Mie scattering interferometer and its application to thestudy of Raman scattering from molecules ata mercury interface
Azriel Z. Genack, King P. Leung, Harry W. Deckman, Premala Chandra, and Joel 1. Gersten
Interference fringes are observed produced by Mie scattering of laser light from a single microstructure orfrom a random array of microstructures supported above a reflecting surface. These fringes are the basisof a simple interferometer which can be used to measure distances from thousands of angstroms to centime-ters. The interferometer is used to measure the height of liquid above a mercury surface. Raman scattering(RS) from the liquid is measured, and an upper limit of 103 is placed on the enhancement of RS from mole-cules at the interface. Enhancement of RS in a wedge between mercury and solid is examined theoreti-cally.
1. Introduction
In this paper we discuss observations of interferencefringes produced by scattering a laser beam from asingle or random array of microstructures supportedabove a reflecting surface. Scatter fringes result fromthe interference between light which is Mie scatteredby the microstructures and then reflected and lightwhich is transmitted through the microstructures andreflected before being scattered by the microstructures.The supported microstructures, which comprise ascatter plate, and the reflecting surface are the com-ponents of an interferometer which exhibits interfer-ence fringes even without careful alignment. It can beused to measure the distance between a scatter plateand a flat surface from thousands of angstroms to cen-timeters. Surface structure can be probed with dif-fraction-limited resolution by measuring the heightabove the surface of a single microstructure as it isscanned laterally above the surface. The interferom-eter is applied here to measure the depth of liquid be-tween the scatter plate and a liquid mercury surfacewhile observing RS from the liquid. This allowed us tosearch for the presence of enhanced RS from a liquidnear a smooth mercury surface as well as near a surface,which was deliberately roughened by contact with thescatter plate.
Joel Gersten is with City College of CUNY, New York, New York10031; the other authors are with Exxon Research & EngineeringCompany, Clinton Township, Route 22 East, Annandale, New Jersey08801.
In the present interferometer, scattering is used asa means of splitting a spatially coherent laser beam.The scattering is from dielectric microstructures withdimensions of the order of the wavelength of light andis, consequently, predominantly in the forward direc-tion. Typically the scatter plate consisted of a sub-monolayer of 0.5-gm polystyrene spheres on a silicadisk. Because the forward scattering of 5145-A lightis 3 orders of magnitude larger than backscattering inthis case,"2 the interpretation of the scatter fringes isgreatly simplified. The predominance of forwardscattering, known as the Mie effect, occurs in scatteringfrom microstructures with dimensions comparable tothe wavelength of light.
Scattering as a means of beam splitting has been usedin the past to produce a variety of scatter plate inter-ferometers.3-9 Incoherent illumination is generallyused, and two or more wave fronts are reimaged onidentical points on the scatter plate. This gives an in-terferogram with intensity related to deviation of aspherical surface from a standard spherical surface. Inthe first scatter plate interferometer3 suitable for testingoptical systems, two identical scatter plates were placed'symmetrically about the sample. This design, due toBurch, is sensitive to vibrations. Shoemaker andMurty 4 modified the Burch interferometer by replacingone of the scatter plates with a plane mirror which rei-mages the scatter plate point by point back on itself andgreatly reduced the sensitivity to vibration. This re-quired critical alignment which can be simplified byfabricating a scatter plate with inversion symmetry.Such a scatter plate7 can be produced from a doublyexposed photograph of a scattering surface which isrotated 180° between exposures. In the present in-terferometer, the coherence of the laser beam alleviates
the need to reimage the part of the beam which is un-scattered in the first pass through the scatter plate toform a coherent interference pattern. However, thepattern from a flat surface is related to the total distancebetween the scattering sphere and the surface ratherthan to the deviation from a standard surface. A Miescattering interferometer can be constructed to probethe deviation from sphericity of a curved mirror byplacing a scattering sphere of the center of curvature ofthe mirror. Such an interferometer is described brieflyat the end of Sec. III, but the emphasis here is on in-terference produced with a flat plate whose character-istics are explored as a function of the distance betweenthe scattering plate and the surface.
The interferometer described here was used to testwhether surface enhanced Raman scattering (SERS)could be observed from molecules above a mercurysurface whose structure is perturbed by contact with arough substrate. We were stimulated by an early reportof SERS from physisorbed pyridine on a mercurydroplet' 0 by Naaman et al. This report seemed to beat variance with previous experimentsl-1 3 and theconventional electrodynamic theory of SERS4-1 7 whichrequired local roughness and sharp localized resonances.Neither of these conditions seemed to hold for liquidmercury because surface tension tends to eradicate localstructure for a liquid, and the optical properties ofmercury are such that the width of a plasmon resonancewould be fairly broad making the plasma enhancementmechanism relatively ineffective. This still leaves openthe possibility of a chemical enhancement mecha-nism.
Although sharp localized or periodic structure onmetals possessing low optical loss has generally beenpresent in cases where SERS is observed, in this workwe explored the possibility that SERS could be inducedby a metal with a large imaginary part of the dielectricfunction when the metal surface is rough. We investi-gate enhancements that might exist for surface struc-ture specifically appropriate to a liquid. These ex-periments set an upper limit of 103 on the enhancementfrom molecules above a textured mercury surface. Thisresult argues against the possibility that SERS on mer-cury could be due to roughness induced by surfacecontaminants.
