antireflection gold surface-relief gratings: experimental characteristics

Antireflection gold surface-relief gratings:experimental characteristics

Nile F. Hartman and Thomas K. Gaylord

A systematic procedure using the effective index method and impedance matching has recently beendeveloped Appl. Opt. 26, 3123 (1987)] for the design of antireflection high-spatial-frequency rectangular-groove gratings on lossy materials including high conductivity metals. The design procedure in turn can beused as a starting point to design antireflection metallic gratings with lower spatial frequencies using rigorouscoupled-wave analysis. These lower spatial-frequency gratings have the advantage of being easier tofabricate. In the present work, a particular antireflection gold grating design (having a period of 1.0 ,um, afilling factor of 50%, and a groove depth of 147.5 nm for use at a freespace wavelength of 500 nm, normalincidence, and polarization parallel to the grooves) was fabricated and its diffraction characteristics experi-mentally measured. The grating indeed showed very nearly zero specular reflection in the blue region of thespectrum. Unlike previously reported antireflection anomalies, the effect is broadband occurring over abroad range of wavelengths and angles of incidence, and for both orthogonal polarizations. This work clearlyshows that the systematic design of zero specular reflection grating surfaces is possible.

I. Introduction

Antireflection surfaces on lossy materials such assemiconductors and metals are useful for eliminatingspecular reflections. A periodic corrugation on thesurface of a material can produce antireflection behav-ior. Such surface-relief grating structures on semicon-ductor materials have been used to increase the effi-ciency of solar cells.1 Similarly, some metallic surface-relief diffraction gratings are known to absorb specificwavelength ranges of the incident radiation ratherthan to diffract them. Wood2 reported this absorp-tion effect in 1902. Later Wood3 showed that this typeof effect can occur when a higher-order diffracted waveis at cutoff. These types of power absorption effectsare commonly called anomalies in the literature.They have been experimentally observed for bothtransverse electric (TE) polarization- 6 and transverse.magnetic (TM) polarization.6-14 Furthermore, theseanomalies have been extensively theoretically investi-gated.9- 31 51 6 These predicted and observed anoma-lies generally occur abruptly in wavelength and/or an-gle of incidence (e.g., Refs. 2, 6-8,10, 12, 17, and 18) butsometimes are broadband (e.g., Refs. 13 and 14). Sim-ilar Brewsterlike effects have been described in struc-tures with multiple layers parallel to the substratesurface.920 Antireflection behavior also has been

The authors are with Georgia Institute of Technology, Atlanta,Georgia 30332.

Received 10 February 1988.0003.6935/88/173738-06$02.00/0.© 1988 Optical Society of America.

predicted theoretically21 22 and observed experimen-tally2324 due to surface-relief gratings on dielectricsurfaces.

A systematic design procedure using the effectiveindex method and impedance matching has recentlybeen developed25 for antireflection high spatial-fre-quency rectangular-groove surface-relief gratings onlossy materials including high conductivity metals.These high spatial-frequency gratings have periodsthat are small compared to the incident wavelength,and, therefore, all diffracted orders are cut off exceptthe zero-order forward and backward diffracted waves.In this long-wavelength limit, the results from theeffective index method rapidly approach the exact re-sults. The design procedure in turn can be used as astarting point to design antireflection metallic gratingswith lower spatial frequencies using rigorous coupled-wave analysis. These lower spatial-frequency grat-ings are, therefore, more easily and economically fabri-cated for applications in the visible and IR regions ofthe spectrum. These larger period gratings, in gener-al, have propagating higher diffracted orders presentin addition to the zero-order waves. More degrees offreedom are available, and additional constraints onthe grating design are possible. For example, by im-posing the constraints of a 50% filling factor and aperiod equal to twice the freespace wavelength, a grat-ing with a groove depth of 147.5 nm is predicted to beantireflecting at a freespace wavelength of 500 nm fornormal incidence and polarization parallel to thegrooves. 2 6

In this paper, the experimentally measured perfor-mance characteristics are presented for a gold surface-

