. If the etching depth did notreach the designed one, another reactive ion etchingis implemented to correct the etching depth untilthe desired etching depth is reached.

Figure 1 is a photograph of the reconstruction ofa beam array with the 64-phase-level kinoform.Measurement of the diffraction efficiency is imple-mented in the following way: First the intensitiesof 5 X 5 diffraction beams were measured with alaser power meter. Then the kinoform was re-placed by a quartz plate with both sides polished andwith the same thickness as that of the kinoform tomeasure the intensity of the incident beam. Thediffraction efficiency is obtained by dividing thesummation of all intensities of the 5 X 5 diffractionbeams with the intensity of the incident beam. Anon-line reference beam is used to measure the varia-tion of the laser power during the measuring proce-dure. Changes in the intensity of the referencebeam are used for correcting all the final measuringvalues. The measured light intensities of the 5 X 5diffractional beam array are also listed in Table 1.The measured diffraction efficiency is 75.56%,which is near the designed value of 79.68%. The de-signed intensity difference [P - P(m, n)flmax/P,where P is the average light intensity, m = -M,....M, n = -N .. ., N] among the 5 X 5 beam array is10.99%, and the measured intensity difference is21.56%. The designed intensity difference is rela-tively large compared with that of the conventionalDammann grating design. One reason is that themerit function is used in the optimization procedure

(7)

where A is the wavelength and n is the deflectionindex of quartz glass.

Fig. 1. Reconstructed pattern of 5 X 5 beam array byusing a transmissive kinoform with 64 phase levels.

May 1, 1992 / Vol. 17, No. 9 / OPTICS LETTERS 687

to have a maximum diffraction efficiency instead ofto have a minimum intensity difference.

In summary, a transmissive kinoform with 64phase levels was designed by using simulated an-nealing and was fabricated by using photolithogra-phy and reactive ion etching. With the designeddiffraction efficiency of 79.68%, the measured dif-fraction efficiency reaches 75.56%. A 5 X 5 beamarray was generated. The measured intensity dif-ference among the different diffraction orders of the5 X 5 beam array is 21.56%, compared with the de-signed value of 10.99%. Each period of the kino-form consists of 10 X 10 cells, and the size of eachcell is 25 tLm X 25 ttm. The total aperture of thekinoform is 10 mm X 10 mm.

This research is partially financed by the HighScience and Technology Program of China and theNatural Science Foundation of China.

2. H. Dammann and K. Gortler, Opt. Commun. 3, 312(1971).

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Sinica 8, 946 (1988).5. J. Walker and J. Jahns, J. Opt. Soc. Am. A 7, 1509

(1990).6. L. Pin, W Minxian, C. Kuofan, and H. Dahsiung, in

Digest of Optical Society of America Annual Meeting(Optical Society of America, Washington, D.C., 1990),paper WA5.

7. L. Pin, W Minxian, C. Baigang, and C. Kuofan, "Opti-mization of a multilevel phase kinoform using phaseand position modulation," Chinese J. Sci. Instrum. (tobe published).

8. L. Pin, W Minxian, C. Kuofan, and H. Dahsiung,presented at the Third Microoptics Conference,Yokohama, Japan, 1991.

9. J. N. Mait, Opt. Lett. 14, 196 (1989).

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