Sharp structure may be produced in liquid mercuryalong its line of contact with a solid dielectric. Thecontact angle is determined by interfacial energies andpersists from macroscopic dimensions down to theatomic scale. Although the irregularity in the electro-magnetic field at a wedge formed along the line of con-tact is weaker than at the tip of an ellipsoid for whichlarge field enhancements are possible, the larger spatialextent of a line may give rise to strong average fieldenhancements. In this work we attempted to roughenthe surface of mercury while monitoring the RS fromliquid above the mercury surface. A calculation of theelectromagnetic enhancement for particular texturesis given in the Appendix. There the local field distri-bution that comes about within the wedge of liquidbetween the mercury and polystyrene spheres is de-
rived. For mercury with a contact angle of 1400, the netenhancements are estimated to be equivalent to thescattering from 102 to 103 monolayers of liquid. Theminimum detectable signal in our experiments was 103monolayers of ethanol, and we were unable to observeresidual RS from thinner layers. For metals other thanmercury, enormous electric fields may be produced nearthe vertex of a wedge giving rise to enhancements of RS104 times greater than for mercury in contact withpolystyrene spheres.
We sought to have a high density of molecules withinthe wedge formed by the contact of mercury and poly-styrene by laying down a densely packed monolayer of0.5-Am polystyrene spheres on a silica plate and im-pressing this on the mercury in either an ethanol orpyridine environment. The Raman scattering wasmonitored as the mercury was raised toward the poly-styrene spheres. When the substrate first made contactwith part of the mercury surface, the mercury vibrationwas greatly reduced and a bright stable fringe patternwas observed in the scattered light. From this pattern,we were able to measure the thickness of the liquid layercontributing to the observed RS. This thicknessmeasurement allowed us to place an upper limit on themagnitude of SERS from molecules above mercury.
The remainder of this paper is organized as follows:The fabrication of a variety of microstructure scatterplates which are the key element of the Mie micro-structure interferometer is described in the next section.In Sec. III examples of interferograms and their inter-pretation are given for scatter plates made from a singlesphere and for a variety of scatter plates with randomroughness. Use of the interferometer to search forSERS at a mercury surface is discussed in Sec. IV. InSec. V we summarize our conclusions. A detailed cal-culation of the enhancement of RS in a wedge and itsimplications for SERS from mercury and other metalsare given in the Appendix.
II. Fabrication of Scatter Plates
Scatter plates used in the interferometer contain ei-ther a single microstructure or a layer of uniform mi-crostructures. Individual microstructures typically haddimensions comparable to the wavelength of light andwere fabricated using the methods of natural lithogra-phy.'8 Scatter plates were fabricated either by de-positing a monolayer of monodisperse colloidal particleson a transparent support or by using this colloidal layeras a mask for etching. The monolayer coating of col-loidal particles used for pattern definition consisted ofuniformly sized polymer spheres. Polymers which canbe polymerized into spherical particles include poly-styrene, polyvinyl toluene, styrene-divinylbenzene co-polymer, and styrene-butadiene copolymer.
To form a scatter plate, polymer spheres are ran-domly arranged on a substrate with an average inter-particle distance that is determined by details of thecolloidal coating process.' 8"19 When a layer of uniformmicrostructures was needed, the average interparticledistance was adjusted to maximize fringe contrast. Insome cases the density was reduced to insure that only
a single microstructure would be within the laser beamdiameter. The standard deviation of particle size forcolloids made from these polymers can be considerably<5%. Colloidal particles used in the present work wereobtained from Dow Diagnostics. Interference patternswere observed using colloidal particle sizes of 0.091 ±0.006, 0.305 0.008, 0.412 0.006, 0.497 i 0.006, 0.6051 0.009, 0.804 ± 0.005, and 2.020 i 0.013,gm.
When a rugged scatter plate composed of glass mi-crostructures was required, the colloidal particle arraywas used as a mask for an etching process. Identicalmicrocolumnar glass posts were fabricated by reactivelyion etching2 0 a polymer sphere mask deposited on aglass substrate. The height and shape of the resultingglass posts were determined by the energy, currentdensity, and reactivity of the ion beam. Typicallyetching conditions were adjusted to produce smoothprolate post structures <1 gim high.
11. Scatter Fringes
To understand the interferogram produced by theMie scattering interferometer, it is simplest to start byconsidering scattering from a single scattering centerabove a plane reflector. The interferometer to be dis-cussed is shown in Fig. 1. Scattering centers are typi-cally 0.5-gtm polystyrene spheres or glass posts on asilica plate, and the light source is a 1-10 mW argon-ionlaser beam. The cylindrical symmetry of the scatteringarrangement results in a circular fringe pattern ap-pearing on the screen in Fig. 2. In our experiments itwas often useful to focus a laser beam on the scatterplate using a lens which also served to collimate thescattered light when the separation between the scatterplate and reflecting surface is small. When observingrelatively weak scattering from a single polystyrenesphere the visibility of the interference fringes was en-hanced by using a spatial filter to eliminate light re-flected from the lens. The spatial filter was made upof a 10-cm focal length lens which focused the lightthrough a 750-gm aperture and a second 10-cm focallength lens to recollimate the light.
The four lowest order scattering processes involvinga single scattering event are shown in Fig. 3. Processes(a) and (b) involve forward scattering and taken to-gether give rise to a common path interference patternwith a bright central fringe. Processes (c) and (d) in-volve backward scattering and taken together give riseto a central spot whose intensity is modulated throughan entire period as the spacing between the scatteringsphere and mirror is changed by X/4. Rapid modula-tion also results from the interference of either forwardscattering process with either backscattering process.