3738 APPLIED OPTICS / Vol. 27, No. 17 / 1 September 1988

'' 0+1

REGION d-11 FA-- A-I -2 - -3 GOLD n3-j3 D

CHROMIUM

GLASS

Fig. 1. Diffraction geometry of gold rectangular-groove surface-relief grating.

relief rectangular-groove grating intentionally de-signed to be antireflecting. Excellent antireflectionbehavior is indeed shown to occur. The grating exhib-its very nearly zero specular reflection in the blueregion of the spectrum. In contrast to previously re-ported antireflection anomalies, the effect is broadband occurring over a comparatively broad range ofwavelengths and angles of incidence and for both or-thogonal polarizations. The specular reflection char-acteristics are found to be very similar to those of theequivalent lossy single layer antireflection coating onwhich the grating design is based.2 5 This work clearlyshows that the systematic design of practical zero spec-ular reflection grating surfaces is possible.

11. Grating Geometry and Diffraction Analysis

The geometry of a lossy rectangular-groove gratingis shown in Fig. 1. An electromagnetic plane wave inregion 1 is incident on the grating. The substrate(region 3) has a complex index of refraction n 3 - K3.

The grating (region 2) is specified by its filling factor Frepresenting the fraction of the grating period occu-pied by the grating material and by its groove depth d.The grating ridges have the same complex index ofrefraction as the substrate.

In the long-wavelength limit, an effective index ofthe grating layer (region 2) may be found using theelectromagnetic boundary conditions on the electricfield E and the electric displacement D.22

,25

,27 Using

impedance matching techniques, the thickness d andthe complex refractive index n2 - jK2 of a single homo-geneous lossy layer to produce zero reflectivity can becalculated.25 From this information, the filling factorand groove depth of a rectangular-groove grating canbe found to make it equivalent to the lossy layer.25

An exact calculation of the diffraction characteris-tics can be performed using the rigorous coupled-waveanalysis for metallic surface-relief gratings.26 A statevariables representation of the coupled-wave ampli-tudes permits the space-harmonic amplitudes of thefields inside the grating region to be obtained in termsof the eigenfunctions and eigenvectors of the coeffi-cient matrix defined by the rigorous coupled waveequations. From the electromagnetic boundary con-ditions the fields inside the grating (region 2) can berelated to the propagating diffracted fields in region 1,and thus the diffraction efficiencies can be deter-mined.

Ill. Antireflection Gold Grating Design

To demonstrate experimentally a grating specifical-ly designed to be antireflecting, the grating materialwas selected to be gold because it is stable and readilyavailable and has accurately known characteristics.The freespace wavelength X0 at which antireflectionoccurs was chosen to be 500 nm in the visible formeasurement convenience. At this wavelength, thecomplex refractive index of gold is well known28

(n3 = 0.803 and K3 = 1.818). Similarly, normal inci-dence (' = 00) in air (n, = 1.00) and optical polariza-tion perpendicular to the grating vector K were select-ed for convenience. Thus E I K and the electric fieldis parallel to the grooves.

From the effective index method for high spatial-frequency gratings together with impedance matchingto produce antireflection, the required homogeneouslayer can be calculated. Its complex refractive indexhas a real part of n2 = 0.78590 and an imaginary part ofK2 = 0.21655. The thickness of the homogeneous layeris d = 0.47779X0. The corresponding antireflectiongrating has a groove depth equal to this thickness, andits filling factor is found to be F = 0.11689.

Using the rigorous coupled-wave analysis, generalgratings can be analyzed, not just high spatial-frequen-cy ones. Larger period gratings, in general, have prop-agating higher-order diffracted waves present in addi-tion to the zero-order waves. More degrees of freedomare available, and additional constraints on the gratingdesign are possible. For ease of fabrication in thepresent case, a filling factor of F = 50% and a periodequal to twice the freespace wavelength (A = 2Xo = 1.00gim) were selected. A grating with a groove depth ofonly d = 147.5 nm (d = 0.295Xo = 0.1475A) is predictedto be antireflecting at a freespace wavelength of 500nm for normal incidence and polarization parallel tothe grooves (see Fig. 6 of Ref. 26). This is the gratingfabricated and tested in this work.