For 0.5-1-gm microstructures having an index ofrefraction of -1.5 the forward Mie scattering intensityis more than 2 orders of magnitude greater than back-scattering,", 2 and the first two processes of Fig. 3 shoulddominate. This is confirmed by an enormous increasein the total intensity of scattered light returned from theplate when a mirror is introduced in front of the scatterplate. Furthermore, we observe that small angle in-terference is modulated only slightly as the separation
Viewing Screen1.
Reflecting Scatter PlateSample Contalning eithera to be Slngle Microstructure * Incident
Studied or Random Array of I LaserMicrostructures Beam
Fig. 1. Schematic diagram of Mie scattering interferometer.
Fig. 2. Fringe pattern observed from a random array of 0 .5 -Ampolystyrene spheres on a scatter plate. Visibility of fringes was en-hanced with a spatial filter which rejected light scattered by the col-lected lens. The shadow of a beam stop used to remove the specularlyreflected laser beam is visible as a line at the bottom of the pattern.
between the scatter plate and the reflecting mirror ischanged by many wavelengths and the central fringeremains bright. This corresponds to a common pathinterference pattern due to forward scattering processesonly. We will, therefore, proceed to calculate the po-sition of the interference maxima by neglecting back-scattering and including only the two lowest order for-ward scattering processes shown in Figs. 3(a) and (b).
The difference in optical path length for the twoforward scattering processes of angle 0 for light focusedat infinity is readily calculated using the constructionshown in Fig. 4. The difference in path length at thetwo forward scattering processes which arises betweenpoint A at which the laser beam first encounters the
Fig. 5. Circular fringe pattern produced from an isolated structureon the scatter plate. In this case, the isolated microstructure was a0.8-,um diam polystyrene sphere. Visibility of fringes was enhanced
with a spatial filter which rejected light scattered by the lens.
Scatter ViewingPlate Screen
Fig. 3. Schematic diagram of the four lowest-order scattering pro-cesses for the interferometer. Processes (a) and (b) involve forward
scattering, while processes (c) and (d) involve backscattering.(a)
D -I -ow-
| - 2d - I]
i t Image Reflecting ScatterPlane Surface Plate
--- Unfolded Beam Path for Forward-Transmitted Beam
(b)Unfolded Beam Path for Transmitted-Forward Beam
Fig. 4. Construction showing unfolded beam paths of the two lowestorder scattering processes shown in Fig. 3. Line AB is the unfoldedbeam path within the interferometer of scattering process (b) shownin Fig. 3. Line BD is the unfolded beam path within the interfer-ometer of scattering process (a) shown in Fig. 3. The optical pathdifference through the interferometer is the distance (BC - AB.).
Fig. 6. (a) Fringe pattern obtained from a submonolayer array of0.5-,4m polystyrene spheres. The spatial filter was used to removelight scattered by the lens. (b) Fringe pattern of the submonolayerarray shown in Fig. 6(a) with spatial filter removed and slightly in-
creased separation d between scatter plate and mirror.
scattering sphere and the wave front drawn perpen-dicular to the propagation direction of the two scatteredlight beams and passing through A are the sides BC andAB of the triangle in Fig. 4. The difference in pathlength for the two forward scattering processes is,therefore, 2d - 2d cosO. The phase shifts on scatteringfor the two forward scattering processes in Fig. 3 areidentical. In addition, the phase shift for small scat-tering angles from a reflecting surface is nearly the sameas for reflections at zero incidence angle. Thus thephase shift introduced by the reflection and scatteringshown in Figs. 3(a) and (b) is essentially that introducedby the path length difference for the two processes. Forlaser wavelength of X and a medium with index of re-fraction n between the scattering sphere and reflector,the phase shift due to the optical path difference is(27rn)/X2d(1 - cos0). Since the Mie scattering functionvaries slowly with angle for objects comparable in sizeto the wavelength of light, maxima in the interferencepattern occur, to a good approximation, whenever thepath length difference is an integer multiple m ofX/n:
2nd(1 - cosO) = mX. (1)
The interference pattern from a single scattering spherefor a spacing d = 13.4gAm observed with a lens with focallength f = 55 mm and aperture D = 46 mm is shown inFig. 5. A spatial filter was used to eliminate reflectionsfrom the lens in Fig. 1 to enhance visibility of the fringes.This pattern can be used to monitor the flatness of thereflecting surface with diffraction-limited lateral anddepth resolution.
Interferograms produced by a random array of mi-crostructures are shown in Fig. 6. The pattern obtainedfrom a random submonolayer of 0.5-grm polystyrenespheres with and without a spatial filter is shown in Figs.6(a) and (b), respectively. The laser speckle, seen inboth these interferograms, arises from the interferencebetween scattering via process 3(a) or (b) from onesphere and scattered light produced by these processesfrom different randomly positioned spheres. Never-theless, the superposition of coherent interferencepatterns produced by the two forward scattering pro-cesses from the same microstructure is clearly discern-ible. A closely spaced interference pattern is seen inFig. 6(b) but is absent in Fig. 6(a). This pattern is dueto interference between the processes shown in Figs.3(a) and (b) and those in Figs. 7(a) and (b). The twoforward scattering processes shown in Fig. 7 arise fromlight reflected off the rear surface of the silica platewhich supports the scattering spheres. This gives riseto a circular interference pattern with a spacing of 2nst,where n, = 1.46 is the index of refraction of silica andt = 0.158 cm is the thickness of the silica disk. Thisadditional interference pattern is not seen in Fig. 6(a)because the light from processes 7(a) and (b) are notimaged in the plane of the pinhole and hence are re-jected.
The grain size in the speckle pattern is determinedby the density of microstructures on the scatter plate.As the density of microstructures is reduced, the grain
a) Forward-Transmitted and Reflected by Silica Plate
Silica Substrate
Reflecting a \ ScatteringSurface Surface
b) Transmitted-Forward and Reflected by Silica Plate
.i _..
Reflecting -' k- ScatteringSurface Surface
:a Substrate
Fig. 7. Scattering process involving reflection of light from rearsurface of silica plate. Basic scattering processes correspond to those
shown in Figs. 3(a) and (b).
Fig. 8. Fringe pattern from a scatter plate with low density of mi-crostructures on the surface. The grain size in the speckle patternis significantly larger than those shown in Figs. 2 and 6. This is pri-
marily due to the difference in density of scattering sites.
size of the speckle pattern increases. Figure 8 shows theeffect of decreasing the density of microstructures onthe scatter plate. As compared with Figs 2 and 6 thegrain size of the speckle pattern is significantly in-creased. In general, the contrast in the pattern im-proves as the density of scatters is reduced.
The collimated scattering has a diameter equal to thelens aperture D. The largest scattered angle collectedO for a lens with focal length f is
______=_(2)-\/D/4 + f2(2The ratio of the distance y from the center of the pat-tern to the mth interference maximum to the radius ofthe lens, Y = D/2, is
y 2f= tanG
Y D
2f\/v4ndmX -m2X2
D(2nd - mX)A fit of the position of the interference maxima for aninterferogram produced with 5145-A light for a spacingof d = 264 gm is shown in Fig. 9. A collecting lens withf = 100 mm and D = 36 mm was used, and the inter-ferometer was immersed in ethanol and index n = 1.36.A comparable fit is obtained using 6470-A light withwider spaced interference fringes. These results
11
10
a
I
II
r.I2.S'5
r
a
7
a
5
4
3
2
0
10
I
I
00
p
0/S~~~~~~~
I
0l
,I _L I lI I I I I I0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8
Ring Radius y [cml
Fig. 9. Index m for interference ring plotted as a function of ringradius y. Solid line is behavior expected for a plate spacing of 264/um. Collecting lens in the interferometer had f = 100 mm and D =
36 mm.
demonstrate that the interference pattern is describedusing the simple model in which only forward scatteringis considered and phase shifts for the two interferingprocesses are assumed identical.
The discussion of interference in scattering from amicrosphere above a reflecting plane suggests that arelated common path interferometer could be con-structed by placing a scattering sphere at the center ofthe curvature of a spherical mirror. An unmodulatedinterference pattern would be expected for a perfectspherical mirror since the path lengths for the two for-ward scattering processes are identical. Any decreaseof intensity of scattered light would correspond to adeviation from sphericity. The intensity of the scat-tered light should be 4F(00)1 2( - cos2b/X), whereF(OO) is the amplitude for Mie scattering of angle (0,/)and is the radial deviation from sphericity of themirror.
IV. Raman Scattering at Mercury Interface
We have used the Mie scattering interferometer tomeasure the height of liquid between a mercury surfaceand a scatter plate supporting polystyrene spheres. Bymeasuring the intensity of RS from the liquid in the il-luminated region as a function of liquid height, thesensitivity of the RS apparatus is determined. Withinthe limits set by this sensitivity we have investigatedwhether RS from molecules above a smooth andtextured mercury surface is enhanced. Roughness wasproduced by impressing a densely packed monolayer of0.5-gm polystyrene spheres or glass posts into themercury surface and also by preparing a stable inter-facial layer of polystyrene spheres on mercury.
Stable interfacial layers of polystyrene spheres areproduced at a mercury-ethanol interface by direct de-position from aqueous colloid. A single layer of spheresis trapped at the interface by exchanging the waterphase with alcohol by continuous washing until spheresare no longer present in the liquid.
To measure the intensity of RS as a function of liquidthickness, a substrate was immersed in the liquid above
10I
E
150
Ethanol
d = 3.6Am
d = 1.1$m
Fig. 10. Raman scattering from 1.1- and 3.6-Amthick ethanol layers trapped between a scatter plate
I Ia~0 I I I I I , with 0.5-,vm polystyrene spheres and a mercuryD 1000 5oo surface. Layer thickness was determined with the
Frequency Shift (cm - ) Mie scattering interferometers.
Fig. 11. Plot of RS intensity from the 808-cm 1 mode of ethanol asa function of layer thickness. The ethanol layer was trapped betweena scatter plate textured with 0.5-,.m polystyrene spheres and a mer-cury surface. The point with the error bar drawn was the thinnestethanol layer which could be obtained. Increasing the contact
pressure did not decrease the layer thickness.
Fig. 12. Expected structure for contact of polystyrene spheres witha mercury surface. Region 1 is mercury, while region 2 may be gas
or liquid.
the mercury surface. The substrate was attached to thetip of a glass funnel so as to exclude liquid in the regionabove the substrate. The distance between the frontsurface of the substrate and the mercury was monitoredby observing the interference pattern from the Miescattering by microstructures present on the substrate.To avoid trapping air bubbles between the substrateand mercury, the substrate was inclined on an angle of15° to the horizontal plane. When the edge of thesubstrate makes contact with the mercury surface, vi-brations are suppressed, and a stable interference pat-tern is obtained from which the liquid thickness in theregion illuminated by the laser beam is determined.
The height of the liquid in the region illuminated bythe laser d was determined using Eq. (1). The numberof interference rings m within the collimated scatteredbeam corresponds to scattering at the maximum angleof 0 defined in Eq. (2). Scattering from a 30-mW Ar+laser beam at 5145 A is collected with a f/2.8 lens withf = 100 mm. Laser plasma lines were eliminated usinga Spex Lasermate spectrometer as the laser beam.