The substrate thickness D should be 10 times great-er than the skin depth to appear to be semi-infinite tothe incident wave. The skin depth 3 is given by 6 = Xo/2 7riK. For gold at Xo = 500 nm, the skin depth is 6 = 21.9nm, and thus the substrate thickness D should be D 2105 = 220 nm.

Due to the relatively large grating period, the i = +1and -1 orders are not cut off. The angles of diffrac-tion of the backward-diffracted (reflected) waves aregiven by the grating equation (from the phase-match-ing requirement)

iXo/n = A(sinO' + sinO), (1)

where i is the diffracted order, ' is the angle of inci-dence in the dielectric of refractive index nj, and 0 isthe angle of diffraction of the ith-order diffracted waveback into the incident region. All angles are positiveas measured counterclockwise. For normal incidenceand the present case of A = 2Xo, the zero-order wave isat O = 0 and the first-order waves are at 01, = ±30.00.From the rigorous coupled-wave analysis, each first-order wave for this grating is predicted to have a dif-fraction efficiency of 25.0%. Thus even though the

1 September 1988 / Vol. 27, No. 17 / APPLIED OPTICS 3739

grating exhibits no specular (zero-order) reflection,there are higher-order diffracted waves present andthe grating is not totally absorbing. The orientation ofthe grating vector can be determined experimentallyfrom positions of the diffracted orders. The gratingvector K lies in the plane of the diffracted waves.

Incidence is at the mth Bragg angle when the Braggcondition mXo/n, = 2A sinO' is satisfied, where m is aninteger. For the present case of A = 2, the first,second, and third Bragg angles are ±14.48, ±30.0, and±48.590, respectively.

IV. Grating Fabrication

The grating fabricated for these measurements isshown schematically in Fig. 1. A 25- X 25-mm sectionfrom a standard chromium coated photolithographicplate (with photoresist dissolved away) was used as asubstrate. The layer of chromium promotes adhesionof the subsequent gold depositions. A gold layer ofthickness d was evaporated onto the chromium. Thethickness was monitored with a quartz crystal monitor,and the deposition was halted when the thickness was150 ± 10 nm. The grating pattern was produced bystandard photolithographic techniques. The gratingpattern with a period of A = 1.0 im was formed by theinterference of two collimated coherent laser beams ofS = 363.8 nm derived from an argon-ion laser. Thebeams had l/e 2 intensity diameters of -100 mm, thusproducing a highly uniform interference pattern overthe entire 25- X 25-mm plate. The angles of incidencewere 0' = 10.48'. The resulting interference patternwas recorded in a 200-nm thick Shipley 1350J positivephotoresist film spun onto the surface. After develop-ing the exposed resist, it was treated with a very lightplasma etch to remove residual resist material remain-ing in the developed areas. This plasma etching stepimproves the overall uniformity of the finished grat-ing. The gold in the resulting resist/gold pattern wasremoved down to the chromium layer by selective etch-ing using a standard gold etchant. Following thisetching operation, the grating was subsequentlywashed with a resist solvent to remove the remainingresist. The patterned substrate was then coated witha second gold film of thickness D 250 nm (greaterthan ten skin depths). This produced the final gratingconfiguration as shown in Fig. 1.

In room light, the finished grating appears to be avery uniform gold-orange color over its entire 25- X 25-mm area. When examined with an optical micro-scope, the filling factor was estimated to be F = 50 i5%. The filling factor is critically dependent on theexposure, development, and thickness of the resistfilm. An average exposure of 7 mJ/cm 2 and a develop-ment time of 40 s were found to provide satisfactoryresults for 200-nm thick resist films.

V. Experimental Configuration and Procedure

To measure the grating reflectance experimentallyas a function of wavelength and polarization, the con-figuration shown in Fig. 2 is used. A broadband halo-gen lamp is used as a source. A He-Ne laser is used to

calibrate the monochromator and to align the testobject (reflector or grating) so that the output beamfrom the monochromator impinges on the test objectat normal incidence. A narrowband of wavelengths isselected by the grating monochromator. The reflect-ed beam (zero-order diffracted wave in the case of agrating) propagates antiparallel to the incident beam.An antireflection-coated cube beam splitter is used todeflect the reflected beam into a detector. Simulta-neously, the beam splitter also reflects a portion of theincident beam onto a second detector. The outputlight from the monochromator is linearly polarizedeither horizontally or vertically by rotating the polariz-er. Due to the diffraction characteristics of the grat-ing in the monochromator, the monochromator outputlight power, IO(XO,P), is a function of the wavelengthand polarization. To eliminate the wavelength andpolarization dependence of the monochromator out-put intensity, a ratiometer is used as indicated in Fig. 2.Furthermore, the wavelength and polarization depen-dence of reflectance and transmittance of the beamsplitter must be known to determine the reflectance ofthe test object.

The power measured by the incident wave detectoris a function of wavelength and polarization and is

A(XP) = rbS(OP)I(XOP), (2)

where rbs(Xo,P) is the reflectance of the beam splitter.The power in the reflected wave as measured by thediffracted wave detector is

B(X0,P) = [1 - rb(XoP)]robj(XoP)rbS(XOP)IO(Xop), (3)

where r0 bj(Xo,P) is the reflectance of the object beingtested. The ratio of these powers is indicated by theratiometer. Thus the ratiometer output is

R(XO,P) = B(X,P)/A(X,,P) = [1 - rbAOP)Irobj(XOP). (4)

The beam splitter reflectance can, therefore, be deter-mined by

rb,(Xo.P) 1 - ___R____P (5)rbj(XOP)

Inserting a known reflector [given r0bj(Xo,P)] as the

DIFFRACTED0 2 tl: WAVE

HALOGEN ! 2c N DETECTORLAMP __io_ 3

|o-~ i2m iL ! GRATING

J CHROMAT

LAS~EIFINCIDENTWAVE

DETECTOR

POWER

METER

Fig. 2. Experimental configuration for measurement of reflectanceat normal incidence as a function of wavelength and polarization.


100

I GOLD FLAT SURFACE

' 60 /

0

'40 -4

H--Hass and Hadley

Hartman and Gaylord20.

400 500 600 700 800

WAVELENGTH, \X (nm)

Fig. 3. Experimentally measured reflectance of gold flat surface atnormal incidence as a function of wavelength from present work

(solid line) and from Handbook of Physics (dashed line).

object in the position labeled grating in Fig. 2 thusallows the beam splitter reflectance to be measured.In the present work, an overcoated aluminum reflector(an Enhanced Visible Aluminum ER.1 mirror fromNewport Corp.2 9 ) was used for the known reflector.The ratio of the beam powers R = B/A was measured asa function of wavelength for both polarizations, andthen the beam splitter reflectance was calculated usingEq. (5). With knowledge of the beam splitter reflec-tance, the reflectance of an arbitrary object can bedetermined from

r~(A P) = R(XoP)(6~' 1 -rb,5(XO,P)(6To test the experimental configuration and proce-

dure, a flat evaporated gold mirror surface was insert-ed as the object (in the position labeled grating in Fig.2). The ratio of the beam intensities R = B/A was thenmeasured as a function of wavelength for both polar-izations. Starting at X0 = 400 nm, the wavelength wasincreased in steps of 25 nm. Then the reflectance wascalculated using Eq. (6). The resulting reflectancesare shown in Fig. 3 as solid circles. For comparison,the standard reflectance data for freshly evaporatedgold from the HANDBOOK OF PHYSICS 28 is alsoshown in Fig. 3. In both cases, a continuous line,calculated by cubic spline interpolation, has been add-ed to connect the data points. As can be seen from Fig.3, the agreement between the two sets of data is quitegood, thus verifying the experimental measurementtechnique.

The fabricated gold grating was then inserted intothe experimental configuration as shown in Fig. 2. Inthe actual experiment the grating vector was orientedperpendicular to the plane of Fig. 2. This caused the+1 and -1 order diffracted beams to be in a planeperpendicular to the plane of the beams and thus madeit easier to isolate them from the detectors. For polar-izations E I K and H I K, the ratio of the beamintensities R = B/A was then measured as a function ofwavelength and the reflectances calculated usingEq. (6).