The scattered light was dispersed in a Spex 1401double monochromator equipped with holographicgratings. Standard photon counting electronics wasused. A resolution of 5 cm- 1 and integrating time of 10sec per data point were employed in these experiments.The RS spectrum from 1 and 3.6gAm of ethanol is shownin Fig. 10. The ethanol layer was trapped between ascatter plate textured with 0.5-gim polystyrene spheresand a mercury surface. A plot of RS intensity from the808-cm-1 mode of ethanol as a function of the thicknessof the ethanol layer is shown in Fig. 11. Two counts persecond are recorded per micron thickness of ethanol.The noise of 0.5 counts/sec corresponds to a minimumdetectable thickness of -0.5 gm.
The y intercept of a straight line drawn through thepoints in Fig. 11 of 0.1 counts/sec indicates that no sig-nificant residual RS is observed. As we continued toraise the mercury cup, increasing the pressure of con-tact, the interference pattern did not change furtherindicating that the laser probed a region of the interfaceat which a 1-gim thick ethanol layer is trapped betweenthe mercury and polystyrene spheres.
Subsequently the interfacial region was examinedwith an optical microscope. The interfacial region wasimaged with a magnification of 800X using an objectivelens which had a numerical aperture of 0.63 and a depthof field of 1 gm. With ethanol between the mercury andthe substrate we found that the edge of the advancingmercury moved continuously through the field of viewas a line. The line indicating the advance of mercuryup the tilted substrate came into focus just as thespheres are blurred. This indicates that the mercurylies -1 gm below the polystyrene spheres, in agreementwith our interferometric measurement. Perhaps directcontact is not established with the polystyrene spheresbecause dust or projections from the surface pin themercury level. Without a liquid phase above the mer-cury, however, we found that the mercury did reach thepolystyrene spheres. The spheres and the edge ofmercury could be brought into sharp focus simulta-neously.
Although the polystyrene spheres did not contactwith the mercury surface when a liquid layer waspresent, the measurement shown in Fig. 11 does serveto calibrate the sensitivity of our apparatus. This cal-ibration can be used to determine the minimum de-tectable enhancement factor for polystyrene spheresbrought into contact with mercury in the presence of gasvapors and organic monolayers.
The expected structure of the mercury surface incontact with the polystyrene spheres is shown in Fig. 12.The surface energy is
S = 13 . dG[2ira2 sinG + ar12(A - ra2 sin24)]
+ 23 d2ra2 sinwhere aij is the surface energy density between regionsi and j, (P is the contact angle, and A is the averagecross-sectional area per polystyrene sphere. The energyextrema are obtained by setting the derivative of Eq. (4)to zero:
From the second derivative we find that the first twosolutions are maxima while the last is a minimum in Sand corresponds to the case where b is the contactangle. A more extended analysis, in which the mercurysurface between the spheres is not constrained to be flat,and in which the effects of gravity are included, intro-duces only a slight variation in the intersphere regionof mercury. For contact among mercury, polystyrene,and ethanol, 4P = 140°.
We searched for RS from molecules at a mercury-polystyrene interface in two different configurations.(1) The scatter plate was impresed into the mercury inthe presence of pyridine vapor and (2) para-nitroben-zoic acid was spin coated on a scatter plate which wasimpressed into the mercury surface. In neither case didwe see additional RS due to the presence of a texturedmercury surface.
With sensitivity similar to that quoted above we in-vestigated RS from a mercury droplet in saturatedpyridine vapor. The experiment was done with 900between the incident and scattered light. By movingthe mercury droplet, RS over a range of incident andscattered angles relative to the normal to the curvedmercury surface was investigated. In no case did weobserve additional RS from pyridine physisorbed on themercury droplet.
The experiments give an upper bound on the en-hancement above both a smooth mercury surface andone in contact with polystyrene spheres. In both cases,the total extra scattering due to the presence of a mer-cury surface was below the detectability limit of scat-tering, which is -103 layers of ethanol. This is wellbelow strong enhancements for monolayers on silversurfaces and below the enhancement reported earlierfor pyridine on mercury.10 The calculation of fieldenhancements in the Appendix for a wetting angle of1400, appropriate to mercury on polystyrene, gives anenhancement of 102_103. Enhancements above theobservation threshold of 103 layers are only predictedfor multilayers on a roughened surface with smallerwetting angles than are characteristic of mercury ondielectric solids.
V. Conclusion
We have developed a Mie scattering interferometerand exploited it to measure the separation betweenscattering microstructures and a flat reflecting surface.Interference fringes are produced with either a randomarray or single-scattering sphere. High contrast fringesare obtained using the Mie effect because of the pre-dominance of forwarding scattering. The observationof interference in scattering from a single microstructureindicates that for a slowly varying structure this inter-ferometer can be used to probe surface structure withdiffraction-limited lateral resolution.
We have used the interferometer to measure thedepth of liquid between a scattering plate and a mercurysurface. By simultaneously measuring the RS from theliquid the sensitivity of the RS apparatus was cali-brated. We were, thereby, able to determine that thenet enhancement of RS from a multilayer above themercury was less than the scattering from 103 layers ofethanol. A calculation for the enhancement of RS dueto the presence of high density of wedges at a mercuryinterface gives 102-103. The enhancement of electro-magnetic fields and of RS in a wedge geometry is de-rived in the Appendix in terms of the angle of the wedgeand the dielectric function of three media which meet,along a line to form the wedge. For some metals andwedge angles, enhancements of 106 are possible.
E 2 E} (1
Z //> /I /// / /, // / /
E3
Fig. 13. Wedge geometry for enhancement calculations. Region1 contains the liquid from which Raman scattering is observed, whileregions 2 and 3 are liquid mercury and a solid which meets in a line.
Appendix
A. Field Enchancement in a Wedge Bounded byMercury and a Dielectric Solid
Consider a sample composed of three media, (1) aliquid from which RS is observed, (2) liquid mercury,and (3) a solid, which meet along a line. A cross sectionof this system is shown in Fig. 13. The dielectric con-stant is
el < O<V/
e(O) = e2 < < 7r -
(3 7r < G < 2r
(Al)
We shall assume that the imaginary part of the dielec-tric function is zero in regions 1 and 3 and that the di-electric function in region 2 has the value 2 = 82 + i 2characteristic of the bulk.
We shall study the region close to the vertex and as-sume that the size of the region under study is less thanthe wavelength of light X. Retardation effects can thenbe neglected, and the electrodynamic problem reducesto electrostatics. We require, then, the solution ofLaplace's equation subject to boundary conditionswhich will be specified shortly;
V24' 0. (A2)
We introduce a scale length R so that R < X. R mightbe related to X or to some physical dimension in the
The parameters Yj are complex eigenvalues which areto be determined. The coefficients Xj, Yj, Zj, Uj, V1,and Wj are fixed by the boundary conditions. Theseconditions are that cb and Do be continuous at 0 = 0,' ,and r for all r. This gives rise to six simultaneousequations which are solvable when the following det-erminental condition is satisfied:
Cl10
det0
0
where
0 -C 3 0 0 -S 3 1-C1 0 Si -Si 0
C2 -C 2 0 S2 -S 2=0,
0 e3S3 el 0 -e3 C3C2 S1 0 ClCl -e 2 C1 0
-E2S2 C3S2 0 c2 C2 -e 3 C2
(A5)
term and assume the coefficient B = 0. The behaviorof cI near the vertex is then dominated by the lowesteigenvalue (the eigenvalue with the smallest real part),and we have
(AS)4 ) A 1 (R-)ilF(0)
The electric field will have components
Er = -al a~r R\R
E =--1 4b -A, (\l-1 dF1 (G)r O R R. dO
The field components will diverge if
Rea - V < 1.
(A9a)
(A9b)
(A10)
The magnitude of the square of the electric field is
JE 2 = A 2(r) 26- 12 + dF (0v12 d .El2-I j I11 iF i( G)l + -(G I(All)
The coefficient A 1 must be determined by the boundaryconditions at a distance from the vertex of order R. Itwill be linear in the applied field E0. Thus from Eq.(All) we conclude that the amplification factor for in-tensity I E/EoI2 will diverge near the origin when theinequality in Eq. (A10) is obeyed. The intensity en-hancement factor is then
(A12)IEOI _ R )
C1 = cosujJ4, S1 = sinaj4,
C2 = cosj7r, S2 = sincjir,
C3 = cos2ir.1, S 3 = sin2roj.
Since both the incident field and the radiating dipoleare enhanced by nearly the same factor, the enhance-ment of surface Raman scattering p is proportional to
(A6) the square of (Eq. A12):
The roots of Eq. (AS) determine the eigenvalues o-j:
Ui= 1j(elE2,E3,) (A7)
For arbitrary angle the roots must be obtained nu-merically.
As indicated in Eq. (A2) a logarithmic solution is alsopossible. This is the potential corresponding to a lineof charge along the vertex. Since we shall mainly beconsidering dielectrics and situations in which the fieldis imposed externally, we shall neglect the logarithmic
IE 4 r 4(v-1)
E0 R(A13)
In Fig. 14 a plot of v vs 4 is given for the case of hw =2.4-eV excitation for which el = 1.78, 2 = -17.5 +i12.19, and e = 6.76 (ethanol, mercury, sapphire).Figure 15 gives v vs hw for fixed angle X = 400, corre-sponding to the mercury contact angle, and for el = 1.78,E2 = 2(co), and 3 = 2.25 (water, mercury, silica). Itshows very little variation in v with exciting laser fre-quency.
1.0
0.9 f w=2.40.8
0.7
0.6-
V 0.5-
0.4-
0.3-
0.2 E,=2e = -1 7.5
0.1 e, =12.19
0 40 80 120 160 200 240 280+(deg)
Fig. 14. Plot of v vs T for hw = 2.4-eV excitation of wedge contactamong ethanol, mercury, and sapphire.
1.0.9
.8
.7
.6
v .5
.4
.3
2.0 3.0-hw [evi
Fig. 15. Plot of v vs hw for fixed angle h = 40° excitation of wedgecontact among water, mercury, and silica.
As we have seen, enhancement is possible in the vi-cinity of the wedge. The net Raman scattering signalmay be maximized by increasing the length of thewedge. This can be done by immersing an array ofspheres in a liquid. Field enhancements will be greatestfor a metallic liquid which has a dielectric function oflarge magnitude. The spheres are made of polystyrene,and the liquid metal is mercury. The field enhance-ment in ethanol which is between the mercury andpolystyrene is to be determined. The geometry isshown in Fig. 12. As shown previously, the mercurysurface is approximately flat and makes a contact angle0 with the spheres of radius a.
The circumference of the line of contact of the threephases is
C = 2ira sinG. (A14)
Looking down at the surface, we assume a close packed2-D array of spheres. The area of a unit cell is
[(2a) (X/-/2)]
so the number of spheres per unit area is
N = . (A15)2a 2 V\/-
The length of wetted line per unit area is thus
L r sinG- a-/, (A16)A a,/3-
As a decreases, this quantity increases in magnitude.A maximum enhancement should occur for spheres withradii comparable to X.