Angular selectivity measurements were made at Xo =500 nm. In this case the zero-order diffracted powerwas measured simply by moving the detector to thecorrect angular position. The diffracted power wasthen divided by the incident power to obtain the dif-fraction efficiency.

VI. Measured Diffraction Characteristics

With the experimental configuration and measure-ment procedure verified as described in the previoussection, the fabricated gold grating was inserted intothe test configuration as shown in Fig. 2. At normalincidence, the ratio R of the intensities of the beamscoming from the beam splitter was measured as afunction of wavelength for both E I K and H I Kpolarizations. The reflectances (zero-order diffrac-tion efficiencies) were then calculated using Eq. (6).The resulting reflectances are shown as solid circles inFig. 4. A dramatic antireflection effect is apparent.The data points have again been connected with acontinuous line for ease of interpretation. The gratingwas designed to be antireflecting at normal incidencefor X0 = 500 nm for the optical electric field E perpen-dicular to the grating vector K (electric field parallel togrooves). The minimum measured value of reflec-tance for E I K polarization was r = 0.768%, whichoccurred at 475 nm. In the absence of the grating (aflat gold surface), the measured reflectance was 40.3%at 475 nm. Therefore, the reflectance has been re-duced by a factor of 52.5 due to the presence of thegrating. Even though the grating was not specificallydesigned to be antireflecting for H I K polarization(electric field perpendicular to the grooves), it never-theless exhibits marked antireflection behavior forthis polarization also. The minimum measured valueof reflectance for H I K polarization was r = 2.70%,which also occurred at 475 nm. The bandwidth of theantireflection effect is seen to be relatively broad.

GOLD ANTIREFLECTION GRATING70

60-

5 ~~~~~~~HK-so-

40 EK

U-30-U

20- H.LK

10 ELK

0400 500 600 700 800

WAVELENGTH, XO (nm)

Fig. 4. Experimentally measured zero-order (specular) reflectanceat normal incidence of gold antireflection grating as a function ofwavelength for E I K polarization (optical electric field parallel togrooves) and for H I K polarization (optical electric field perpen-dicular to grooves). A very pronounced antireflection effect is ap-

parent in the neighborhood of Xo = 475 nm.


This is in contrast to the narrow bandwidths that havepreviously been observed (e.g., Refs. 2, 6-8, 10, 12, 17,and 18). The functional form of the reflectance curvesin Fig. 4 is similar to those of a single layer antireflec-tion coating.

With the alternative experimental configuration de-scribed in Sec. V, the angular selectivity of the specularreflectance (zero-order diffraction efficiency) of thegold grating was measured for E I K polarization atthe design wavelength of X0 = 500 nm. The measuredreflectances as a function of angle of incidence ' areshown as open circles in Fig. 5. The angle of incidencerange for antireflection behavior is seen to be verybroad. This is in stark contrast to the previouslyreported antireflection anomalies that occur over anangular range of 1 or 20 (e.g., Refs. 6-8, 12, 17, and 18).At \0 = 500 nm, the normal incidence (6' = 0) reflec-tance is 2.26%. As the angle of incidence is increasedthe measured reflectance increases only very slowly asshown. At ' = 400, the gold grating reflectancereaches only 12.5%. For comparison, the exact calcu-lation of the zero-order diffraction efficiency using therigorous coupled-wave analysis (see Fig. 7 of Ref. 26) isshown as a solid line in Fig. 5. These calculated datashow a similarly broad angular selectivity. The slopediscontinuity in the reflectance at 0' = 30° occurs dueto the i = -1 diffracted order changing from propagat-ing to cutoff and the i = +2 diffracted order changingfrom cutoff to propagating.

For further comparison, the reflectance of the homo-geneous lossy layer that is equivalent to the small-period grating design is shown as a dashed line in Fig. 5.As described in Sec. III, the complex refractive index ofthis antireflecting layer has a real part of n 2 = 0.78590,an imaginary part of K2 = 0.21655, and a thickness of d= 0.47779Xo. It also predicts a similarly very broadangular selectivity as shown.