Let us introduce the polarization dependence of theelectric field by writing
A = cosx, (A17)
where X is the angle between the applied electric fieldand the wedge line. The angle X will vary from pointto point on the circle. In place of Eq. (A13), we write
10
10-'
Ho[cm]
10-2
10-3
10-4 0 0.2 0.4 0.6 0.8 1.00 0.2 0.4 0.6 0.8 1.0
Fig.16. Plot of H0 vs v for h = 40,20, and 1400. Values of a, R, andRo were taken to be 0.5 Am, 0.5,am, and 5°, respectively.
The quantity R is the sum of two terms. The first mayget to be large if 4v - 2 < 0, or v - 0.5 < 0, while thesecond may become large if 4v - 1 < 0 or v < 0.25. Rrepresents the contribution from a single sphere.Multiplying it by N of Eq. (A16) gives the contributionper unit area:
P = (r)4(-i) cos4X.(A18)
Consider now the region near the wedge. The volumeelement is
dV = (a sinO - r cosO)rdrdOdX. (A19)
We will introduce a cutoff on the r integration Ro so thatRo ' r < R. The specific contribution of the wedge tothe integrated enhancement factor for Raman scatter-ing is
X=fpdV= f r 4(v-) cos4 X(a sinG + r cosG)rdrd~dx.
Evaluation of the integral gives
R = 3r R2 faG sin I_ Ro )4-2 + R sin 1 _ IRo 4-l
4 4v-2 ( 4v-1 R
NR = 37r w( 52 al sinl G, _ F 4-12Vf3\a- 4v-2 L kR )I+R sin _RO4- Ho.
4" -l1 L kR/(A22)
Ho has the dimensions of a length and describes thedepth of liquid in a homogeneous situation which wouldbe needed to produce a similar Raman signal. Thelower limit Ro is determined by the effect of nonlocalelectrodynamics or by the breakdown of the well-de-fined macroscopic angle of the wedge due to atomisticeffects. This is typically of the order of 5 A, which is thevalue we take in our calculations. A plot of Ho as afunction of v is given in Fig. 16 for several angles 4'. Thevalues of a, R, and Ro were taken to be 0.5 gm, 0.5 gm,and 5 A, respectively. We see that there is a dramaticfalloff of Ho with increasing index v for all angles. InFig. 17 we present Ho as a function of 4 for several val-ues of v. In all cases there appears to be a maximum ofHo at an angle 4 of 70°.
Fig. 17. Plot of Ho as a function of IF for several values of v.
B. Monolayer CaseSuppose there were only a monolayer on the mercury
surface. How large would the SERS signal be? Let N,be the number of adsorbed molecules per unit area.The SERS signal from the roughened geometry of Fig.12 is
I = NN, dA I r-) cos4 x, (A23)
where the integration is over the mercury-ethanol in-terface for a unit cell and
dA = (a sinO + r)drdX. (A24)
As a crude estimate, let us choose the upper limit of theintegration R, as that for which
NirRl = 1. (A25)
ThenRl ~~~~~1
5 (a sinO + r)drdx = -' (A26)
or
7rR' + 27rRia sinO = 1/N. (A27)
The SERS signal is
I NNS I (a sinO + r)drdx lr-) cos4xI 0 W X~(r4(-i
Table 1. The SERS Enhancement Ratio, p, for a Monolayer of Moleculeson the Surface of a Metal Wedge Produced by Polystyrene Spheres of
Radius a for the case R = 0.5jsm, Ro = 5A and 0 = 30°; theseParameters are Defined in the Appendix.
v P
0.7 6.80.6 360.5 3400.4 38480.3 474350.2 6.2 X 1050.1 8.2 X 106
= - NNsR fa4 14v-3
X [(R1 4v-3 (Ro)4v-3 R 4v R 1 4)-2 _ kR IJ4-2IR} IR 4v-2 |R} |R} (A28)
Assuming that R0 << R1 the SERS enhancement ratio becomes
_ 37r RU sinO (R 13-4 1 (R\( R 2-41 .11 I= l 11 + I-lI (A29)83 \a113-4v \Ro 2-4v aJ\Ro
For R/Ro- >> 1 the first term is the more singular, andthe second term can generally be disregarded. A tableof pT for various values of v is given in Table I for the caseof a = 0.5 gm, R = 0.5 gm, Ro = 5 A and with 0 chosento be 30°. The large enhancement for small values ofv indicates that for appropriate choice of liquid metaland laser frequency, large enhancements might be ob-served.
Referencesi. H. Blumer, Z. Phys. 38, 304 (1926).2. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford,
1980).3. J. M. Burch, "Scatter Fringes of Equal Thickness," Nature
London 171, 889 (1953).4. A. H. Shoemaker and M. V. R. K. Murty, "Some Further Aspects
of Scatter-Fringe Interferometry," Appl. Opt. 5, 603 (1966).5. R. M. Scott, "Scatter Plate Interferometry," Appl. Opt. 8, 531
(1969).6. J. M. Burch, Optical Instruments and Techniques, J. H. Dickson,
Ed. (Oriel, London, 1979).7. S. Mallick, Optical Shop Testing, D. Malacara, Ed. (Wiley, New
York, 1978).8. J. B. Houston, Jr., "Optical Systems Manufacturing Technology,"
Opt. Spectra 4, 32 (1970).9. J. Dyson, "Very Stable Common Path Interferometers and Ap-
plications," J. Opt. Soc. Am. 53, 690 (1963).10. R. Naaman, S. J. Buelow, 0. Cheshnovsky, and D. R. Herschbach,
11. C. Y. Chen, E. Burstein, and S. Lundquist, "Giant Raman Scat-tering by Pyridine and CN- Adsorbed on Silver," Solid StateCommun. 32, 63 (1979).
12. J. E. Rowe, C. V. Shank, D. A. Zwemer, and C. A. Murray,"Ultra-High-Vacuum Studies of Enhanced Raman Scatteringand Pyridine on Silver Surfaces," Phys. Rev. Lett. 44, 1770(1980).
13. D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten,"Anomalous Low-Frequency Raman Scattering for Rough MetalSurfaces and the Origin of Surface-Enhanced Raman Scattering,"Phys. Rev. Lett. 45, 355 (1980).
14. J. I. Gersten, "The Effect of Surface Roughness on Surface En-hanced Raman Scattering," J. Chem. Phys. 72, 5779 (1980).
15. S. L. McCall, P. M. Platzman, and P. A. Wolff, "Surface EnhancedRaman Scattering," Phys. Lett. A 77, 381 (1980).
16. J. I. Gersten and A. Nitzan, "Electromagnetic Theory of En-hanced Raman Scattering by Molecules Adsorbed on RoughSurfaces," J. Chem. Phys. 73, 3023 (1980).
17. M. Kerker, D.-S. Wang, and H. W. Chew, "Surface EnhancedRaman Scattering (SERS) by Molecules Adsorbed at SphericalParticles: Errata," Appl. Opt. 19, 4159 (1980).
18. H. W. Deckman and J. H. Dunsmuir, "Natural Lithography,"Appl. Phys. Lett. 41, 377 (1982).
19. H. W. Deckman and J. H. Dunsmuir, "Applications of SurfaceTextures Produced with Natural Lithography," J. Vac. Sci.Technol. B1, 1109 (1983).
20. J. L. Vossen and W. Kern, Thin Film Processes (Academic, NewYork, 1978).
Of Optics continued from page 4367Fabry-Perot laser diodes exhibit multilongitudinal mode emission.This can cause overall system bandwidth reduction in a single-modecommunications link compared to the potential link bandwidth. Thedistributed feedback (DFB) laser can operate in a single longitudinalmode under narrow pulse operation. Hitachi's DFB laser develop-ment is aimed at single-mode operation at 1.55 pm with distributedfeedback built into the InP guiding layers.
The Hitachi Central Research Laboratory has been strongly in-terested in the transverse mode stabilized high power laser for use asa light source for optical information processing such as laser beamprinters and optical disk direct reading. To meet this need, GaAlAshigh power visible lasers with a self-aligned stripe buried hetero-structure (SSBH) have been developed. SSRH lasers have a widewaveguide layer which is self-aligned to the narrow active layer.Stable oscillation in the fundamental transverse mode up to about50 MW of output power at wavelengths around 780 nm have beenreported. Growth of the short (visible) wavelength GaAIAs is not aneasy task, since the second liquid phase epitaxial growth having highAlAs composition is difficult.
Optical electronics integrated circuits (OEIC) is also an active re-search area at Hitachi. OEIC research is conducted in many indus-trial laboratories and is coordinated by the Optoelectronic Industryand Technology Association established by the Ministry of Interna-tional Trade and Industry (MITI). In the Hitachi Central ResearchLaboratory, one laser diode, one photodiode, and six GaAs FETs aremonolithically integrated to form a laser transmitter. Six GaAs FETsand a photodiode are fabricated on one GaAs chip, which is to be usedas a laser driver.
Investigation is also in progress on fabrication of 1.3-p1m lightemitting diodes (LEDs) for high speed operation in the 200-MHz to300-MHz region. It is found that the rise time of an LED is about 2to 3 nsec and the fall time is about 10 nsec. It is speculated that thedifference in rise and fall times is due to current spreading. As thecurrent density falls, carrier recombination time will increase sinceit takes a longer time for recombination between electrons and holesto take place at a low carrier density.
The most popular Hitachi laser structures are the buried hetero-structure (BH) and the channeled substrate planar stripe (CSP) laser.The BH laser is an index-guided device, while the CSP laser is aweakly index-guided realization. Another laser structure is themodified channeled substrate planar stripe laser (MCSP), which isan index-guided laser. The main difference between BH and MCSPlasers lies in the manufacturing procedure. The BH laser needstwo-step epitaxial growing processes, while a one-step epitaxial growthprocess is sufficient for MCSP laser fabrication.
The research activity in guided wave optics is conducted in thesecond department with a staff of about eighteen. Single-mode po-larization-preserving fiber manufactured by Hitachi has a loss of 0.8dB/km at 1.55 Am. The extinction ratio between two orthogonalpolarizations is 30 dB. We were shown a length of this optical fiberincorporated into an optical fiber gyroscope. The interference fringepattern in the experimental gyroscope is stable even under pertur-bation caused by a finger touching the elliptical (polarization pre-served) fiber. An integrated optical switch operated at 1 MHz wasalso demonstrated with an extinction ratio somewhat less than 20 dI.Optical isolators with 20-dB extinction ratio have also been builtexperimentally. Solgel fiber has been fabricated with an attenuationof 20 dB/km.
Development of optical communication systems is undertaken inthe fifth department with approximately thirteen scientists and en-gineers. Duplex analog CATV transmission was experimentallydemonstrated in the laboratory using wavelength division multi-plexing over a single fiber of 2-km length. For transmitting commandsignals and video signals to subscribers, 0.81-pm and 1.3-ttm laserswere used, while an 0.89-pm laser was utilized for transmitting requestsignals from subscribers.