VII. Discussion and Summary

A gold rectangular-groove surface-relief grating wasfabricated according to an antireflection design(groove depth d = 147.5 nm, filling factor F = 50%,period A = 1.0 gim) for operation at normal incidencewith a freespace wavelength of 500 nm and E I Kpolarization. The grating indeed showed very nearlyzero specular reflectivity in the blue region of the spec-trum. The wavelength response (Fig. 4) and the angu-lar selectivity (Fig. 5) are relatively broad band and aresimilar to those of a single layer antireflection coatingindicating that the grating is acting like a homoge-neous lossy layer in this regard. In addition, the grat-ing antireflects not only for the design polarization(E I K) but also rather well for the orthogonal polar-ization (H I K). This is in contrast to gratings thathave high reflectance for one polarization and low re-flectance for the other to enable their use as polariz-ers.'4 These response characteristics are much broad-er than the abrupt antireflection anomalies measuredby others. Furthermore, comparison to the angularresponse from rigorous coupled-wave analysis26 clearlyshows that this behavior should be expected. Thus

20-

0ui

j 10-

ILU.

GOLD ANTIREFLECTION GRATING

-Rigorous Coupled-Wave Analysis-- Homogeneous Layer Model

0 Measured

0 /

///. ) ° 0// 0

10 20 30

ANGLE OF INCIDENCE, ' (degrees)

40

Fig. 5. Zero-order (specular) reflectance of gold antireflection grat-ing as a function of angle of incidence at X0 = 500 nm. Experimen-tally measured values (open circles), calculated values from rigorouscoupled-wave analysis (solid line), and calculated values from thehomogeneous lossy layer that is equivalent to the grating in theshort-period limit (dashed line) are shown. The very broad angular

selectivity of the grating is apparent in all three sets of data.

the design approach is valid. The grating acts as animpedance matching layer.

The gold grating described in this work representsan attempt to fabricate a grating that was intentionallydesigned to be antireflecting. No subsequent refine-ments or adjustments in the fabrication process haveyet been made. The actual groove depth (140 nm < d< 160 nm) and the actual filling factor (45% < F < 55%)probably differ from the exact design values of d =147.5 nm and F = 50%. Nevertheless, the antireflec-tion behavior is still dramatically apparent. Previouswork2225 in fact has shown that the reflectance can berather insensitive to groove depth and the filling factorin many cases. In addition to these factors, the shift ofthe reflectance minimum from the 500-nm designwavelength is also probably related to the natural de-crease in the reflectance of a flat gold surface as thewavelength decreases toward 475 nm (see Fig. 3).

This particular gold grating has a relatively largeperiod of A = 1.0 gim, and thus the i = 1 diffractedorders are also propagating. With higher spatial fre-quency gratings, all orders except i = 0 will be cut off.In the limit of small periods (equivalent to the long-wavelength limit), the reflection and transmission be-havior of the grating become identically the same asthose of the equivalent homogeneous lossy layer on thesame substrate.25 With all orders cut off except the i =0 transmitted and reflected waves, the grating wouldbe totally absorbing as well as producing zero specularreflection. Metallic grating absorbers have the poten-tially desirable feature that they can be water-cooled ifnecessary for high power applications.

The equivalence of gratings and homogeneous layersin the limit of small periods indicates that a stairstepsurface-relief profile consisting of N steps could beused to simulate a coating of N individual homoge-neous layers. Thus the use of a stairstep grating wouldallow further broadbanding both in wavelength andangle of incidence.

In summary, starting from an antireflection homo-geneous lossy layer design, an equivalently antireflect-ing gold grating was designed and fabricated. This is


U I . - . .v

the first time, to the authors' knowledge, that a metalgrating has been fabricated specifically to be antire-flecting. The grating indeed was measured to havevery nearly zero specular reflectance in the blue regionof the spectrum. This antireflection effect occurs overa broad range of wavelengths and angles of incidence,and for both orthogonal polarizations, thus indicatingthat the grating is acting much like a single homoge-neous lossy layer and that the systematic design of zerospecular reflection grating surfaces is possible.

This research was sponsored in part by a grant fromthe Joint Services Electronics Program under contractDAAG29-84-K-0024.

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antireflection gold surface-relief gratings: experimental characteristics

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